ISSN 1854-6250 APEM journal Advances in Production Engineering & Management Volume 17 | Number 3 | September 2022 Published by CPE apem-journal.org Advances in Production Engineering & Management Identification Statement APEM journal ISSN 1854‐6250 | Abbreviated key title: Adv produc engineer manag | Start year: 2006 ISSN 1855‐6531 (on‐line) Published quarterly by Chair of Production Engineering (CPE), University of Maribor Smetanova ulica 17, SI – 2000 Maribor, Slovenia, European Union (EU) Phone: 00386 2 2207522, Fax: 00386 2 2207990 Language of text: English APEM homepage: apem‐journal.org University homepage: www.um.si APEM Editorial Editor‐in‐Chief Miran Brezocnik editor@apem‐journal.org, info@apem‐journal.org University of Maribor, Faculty of Mechanical Engineering Sme‐ tanova ulica 17, SI – 2000 Maribor, Slovenia, EU Desk Editor Website Technical Editor Martina Meh Lucija Brezocnik desk1@apem‐journal.org desk3@apem‐journal.org Janez Gotlih desk2@apem‐journal.org Editorial Board Members Eberhard Abele, Technical University of Darmstadt, Germany Bojan Acko, University of Maribor, Slovenia Joze Balic, University of Maribor, Slovenia Agostino Bruzzone, University of Genoa, Italy Borut Buchmeister, University of Maribor, Slovenia Ludwig Cardon, Ghent University, Belgium Nirupam Chakraborti, Indian Institute of Technology, Kharagpur, India Edward Chlebus, Wroclaw University of Technology, Poland Igor Drstvensek, University of Maribor, Slovenia Illes Dudas, University of Miskolc, Hungary Mirko Ficko, University of Maribor, Slovenia Vlatka Hlupic, University of Westminster, UK David Hui, University of New Orleans, USA Pramod K. Jain, Indian Institute of Technology Roorkee, India Isak Karabegović, University of Bihać, Bosnia and Herzegovina Janez Kopac, University of Ljubljana, Slovenia Qingliang Meng, Jiangsu University of Science and Technology, China Lanndon A. Ocampo, Cebu Technological University, Philippines Iztok Palcic, University of Maribor, Slovenia Krsto Pandza, University of Leeds, UK Andrej Polajnar, University of Maribor, Slovenia Antonio Pouzada, University of Minho, Portugal R. Venkata Rao, Sardar Vallabhbhai National Inst. of Technology, India Rajiv Kumar Sharma, National Institute of Technology, India Katica Simunovic, J. J. 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Advances in Production Engineering & Management is indexed and abstracted in the WEB OF SCIENCE (maintained by Clarivate Analytics): Science Citation Index Expanded, Journal Citation Reports – Science Edition, Current Contents – Engineering, Computing and Technology • Scopus (maintained by Elsevier) • Inspec • EBSCO: Academic Search Alumni Edition, Academic Search Complete, Academic Search Elite, Academic Search Premier, Engineering Source, Sales & Marketing Source, TOC Premier • ProQuest: CSA Engineering Research Database – Cambridge Scientific Abstracts, Materials Business File, Materials Research Database, Mechanical & Transportation Engineering Abstracts, ProQuest SciTech Collection • TEMA (DOMA) • The journal is listed in Ulrich’s Periodicals Directory and Cabell's Directory Chair of Production Engineering (CPE) Advances in Production Engineering & Management Volume 17 | Number 3 | September 2022 | pp 259–396 Contents Scope and topics Financing and information sharing in capital-constrained supply chain 262 263 Effect of printing parameters on the mechanical behaviour of the thermoplastic polymer processed by FDM technique: A research review 279 Evolutionary game analysis of company collaborative strategy in cloud manufacturing platform environment 295 Development of a flexible tooling system for sheet metal bending 311 A new approach for quality prediction and control of multistage production and manufacturing process based on Big Data analysis and Neural Networks 326 Experimental determination of influences on a gauge block’s stack length 339 Last-mile delivery optimization considering the demand of market distribution methods: A case studies using Adaptive Large Neighborhood Search algorithm 350 Modelling surface roughness in finish turning as a function of cutting tool geometry using the response surface method, Gaussian process regression and decision tree regression 367 Multi-objective Intuitionistic Fuzzy Linear Programming model for optimization of industrial closed-loop supply chain network 381 Calendar of events Notes for contributors 394 395 Duan, H.W.; Wang, M.T.; Ye, Y.S. Tripathy, C.R.; Sharma, R.K.; Rattan, V.K. Xiao, M.; Tian, Z.Y. Stefanovska, E.; Pepelnjak, T. Tian, S.; Zhang, Z.; Xie, X.; Yu, C. Lipus, L.C.; Acko, B.; Tompa, J. Huang, Q.L.; Wang, W.J.; Liang, X.J.; Xu, L.; Niu, X.Y.; Yang, X.Y. Vukelic, D.; Simunovic, K.; Kanovic, Z.; Saric, T.; Doroslovacki, K.; Prica, M.; Simunovic, G. Kousar, S.; Batool, M.; Kausar, N.; Pamucar, D.; Ozbilge, E.; Tantay, B. Journal homepage: apem-journal.org ISSN 1854-6250 (print) ISSN 1855-6531 (on-line) Published by CPE, University of Maribor. Scope and topics Advances in Production Engineering & Management (APEM journal) is an interdisciplinary refereed international academic journal published quarterly by the Chair of Production Engineering at the University of Maribor. The main goal of the APEM journal is to present original, high quality, theoretical and application-oriented research developments in all areas of production engineering and production management to a broad audience of academics and practitioners. In order to bridge the gap between theory and practice, applications based on advanced theory and case studies are particularly welcome. For theoretical papers, their originality and research contributions are the main factors in the evaluation process. General approaches, formalisms, algorithms or techniques should be illustrated with significant applications that demonstrate their applicability to real-world problems. Although the APEM journal main goal is to publish original research papers, review articles and professional papers are occasionally published. Fields of interest include, but are not limited to: Additive Manufacturing Processes Advanced Production Technologies Artificial Intelligence in Production Assembly Systems Automation Big Data in Production Block Chain in Manufacturing Computer-Integrated Manufacturing Cutting and Forming Processes Decision Support Systems Deep Learning in Manufacturing Discrete Systems and Methodology e-Manufacturing Evolutionary Computation in Production Fuzzy Systems Human Factor Engineering, Ergonomics Industrial Engineering Industrial Processes Industrial Robotics Intelligent Manufacturing Systems Joining Processes Knowledge Management Logistics in Production 262 Machine Learning in Production Machine-to-Machine Economy Machine Tools Machining Systems Manufacturing Systems Materials Science, Multidisciplinary Mechanical Engineering Mechatronics Metrology in Production Modelling and Simulation Numerical Techniques Operations Research Operations Planning, Scheduling and Control Optimisation Techniques Project Management Quality Management Risk and Uncertainty Self-Organizing Systems Smart Manufacturing Statistical Methods Supply Chain Management Virtual Reality in Production Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 3 | September 2022 | pp 263–278 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.3.435 Original scientific paper Financing and information sharing in capital-constrained supply chain Duan, H.W.a, Wang, M.T.a, Ye, Y.S.b,* a Xihua University, School of Management, Chengdu, Sichuan, P.R. China University, Institute for Disaster Management and Reconstruction, Chengdu, Sichuan, P.R. China bSichuan ABSTRACT ARTICLE INFO This paper focuses on financing choices and information-sharing strategies in the capital-constrained supply chain. We model four scenarios with the capital constraints of the respective manufacturer and retailer using bank credit financing (BCF) and trade credit financing (TCF) approaches to address financing problems, and investigate the retailer’s willingness to share demand forecasting information. We find that TCF is an equilibrium financing choice for a capital-constrained supply chain. However, when a capital-constrained member chooses TCF, sharing demand information over the supply chain becomes more difficult. The interactions between the choices of financing approach and information sharing based on the game equilibriums, as well as the conditions that encourage the well-funded member to offer TCF in the capital-constrained supply chains, have also been analytically explored and numerically verified. Additional managerial insights are provided for discussions. Keywords: Supply chain; Capital constraint; Information sharing; Financing choice; Game equilibrium *Corresponding author: moriye@scu.edu.cn (Ye, Y.S.) Article history: Received 2 May 2022 Revised 27 July 2022 Accepted 10 Aug 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Capital is the basic guarantee for smooth operations and management of supply chains, nevertheless, many enterprises are capital-constrained during startup phases [1]. According to Enterprise Surveys (World Bank Group, 2018), which encompass more than 135,000 enterprises in 139 countries, 53.6 % of the enterprises require a loan, and 26.5 % cited access to finance as a major restriction. Both the manufacturer and the retailer may face capital constraints. In March 2018, Peugeot Citroen immediately issued a supply disruption warning when noticed that up to 85 % of the major suppliers were facing financing difficulties. A total of 19 % of U.S. retailers closed their stores due to capital-constrained reasons in the first half of 2019, and more than 7,000 retail stores were finally closed. In 2020, the outbreak of the COVID-19 pandemic posed great challenges to the stability of the supply chain system and undermined the shortage of funds in the supply chain [2]. Many companies suffer from budget pressure had to close down a mass of their factories and stores. On March 23, 2020, Tesla temporarily suspended production at its two plants in New York and California. In May, the first major fashion retailer, J. Crew Group Inc. filed for bankruptcy, followed by Neiman Marcus, a luxury department store, and in 263 Duan, Wang, Ye December, Debenhams, a British retail giant with more than 230 years of history, declared bankruptcy. To ease the capital constraints, a firm may have access to more than one financing sources. Bank credit financing (BCF) is a common financing approaches provided by banks for firms to meet the financing requirements. In 2016, 20 % of China's small and medium-sized firms (SMEs) borrowed from banks [3], To increase the overall efficiency of the entire supply chain, large well-funded firms often provide trade credit financing (TCF) to the participants within the supply chain in practice. Ford Motor Credit Company LLC, a wholly-owned subsidiary of Ford Motor Company, offers wholesale loans to dealers to finance the purchase of vehicle inventory, as well as loans to dealers to finance working capital and enhancements to dealership facilities [4]. And Haier provides trade credit to its small partners to alleviate their financial strain [5]. However, the related research seem to have opposing opinions on whether capital-constrained buyers/retailers should adopt BCF or TCF. Through numerical research, Zhou and Groenevelt [6] contend that bank credit is better than trade credit. Whereas Kouvelis and Zhao [7] pointed out that if the retailer is provided an effectively constructed scheme, they would always choose supplier financing over bank financing. Jing et al. [8] demonstrate that TCF (BCF) is the unique financing equilibrium when production costs are below (above) a certain threshold, when both bank credit and trade credit are available. Specifically, for the capital-constrained supply chain with the coexistence of bank and trade credits, demand uncertainty and information asymmetry should also be emphasized. Demand uncertainty would not only aggravate the internal difficulties of enterprises’ operations but also exert external financing pressure on capital-constrained enterprises [9]. Internally, it necessitates greater financial investment in inventory management to prevent stock-outs, while externally, the uncertain sales revenue makes it harder for firms to maintain robust cash flow and may raise the risk of default, a critical factor for their lending agents or institutions in determining the interest rate. Wang et al. [1] have shown that increased demand uncertainty may prompt lenders to charge a higher interest rate, which would further impact the decisions and performance of supply chain participants in the lending market. Therefore, demand forecasting is important for capital-constrained enterprises because it is an effective way to reduce demand uncertainty [10]. If the retailer shares demand information with the upstream manufacturer, it would help the manufacturer improve the accuracy of demand forecasting. Thus, the problem would be whether the retailer decides to share private demand information with the upstream manufacturer in a capital-constrained supply chain. Given that both manufacturers and retailers may face increasing capital constraints, wherein the uncertain demand and asymmetric information further complicate the financing for the capital-constrained member, this paper addresses the following issues: How does a capital-constrained member make financing choices in the face of asymmetric demand information? Will the retailer share demand information when the capital-constrained member addresses the financing problem through BCF and TCF respectively? How will the information be shared with different financing choices? All the abovementioned problems are key to capital-constrained supply chain management under information asymmetry. However, while the theoretical studies on respective financing and information sharing are abundant, there is limited research focusing on supply chain management that considers both demand information asymmetry and capital constraints at an operational level. This paper shows the equilibrium choices of financing and information-sharing strategies for an information-asymmetric supply chain with either capital-constrained manufacturers or retailers. Based on the game equilibriums, the interactions between the above two strategies (i.e., financing vs. information sharing) are analysed, and the conditions that the well-funded member is willing to provide TCF are further discussed. This paper contributes to the state-of-the-art research in three ways: First, we identify the financing choices, i.e., BCF or TCF, that the capital-constrained manufacturer/retailer prefers to take in the face of asymmetric demand information. We find that TCF is an equilibrium financing choice in both scenarios with capital constraints of manufacturer and retailer. Second, we further analyse the correlation between the choice of financing approach and information sharing. 264 Advances in Production Engineering & Management 17(3) 2022 Financing and Information sharing in capital-constrained supply chain Although the capital-constrained member’s financing choice does not directly affect the retailer's information-sharing strategy, the value of information sharing has changed: when the capitalconstrained member opts for TCF, the retailer is less willing to share demand information in case of losing profits. Third, we consider the bank deposit and loan rates for the choice of BCF in the construction of the game model and numerically analyse the ranges of deposit and loan rates that urge the well-funded member become willing to provide TCF. The rest of the paper is organized as follows. Section 2 reviews the relevant literature and Section 3 introduces the model framework. In Section 4, the game model when capitalconstrained manufacturer adopts BCF and TCF are built respectively, and the equilibrium solutions are discussed. And the game equilibriums of the model when capital-constrained retailer adopts BCF and TCF are analysed in Section 5. Based on the equilibrium results, the impact of the financing approach on the value of information sharing is explored in Section 6, and the willingness of the well-funded member to provide TCF in Section 7. Section 8 is the numerical study. The last section summarizes the conclusions and provides additional managerial insights for discussions. 2. Literature review This is an interface study of operations management and finance in which the financing options in a capital-constrained supply chain are investigated. It is a typical practice for enterprises suffering capital constraint to establish alternate financing approaches with distinct decisional dynamics amongst supply chain participants. Numerous studies have investigated the selection of financing approaches in a capital-constrained supply chain when alternative capital sources are available [11-16], wherein a significant amount of research has shown the effect of demand uncertainty on the efficiency of BCF and TCF. Jing et al. [8] conclude that BCF should be used under high demand uncertainty to increase channel efficiency. Overall, TCF is more lucrative than BCF for the manufacturer provided manufacturing costs and demand fluctuation are modest but is less profitable otherwise. Based on this study, Chen et al. [17] further verify that TCF improves the efficiency of the channel compared with bank credit. The retailer shares the demand risk with the manufacturer under TCF, and the manufacturer's risk sharing effectively reduces the retailer's marginal cost, which causes the retailer to increase the order quantity. Increased inventory at the store improves anticipated product sales, hence increasing the manufacturer's earnings. They conclude that trade credit is the only financing equilibrium in wholesale price contracts. According to Zhao and Arnd [18], the retailer may select between two pre-shipment finance mechanisms (APD, advance payment discount; BPOF, buyer-backed purchase order financing) to alleviate the supplier's financial difficulties. They discover that the retailer chooses APD over BPOF until the marginal cost of financial hardship outweighs the value of the unit discount. They demonstrate that the financing equilibrium zone of APD grows with both the retailer's internal capital level and demand fluctuation. The decisional dynamics of a supply chain that includes a supplier and a capital-constrained retailer that selects between BCF and TCF are examined by Shi et al. [9] in relation to demand uncertainty reduction (DUR). They recommend that when DUR is high and wholesale price is exogenous and cheap, the retailers should take TCF. And retailers should only take TCF, when the wholesale price is determined endogenously. and both DUR and manufacturing costs are low. Notably, the research described above has mostly focused on choosing a financing approach, and some of them have shown that reducing demand uncertainty would impact the efficacy of BCF and TCF. But all the above literature is conducted under information symmetry. None of them has examined the information-sharing decision of retailers in a capital-constrained supply chain. Information sharing decision, that is, whether to share information based on the selfinterest of the information holder, is the core issue in the field of information sharing. In recent years, much study has been undertaken on the relationship between information sharing and supply chain operation decisions. Mishra et al. [19] demonstrate that in both make-to-order and make-to-stock situations, sharing the forecast unconditionally by the retailer is advantageous for the manufacturer but detrimental for the retailer. However, Li and Zhang [20] conclude that if Advances in Production Engineering & Management 17(3) 2022 265 Duan, Wang, Ye the level of demand uncertainty is moderate, the retailer has an incentive to voluntarily share the information manufacturer in the make-to-stock situations. Lai et al. [21] demonstrate that forecast sharing from the port can not only increase profitability for both partners, but also encourage investments in sustainability, even when the carrier is risk-averse in the marine supply chain. Liu et al. [22] investigate information sharing in a fresh-produce e-commerce supply chain in which the supplier provides freshness-keeping effort, and the e-tailer offers value-added services. They discover that information sharing is more likely to happen when the supplier is more cost-effective in investment in freshness-keeping or when the e-tailer is more effective in service investment. Li et al. [23] focus on a supply chain in which the manufacturer buys a component from the supplier who has private information on supply disruption risk. They discover that when the supplier's initial reliability is low in the pull regime, greater information transparency may be damaging to the manufacturer, but the high-type supplier might surprise provide a significant return under information asymmetry. Wang et al. [24] investigate information sharing in secondary supply chains in the presence of potential supplier intrusion and find that the degree of information sharing by retailers was not related to supplier intrusion. Liu et al. [25] study the information-sharing problem in a secondary supply chain consisting of two homogeneous manufacturers and a value-added retailer and find that when value-added services are cost-inefficient, the manufacturer's receipt of information shared by the retailer hurts its profit instead. Guan et al. [26] develop the information-sharing strategies for two competing supply chains and conclude that when one supply chain chooses an information-sharing strategy will affect the strategy choice of the other supply chain. Yan et al. [27] analyse the impact of blockchain technology on supply chain information coordination and conclude that blockchain technology can effectively reduce supply chain operating costs. However, very few studies consider the effect of information sharing on the financing options of a capital-constrained supply chain, as far as we are aware. To take advantage of this research opportunity, this research seeks to analyse the equilibrium choices of financing approach and information-sharing strategy in a capital-constrained supply chain with the analysis of the interactions between financing channel choice and information-sharing decisions. 3. Model framework Consider a capital-constrained supply chain consisting of a manufacturer (he) and a retailer(she) with asymmetric demand information. The manufacturer or the retailer facing capital constraints chooses between BCF and TCF when challenged with financing problems. BCF is a common financing approach whereby capital constraints are eased by bank loans, whereas TCF with capital-constrained manufacturer/retailer differs. When the manufacturer faces capital constraints, the retailer can offer TCF through advance payment. On the other hand, if the retailer is capital-constrained, TCF is provided via deferred payment from the manufacturer. Thus, it is important for the capital-constrained member to determine which financing approach should be adopted. The proximity to the customers facilitates the retailer to receive more accurate information about the market demand than the manufacturer does. It enables the retailer to determine whether to share the demand information with the manufacturer. This paper explores the equilibrium financing decision of the capital-constrained member and the equilibrium information-sharing decision of the retailer, as well as the interplay of the above two decisions. The sequence of the game when manufacturer faces capital constraints is as follows. Before the selling season, the retailer decides whether to share the information, and the manufacturer decides whether to accept the information if retailer is willing to share. Then the manufacturer determines wholesale price 𝑤𝑤 (𝑤𝑤 > 𝑐𝑐), and the retailer determines retail price retail price 𝑝𝑝 (𝑝𝑝 > 𝑤𝑤) and places the order. After receiving the order, the manufacturer begins production with perunit production cost 𝑐𝑐 if he has sufficient funds, otherwise, he resorts to TCF or BCF for financing. When production is completed, the manufacturer sells the products to the retailer at 𝑤𝑤 and deposits profits into bank. During the selling season, the retailer sells products in the market at 𝑝𝑝, and also deposits the sales proceeds on zero deposit and withdrawal. At the end of the sales season, the manufacturer and retailer take back the principal and interest on the deposit, and 266 Advances in Production Engineering & Management 17(3) 2022 Financing and Information sharing in capital-constrained supply chain the manufacturer pays off the debt. If the retailer is capital-constrained, she pays for the product upon receipt by taking out a loan from the bank or at the end of the sale season through a deferred payment option offered by the manufacturer. 3.1 Demand function The demand function is written as 𝐷𝐷 = 𝑎𝑎 − 𝑏𝑏𝑏𝑏 + 𝜀𝜀, where 𝑎𝑎 refers to the market size and b the demand elasticity of retail price. 𝜀𝜀 is the randomness of market demand, which is assumed to be normally distributed with a mean of 0 and a variance of 𝜎𝜎 2 . We assume that the retailer has private demand forecasting information 𝛾𝛾, i.e., 𝛾𝛾 = 𝜀𝜀 + 𝛿𝛿 , where 𝛿𝛿 captures the noise in the forecast error, which is also normally distributed with a mean of 0 and a variance of 𝜎𝜎02 . According to the existing literature [19, 21], we denote 𝐻𝐻 = 𝐸𝐸[𝜀𝜀|𝛾𝛾] = refers to the market demand fluctuation. 𝜎𝜎 2 𝛾𝛾 𝜎𝜎02 +𝜎𝜎2 3.2 Model assumptions 𝜎𝜎 2 𝜎𝜎 2 and 𝑉𝑉𝑉𝑉𝑉𝑉[𝜀𝜀|𝛾𝛾] = 𝜎𝜎2 +𝜎𝜎02, where 𝐻𝐻 0 To facilitate the construction of the models, we have the following assumptions: (1) The capital-constrained member's initial capital is assumed to be zero. (2) No moral hazard exists. Both the manufacturer and retailer are creditworthy and the loan will be repaid at the conclusion of the sales period;. (3) No bankruptcy risk happens. The supply chain system and the bank operate in good conditions in the game and there are no extreme changes in the market environment. (4) During the s season, the retailer deposits the sales revenue in the bank on a zero-deposit basis, disregarding the self-retaining non-deposit. 4. Manufacturer's choice with capital constraints 4.1 Analysis of trade credit financing The retailer can ease the manufacturer's capital constraints by paying in advance, which is a typical type of TCF. The sequence of the game when a capital-constrained manufacturer adopts TCF is shown in Fig. 1. When the retailer is not willing to share demand information, the manufacturer has to determine the wholesale price according to his private information. The expected profit functions of the manufacturer and the retailer can be described as follows: 𝑀𝑀𝑀𝑀 ] 𝐸𝐸[𝜋𝜋𝑀𝑀1 = (1 + 𝐼𝐼𝑀𝑀 )(𝑤𝑤1𝑀𝑀𝑀𝑀 − 𝑐𝑐)(𝑎𝑎 − 𝑏𝑏𝑝𝑝1𝑀𝑀𝑀𝑀 + 𝐸𝐸[𝜀𝜀]) 𝑀𝑀𝑀𝑀 ] 𝐸𝐸[𝜋𝜋𝑅𝑅1 = [(1 + 𝐼𝐼𝑅𝑅 )𝑝𝑝1𝑀𝑀𝑀𝑀 − 𝑤𝑤1𝑀𝑀𝑀𝑀 ](𝑎𝑎 − 𝑏𝑏𝑝𝑝1𝑀𝑀𝑀𝑀 (1) (2) + 𝐸𝐸[𝜀𝜀|𝛾𝛾]) where 𝐼𝐼𝑀𝑀 and 𝐼𝐼𝑅𝑅 refer to the deposit rate of the manufacturer and the retailer. We express 𝐼𝐼𝑀𝑀 = (𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 + 𝑡𝑡𝑠𝑠𝑠𝑠 )𝑖𝑖𝑀𝑀 and 𝐼𝐼𝑅𝑅 = 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑅𝑅 , wherein 𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 denotes the length of lead time, 𝑡𝑡𝑠𝑠𝑠𝑠 the length of sales period, 𝑖𝑖𝑀𝑀 the bank deposit rate and 𝑖𝑖𝑅𝑅 the deposit rate for zero deposit and withdrawal. Retailer Manufacturer Forecast market demand Decide whether to share information Determine retail price & place order Decide whether to accept Determine the information if retailers wholesale price are willing to share Pay for goods Produce Advance Period Deposit profit into the bank Deposit profit into the bank Fig. 1 The sequence of events with manufacturer’s choice of TCF Advances in Production Engineering & Management 17(3) 2022 Recover principal and interest on deposit Recover principal and interest on deposit Sales Season 267 Duan, Wang, Ye When the retailer decides to share her private demand forecasting information, the manufacturer determines the wholesale price depending on the information shared by the retailer. The expected profit functions of the manufacturer and the retailer are written as: 𝑀𝑀𝑀𝑀 ] 𝐸𝐸[𝜋𝜋𝑀𝑀1 = (1 + 𝐼𝐼𝑀𝑀 )(𝑤𝑤1𝑀𝑀𝑀𝑀 − 𝑐𝑐)(𝑎𝑎 − 𝑏𝑏𝑝𝑝1𝑀𝑀𝑀𝑀 + 𝐸𝐸[𝜀𝜀|𝛾𝛾]) 𝑀𝑀𝑀𝑀 ] 𝐸𝐸[𝜋𝜋𝑅𝑅1 = [(1 + 𝐼𝐼𝑅𝑅 )𝑝𝑝1𝑀𝑀𝑀𝑀 − 𝑤𝑤1𝑀𝑀𝑀𝑀 ](𝑎𝑎 − 𝑏𝑏𝑝𝑝1𝑀𝑀𝑀𝑀 (3) (4) + 𝐸𝐸[𝜀𝜀|𝛾𝛾]). By solving with back induction, we can get the equilibriums of the game with retailer’s sharing or not sharing demand information as shown in Table 1. Table 1 The game equilibriums with manufacturer’s choice of TCF No information sharing (3𝑎𝑎 + 2𝐻𝐻)(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏 𝑝𝑝1𝑀𝑀𝑀𝑀∗ = 4𝑏𝑏(1 + 𝐼𝐼𝑅𝑅 ) 𝑝𝑝1∗ 𝑤𝑤1∗ ∗ 𝜋𝜋𝑅𝑅1 ∗ 𝜋𝜋𝑀𝑀1 ∗ 𝜋𝜋𝑆𝑆𝑆𝑆1 𝑤𝑤1𝑀𝑀𝑀𝑀∗ = 𝑝𝑝1𝑀𝑀𝑀𝑀∗ 𝑎𝑎(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏 2𝑏𝑏 𝑤𝑤1𝑀𝑀𝑀𝑀∗ = 𝑀𝑀𝑀𝑀∗ 𝜋𝜋𝑅𝑅1 = 𝐴𝐴1 𝐻𝐻 2 (1 + 𝐼𝐼𝑅𝑅 )(1 + 𝐼𝐼𝑀𝑀 ) 8𝑏𝑏 𝐻𝐻 2 (1 + 𝐼𝐼𝑅𝑅 )(1 + 𝐼𝐼𝑀𝑀 ) = 𝐴𝐴1 + (1 + 𝐼𝐼𝑀𝑀 )𝐶𝐶1 − 8𝑏𝑏 𝑀𝑀𝑀𝑀∗ 𝜋𝜋𝑀𝑀1 = (1 + 𝐼𝐼𝑀𝑀 )𝐶𝐶1 − 𝑀𝑀𝑀𝑀∗ 𝜋𝜋𝑆𝑆𝑆𝑆1 )−𝑏𝑏𝑏𝑏]2 )−𝑏𝑏𝑏𝑏]2 Information sharing 3(𝑎𝑎 + 𝐻𝐻)(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏 = 4𝑏𝑏(1 + 𝐼𝐼𝑅𝑅 ) )−𝑏𝑏𝑏𝑏]2 (𝑎𝑎 + 𝐻𝐻)(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏 2𝑏𝑏 𝑀𝑀𝑀𝑀∗ 𝜋𝜋𝑅𝑅1 = 𝐵𝐵1 𝑀𝑀𝑀𝑀∗ 𝜋𝜋𝑀𝑀1 = 2(1 + 𝐼𝐼𝑀𝑀 )𝐵𝐵1 𝑀𝑀𝑀𝑀∗ 𝜋𝜋𝑆𝑆𝑆𝑆1 = (3 + 2𝐼𝐼𝑀𝑀 )𝐵𝐵1 [(𝑎𝑎+𝐻𝐻)(1+𝐼𝐼𝑅𝑅 [(𝑎𝑎−𝐻𝐻)(1+𝐼𝐼𝑅𝑅 𝑅𝑅 Note: 𝐴𝐴1 = [(𝑎𝑎+2𝐻𝐻)(1+𝐼𝐼 , 𝐵𝐵1 = , 𝐶𝐶1 = . The deposit rate of the respective 16𝑏𝑏(1+𝐼𝐼𝑅𝑅 ) 16𝑏𝑏(1+𝐼𝐼𝑅𝑅 ) 16𝑏𝑏(1+𝐼𝐼𝑅𝑅 ) manufacturer and retailer and the bank loan rate is denoted as 𝐼𝐼𝑀𝑀 = (𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 + 𝑡𝑡𝑠𝑠𝑠𝑠 )𝑖𝑖𝑀𝑀 , 𝐼𝐼𝑅𝑅 = 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑅𝑅 where 𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 , 𝑡𝑡𝑠𝑠𝑠𝑠 , 𝑖𝑖𝑀𝑀 , and 𝑖𝑖𝑅𝑅 represent the length of lead time, the length of sales period, the bank deposit rate and the deposit rate for zero deposit and withdrawal respectively. According to the game equilibriums, when the manufacturer faces capital constraints and adopts TCF, the optimal wholesale price is positively related to the retailer's deposit rate and deposit time regardless of whether she shares demand information. Inversely, the optimal retail price is negatively related to the retailer's deposit rate and deposit time. Both the optimal wholesale price and retail price are independent of the manufacturer's deposit rate and deposit time. The retailers' profits are only positively related to the retailer's time deposit rate of small savings for lump-sum withdrawal over time, which is independent of the manufacturers' deposit rate and time. In contrast, the manufacturers' profits are positively correlated not only with both members’ deposit rates and time but also with the retailer's time deposit rate of small savings for lump-sum withdrawal over time. 4.2 Analysis of bank credit financing BCF refers to the financing channel where the manufacturer raises seed money from bank loans. The sequence of events when a capital-constrained manufacturer adopts BCF is shown in Fig. 2. Retailer Forecast Decide whether to market share information demand Determine retail price & place order Pay for goods Deposit profit into the bank Manufacturer Take out a Decide whether to accept Determine the information if retailers wholesale price bank loan & produce are willing to share Repay the debt & deposit the profit into the bank （pay cash point） Fig. 2 The sequence of events with manufacturer’s choice of BCF 268 Recover principal and interest on deposit Recover principal and interest on deposit Sales Season Advances in Production Engineering & Management 17(3) 2022 Financing and Information sharing in capital-constrained supply chain When the retailer does not share demand information, the manufacturer can only determine the wholesale price based on his private information. The expected profit functions of the manufacturer and the retailer are as follows: 𝑀𝑀𝑀𝑀 ] 𝐸𝐸[𝜋𝜋𝑀𝑀2 = [(1 + 𝐼𝐼𝑀𝑀 )𝑤𝑤2𝑀𝑀𝑀𝑀 − (1 + 𝐼𝐼𝑀𝑀 + 𝐽𝐽𝑀𝑀 )𝑐𝑐](𝑎𝑎 − 𝑏𝑏𝑝𝑝2𝑀𝑀𝑀𝑀 + 𝐸𝐸[𝜀𝜀]) (5) 𝑀𝑀𝑀𝑀 ] 𝐸𝐸[𝜋𝜋𝑅𝑅2 = [(1 + 𝐼𝐼𝑅𝑅 )𝑝𝑝2𝑀𝑀𝑀𝑀 − 𝑤𝑤2𝑀𝑀𝑀𝑀 ](𝑎𝑎 − 𝑏𝑏𝑝𝑝2𝑀𝑀𝑀𝑀 + 𝐸𝐸[𝜀𝜀|𝛾𝛾]) (8) 𝑀𝑀𝑀𝑀 ] 𝐸𝐸[𝜋𝜋𝑅𝑅2 = [(1 + 𝐼𝐼𝑅𝑅 )𝑝𝑝2𝑀𝑀𝑀𝑀 − 𝑤𝑤2𝑀𝑀𝑀𝑀 ](𝑎𝑎 − 𝑏𝑏𝑝𝑝2𝑀𝑀𝑀𝑀 + 𝐸𝐸[𝜀𝜀|𝛾𝛾]) (6) On the other hand, if the retailer shares her private demand forecasting information with the manufacturer, the wholesale price is chosen according to the information that is shared by retailer. The expected profit functions of the manufacturer and the retailer can be described as follows: 𝑀𝑀𝑀𝑀 ] (7) 𝐸𝐸[𝜋𝜋𝑀𝑀2 = [(1 + 𝐼𝐼𝑀𝑀 )𝑤𝑤2𝑀𝑀𝑀𝑀 − (1 + 𝐼𝐼𝑀𝑀 + 𝐽𝐽𝑀𝑀 )𝑐𝑐](𝑎𝑎 − 𝑏𝑏𝑝𝑝2𝑀𝑀𝑀𝑀 + 𝐸𝐸[𝜀𝜀|𝛾𝛾]) By solving the above formulas, we derive the game equilibriums with alternative information-sharing decisions of the retailer, which is shown in Table 2. Table 2 The game equilibriums with manufacturer’s choice of BCF 𝑝𝑝2∗ 𝑤𝑤2∗ ∗ 𝜋𝜋𝑅𝑅2 ∗ 𝜋𝜋𝑀𝑀2 ∗ 𝜋𝜋𝑆𝑆𝑆𝑆2 No information sharing (3𝑎𝑎 + 2𝐻𝐻)(1 + 𝐼𝐼𝑀𝑀 )(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏(1 + 𝐼𝐼𝑀𝑀 + 𝐽𝐽𝑀𝑀 ) 𝑝𝑝2𝑀𝑀𝑀𝑀∗ = 4𝑏𝑏(1 + 𝐼𝐼𝑀𝑀 )(1 + 𝐼𝐼𝑅𝑅 ) )(1 𝑎𝑎(1 + 𝐼𝐼𝑀𝑀 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏(1 + 𝐼𝐼𝑀𝑀 + 𝐽𝐽𝑀𝑀 ) 𝑤𝑤2𝑀𝑀𝑀𝑀∗ = 2𝑏𝑏(1 + 𝐼𝐼𝑀𝑀 ) 𝑀𝑀𝑀𝑀∗ 𝜋𝜋𝑅𝑅2 = 𝐴𝐴2 𝐻𝐻 2 (1 + 𝐼𝐼𝑀𝑀 )(1 + 𝐼𝐼𝑅𝑅 ) 8𝑏𝑏 𝐻𝐻 2 (1 + 𝐼𝐼𝑀𝑀 )(1 + 𝐼𝐼𝑅𝑅 ) = 𝐴𝐴2 + 𝐶𝐶2 − 8𝑏𝑏 Information sharing 3(𝑎𝑎 + 𝐻𝐻)(1 + 𝐼𝐼𝑀𝑀 )(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏(1 + 𝐼𝐼𝑀𝑀 + 𝐽𝐽𝑀𝑀 ) 𝑝𝑝2𝑀𝑀𝑀𝑀∗ = 4𝑏𝑏(1 + 𝐼𝐼𝑀𝑀 )(1 + 𝐼𝐼𝑅𝑅 ) (𝑎𝑎 + 𝐻𝐻)(1 + 𝐼𝐼𝑀𝑀 )(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏(1 + 𝐼𝐼𝑀𝑀 + 𝐽𝐽𝑀𝑀 ) 𝑤𝑤2𝑀𝑀𝑀𝑀∗ = 2𝑏𝑏(1 + 𝐼𝐼𝑀𝑀 ) 𝑀𝑀𝑀𝑀∗ 𝜋𝜋𝑅𝑅2 = 𝐵𝐵2 𝑀𝑀𝑀𝑀∗ 𝜋𝜋𝑀𝑀2 = 2(1 + 𝐼𝐼𝑀𝑀 )𝐵𝐵2 𝑀𝑀𝑀𝑀∗ 𝜋𝜋𝑀𝑀2 = 𝐶𝐶2 − 𝑀𝑀𝑀𝑀∗ 𝜋𝜋𝑆𝑆𝑆𝑆2 )(1+𝐼𝐼 )−𝑏𝑏𝑏𝑏(1+𝐼𝐼 )]2 [(𝑎𝑎+𝐻𝐻)(1+𝐼𝐼 )(1+𝐼𝐼 )−𝑏𝑏𝑏𝑏(1+𝐼𝐼 )]2 𝑀𝑀𝑀𝑀∗ 𝜋𝜋𝑆𝑆𝑆𝑆2 = (3 + 2𝐼𝐼𝑀𝑀 )𝐵𝐵2 )(1+𝐼𝐼 )−𝑏𝑏𝑏𝑏(1+𝐼𝐼 )]2 [(𝑎𝑎−𝐻𝐻)(1+𝐼𝐼𝑅𝑅 𝑅𝑅 𝑀𝑀 𝑀𝑀 +𝐽𝐽𝑀𝑀 𝑅𝑅 𝑀𝑀 𝑀𝑀 +𝐽𝐽𝑀𝑀 𝑀𝑀 𝑀𝑀 +𝐽𝐽𝑀𝑀 Note: 𝐴𝐴2 = [(𝑎𝑎+2𝐻𝐻)(1+𝐼𝐼 , 𝐵𝐵2 = , 𝐶𝐶2 = . 16𝑏𝑏(1+𝐼𝐼𝑅𝑅 )(1+𝐼𝐼𝑀𝑀 )2 16𝑏𝑏(1+𝐼𝐼𝑅𝑅 )(1+𝐼𝐼𝑀𝑀 )2 16𝑏𝑏(1+𝐼𝐼𝑅𝑅 )(1+𝐼𝐼𝑀𝑀 )2 The deposit rate of the respective manufacturer and retailer and the bank loan rate is denoted as 𝐼𝐼𝑀𝑀 = 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 , 𝐼𝐼𝑅𝑅 = 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑅𝑅 and 𝐽𝐽𝑀𝑀 = 𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 𝑗𝑗𝑀𝑀 , where 𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 , 𝑡𝑡𝑠𝑠𝑠𝑠 , 𝑖𝑖𝑀𝑀 , 𝑖𝑖𝑅𝑅 and 𝑗𝑗𝑀𝑀 represent the length of lead time, the length of sales period, the bank deposit rate, the deposit rate for zero deposit and withdrawal and the bank loan rate respectively. A comparison with the previous conclusions in Section 4.1 shows that when the manufacturer faces capital constraints and adopts BCF, both the optimal wholesale price and the optimal retail price are related to the manufacturer's bank deposit and loan interest rate, as well as the length of lead time and sales period. Meanwhile, the profits of both the retailer and manufacturer depend on the manufacturer’s loan rate and the length of lead time. The rest of the conclusions are similar to those in the previous section. 4.3 Information sharing strategy with manufacturer's capital constraints By comparing the game equilibriums in the scenarios with retailer’s sharing or not sharing demand information, we have the following analytical results for the information-sharing strategy when the manufacturer is capital-constrained. Proposition 1: The retailer’s equilibrium information sharing strategy with the manufacturer’s capital constraints is given as: (1) When the actual market demand fluctuates positively (i.e., 𝐻𝐻 > 0), regardless of the capitalconstrained manufacturer’s choice of TCF or BCF, the wholesale price and the retail price will both increase if the retailer shares demand information, i.e., 𝑤𝑤1𝑀𝑀𝑀𝑀∗ > 𝑤𝑤1𝑀𝑀𝑀𝑀∗ , 𝑤𝑤2𝑀𝑀𝑀𝑀∗ > 𝑤𝑤2𝑀𝑀𝑀𝑀∗ , 𝑝𝑝1𝑀𝑀𝑀𝑀∗ > 𝑝𝑝1𝑀𝑀𝑀𝑀∗ and 𝑝𝑝2𝑀𝑀𝑀𝑀∗ > 𝑝𝑝2𝑀𝑀𝑀𝑀∗. Meanwhile, the retailer's profit will decrease while the manufac𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ > 𝜋𝜋𝑅𝑅1 , 𝜋𝜋𝑅𝑅2 > 𝜋𝜋𝑅𝑅2 , 𝜋𝜋𝑀𝑀1 < 𝜋𝜋𝑀𝑀1 and 𝜋𝜋𝑀𝑀2 < 𝜋𝜋𝑀𝑀2 . Thus, it is turer’s profit grows, i.e., 𝜋𝜋𝑅𝑅1 not wise for the retailer to share demand information. Advances in Production Engineering & Management 17(3) 2022 269 Duan, Wang, Ye (2) When the actual market demand fluctuates negatively (i.e., 𝐻𝐻 < 0), regardless of the capitalconstrained manufacturer’s choice of TCF or BCF, the wholesale price and the retail price will go down with the retailer’s information sharing decision, i.e., 𝑤𝑤1𝑀𝑀𝑀𝑀∗ < 𝑤𝑤1𝑀𝑀𝑀𝑀∗ , 𝑤𝑤2𝑀𝑀𝑀𝑀∗ < 𝑤𝑤2𝑀𝑀𝑀𝑀∗ , 𝑝𝑝1𝑀𝑀𝑀𝑀∗ < 𝑝𝑝1𝑀𝑀𝑀𝑀∗ and 𝑝𝑝2𝑀𝑀𝑀𝑀∗ < 𝑝𝑝2𝑀𝑀𝑀𝑀∗ . Meanwhile, the retailer’s profit will be improved and the manufacturer’s 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ < 𝜋𝜋𝑅𝑅1 , 𝜋𝜋𝑅𝑅2 < 𝜋𝜋𝑅𝑅2 , 𝜋𝜋𝑀𝑀1 > 𝜋𝜋𝑀𝑀1 and 𝜋𝜋𝑀𝑀2 > 𝜋𝜋𝑀𝑀2 . As a result, profit will decrease, i.e., 𝜋𝜋𝑅𝑅1 the manufacturer will not accept the offer of information sharing even if the retailer is willing to. In conclusion, with positively fluctuating demand, the manufacturer may raise the wholesale price given the demand information shared by the retailer, which will exacerbate the double marginalization effect. It results in the retailer’s no willingness of sharing demand information. In contrast, with negatively fluctuating demand, the demand information shared by the retailer may force the manufacturer to reduce the wholesale price. Even if it encourages the retailer to share demand information, the manufacturer will not accept it because his profit will be reduced. In summary, information sharing can't be realized in a supply chain with a capitalconstrained manufacturer. 4.4 Manufacturer's financing choice with capital constraints Given the game equilibriums of the capital-constrained manufacturer adopting TCF and BCF, we have the following analytical results for the equilibrium financing approach for the manufacturer. Proposition 2: The profits of both the retailer and the manufacturer will be improved if the capital-constrained manufacturer chooses TCF, regardless of whether the retailer shares demand 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ information or not, i.e., 𝜋𝜋𝑀𝑀1 > 𝜋𝜋𝑀𝑀2 , 𝜋𝜋𝑅𝑅1 > 𝜋𝜋𝑅𝑅2 , 𝜋𝜋𝑀𝑀1 > 𝜋𝜋𝑀𝑀2 and 𝜋𝜋𝑅𝑅1 > 𝜋𝜋𝑅𝑅2 . Therefore, TCF is the equilibrium financing choice for the capital-constrained manufacturer. 5. Retailer's choice with capital constraints 5.1 Analysis of trade credit financing The retailer’s financing problem is possibly solved by deferred payment, which is a typical type of TCF provided by the manufacturer. The sequence of decisions when the capital-constrained retailer adopts TCF is shown in Fig. 3. Retailer Manufacturer Forecast market Decide whether to demand share information Determine retail price & place order Decide whether to accept Determine the information if retailers wholesale price are willing to share Deposit profit into the bank Recover principal and interest on deposit & pay for goods Receive payment for goods Produce Sales Season Fig. 3 The sequence of events with capital-constrained retailer’s choice of TCF For the retailer’s decision not to share demand information, the manufacturer can only determine the wholesale price based on private information. The expected profit functions of the manufacturer and the retailer can be described as follows: 𝑅𝑅𝑅𝑅 ] 𝐸𝐸[𝜋𝜋𝑀𝑀3 = (𝑤𝑤3𝑅𝑅𝑅𝑅 − 𝑐𝑐)(𝑎𝑎 − 𝑏𝑏𝑝𝑝3𝑅𝑅𝑅𝑅 + 𝐸𝐸[𝜀𝜀]) 𝑅𝑅𝑅𝑅 ] 𝐸𝐸[𝜋𝜋𝑅𝑅3 = [(1 + 𝐼𝐼𝑅𝑅 )𝑝𝑝3𝑅𝑅𝑅𝑅 − 𝑤𝑤3𝑅𝑅𝑅𝑅 ](𝑎𝑎 − 𝑏𝑏𝑝𝑝3𝑅𝑅𝑅𝑅 + 𝐸𝐸[𝜀𝜀|𝛾𝛾]) (9) (10) When the retailer shares her private demand forecasting information, the manufacturer determines the wholesale price depending on the information shared by the retailer. The expected profit function of the manufacturer and the retailer are given as: 270 Advances in Production Engineering & Management 17(3) 2022 Financing and Information sharing in capital-constrained supply chain 𝑅𝑅𝑅𝑅 ] 𝐸𝐸[𝜋𝜋𝑀𝑀3 = (𝑤𝑤3𝑅𝑅𝑅𝑅 − 𝑐𝑐)(𝑎𝑎 − 𝑏𝑏𝑝𝑝3𝑅𝑅𝑅𝑅 + 𝐸𝐸[𝜀𝜀|𝛾𝛾]) (11) 𝑅𝑅𝑅𝑅 ] 𝐸𝐸[𝜋𝜋𝑅𝑅3 = [(1 + 𝐼𝐼𝑅𝑅 )𝑝𝑝3𝑅𝑅𝑅𝑅 − 𝑤𝑤3𝑅𝑅𝑅𝑅 ](𝑎𝑎 − 𝑏𝑏𝑝𝑝3𝑅𝑅𝑅𝑅 + 𝐸𝐸[𝜀𝜀|𝛾𝛾]) (12) Solving with the back induction method, we show the game equilibriums when the retailer shares demand information or not in Table 3. Table 3 The game equilibriums with capital-constrained retailer’s choice of TCF 𝑝𝑝3∗ 𝑤𝑤3∗ 𝑝𝑝3𝑅𝑅𝑅𝑅∗ ∗ 𝜋𝜋𝑆𝑆𝑆𝑆3 Information sharing (3𝑎𝑎 + 2𝐻𝐻)(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏 = 4𝑏𝑏(1 + 𝐼𝐼𝑅𝑅 ) 𝑤𝑤3𝑅𝑅𝑅𝑅∗ = ∗ 𝜋𝜋𝑅𝑅3 ∗ 𝜋𝜋𝑀𝑀3 No information sharing 𝑝𝑝3𝑅𝑅𝑅𝑅∗ = 𝑎𝑎(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏 2𝑏𝑏 𝑤𝑤3𝑅𝑅𝑅𝑅∗ = 𝑅𝑅𝑅𝑅∗ 𝜋𝜋𝑅𝑅3 = 𝐴𝐴3 𝐻𝐻 2 (1 + 𝐼𝐼𝑅𝑅 ) 8𝑏𝑏 𝐻𝐻 2 (1 + 𝐼𝐼𝑅𝑅 ) = 𝐴𝐴3 + 𝐶𝐶3 − 8𝑏𝑏 )−𝑏𝑏𝑏𝑏]2 )−𝑏𝑏𝑏𝑏]2 (𝑎𝑎 + 𝐻𝐻)(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏 2𝑏𝑏 𝑅𝑅𝑅𝑅∗ 𝜋𝜋𝑅𝑅3 = 𝐵𝐵3 𝑅𝑅𝑅𝑅∗ 𝜋𝜋𝑀𝑀3 = 2𝐵𝐵3 𝑅𝑅𝑅𝑅∗ 𝜋𝜋𝑀𝑀3 = 𝐶𝐶3 − 𝑅𝑅𝑅𝑅∗ 𝜋𝜋𝑆𝑆𝑆𝑆3 3(𝑎𝑎 + 𝐻𝐻)(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏 4𝑏𝑏(1 + 𝐼𝐼𝑅𝑅 ) 𝑅𝑅𝑅𝑅∗ 𝜋𝜋𝑆𝑆𝑆𝑆3 = 3𝐵𝐵3 [(𝑎𝑎−𝐻𝐻)(1+𝐼𝐼 )−𝑏𝑏𝑏𝑏]2 [(𝑎𝑎+𝐻𝐻)(1+𝐼𝐼𝑅𝑅 𝑅𝑅 𝑅𝑅 Note: 𝐴𝐴3 = [(𝑎𝑎+2𝐻𝐻)(1+𝐼𝐼 , 𝐵𝐵3 = , 𝐶𝐶3 = . Denote 𝐼𝐼𝑅𝑅 = 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑅𝑅 as the retailer’s 16𝑏𝑏(1+𝐼𝐼𝑅𝑅 ) 16𝑏𝑏(1+𝐼𝐼𝑅𝑅 ) 8𝑏𝑏(1+𝐼𝐼𝑅𝑅 ) deposits, where 𝑡𝑡𝑠𝑠𝑠𝑠 refers to the length of sales period, 𝑖𝑖𝑅𝑅 the deposit rate for zero deposit and withdrawal. 5.2 Analysis of bank credit financing The retailer may also go for bank loans to deal with the financing problem. The sequence of decisions when the capital-constrained retailer adopts BCF is shown in Fig. 4. Without information sharing from the retailer, the manufacturer chooses the wholesale price solely dependent on his private information. The expected profit functions of the manufacturer and the retailer are as follows: 𝑅𝑅𝑅𝑅 ] 𝐸𝐸[𝜋𝜋𝑀𝑀4 = (1 + 𝐼𝐼𝑀𝑀 )(𝑤𝑤4𝑅𝑅𝑅𝑅 − 𝑐𝑐)(𝑎𝑎 − 𝑏𝑏𝑝𝑝4𝑅𝑅𝑅𝑅 + 𝐸𝐸[𝜀𝜀]) (13) 𝑅𝑅𝑅𝑅 ] 𝐸𝐸[𝜋𝜋𝑅𝑅4 = [(1 + 𝐼𝐼𝑅𝑅 )𝑝𝑝4𝑅𝑅𝑅𝑅 − (1 + 𝐽𝐽𝑅𝑅 )𝑤𝑤4𝑅𝑅𝑅𝑅 ](𝑎𝑎 − 𝑏𝑏𝑝𝑝4𝑅𝑅𝑅𝑅 + 𝐸𝐸[𝜀𝜀|𝛾𝛾]) (14) While the retailer decides to share, the manufacturer determines the wholesale price according to the information shared by the retailer. The expected profit functions of the manufacturer and the retailer are described as: 𝑅𝑅𝑅𝑅 ] 𝐸𝐸[𝜋𝜋𝑀𝑀4 = (1 + 𝐼𝐼𝑀𝑀 )(𝑤𝑤4𝑅𝑅𝑅𝑅 − 𝑐𝑐)(𝑎𝑎 − 𝑏𝑏𝑝𝑝4𝑅𝑅𝐼𝐼 + 𝐸𝐸[𝜀𝜀|𝛾𝛾]) 𝑅𝑅𝑅𝑅 ] 𝐸𝐸[𝜋𝜋𝑅𝑅4 = [(1 + 𝐼𝐼𝑅𝑅 )𝑝𝑝4𝑅𝑅𝑅𝑅 − (1 + 𝐽𝐽𝑅𝑅 )𝑤𝑤4𝑅𝑅𝑅𝑅 ](𝑎𝑎 − 𝑏𝑏𝑝𝑝4𝑅𝑅𝑅𝑅 (15) (16) + 𝐸𝐸[𝜀𝜀|𝛾𝛾]) Thus, we have the game equilibriums when the retailer shares or does not share demand information, as summarized in Table 4. Retailer Manufacturer Forecast Decide whether market to share demand information Determine retail price & place order Take out a bank loan & pay for goods Delivery product & Determine Produce Decide whether to accept deposit profit in to the the information if retailers wholesale price bank are willing to share （ cash pay point） Deposit profit into the bank Recover principal and interest on deposit & repay the debt Recover principal and interest on deposit Sales Season Fig. 4 The sequence of events with capital-constrained retailer’s choice of BCF Advances in Production Engineering & Management 17(3) 2022 271 Duan, Wang, Ye Table 4 The game equilibriums with capital-constrained retailer’s choice of BCF 𝑝𝑝4∗ 𝑤𝑤4∗ ∗ 𝜋𝜋𝑅𝑅4 No information sharing (3𝑎𝑎 + 2𝐻𝐻)(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏(1 + 𝐽𝐽𝑅𝑅 ) 𝑝𝑝4𝑅𝑅𝑅𝑅∗ = 4𝑏𝑏(1 + 𝐼𝐼𝑅𝑅 ) 𝑎𝑎(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏(1 + 𝐽𝐽𝑅𝑅 ) 𝑤𝑤4𝑅𝑅𝑅𝑅∗ = 2𝑏𝑏(1 + 𝐽𝐽𝑅𝑅 ) 𝑅𝑅𝑅𝑅∗ 𝜋𝜋𝑅𝑅4 = 𝐴𝐴4 ∗ 𝜋𝜋𝑀𝑀4 ∗ 𝜋𝜋𝑆𝑆𝑆𝑆4 Information sharing 3(𝑎𝑎 + 𝐻𝐻)(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏(1 + 𝐽𝐽𝑅𝑅 ) 𝑝𝑝4𝑅𝑅𝑅𝑅∗ = 4𝑏𝑏(1 + 𝐼𝐼𝑅𝑅 ) (𝑎𝑎 + 𝐻𝐻)(1 + 𝐼𝐼𝑅𝑅 ) + 𝑏𝑏𝑏𝑏(1 + 𝐽𝐽𝑅𝑅 ) 𝑤𝑤4𝑅𝑅𝑅𝑅∗ = 2𝑏𝑏(1 + 𝐽𝐽𝑅𝑅 ) 𝑅𝑅𝑅𝑅∗ 𝜋𝜋𝑀𝑀4 = (1 + 𝐼𝐼𝑀𝑀 )𝐶𝐶4 )−𝑏𝑏𝑏𝑏(1+𝐽𝐽 2 𝑅𝑅𝑅𝑅∗ 𝜋𝜋𝑆𝑆𝑆𝑆4 = 𝐴𝐴4 + (1 + 𝐼𝐼𝑀𝑀 )𝐶𝐶4 )−𝑏𝑏𝑏𝑏(1+𝐽𝐽 𝑅𝑅𝑅𝑅∗ 𝜋𝜋𝑅𝑅4 = 𝐵𝐵4 2(1 + 𝐼𝐼𝑀𝑀 ) 𝐵𝐵 (1 + 𝐽𝐽𝑅𝑅 ) 4 (3 + 2𝐼𝐼𝑀𝑀 + 𝐽𝐽𝑅𝑅 ) = 𝐵𝐵4 (1 + 𝐽𝐽𝑅𝑅 ) 𝑅𝑅𝑅𝑅∗ 𝜋𝜋𝑀𝑀4 = 2 𝑅𝑅𝑅𝑅∗ 𝜋𝜋𝑆𝑆𝑆𝑆4 )−𝑏𝑏𝑏𝑏(1+𝐽𝐽 )]2 2 (1+𝐼𝐼 )2 [(𝑎𝑎+𝐻𝐻)(1+𝐼𝐼𝑅𝑅 [(𝑎𝑎−𝐻𝐻)(1+𝐼𝐼𝑅𝑅 −𝐻𝐻 𝑅𝑅 𝑅𝑅 )] 𝑅𝑅 )] 𝑅𝑅 𝑅𝑅 Note: 𝐴𝐴4 = [(𝑎𝑎+2𝐻𝐻)(1+𝐼𝐼 , 𝐵𝐵4 = , 𝐶𝐶4 = . The deposit 16𝑏𝑏(1+𝐼𝐼𝑅𝑅 ) 16𝑏𝑏(1+𝐼𝐼𝑅𝑅 ) 8𝑏𝑏(1+𝐼𝐼𝑅𝑅 )(1+𝐽𝐽𝑅𝑅 ) rate of the respective manufacturer and retailer and the bank loan rate is denoted as 𝐼𝐼𝑀𝑀 = 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 , 𝐼𝐼𝑅𝑅 = 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑅𝑅 and 𝐽𝐽𝑀𝑀 = 𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 𝑗𝑗𝑀𝑀 , where 𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 , 𝑡𝑡𝑠𝑠𝑠𝑠 , 𝑖𝑖𝑀𝑀 , 𝑖𝑖𝑅𝑅 and 𝑗𝑗𝑀𝑀 represent the length of lead time, the length of sales period, the bank deposit rate, the deposit rate for zero deposit and withdrawal and the bank loan rate respectively. 5.3 Information sharing strategy with retailer's capital constraints Comparing the game equilibriums obtained from Table 5 (i.e., information sharing vs. no information sharing), we have the following propositions with regard to the information-sharing strategy when the retailer faces capital constraints. Proposition 3: The equilibrium information-sharing strategy in a supply chain with retailer’s capital constraints is provided as follows: (1) When the actual market demand fluctuates positively (i.e., 𝐻𝐻 > 0), regardless of whether the financially constrained retailer takes TCF or BCF, the wholesale price and the retail price will be improved if the retailer shares demand information, i.e., 𝑤𝑤3𝑅𝑅𝑅𝑅∗ > 𝑤𝑤3𝑅𝑅𝑅𝑅∗ , 𝑤𝑤4𝑅𝑅𝑅𝑅∗ > 𝑤𝑤4𝑅𝑅𝑅𝑅∗ , 𝑝𝑝3𝑅𝑅𝑅𝑅∗ > 𝑝𝑝3𝑅𝑅𝑅𝑅∗ and 𝑝𝑝4𝑅𝑅𝑅𝑅∗ > 𝑝𝑝4𝑅𝑅𝑅𝑅∗ . Meanwhile, the retailer’s profit will decrease while the manufacturer’s profit 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ > 𝜋𝜋𝑅𝑅3 , 𝜋𝜋𝑅𝑅4 > 𝜋𝜋𝑅𝑅4 , 𝜋𝜋𝑀𝑀3 < 𝜋𝜋𝑀𝑀3 and 𝜋𝜋𝑀𝑀4 < 𝜋𝜋𝑀𝑀4 . As a consequence, the retailgrows, i.e., 𝜋𝜋𝑅𝑅3 er has no motives to share demand information. (2) When the actual market demand fluctuates negatively (i.e., 𝐻𝐻 < 0), regardless of whether the financially constrained retailer takes TCF or BCF, the wholesale price and the retail price will be reduced if the retailer shares demand information, i.e., 𝑤𝑤3𝑅𝑅𝑅𝑅∗ < 𝑤𝑤3𝑅𝑅𝑅𝑅∗ , 𝑤𝑤4𝑅𝑅𝑅𝑅∗ < 𝑤𝑤4𝑅𝑅𝑅𝑅∗ , 𝑝𝑝3𝑅𝑅𝑅𝑅∗ < 𝑝𝑝3𝑅𝑅𝑅𝑅∗ and 𝑝𝑝4𝑅𝑅𝑅𝑅∗ < 𝑝𝑝4𝑅𝑅𝑅𝑅∗ . Meanwhile, the retailer's profit will increase while that of the manufacturer 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ < 𝜋𝜋𝑅𝑅3 , 𝜋𝜋𝑅𝑅4 < 𝜋𝜋𝑅𝑅4 , 𝜋𝜋𝑀𝑀3 > 𝜋𝜋𝑀𝑀3 and 𝜋𝜋𝑀𝑀4 > 𝜋𝜋𝑀𝑀4 . Therefore, the manufacdecreases, i.e., 𝜋𝜋𝑅𝑅3 turer will choose not to accept the information-sharing offer even if the retailer has a willingness to share. In conclusion, with positively fluctuating demand, the manufacturer may raise the wholesale price given the demand information shared by the retailer, which will exacerbate the double marginalization effect. It results in the retailer’s no willingness of sharing demand information. In contrast, with negatively fluctuating demand, the demand information shared by the retailer may force the manufacturer to reduce the wholesale price. Even if it encourages the retailer to share demand information, the manufacturer will not accept it because his profit will be reduced. In summary, information sharing can't be realized in a supply chain with a capitalconstrained retailer. 272 Advances in Production Engineering & Management 17(3) 2022 Financing and Information sharing in capital-constrained supply chain 5.4 Retailer’s financing choice with capital constraints Given the game equilibriums of the capital-constrained manufacturer’s choice between TCF and BCF, we have the following analytical results for the equilibrium financing strategy when the retailer is capital-constrained. Proposition 4: The profits of both the retailer and the manufacturer will be improved if the capital-constrained retailer chooses TCF, regardless of whether the retailer shares demand infor𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ 𝑅𝑅𝑅𝑅∗ > 𝜋𝜋𝑀𝑀4 , 𝜋𝜋𝑅𝑅3 > 𝜋𝜋𝑅𝑅4 , 𝜋𝜋𝑀𝑀3 > 𝜋𝜋𝑀𝑀4 and 𝜋𝜋𝑅𝑅3 > 𝜋𝜋𝑅𝑅4 . Therefore, TCF is the mation or not, i.e., 𝜋𝜋𝑀𝑀3 equilibrium financing choice for the capital-constrained retailer. Because BCT increases the cost of retailer. 6. Impact of financing choice on the value of information sharing According to Proposition 1 and Proposition 3, we conclude that it is not wise for the retailer to share demand forecasting information regardless of the capital-constrained member’s financing choice (i.e., TCF vs. BCF). However, will the financing choice have an impact on the value of information sharing? Is information sharing beneficial to the whole supply chain? Can manufacturer incentivize the retailer to share demand forecasting information through unilateral payment? To answer the above questions, we conduct the value analysis of information sharing based on the game equilibriums for the capital-constrained member adopting TCF and BCF respectively to look at the impact of capital constraints and financing choices on the value of information sharing. 𝑖𝑖 𝑖𝑖 , 𝑣𝑣𝑅𝑅𝑗𝑗 , and The value of information sharing to the manufacturer and retailer is denoted as 𝑣𝑣𝑀𝑀𝑗𝑗 the value of information sharing to the supply chain as 𝑣𝑣𝑗𝑗 .Then we have: 𝑖𝑖 𝑖𝑖𝑖𝑖∗ 𝑖𝑖𝑖𝑖∗ 𝑣𝑣𝑀𝑀𝑀𝑀 = 𝜋𝜋𝑀𝑀𝑀𝑀 − 𝜋𝜋𝑀𝑀𝑀𝑀 𝑖𝑖 𝑖𝑖𝑖𝑖∗ 𝑖𝑖𝑖𝑖∗ 𝑣𝑣𝑅𝑅𝑅𝑅 = 𝜋𝜋𝑅𝑅𝑅𝑅 − 𝜋𝜋𝑅𝑅𝑅𝑅 𝑖𝑖 𝑖𝑖 𝑣𝑣𝑗𝑗 = 𝑣𝑣𝑀𝑀𝑀𝑀 + 𝑣𝑣𝑅𝑅𝑅𝑅 (17) (18) (19) where 𝑖𝑖 = 𝑀𝑀, 𝑅𝑅, j = 1, 2, 3, 4, 𝑀𝑀 means the manufacturer faces capital constraints, 𝑅𝑅 means the retailer faces capital constraints, 1 means the capital-constrained manufacturer adopts TCF, 2 means the capital-constrained manufacturer adopts BCF, 3 means the capital-constrained retailer adopts TCF, 4 means the capital-constrained retailer adopts BCF. The value of information sharing calculated based on Eqs. 17 to 19, and the following results can be derived. 𝑀𝑀 Result 1: When 𝐻𝐻 > 0, the value of information sharing to the retailer is negative with �𝑣𝑣𝑅𝑅1 �> 𝑀𝑀 𝑅𝑅 𝑅𝑅 �𝑣𝑣𝑅𝑅2 � and�𝑣𝑣𝑅𝑅3 � > �𝑣𝑣𝑅𝑅4 �, which suggests that the retailer loses more profit from sharing demand information so that she is less willing to share while TCF is used. When 𝐻𝐻 < 0, the value of in𝑀𝑀 𝑀𝑀 𝑅𝑅 𝑅𝑅 formation sharing to the manufacturer is negative with �𝑣𝑣𝑀𝑀1 � > �𝑣𝑣𝑀𝑀2 � and �𝑣𝑣𝑀𝑀3 � > �𝑣𝑣𝑀𝑀4 �, whereby the manufacturer suffers greater profit loss if he accepts the demand information shared by the retailer. Thus, the manufacturer becomes passive toward retailer’s information sharing under TCF. From Result 1, it is clear that information sharing is more difficult to achieve when the capital-constrained member adopts TCF, notwithstanding cost savings and efficiency improvements in financing. Result 2：When TCF is adopted, the retailer’s profit loss from sharing information is equal under 𝑀𝑀 𝑅𝑅 capital constraints of alternative supply chain members, i.e., 𝑣𝑣𝑅𝑅1 = 𝑣𝑣𝑅𝑅3 . On the other hand, with BCF on condition that 1 + 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 − 𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 𝑗𝑗𝑅𝑅 𝑡𝑡𝑠𝑠𝑠𝑠 𝑗𝑗𝑅𝑅 > 0, the retailer’s profit loss from sharing information is higher under the manufacturer's capital constraints, whereas it would remain higher under the retailer's capital constraints if 1 + 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 − 𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 𝑗𝑗𝑅𝑅 𝑡𝑡𝑠𝑠𝑠𝑠 𝑗𝑗𝑅𝑅 < 0. Advances in Production Engineering & Management 17(3) 2022 273 Duan, Wang, Ye From Result 2, what is interesting is that the capital constraint concern has zero effect on the value of information sharing to the retailer once TCF is used. However, this conclusion does not hold when the capital-constrained member prefers BCF. Result 3：In a capital-constrained supply chain with either TCF or BCF being chosen, when the actual market demand fluctuates positively (i.e., 𝐻𝐻 > 0), the value of information sharing to the supply chain remains positive, i.e., 𝑣𝑣1 > 0, 𝑣𝑣2 > 0, 𝑣𝑣3 > 0, and 𝑣𝑣4 > 0. At this point, information sharing can increase the overall profits of the supply chain. When the actual market demand fluctuates negatively (i.e., 𝐻𝐻 < 0), the value of information sharing to the supply chain remains negative, i.e., 𝑣𝑣1 < 0, 𝑣𝑣2 < 0, 𝑣𝑣3 < 0, and 𝑣𝑣4 < 0. At this point, information sharing can’t increase the overall profits of the supply chain. When the actual market demand fluctuates positively, result 3 further verifies that information sharing brings benefits to the whole supply chain, which is expected to achieve through contract design such as a single-sided payment contract. 7. Well-funded member’s willingness to offer trade credit financing The above analysis concludes that TCF is an equilibrium financing choice for capital-constrained supply chains. However, the well-funded member’s offering of TCF leads to his/her loss of the interest earned from depositing the fund in the bank. Thus, the well-funded member needs to trade off the gains and losses of providing TCF. In the following, we derive the conditions on which the well-funded member is willing to offer TCF with the respective capital-constrained manufacturer and retailer. Result 4: Given the capital constraints for the manufacturer, if the retailer shares demand information, the condition that the retailer is willing to provide TCF is 𝑏𝑏𝑏𝑏𝑗𝑗𝑀𝑀 �2(𝑎𝑎 + 𝐻𝐻)𝑊𝑊 − 𝑏𝑏𝑏𝑏�2 + 2𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 + 𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 𝑗𝑗𝑀𝑀 �� > 1, 2𝑖𝑖𝑅𝑅 [(𝑎𝑎 + 𝐻𝐻)2 𝑊𝑊 2 − 𝑏𝑏 2 𝑐𝑐 2 (1 + 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 )2 ] (20) 𝑏𝑏𝑏𝑏𝑗𝑗𝑀𝑀 �2(𝑎𝑎 + 2𝐻𝐻)𝑊𝑊 − 𝑏𝑏𝑏𝑏�2 + 2𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 + 𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 𝑗𝑗𝑀𝑀 �� > 1, 2𝑖𝑖𝑅𝑅 [𝑎𝑎(𝑎𝑎 + 2𝐻𝐻)𝑊𝑊 2 − 𝑏𝑏 2 𝑐𝑐 2 (1 + 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 )2 + 2𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻(1 + 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 )] (21) (1 + 𝑡𝑡𝑠𝑠𝑠𝑠 𝑗𝑗𝑅𝑅 )(1 − 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 )[𝑁𝑁 + 𝐻𝐻𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑅𝑅 ]2 > 1, (1 + 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 )[𝑁𝑁 + 𝐻𝐻𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑅𝑅 − 𝑏𝑏𝑏𝑏𝑡𝑡𝑠𝑠𝑠𝑠 𝑗𝑗𝑅𝑅 ]2 (22) (1 + 𝑡𝑡𝑠𝑠𝑠𝑠 𝑗𝑗𝑅𝑅 )(1 − 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 ){𝑁𝑁 2 − 2𝐻𝐻𝐻𝐻} > 1, (1 + 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 ){[𝑁𝑁 − 𝑏𝑏𝑏𝑏𝑡𝑡𝑠𝑠𝑠𝑠 𝑗𝑗𝑅𝑅 ]2 − 2𝐻𝐻(1 + 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑅𝑅 )[𝑁𝑁 − 𝑏𝑏𝑏𝑏𝑡𝑡𝑠𝑠𝑠𝑠 𝑗𝑗𝑅𝑅 ]} (23) whereas if the retailer does not share demand information, the condition that the retailer is willing to provide TCF is where 𝑊𝑊 = (1 + 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑅𝑅 )(1 + 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑀𝑀 ). Result 5: Given the capital constraints for the retailer, if the retailer shares information, the conditions that the manufacturer is willing to provide TCF is whereas if the retailer does not share information, the conditions that the manufacturer is willing to provide TCF is, where 𝑁𝑁 = 𝑎𝑎(1 + 𝑡𝑡𝑠𝑠𝑠𝑠 𝑖𝑖𝑅𝑅 ) − 𝑏𝑏𝑏𝑏. We observe that the willingness of the well-funded member to provide internal financing to the capital-constrained member is related to the demand fluctuation type and the deposit and loan rates for the respective manufacturer and retailer. In the following section, we will derive the varying ranges of 𝑗𝑗𝑀𝑀 , 𝑖𝑖𝑅𝑅 , and H for retailer’s willingness to offer TCF, and the ranges of 𝑗𝑗𝑅𝑅 , 𝑖𝑖𝑀𝑀 and 𝐻𝐻 for manufacturer’s willingness to offer TCF using numerical analysis. 274 Advances in Production Engineering & Management 17(3) 2022 Financing and Information sharing in capital-constrained supply chain 8. Numerical analysis In this section, we first numerically verify the relevant conclusions, and then we analyse the willingness of the well-funded member to provide TCF. Parameters are set as follows: 𝑎𝑎 = 130, 𝑏𝑏 = 1, 𝑐𝑐 = 10, 𝐻𝐻𝐻𝐻(−40,40), 𝑖𝑖𝑅𝑅 = 0.1, 𝑖𝑖𝑀𝑀 = 0.1, 𝑗𝑗𝑀𝑀 = 0.15, 𝑗𝑗𝑅𝑅 = 0.15, and 𝑡𝑡𝑠𝑠𝑠𝑠 = 𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 = 1. 8.1 Impact of financing choices on the value of information sharing The impacts of the financing choices on the value of information to the manufacturer and the retailer are depicted in Fig. 5 and Fig. 6. The x-axis represents market demand fluctuation in Fig. 5 and Fig. 6. The y-axis represents the profit of retailer in Fig. 5, and y-axis represents the profit of manufacturer in Fig. 6. From Fig. 5, the absolute value of information sharing to the retailer adopting TCF is greater than that adopting TCF. When 𝐻𝐻 > 0, the value of information sharing to the retailer is negative, where the retailer suffers greater profit loss adopting TCF and becomes more reluctant to share demand information. When 𝐻𝐻 < 0, the value of information sharing to the retailer is positive, which suggests that the retailer enjoys improved profits adopting TCF and is more willing to share demand information. The conclusions are independent of the takers of capital constraints in the supply chain. As shown in Fig. 6, the value of information sharing to the manufacturer is positive when 𝐻𝐻 > 0, which indicates that the manufacturer gains more from information sharing while adopting TCF. When 𝐻𝐻 < 0, the conclusion is the opposite. The arithmetic analysis is consistent with the conclusions from Result 1. In summary, we numerically verify that sharing information benefits the manufacturer rather than the retailer when the actual market demand fluctuates positively, and vice versa if the actual market demand fluctuates negatively, which is irrelevant with the takers of capital constraints in the supply chain. In particular, when TCF is adopted, it should be also noted that the capitalconstrained member’s financing choice may exert a more numerically significant effect on the value of information. (a) Manufacturer's capital constraints (b) Retailer's capital constraints Fig. 5 Impact of financing choices on the value of information sharing to retailer (a) Manufacturer's Capital constraints (b) Retailer's Capital constraints Fig. 6 Impact of financing choices on the value of information sharing to manufacturer Advances in Production Engineering & Management 17(3) 2022 275 Duan, Wang, Ye 8.2 Willingness analysis of well-funded member to provide trade credit financing Firstly, we capture the conditions for the retailer's willingness to offer TCF to the capitalconstrained manufacturer, as shown in Fig. 7. Assume that 𝐻𝐻 = 10, the x-axis represents the retailer's deposit rate and the y-axis is the manufacturer's loan rate. The vertical axis gives 𝑀𝑀𝑀𝑀∗ 𝑀𝑀𝑀𝑀∗ − 𝜋𝜋𝑅𝑅2 − 𝑤𝑤1𝑀𝑀𝑀𝑀∗ (𝑎𝑎 − 𝑏𝑏𝑝𝑝1𝑀𝑀𝑀𝑀∗ + 𝐻𝐻)𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝 𝑖𝑖𝑅𝑅 ), which indicates the difference between 𝑀𝑀 (i. e. , 𝑀𝑀 = 𝜋𝜋𝑅𝑅1 the incremental revenue and reduced interest income when the retailer provides TCF. Specifically, 𝑀𝑀 > 0 means that the retailer is willing to offer TCF, while 𝑀𝑀 < 0 indicates that the retailer is reluctant to offer TCF. With information sharing from the retailer, the impact of the loan rate and deposit rate on the retailer's willingness to provide TCF is shown in Fig. 7(a). We observe that the varying range of the rates that encourage the retailer to offer TCF satisfies 𝑥𝑥𝑥𝑥[0.16,1], 𝑦𝑦𝑦𝑦[0.01,0.06]. When the retailer chooses not to share demand information, the impact of the loan rate and the deposit rate on the retailer's willingness to provide TCF is depicted in Fig. 7(b), wherein the varying range of the rates that encourages the retailer to offer TCF locate within 𝑥𝑥𝑥𝑥[0.15,1] and 𝑦𝑦𝑦𝑦[0.01,0.06]. Then, we capture the conditions for the manufacturer's willingness to offer TCF to the capitalconstrained retailer in Fig. 8. Likewise, the x-axis denotes the manufacturer’s deposit rate and the y-axis the retailer's loan rate. With the retailer's information sharing, the condition that allows the manufacturer to accept delayed payment (i.e., offer TCP) is given as 𝑥𝑥𝑥𝑥[0,0.4], 𝑦𝑦𝑦𝑦[0.01,1], whereas the counterpart condition without the retailer's information sharing satisfies 𝑥𝑥 𝜖𝜖[0,0.41], y𝜖𝜖[0,1]. According to our numerical analysis, we show that the deposit rate of the well-funded member that allows for offering TCF varies much lower for the manufacturer than for the retailer, while the varying condition of the bank loan rate that encourages the capital-constrained member to choose TCF is much laxer for the manufacturer than for the retailer. It may suggest that TCF is possible to be a popular financing approach if the manufacturer is capital-constrained. Moreover, the impacts of the retailer’s information sharing decisions on the varying ranges of the rates are very slight, regardless of the capital constraint of either the manufacturer or the retailer. (a) With retailer's information sharing (b) Without retailer's information sharing Fig. 7 The conditions for the retailer's willingness to offer TCF to the capital-constrained manufacturer (a) With retailer's information sharing 276 (b) Without retailer's information sharing Fig. 8 The conditions for the manufacturer's willingness to offer TCF to the capital-constrained retailer Advances in Production Engineering & Management 17(3) 2022 Financing and Information sharing in capital-constrained supply chain 9. Conclusion We model four scenarios of the capital-constrained supply chain using BCF and TCF to address financing problems, with the consideration of the retailer’s decisions on sharing demand information or not. We derive the equilibrium financing and information-sharing strategies with the capital constraints of the manufacturer and the retailer respectively and find that TCF is an equilibrium financing choice for a capital-constrained supply chain. The retailer has no willingness to share demand forecasting information if the actual demand fluctuates positively, whereas she prefers to share when the actual demand fluctuates negatively but the manufacturer is reluctant to accept in case of profit loss. By comparing the equilibriums of the game, we further analyse the interactions between the financing and information-sharing strategies and provide useful managerial insights. First, when a capital-constrained member chooses TCF, it becomes more difficult to share demand information over the supply chain. Second, when the capital-constrained member, either manufacturer or retailer, adopts TCF, the value of information sharing to the retailer would not change; however, this conclusion does not hold if BCF is used in the capital-constrained supply chain. Third, sharing demand information over the supply chain is always beneficial to the system, whereby the contract design, such as a single-sided payment contract, should be emphasized to facilitate information sharing. Finally, we provide the conditions that encourage the well-funded member to offer TCF in the capital-constrained supply chain. Given the benefits that TCF brings to the reduction of financing costs and the improvement of financing efficiency, we suggest that capital-constrained companies should respond to financial crises through TCF. To improve demand forecasting information sharing over the supply chain, the design of incentive mechanisms in capital-constrained supply chains is necessary and imperative. This will be one of the future directions of our research. In addition, this paper assumes that there is no insolvency risk for capital-constrained firms, which deserves a further understanding in the future research of capital-constrained supply chains. Also, it should be emphasized that the concerns of international crises, such as wars, pandemics and lack of raw materials, become an urgent and imperative topic in today’s capital-constrained supply chains, which needs more targeted modelling and discussion in our extension studies. References [1] Wang, F., Yang, X., Zhuo, X., Xiong, M. (2019). Joint logistics and financial services by a 3PL firm: Effects of risk preference and demand volatility, Transportation Research Part E: Logistics and Transportation Review, Vol. 130, 312-328, doi: 10.1016/j.tre.2019.09.006. [2] Duan, W., Ma, H., Xu, D.S. (2021). Analysis of the impact of COVID-19 on the coupling of the material flow and capital flow in a closed-loop supply chain, Advances in Production Engineering & Management, Vol. 16, No. 1, 522, doi: 10.14743/apem2021.1.381. [3] SME Finance Forum. China MSME finance report 2016, from https://www.smefinanceforum.org/post/chinamsme-finance-report-2016, accessed March 25, 2022. [4] Hua, S., Liu, J., Cheng, T.C.E., Zhai, X. (2019). Financing and ordering strategies for a supply chain under the option contract, International Journal of Production Economics, Vol. 208, 100-121, doi: 10.1016/j.ijpe.2018.10.008. [5] Jin, W., Zhang, Q., Luo, J. (2019). Non-collaborative and collaborative financing in a bilateral supply chain with capital constraints, Omega, Vol. 88, 210-222, doi: 10.1016/j.omega.2018.04.001. [6] Zhou, J., Groenevelt, H. (2007). Impacts of financial collaboration in a three-party supply chain, Working paper, The Simon School, University of Rochester, New York, USA. [7] Kouvelis, P., Zhao, W. (2012). Financing the newsvendor: Supplier vs. bank, and the structure of optimal trade credit contracts, Operations Research, Vol. 60, No. 3, 566-580, doi: 10.1287/opre.1120.1040. [8] Jing, B., Chen, X., Cai, G. (2012). Equilibrium financing in a distribution channel with capital constraint, Production and Operations Management, Vol. 21, No. 6, 1090-1101, doi: 10.1111/j.1937-5956.2012.01328.x. [9] Shi, J., Li, Q., Chu, L.K., Shi, Y. (2021). Effects of demand uncertainty reduction on the selection of financing approach in a capital-constrained supply chain, Transportation Research Part E: Logistics and Transportation Review, Vol. 148, Article No. 102266, doi: 10.1016/j.tre.2021.102266. [10] Li, L., Zhang, H. (2008). Confidentiality and information sharing in supply chain coordination, Management Science, Vol. 54, No. 8, 1467-1481, doi: 10.1287/mnsc.1070.0851. [11] Yan, X., Wang, Y. (2014). A newsvendor model with capital constraint and demand forecast update, International Journal of Production Research, Vol. 52, No. 17, 5021-5040, doi: 10.1080/00207543.2014.894261. Advances in Production Engineering & Management 17(3) 2022 277 Duan, Wang, Ye [12] Cao, E., Du, L., Ruan, J. (2019). Financing preferences and performance for an emission-dependent supply chain: Supplier vs. bank, International Journal of Production Economics, Vol. 208, 383-399, doi: 10.1016/j.ijpe. 2018.08.001. [13] Zhen, X., Shi, D., Li, Y., Zhang, C. (2020). Manufacturer’s financing strategy in a dual-channel supply chain: Thirdparty platform, bank, and retailer credit financing, Transportation Research Part E: Logistics and Transportation Review, Vol. 133, Article No. 101820, doi: 10.1016/j.tre.2019.101820. [14] Shen, B., Wang, X., Cao, Y., Li, Q. (2020). Financing decisions in supply chains with a capital-constrained manufacturer: Competition and risk, International Transactions in Operational Research, Vol. 27, No. 5, 2422-2448, doi: 10.1111/itor.12670. [15] Shi, J., Guo, J., Du, Q., Lin, F., Lai, K.K., Cheng, T.C.E. (2020). Optimal financing mode selection for a capitalconstrained retailer under an implicit bankruptcy cost, International Journal of Production Economics, Vol. 228, Article No. 107657, doi: 10.1016/j.ijpe.2020.107657. [16] Yang, H., Zhuo, W., Shao, L., Talluri, S. (2021). Mean-variance analysis of wholesale price contracts with a capitalconstrained retailer: Trade credit financing vs. bank credit financing, European Journal of Operational Research, Vol. 294, No. 2, 525-542, doi: 10.1016/j.ejor.2021.01.042. [17] Chen, X. (2015). A model of trade credit in a capital-constrained distribution channel, International Journal of Production Economics, Vol. 159, 347-357, doi: 10.1016/j.ijpe.2014.05.001. [18] Zhao, L., Huchzermeier, A. (2019). Managing supplier financial distress with advance payment discount and purchase order financing, Omega, Vol. 88, 77-90, doi: 10.1016/j.omega.2018.10.019. [19] Mishra, B.K., Raghunathan, S., Yue, X. (2009). Demand forecast sharing in supply chains, Production and Operations Management, Vol. 18, No. 2, 152-166, doi: 10.1111/j.1937-5956.2009.01013.x. [20] Li, T., Zhang, H. (2015). Information sharing in a supply chain with a make-to-stock manufacturer, Omega, Vol. 50, 115-125, doi: 10.1016/j.omega.2014.08.001. [21] Lai, X., Tao, Y., Wang, F., Zou, Z. (2019). Sustainability investment in maritime supply chain with risk behavior and information sharing, International Journal of Production Economics, Vol. 218, 16-29, doi: 10.1016/j.ijpe. 2019.02.021. [22] Liu, M., Dan, B., Zhang, S., Ma, S. (2020). Information sharing in an E-tailing supply chain for fresh produce with freshness-keeping effort and value-added service, European Journal of Operational Research, Vol. 290, No. 2, 572584, doi: 10.1016/j.ejor.2020.08.026. [23] Li, G., Liu, M., Bian, Y., Sethi, S.P. (2020). Guarding against disruption risk by contracting under information asymmetry, Decision Sciences, Vol. 51, No. 6, 1521-1559, doi: 10.1111/deci.12437. [24] Wang, J., Zhuo, W. (2020). Strategic information sharing in a supply chain under potential supplier encroachment, Computers & Industrial Engineering, Vol. 150, Article No. 106880, doi: 10.1016/j.cie.2020.106880. [25] Liu, M., Zhao, Y., Huang, R., Perera, S. (2021). Vertical value-added cost information sharing in a supply chain, Annals of Operations Research, Vol. 2021, 1-34, doi: 10.1007/s10479-021-04021-3. [26] Guan, Z., Zhang, X., Zhou, M, Dan, Y. (2020). Demand information sharing in competing supply chains with manufacturer-provided service, International Journal of Production Economics, Vol. 220, Article No. 107450, doi: 10.1016/j.ijpe.2019.07.023. [27] Yan, K., Cui, L., Zhang, H., Liu, S., Zuo, M. (2022). Supply chain information coordination based on blockchain technology: A comparative study with the traditional approach, Advances in Production Engineering & Management. Vol. 17,No. 1, 5-15, doi: 10.14743/apem2022.1.417. 278 Advances in Production Engineering & Management 17(3) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 3 | September 2022 | pp 279–294 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.3.436 Original scientific paper Effect of printing parameters on the mechanical behaviour of the thermoplastic polymer processed by FDM technique: A research review Tripathy, C.R.a,*, Sharma, R.K.b, Rattan, V.K.a aGNA University, Phagwara, Punjab, India Institute of Technology, Hamirpur, India bNational ABSTRACT ARTICLE INFO Fused deposition modelling (FDM) is an additive-based manufacturing technique used by various industries due to its effectiveness & ability to make complicated geometries possible. This technique requires sufficient knowledge about the process and its parameters including their effect on the component’s mechanical characteristics. Thus, it is crucial to review the available articles on this topic not only to identify the practical and useful aspects, limitations, and process variables but also to understand how the results of the literature are relevant to be used for real applications and further studies. A systematic literature review is carried out based on the type of 3D printing materials. The printing parameters which influence the mechanical characteristics of the FDM specimens are discussed based on the results presented in the literature. From the present study, it has been found that the process variables such as orientation, raster angle, raster width, layer height, and contours directly affect the quality of the 3D-printed parts. It has also been found that the effect of these process variables also varies with the type of thermoplastic materials. The present article will help researchers to select FDM processed material and appropriate process variables for further research. Keywords: 3D printing; Additive manufacturing; Fused deposition modeling (FDM); Process parameters; Mechanical properties; Thermoplastic polymer; Review study *Corresponding author: chittatripathy@rediffmail.com (Tripathy, C.R.) Article history: Received 13 May 2022 Revised 14 August 2022 Accepted 12 September 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Plastic manufacturing is one of the cutting-edge market that produces plastic components at a low price and least time [1]. There are many processes available to manufacture plastic components like injection moulding, Blow moulding, etc. These processes are beneficial for large volume production as mould development for a specific component is quite costly. In contrast, other techniques are also available which are cheaper for low volume production, such as fused deposition modelling (FDM) or fused filament fabrication (FFF) [2]. FDM uses 3D CAD data for creating a physical model with the help of CAD softwares and 3D printing machines. This technique rapidly transfers design ideas into functional prototypes from the regular CAD model. It builds the product with complex geometry and is hard to be fabricated using conventional manufacturing techniques at low costs. It uses a 3D scanner for an existing product and CAD software for a new product to generate virtual CAD model and build physical products using different AM technologies. 279 Tripathy, Sharma, Rattan These technologies are used in various manufacturing sectors like defence, aerospace, medical, art and design for customization and rapid production [3-5]. Additive manufacturing is a modern manufacturing technique to create components by depositing materials layer by layer using a virtual model developed in CAD. In this process, the CAD model is exported into stereolithographic (*.stl) format, which defines the entire model into a series of 2D cross-sections. The converted file is then transferred to any of the AM machines for creating the physical part [6, 7] with more accuracy, stability, and durability. Additive manufacturing is generally designated as (ISO/ASTM standard 52900:2021 [1]). • Stereolithography (SLA): The final product is generated with the help of an ultraviolet laser inside a vat of resin. This method uses light-sensitive polymers, whose limited availability limits the application of this technique. Though, it provides a better surface finish and lesser raw material wastage. • Selective laser sintering (SLS): This process uses powder as raw material which is melted and fused with the help of a laser beam. The fused powder is then stacked layer upon layer to form the part based on CAD data. The performance of the components sintered through SLS process is significantly affected by the quality of powder used. • Polyjet 3D printing (PJP): This technology uses a variety of printing materials. In the dentistry and medical field, patient anatomy can be better understood by printing the model using this technique. • Inkjet 3D printing (IJP): This technique uses the liquid formed of polymer solution to build parts layer by layer. It is economically good for printing the part using a variety of materials. • Laminated object manufacturing (LOM): it uses material sheets to fabricate components layer by layer with the help of a laser, which cut the sheets as per the requirement. The layer of the sheet is combined using adhesives, and the part is fabricated by repeating the steps. • Multi-Jet-Printing (MJP): In this technique, a thin solid layer of ceramic or metallic powder is created by spraying a liquid binder through a nozzle. In order to have higher strength the fabricated part is sintered in the furnace. • Colour-Jet Printing (CJP): This technique is frequently used in medical applications due to its ability to print coloured products. In this technique, powder and binder are used as core material and resin respectively. The powder is spread over a platform with the help of a roller to form a layer and then the binder is sprayed through a printing head jet over each layer at a point specified by CAD software to form the final product. • Fused Deposition Modelling (FDM): This technique is based on the extrusion method, in which, the thermoplastic material is melted through heating and deposited layer by layer over a printer bed to fabricate a model. These techniques vary according to the building layers and based on the materials type that can be used for part fabrication. Among the available additive manufacturing technology, the FDM process is best to manufacture thermoplastic components due to its low initial investment, less material wastage, simplicity of the process, and easy availability of 3D printing software [8]. 2. The FDM technique The brief layout of FDM technique is graphically represented in Fig. 1. In this process, the part is modelled using CAD software and converted to STL format. Almost all CAD software can generate this format and sent it to RPT software to check the defects in the model [9]. In the FDM process, wire of polymer is liquified and extruded along a precise toolpath creating the shape of each layer. The system extrudes both build material and temporal support material with the help of nozzles mounted on the extruder [10]. The movement of the extruder head is controlled through the motor, and the low temperature of the printing bed allows the deposited material to solidify very fast [11]. The system repeats the step until the part is finalized. After completion of the process, parts are moved out of the machine bed and support material is removed using a different technique. In the fused deposition modelling process, as described above, two forms of materials are used. One is to build the physical model, and another is for generating a support structure. 280 Advances in Production Engineering & Management 17(3) 2022 Effect of printing parameters on the mechanical behaviour of the thermoplastic polymer processed by FDM technique: A … Fig. 1 Simplified layout for FDM process Fig. 2 Fused deposition modelling process flow diagram This process produces low stiffness products of thermoplastic polymer material. ABS and PLA polymers are compatible and cheap; therefore, it is widely used with 3D printers. Recently, NASA designed a space exploration vehicle for transporting humans to Mars with almost 70 FDM parts onboard such as vents, ducts, etc. [15]. An ability of functional efficiency under a cryogenic environment made PLA and ABS to be used for the fabrication of the rover. The performance of PLA is quite well under low temperatures and has also been used in the medical field [16]. However, the low toughness characteristic of PLA made it to use with the composition of ABS [17]. ABS found its wide application in automobile sectors [18]. For complete understanding of the FDM process, one has to perform many trials, although many researchers have investigated the mechanical behaviour of FDM built components and found that those are affected by various process variables/parameters. All these parameters are represented through the fishbone diagram shown in Fig. 3. The present work is focused on identifying how these variables affect the 3D printed part quality. The selection of appropriate process parameters has made FDM a complicated manufacturing process. Understanding the selection of these parameters is quite difficult [19, 20]. Fig. 3 Parameters/variables affecting FDM part quality Advances in Production Engineering & Management 17(3) 2022 281 Tripathy, Sharma, Rattan 3. A research review and discussion 3.1 FDM process parameters The mechanical behaviour of FDM based parts is affected by various process parameters like infilldensity, pattern (via honeycomb, rectilinear, concentric), raster-width, layer thickness (h), temperature, extruder speed, the air-gap in the same layer or between the layers, raster-angle (via 0°, 45°and 90°), nozzle diameter, build-orientation (via on-edge, upright, and Flat), etc [21, 22]. The different process variables affecting the mechanical characteristics of the part are described as follows. • Layer thickness: when a material is extruded from the tip of the nozzle to form a layer, the height of that layer along a vertical direction is termed layer height or thickness (Fig. 5). The layer height value is always lower than the diameter of the nozzle tip [22]. The selection of layer thickness is based on: − The diameter of nozzle tip [19] − The material [19] • Build-orientation: It is the alignment of the built component within the printing bed along X-axis (Flat), Y-axis (Up-right), or Z-axis (On-edge) of the 3D printing machine [19, 23] Build-orientation of the part is shown in Fig. 4. Fig. 4 Build-orientation of the Component • Raster-angle: It is the inclination of extruded material with the X-axis of a printing bed (Fig. 5). This angle ranges from 0° to 90° [19, 23]. • Air-gap: The free space between two successive beads on the same layer of the 3D printed part is termed as air-gap [19, 23] (Fig. 5). • Build-style: Build-style is the way rasters are filled to build the part. The build-style of any component defines its density. The parts can be fabricated with three different Build-styles [19]. − Solid normal: This build-style completely fills the interior of the part and provides a strong interior. − Sparse: This Build-style leaves the gap while material deposition uses a unidirectional raster thereby minimizing the material consumption and part-build time. − Sparse double dense: This build-style uses a crosshatch raster pattern, which reduces material consumption and part-build time. • Support-style: It helps to prevent the collapsing of components during fabrication by extending the surface of the model [19]. It can be provided in four different ways. − Basic: it is the default support-style, which provides support to all the part features using small support raster curves. − Sparse: Compared to basic support, it utilizes less amount of material, which reduces the support material consumption. − Surround: It is used for all the parts to fill the small features or small components. − Break-away: It's equivalent to "Sparse," except it has separate blocks that are easier to remove compared to the other three types of support styles. 282 Advances in Production Engineering & Management 17(3) 2022 Effect of printing parameters on the mechanical behaviour of the thermoplastic polymer processed by FDM technique: A … • Extrusion temperature: It is the temperature with which the polymeric filaments are treated within the nozzles prior it extruded. Its value varies with the type of material and printing speed [23]. • Print Speed: It is the movement of nozzle tip along the printing bed plane for fabrication of the part [23]. • Nozzle diameter: It is defined as the diameter of the nozzle tip of the extruder [24] • Infill pattern: It is defined as the pattern in which extrusion of material takes place to fill the internal zone of a 3D printed part. Some of the widely used infill patterns are cross, linear infill, diamond, and honeycomb [23]. Honeycomb infill pattern has the capacity to resist a higher load compared to others [24]. • Raster/bead width: It is the beads size that are extruded on the printing bed to create rasters. The raster width for depositing any material is selected based on the diameter of the nozzle tip mounted on the extruder head [23, 19] (Fig. 5). • Infill-density: The infill-density reflects the internal structure solidity of the fabricated component. Unlike the external structure of the part, Inside, the structure isn't always solid; it can be sparse, with a variety of shapes, sizes, and infill patterns [23, 24]. • Contour Number: Number of outer solid layers surrounding internal structure of the 3D printed component [19]. This process variable can also be referred to as perimeter (Fig. 5). • Contour width/Perimeter width: It is defined as the thickness of each contour/perimeter measured horizontally [19] as shown in Fig. 5. • Contour to contour air-gap: The free space between two successive perimeters [19] as shown in Fig. 5. Fig. 5 FDM Tool path parameters 3.2 Influence of process parameters on mechanical behaviour of parts It is mandatory to investigate the influence of FDM printing variables on part characteristics, since, the influence of layer height on the part characteristics with flat orientation-built components is vague [25]. Some researchers reported that an increase of layer height causes decrease in mechanical behaviour [26-28]. Whereas Abbott et al. [29] reported the opposite behaviour. Wu et al. [30] found that, for P-E-E-K, an increase of layer height from 200 μm to 300 μm increased the bending, compressive, and tensile strength but a further increase of layer thickness causes a decrease in these properties. Samples fabricated with the lower speed along with lower layer height have higher tensile strength [31]. Rouf et al. [32] investigated the impact of various process variables on the mechanical behaviour of the component, and it was found that along with the strength of the component the process parameter also affects tribological properties [33-35]. Bhosle et al. [36] analysed the Impact of layer height, Printing speed, and infill percentage on tensile strength, printing time, and surface finish. From the analysis, it was found that layer height and infill percentage are highly contributing to the surface roughness and strength [37-38] of the build parts. The author suggested keeping layer height lower to improve the performance of FDM for surface roughness and tensile strength. Kaur et al. [13] analysed the impact of printing variables on the tribological behaviour of ABS polymer. The authors found that FDM process parameters not only improve strength but also improve surface finish and tribological behaviour. These improvements are obtained through optimization of the process variables as well as the addition of material to the raw polymer. Advances in Production Engineering & Management 17(3) 2022 283 Tripathy, Sharma, Rattan Kumar and Ranjan [39] analysed the effect of bed temperature, infill percentage, and outer perimeter on the elongation behaviour of Nylon 6. The authors found that at 100 infill per-centage, 60° C bed temperature, and four contour numbers provide maximum elongation in the component and thereby increase the tensile strength. They also found that infill percentage was more significant followed by bed temperature and outer perimeter. Patil et al. [14] optimized some of the input variables viz. infill percentage, infill pattern, print speed, and layer thickness using multi-objective optimization for achieving better surface roughness, printing time, and filament length consumed for PLA. They reported the best response after the optimum setting of the parameters to the triangular pattern with 70 % infill, 100 mm/h printing speed, and 0.2 mm layer height. Casavola et al. [20] explored the influence of raster orientation on the residual stresses that occur in FDM-fabricated ABS material parts due to the sudden change in temperature during processing. The authors concluded that components fabricated at a ±30° raster orientation is the worst configuration because the component exhibited higher residual stress, whereas the part fabricated with ±45° was the best configuration with the lowest residual stress. Chacon et al. [40] analysed the impact of layer height, build direction, and feed-rate on the flexural and tensile behaviour of PLA specimens. The authors found that with an increase of layer height the mechanical properties decreased for flat oriented built specimens. However, for onedge built orientation, the flexural strength was found lower at low layer height. On the contrary, for upright built orientation, specimens with high layer thickness possessed higher mechanical properties. Shubham et al. [41] analysed the impact of layer height on impact, hardness, and tensile characteristics of ABS samples. The authors reported that Izod impact and tensile strength increased with the reduction of layer height. Whereas, the hardness value was first decreased and then increased with the increase of layer height. Later on, Shubham et al. [42] optimised the various printing parameters (viz. infill percentage, nozzle temperature, and layer height) by reporting the dynamic mechanical characteristics of ABS built components. The authors found the highest storage modulus at higher values of printing parameters. They also found that the impact of layer height and percentage of infill on dynamic mechanical behaviour was most significant, whereas the impact of nozzle temperature was low. Daminabo et al. [43] gave an overview of AM techniques. The authors focused on FDM technique due to its cost efficiency, scalability, and ability to process a variety of materials. They suggested the use of biodegradable, bio-based, and eco-friendly materials having the capability of multi-functionality for future research and development. Ramesh and Paneerselvam [44] analysed the effect of various input variables like print speed, layer height, and infill percentage on the mechanical behaviour of fabricated nylon samples. Through the analysis, the authors found that parts printed with 100 infill percent exhibit optimum (max) flexural strength, Shore-D hardness, and UTS. This is due to the fact that 100 % infill don’t have pores and therefore, the sample strength increased. The infill percent was found to have the highest impact on the mechanical behaviour of the fabricated components. Complete filling of the material eliminates the space caused for the crack growth of the sample. The layer height of 0.1 mm has affected the mechanical characteristics like impact, tensile and flexural strength. However, maximum Shore-D hardness was found at 0.3 mm layer height. The selected parameter of print speed didn’t have a effective influence on the mechanical behaviour however, low speed causes heat-affected zones and higher speed causes the wrapping defect. The authors have suggested extending this work through the use of fillers in the nylon matrix and evaluating and comparing the related properties with pure material. Pazhamannil et al. [45] assessed the effect of various process variables on the UTS of PLA component using the Taguchi technique. The values of UTS were predicted using an artificial neural network. The authors found that the tensile strength of the specimens increases at reduced layer height due to improved inter-layer bonding at reduced layer thickness. They also found the higher tensile strength with increased nozzle temperature due to quick growth of the neck caused by long-duration intermolecular diffusion across the interface. The authors concluded that infill speed did not influence the tensile property of the component significantly. Therefore, one can 284 Advances in Production Engineering & Management 17(3) 2022 Effect of printing parameters on the mechanical behaviour of the thermoplastic polymer processed by FDM technique: A … alter the infill speed without affecting the strength of the component. In order to get better tensile properties, one should keep a high nozzle temperature with a low layer height. Yadav et al. [46] analysed the impact of printing variables like material density, layer height, and extrusion temperature on the tensile behaviour of different materials like ABS, PETG, and their different compositions. The analysis showed that extrusion temperature was found more dominant factor for the tensile strength compared to other considered parameters. The maximum tensile strength for PETG material was found at an extrusion temperature of 225 °C and 0.1 mm layer height. The authors suggested analysing the influence of other printing variables using the ANFIS model, or other models can also be developed to analyse these parameters. Gebisa and Lemu [47] carried out a study to analyse the tensile behaviour of ULTEM-9085 material using the design of an experiment by varying some of the printing variables. The authors considered five printing variables viz. raster-angle, raster-width, air-gap, contour width, and contour number and found only the raster-angle to have a substantial influence on the tensile behaviour of the material. They suggested doing the flexural and impact test to analyse the parameters. Wankhede et al. [48] analysed the influence of the printing variables viz. support-style, layer height, and infill percentage on the build-time and surface roughness of part made of ABS material. The authors performed the experiment using Taguchi’s L8 Orthogonal Array. The significant behaviour of the parameters was presented using the Analysis of Variance (ANOVA) technique. From ANOVA results, they found that the layer height has a more dominant effect on surface roughness and build-time among all the process parameters considered. Solomon et al. [49] reviewed the development of the various samples and input parameter optimisation for the FDM technique. Through this review, the authors found that layer thickness or layer height was considered to be more significant factor in evaluating the part quality. It was also observed that the raster orientation dominates in evaluating the mechanical behaviour of the fabricated component. They also found that much work has been done on the printing variables and their optimisation; still, many unknown factors affect the part quality and process efficiency that need to be explored and suggested exploring more material as filament. Vicente et al. [50] analysed the influence of two input variables, i.e., density and pattern of the infill, on the mechanical characteristics of ABS components. Through the experiment, 5 % variation in maximum tensile strength was observed with variation of infill pattern. This variation was significantly improved by varying the infill-density. Maximum tensile strength was observed for the component fabricated with rectilinear pattern and 100 infill percentage. The authors have reported that if the density is kept constant, then the honeycomb pattern exhibits a better tensile strength. Rajpurohit and Dave [51] highlighted the impact of input variables like. layer thickness, rasterwidth, and raster-angle on the material characteristics of 3D printed PLA material. The authors chose tensile strength to analyse the mechanical behaviour of the fabricated component. They used the Taguchi method to optimise the process variables and also used the ANOVA tool to predict the significant process variables. Based on the experimental results, they observed the maximum tensile at a raster-angle of 45°, and it was also observed that tensile strength increases with increase of layer height. Among the selected parameters, raster-width was found to be the most significant process variable affecting strength. Dawoud et al. [52] compared FDM and injection moulding techniques by analysing the mechanical behaviour of ABS material. The authors explored the potential of the FDM technique by varying the parameters like raster angle and gap. They varied the raster angle of odd as well as even layers. Through the investigation, they found the raster gap as a significant input for FDM, where denser components equivalent to moulded parts can be fabricated using a negative gap of −0.05 mm. It was also observed that the flexural and tensile strength of the FDM component fabricated with +45° raster-angle of even layer, −45° raster-angle of odd layer, and gap of −0.05 was able to attain 86 % and 91 % respectively of the moulded parts strength respectively. The FDM technique showed the dimensional accuracy acceptable and found within the specified range of size. Further, raster angle and gap did not find to be affecting the dimensional preciseness of the component. Advances in Production Engineering & Management 17(3) 2022 285 Tripathy, Sharma, Rattan Wang et al. [53] analysed the impact of input variables on the mechanical behaviour of 3D printed PEEK material. The authors reported the impact of process parameters like the layer height, printing speed, and printing temperature on the microstructure, mechanical characteristics, and surface quality of the fabricated component. Through the analysis, they found that components possessed maximum density, along with improved surface quality and reduced internal defects when printed with a small printing layer height of 0.1 mm, a higher printing temperature of 440 °C, and a printing speed of 20 mm/s. Though the author considered some of the input parameters, the effect of other parameters still needs to be investigated like density, pattern, line direction, overlap percentage of infill, the diameter of nozzle and filament, the flow of filament, orientation of rasters, print direction, enable print cooling, UV Light, etc. The authors only focused on analysing the tensile characteristics and density of the part whereas, the other parameters like flexural strength, impact strength, etc. need to be analysed. Kaplun et al. [54] explored the impact of raster patterns and print orientation on the mechanical behaviour of 3D-printed 9085 and Antero 840CN03 (PEKK) for their potential use in aerospace and defence-grade polymers. Through the analysis, the authors found that the mechanical strength of PEKK was higher than ULTEM 9085. They concluded that raster angle and pattern both play a major role to enhance the mechanical characteristics of FDM parts. Sheoran and Kumar [12] reviewed the literature on the optimisation of FDM parameters and found that limitations in physical parameters, like availability of nozzle diameter and some specific values of layer height, restrict the integration of DOE and optimisation techniques. Thus, this limitation has to be addressed by coupling statistical DOE tools and modern optimisation techniques. Consequently, a newer mathematical modelling approach needs to be developed. Kumar et al. [55] presented the influence of print orientation and fill density on flexural and tensile strength for a standard ASA material. The authors have followed ASTM standards to fabricate and test the specimen. Through the testing, the tensile strength was reported with 52.2 MPa when printed with Z-90 print orientation and 100 % fill density. The results were compared with injection moulded components and were found with higher tensile strength. Whereas, components fabricated with Y-90 print orientation and 25 % fill density exhibit high flexural strength of 65.7 MPa. Szykiedans et al. [56] explored the mechanical behaviour of 3D printed PET-G. The authors only focused on tensile strength and elastic modulus. The author found variation in tensile modulus due to the presence of air-gap in the print structure Durgashyam et al. [57] perceived the impact of printing variables on tensile and flexural properties of PET-G material fabricated using the FDM technique. They considered the process parameters like infill-density, feed-rate, and layer height to analyse their effectiveness. They found that the components with lower layer height and feed-rate and with higher infill-density have shown good tensile properties. In contrast, the material showed good flexural strength at minimum layer height, a lesser percentile of infill-density, and a moderate feed-rate. Through, this work authors concluded that among layer height, infill-density, and feed-rate, the significance of layer height is much higher compared to other process parameters. Gebisa and Lemu [58] investigated the impact of FDM processing variables on the flexural strength of ULTEM 9085 considering five processing variables viz. air-gap, raster-angle, rasterwidth, contour width, and contour number. They found that raster-angle and raster-width have influenced the flexural property of the material to a larger extent. Mohamed et al. [59] analysed the impact of printing variables on the dynamic mechanical characteristics of PC-ABS components fabricated using the FDM method. Through this analysis, they showed that air-gap, contour number, and layer height have the highest influence on the mechanical characteristics of the part. The authors also varied layer thickness, raster angle, air gap, build orientation, and road width to analyse the dynamic and cyclic conditions of 3D printed parts [60]. The authors used same material as before to optimise the parameters with a combination of artificial neural network and fractional factorial design. They found that dynamic modulus of elasticity increases with increase of layer thickness; whereas reverse trend was found with increase of other parameters. 286 Advances in Production Engineering & Management 17(3) 2022 Effect of printing parameters on the mechanical behaviour of the thermoplastic polymer processed by FDM technique: A … Ahn et al. [61] analysed the impact of bead width, raster orientation, model temperature, airgap, and material colour on the compressive and tensile behaviour of ABS parts fabricated using the FDM method. Their analysis showed that the mechanical behaviour of the fabricated components was found to be anisotropic and parameter-dependent. They also revealed that raster orientation and air-gap have an impact on the mechanical characteristics of the part. Deng et al. [62] studied the optimisation of the mechanical behaviour of P-E-E-K in terms of printing variables. The authors considered layer height, printing speed, filling ratio, and extrusion temperature to analyse the tensile characteristics of the component. They revealed the optimum mechanical characteristics that can be obtained for the process parameters with a set of filling ratio at 40 %, printing speed at 60 mm/s, layer height at 0.2 mm, and extrusion temperature at 370 °C. Onwubolu and Rayegani [63] looked at the impact of raster-angle, width, orientation, air-gap, and layer height on the tensile behaviour of ABS components fabricated using the FDM technique. Their study revealed that the optimal process variables that could enhance the tensile behaviour of the component are increased raster-angle, minimum raster-width, minimum layer height, and negative air-gap. It has also been observed that for zero-part orientation, maximum tensile strength is obtained. Bagsik et al. [64] reported the impact of build direction on the compressive and tensile behaviour of ULTEM-9085-part build with FDM technology. The authors showed that the build-direction of the edge exhibits the highest tensile strength among all build directions, i.e., edge, upright and flat. Their investigation also revealed that compressive strength was maximum for the part built along upright-direction. Bagsik and Schöppner [65] also explored the influence of other process variables like rasterto-perimeter and raster-to-raster air-gap, build-orientation, raster-angle, and raster-width. The tensile behaviour of the same material fabricated using FDM technology. Their study revealed that for all build directions with a negative raster air-gap, the tensile strength was highest. They also revealed that thicker filament can enhance the tensile behaviour for both build directions, i.e., edge and upright. However, the tensile behaviour for the components fabricated with build-orientation flat can be enhanced by using a thinner filament. Motaparti et al. [66] analysed the impact of printing variables on the compressive nature of 3Dprinted ULTEM-9085 component. The authors considered three process variables, like, build-orientation, raster-angle, and air-gap. They concluded that the compressive strength of the component gets affected by raster-angle and build-orientation. Motaparti et al. [67] also highlighted the influence of the process variables like air-gap, rasterangle, and printing direction on the flexural behaviour of ULTEM 9085 fabricated using the FDM process with Build-styles of sparse and solid. Their analysis uncovered that the build-orientation of vertical or on-edge could provide higher flexural yield strength compared to other build directions. Masood et al. [68] presented the impact of the airgap, raster-angle, and raster-width on the tensile strength of Polycarbonate (PC) polymer. The authors found the highest tensile strength of the selected material on a process parameter setting as in air-gap type of solid normal, rasterwidth of 0.6064 mm and raster-angle of 45°. Gorski et al. [69] presented the impact of part orientation on tensile, bending, and impact strength of the part fabricated by ABS. The result showed that with a change in the orientation, the values of strength increased due to a change in macroscopic material behaviour. Durgun and Ertan [70] explored the influence of part orientation and raster-angle on surface roughness, tensile and flexural characteristics. Through the result, the authors suggested that the part orientation has the highest influence on the product quality and mechanical properties of the part compared to the raster-angle. The result also showed that surface roughness has a close relationship with mechanical behaviour. Ognzan et al. [71] explored the influence of deposition angle, layer height, and infill on the flexural strength of FDM samples fabricated using PLA material. The results showed that layer height has a dominant effect on flexural strength compared to the other two parameters. Table 1 shows an overview of the various process parameters for different polymers. Advances in Production Engineering & Management 17(3) 2022 287 Tripathy, Sharma, Rattan Ref. Al-Ghamdi [72] Mat. ABS Table 1 Some published work on FDM process parameters Input parameters Fill density, Layer thickness, Shell thickness, Feed-rate, Remarks Specific mass was not affected by feed-rate. The specific time and energy both decrease with the decrease of layer height and infill-density and by increasing feed-rate. Printing, Speed, Extruder temperature, Fill density, Bed temperature, Layer height Extruder temperature and print speed were found to be the most dominant parameters of surface roughness followed by the layer thickness and infill-density. Injection-moulded part exhibits higher tensile properties, and low layer thickness showed better mechanical properties among FDM printed samples. FDM specimens showed excellent flexural strength compared to moulded ones, and 0.15 mm layer thickness gave optimum flexural strength. 0.2 mm layer thickness showed the most preferable compressive strength. The surface finish of moulded samples was found to be better than FDM. Garzon-Hernandez et al. [73] ABS Galeja et al. [75] ABS Divyathej et al. [76] ABS Layer height Kuznetsov et al. [77] PLA Nozzle diameter, Printing The Layer height has affected the intra-layer cohesion to a speed, Layer thickness greater extent. An increase in layer height reduces the part strength for all nozzle diameters. Pramanik et al. ABS [74] Layer height, Number of Maximum stress and higher elastic modulus were found for layers, Raster orientation, lower layer thickness and longitudinal raster direction. low mechanical property with an increased number of layers. Raster-angle (Fill angle) RodríguezPanes et al. [78] ABS, PLA Arif et al. [79] PEEK Part orientation Mishra et al. [81] ABS Samykano [82] PLA Contour number, Layer thickness, Raster-width, Part orientation, Raster angle and air-gap Flexural strength was increased with increase of external perimeter (Contour). The failure also shifted from the edge to the centre. Anisotropy of the specimen was also reduced at 30° raster angle. Layer height, Extruded line width, Top layer thickness, Number of walls, Infill percent, Infill pattern, Print speed, Part orientation etc. Top layer height, Shape of the top layer, and print speed were found most influencing the roughness at the top of the fabricated part. Overall layer height, part orientation, and wall printing speed were found to be dominating for wall roughness. Rinaldi et al. [80] Mendricky and Fris [83] PEEK PLA Layer height, Infill density, Part orientation With an increase in raster-angle, the strength of the component reduces. However, maximum strength is obtained at a raster-angle of 55°. Infill density, Part orientation The results for ABS showed a lower variation compared to PLA. The infill percentage has a higher influence on the mechanical characteristics of the part, although this effect is higher in PLA compared to ABS. The specimens fabricated using PLA having higher tensile strength than ABS due to their more rigid nature. The part orientation H-0° was found to be best for tensile, flexural, and fracture toughness, followed by H-90° and V-90°. The mechanical properties of FDM and injection moulded samples were found same for 100 % infill printed in the X-Y plane, whereas, samples printed in the Z direction were found to be extremely brittle with premature failures. Low mechanical properties were found in the samples fabricated with a low infill percentage. Fill percentage, Raster an- Infill percentage significantly influenced the tensile strength out gle and layer height of selected input parameters. The effect of main process variables on the mechanical behaviour are presented in Table 2. The table also consists of most frequently used optimisation techniques. It is also observed that Taguchi and ANOVA based method is most often used for almost all the parameters. However, machine learning methods based on ANN and fuzzy is implemented with few parameters. The ANN and fuzzy based optimisation methods have proved to be more accurate in providing optimal set of parameters value. 288 Advances in Production Engineering & Management 17(3) 2022 Effect of printing parameters on the mechanical behaviour of the thermoplastic polymer processed by FDM technique: A … Table 2 The effect of the main process variables on the mechanical behaviour Process parameters Influence on the mechanical behaviour Optimisation technique used Raster angle Layer thickness Raster width Contour number Infill density Infill pattern Build orientation Air gap Support style Tensile strength, Flexural strength, Impact strength, Surface roughness, Dimensional accuracy Tensile strength, Flexural strength, Impact strength, Hardness, Compressive strength, Dimensional accuracy, Surface roughness Elasticity, Tensile strength, Flexural strength, Impact strength, Dimensional accuracy Taguchi method [19, 84], Gray relation analysis [84], ANOVA [84], Fuzzy Logic [85, 86], Artificial Neural Network (ANN), GA Taguchi method [84], Hybrid particle swarm, Bacterial forage optimization, Artificial Neural Network (ANN), Gray relation analysis [84], ANOVA [84], Fuzzy logic [85, 86] Taguchi method [84], ANOVA [84], Artificial Neural Network (ANN), Fuzzy logic [85, 86] Elasticity, Tensile strength, Impact strength, Taguchi method, ANOVA, Regression analFlexural strength, Impact strength, Dimensional ysis [88] accuracy Flexural strength, Tensile strength, % Elongation Surface roughness, Hardness, Flexural Modulus, Tensile strength RSM, ANOVA, Taguchi method [89], GA, GA-ANN, GA-ANFIS [90] Taguchi method, ANOVA, Regression analysis [87] Tensile strength, Flexural strength, Impact strength, ANOVA [84], Regression analysis, Taguchi method [84], Fuzzy logic [85, 86] Tensile strength, Flexural strength, Fracture toughness Tensile strength, Dimension accuracy, Surface roughness Fuzzy Logic [85, 86], ANOVA [84], Regression analysis, Taguchi method [84] ANOVA along with gray relational analysis, Taguchi method [91] 4. Challenges and future scope From the above discussion, it has been found that the process variables influence the quality of the FDM product to a great extent. Manufacturers and users are mainly concerned with the mechanical characteristics of the component like tensile strength, compressive strength, yield strength, flexural strength, impact strength, hardness, dimensional accuracy, production time, surface roughness, and durability. Therefore, researchers are investigating the most significant process parameter to enhance the mechanical characteristic of the component. However, there are still no unique significant parameters found for all materials, parts, and mechanical properties. There is always a need to adjust most of the parameters to meet the required part quality. After all these parameter adjustments, porosity remains within the FDM fabricated component because of its layering approach. The presence of porosity within the components fabricated through the FDM technique leads to having lower mechanical properties compared to the injection-moulded components. To enhance the mechanical behaviour and quality of these components, it is necessary to develop the relationship between printing variables and material characteristics through mathematical modelling approaches. From the literature review, it has been found that various printing variables (parameters) influence the quality of the component fabricated using the FDM technique. Hence, it is required to identify the critical parameters and determine their optimum values to improve the quality of the component. However, there are very few authors who have developed the relationships of the process variables with the mechanical behaviour and part quality, which is not enough for all types of FDM processed materials. Many authors have analysed the influence of FDM process variables on PLA, ABS, ULTEM 9085, PETG, Nylon-6 built parts. However, very few authors have reported on other FDM processed materials, both in terms of FDM process optimisation and material characterization. Therefore, it is necessary to fabricate and identify the significant process parameters for other FDM processed materials like ASA, PEEK, PEKK, PET-G, and nylon-12. Advances in Production Engineering & Management 17(3) 2022 289 Tripathy, Sharma, Rattan As far as material behaviour is concerned, most authors have reported on the optimisation of the printing input variables for enhancing the material characteristics of the parts fabricated using the FDM technique. However, very few authors have worked on the optimisation technique of FDM printing input variables for chemical, dynamic mechanical characteristics, chemical resistance, UV resistance and thermal of the parts printed using the FDM technique. Therefore, the impact of process variables on these factors needs to be investigated. The impact of printing variables on surface roughness, dimensional accuracy, impact, flexural, compressive, and tensile strength have been studied thoroughly by the authors. However, the other types of material properties like stress-strain behaviour at high-strain-rate loading conditions, porosity, product and process cost, vibration, production time, creep, and hardness need to be studied. The researchers should also work on the application of new optimisation techniques integrated with DOE, modelling techniques, and new statistical designs in the future, and identify the optimum setting of printing variables, and should also test the functionality of parts fabricated using the FDM technique. Environmental factors like relative humidity and temperature also affect the part quality. These factors may affect the surface quality and the dimensional accuracy of the FDM processed parts of materials like ABS, PLA, nylon-12, etc. Therefore, it is necessary to determine the optimal sets of humidity and temperature for FDM processed materials. The process of FDM machines is restricted by some physical constraints and has an impact on the setting of the optimum values of process variables, which must be addressed in future research. Among these constraints, the most crucial is the layer thickness whose value depends on the nozzle diameter; therefore, the user cannot select the layer thickness values other than specified values for that particular machine. The second constraint is imposed on nozzle diameter, which has a specified range of raster-width. In these conditions, the user cannot use any arbitrary values other than those defined by their range. These constraints complicate the optimisation of the FDM process variables and their selection on the machine for fabricating the component. Therefore, it is difficult to solve FDM process-related problems using traditional DOE techniques. Thus, the development of new mathematical modelling and optimisation approach is required for solving the constraints-related problems for the selection of optimum values of process variables beyond the specified range and also make it possible and feasible for practical applications. 5. Conclusion This work presents the various process parameters of fused deposition modelling-based additive manufacturing technique and their effect on mechanical characteristics of 3D-Printed components made of different thermoplastic materials. Through this study, it has been found that many researchers have worked on ABS, ABS+, PLA, ULTEM 9085; however, there exists future scope to analyse the influence of FDM process variables on the mechanical behaviour of other thermoplastic materials like ASA, PET-G, PEEK, and PEKK, etc. The present study also identified that printing process parameters have their roles and influence. Among all the process parameters, layer height has the highest influence on surface finish, build time, and strength of the component. Maximum strength is obtained with a rectilinear pattern,100 % infill-density, and increased layer thickness. Raster width, raster angle, and contour numbers also affect the mechanical property of the component. It has also been found that most of the researchers analysed the influence on tensile and flexural properties; however, very few researchers have analysed the effect on impact strength. Overall, the parameters like part orientation, layer height, raster-angle, raster width, and contours directly affect the quality of the 3Dprinted part. From the investigation, the input variables which affect the mechanical behaviour of the part can be set with most significant (layer height, raster-angle, and raster-width), significant (contour width and contour number) and least significant (air-gap). Although many authors have suggested a minus air-gap for enhancing the mechanical characteristics of the component, it was observed that minus air-gap has some drawbacks. Its effect can differ based on the thermoplastic used for 290 Advances in Production Engineering & Management 17(3) 2022 Effect of printing parameters on the mechanical behaviour of the thermoplastic polymer processed by FDM technique: A … processing. Although FDM process saves time and cost for low volume production, whereas, mechanical behaviour of its product doesn’t exceed injection moulded product. Hence, one should investigate other methods to improvise the properties of FDM products. Here, an effort is made to help researchers toward the selection of FDM processed material and variables for further research. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] Marwah, O.M.F., Darsani, A., Johar, M.A., Rosden, A.A., Mohamad, E.J., Shaari, M.F., Haq, R.H.A., Amin, A.M. (2017). Evaluation of injection molding process parameters for manufacturing polyethylene terephthalate, MATEC Web of Conferences, Vol. 135, 1-10, doi: 10.1051/matecconf/201713500037. Meekers, I., Refalo, P., Rochman, A. (2018). Analysis of process parameters affecting energy consumption in plastic injection moulding, Procedia CIRP, Vol. 69, 342-347, doi: 10.1016/j.procir.2017.11.042. Ganeshkar, J., Kamble, D. (2014). Design and manufacturing of plastic injection mould, Pertanika Journal of Science and Technology Supplement, Vol. 2, No. 5, 439-442. Knezovic, N., Dolsak, B. (2018). In‐process non-destructive ultrasonic testing application during wire plus arc additive manufacturing, Advances in Production Engineering & Management, Vol. 13, No. 2, 158-168, doi: 10.14743/ apem2018.2.281. Patalas-Maliszewska, J., Topczak, M. (2021). A new management approach based on additive manufacturing technologies and Industry 4.0 requirements, Advances in Production Engineering & Management, Vol. 16, No. 1, 125135, doi: 10.14743/apem2021.1.389. Javaid, M., Haleem, A. (2019). Current status and applications of additive manufacturing in dentistry: A literaturebased review, Journal of Oral Biology and Craniofacial Research, Vol. 9, No. 3, 179-185, doi: 10.1016/j.jobcr. 2019.04.004. Sarı, T., Güleş, H.K., Yiğitol, B. (2020). Awareness and readiness of Industry 4.0: The case of Turkish manufacturing industry, Advances in Production Engineering & Management, Vol. 15, No. 1, 57-68, doi: 10.14743/apem2020. 1.349. Song, Y., Li, Y., Song, W., Yee, K., Lee, K.-Y., Tagarielli, V.L. (2017). Measurements of the mechanical response of unidirectional 3D-printed PLA, Materials & Design, Vol. 123, 154-164, doi: 10.1016/j.matdes.2017.03.051. Tak, A., Ingavale, P., Khopatkar, C., Bhure, S., Barve, V., Rajurkar, A. (2015). Effect of 3D printing parameters on dimensional accuracy & shrinkage on printed parts, In: Proceedings of National Conference on Modeling, Optimization and Control - NCMOC – 2015, Pune, Maharashtra, India. Pham, D.T., Dimov, S.S. (2012). Rapid manufacturing: The technologies and applications of rapid prototyping and rapid tooling, Springer, London, United Kingdom. Shofner, M.L., Lozano, K., Rodríguez-Macías F.J., Barrera, E.V. (2003). Nanofiber-reinforced polymers prepared by fused deposition modeling, Journal of Applied Polymer Science, Vol. 89, No. 11, 3081-3090, doi: 10.1002/app. 12496. Sheoran, A.J., Kumar, H. (2020). Fused deposition modeling process parameters optimization and effect on mechanical properties and part quality: Review and reflection on present research, Materials Today Proceedings, Vol. 21, Part 3, 1659-1672, doi: 10.1016/j.matpr.2019.11.296. Kaur, G., Singari, R.M., Kumar, H. (2022). A review of fused filament fabrication (FFF): Process parameters and their impact on the tribological behavior of polymers (ABS), Materials Today Proceedings, Vol. 51, Part 1, 854-860, doi: 10.1016/J.MATPR.2021.06.274. Patil, P., Singh, D., Raykar, S.J., Bhamu, J. (2021). Multi-objective optimization of process parameters of Fused Deposition Modeling (FDM) for printing Polylactic Acid (PLA) polymer components, Materials Today Proceedings, Vol. 45, Part 6, 4880-4885, doi: 10.1016/j.matpr.2021.01.353. Ortiz-Acosta, D., Moore, T. (2019). Functional 3D printed polymeric materials, In: Sahu, D. (ed.), Functional Materials, IntechOpen, London, United Kingdom, doi: 10.5772/intechopen.80686. Hamad, K., Kaseem, M., Yang, H.W., Deri, F., Ko, Y.G. (2015). Properties and medical applications of polylactic acid: A review, Express Polymer Letters, Vol. 9, No. 5, 435-455, doi: 10.3144/expresspolymlett.2015.42. Jo, M.Y., Ryu, Y.J., Ko, J.H., Yoon, J.-S. (2012). Effects of compatibilizers on the mechanical properties of ABS/PLA composites, Journal of Applied Polymer Science, Vol. 125, No. 2, 231-238, doi: 10.1002/app.36732. Raj, S.A., Muthukumaran, E., Jayakrishna, K. (2018). A case study of 3D printed PLA and its mechanical properties, Materials Today Proceedings, Vol. 5, No. 5, Part 2, 11219-11226, doi: 10.1016/j.matpr.2018.01.146. Mohamed, O.A., Masood, S.H., Bhowmik, J.L. (2015). Optimization of fused deposition modeling process parameters: A review of current research and future prospects, Advances in Manufacturing, Vol. 3, 42-53, doi: 10.1007/s40436-014-0097-7. Casavola, C., Cazzato, A., Moramarco, V., Pappalettera, G. (2017). Residual stress measurement in Fused Deposition Modelling parts, Polymer Testing, Vol. 58, 249-255, doi: 10.1016/j.polymertesting.2017.01.003. Hossain, M.S., Ramos, J., Espalin, D., Perez, M., Wicker, R. (2013). Improving tensile mechanical properties of FDMmanufactured specimens via modifying build parameters, In: 2013 International Solid Freeform Fabrication Symposium, University of Texas at Austin, 380-392. Sood, A.K., Ohdar, R.K., Mahapatra, S.S. (2010). Parametric appraisal of fused deposition modelling process using the grey Taguchi method, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, Vol. 224, No. 1, 135-145, doi: 10.1243/09544054JEM1565. Advances in Production Engineering & Management 17(3) 2022 291 Tripathy, Sharma, Rattan [23] Dey, A., Yodo, N. (2019). A systematic survey of FDM process parameter optimization and their influence on part characteristics, Journal of Manufacturing and Materials Processing, Vol. 3, No. 3, Article No. 64, doi: 10.3390/ jmmp3030064. [24] Moradi, M., Meiabadi, S., Kaplan, A. (2019). 3D printed parts with honeycomb internal pattern by Fused Deposition Modelling; Experimental characterization and production optimization, Metals and Materials International, Vol. 25, 1312-1325, doi: 10.1007/s12540-019-00272-9. [25] Rankouhi, B., Javadpour, S., Delfanian, F., Letcher, T. (2016). Failure analysis and mechanical characterization of 3D printed ABS with respect to layer thickness and orientation, Journal of Failure Analysis and Prevention, Vol. 16, No. 3, 467-481, doi: 10.1007/s11668-016-0113-2. [26] Selva Priya, M., Naresh, K., Jayaganthan, R., Velmurugan, R. (2019). A comparative study between in-house 3D printed and injection molded ABS and PLA polymers for low-frequency applications, Materials Research Express, Vol. 6, No. 8, Article No. 085345, doi: 10.1088/2053-1591/ab2776. [27] Vaezi, M., Chua, C.K. (2011). Effects of layer thickness and binder saturation level parameters on 3D printing process, International Journal of Advanced Manufacturing Technology, Vol. 53, No. 1-4, 275-284, doi: 10.1007/s00170010-2821-1. [28] Noori, H. (2019). Interlayer fracture energy of 3D-printed PLA material, International Journal of Advanced Manufacturing Technology, Vol. 101, 1959-1965, doi: 10.1007/s00170-018-3031-5. [29] Abbott, A.C., Tandon, G.P., Bradford, R.L., Koerner, H., Baur, J.W. (2018). Process-structure-property effects on ABS bond strength in fused filament fabrication, Additive Manufacturing, Vol. 19, 29-38, doi: 10.1016/j.addma. 2017.11.002. [30] Wu, W., Geng, P., Li, G., Zhao, D., Zhang, H., Zhao, J. (2015). Influence of layer thickness and raster-angle on the mechanical properties of 3D-printed PEEK and a comparative mechanical study between PEEK and ABS, Materials, Vol. 8, No. 9, 5834-5846, doi: 10.3390/ma8095271. [31] Bin Sukindar, N.A., Bin Mohd Ariffin, M.K.A., Bin Baharudin, B.T.H.T., Binti Jaafar, C.N.A., Bin Ismail, M.I.S. (2017). Analysis on the impact process parameters on tensile strength using 3d printer repetier-host software, ARPN Journal of Engineering and Applied Sciences, Vol. 12, No. 10, 3341-3346. [32] Rouf, S., Raina, A., Irfan Ul Haq, M., Naveed, N., Jeganmohan, S., Farzana Kichloo, A. (2022). 3D printed parts and mechanical properties: Influencing parameters, sustainability aspects, global market scenario, challenges and applications, Advanced Industrial and Engineering Polymer Research, Vol. 5, No. 3, 143-158, doi: 10.1016/J.AIEPR. 2022.02.001. [33] Roy, R., Mukhopadhyay, A. (2021). Tribological studies of 3D printed ABS and PLA plastic parts, Materials Today Proceedings, Vol. 41, Part 4, 856-862, doi: 10.1016/j.matpr.2020.09.235. [34] Norani, M.N.M., Abdollah, M.F.B., Abdullah, M.I.H.C., Amiruddin, H., Ramli, F.R., Tamaldin, N. (2021). 3D printing parameters of acrylonitrile butadiene styrene polymer for friction and wear analysis using response surface methodology, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, Vol. 235, No. 2, 468-477, doi: 10.1177/1350650120925601. [35] Dangnan, F., Espejo, C., Liskiewicz, T., Gester, M., Neville, A. (2020). Friction and wear of additive manufactured polymers in dry contact, Journal of Manufacturing Processes, Vol. 59, 238-247, doi: 10.1016/j.jmapro.2020.09.051. [36] Bhosale, V., Gaikwad, P., Dhere, S., Sutar, C., Raykar, S.J. (2022). Analysis of process parameters of 3D printing for surface finish, printing time and tensile strength, Materials Today Proceedings, Vol. 59, Part 1, 841-846, doi: 10.1016/J.MATPR.2022.01.210. [37] Raj Mohan, R., Venkatraman, R., Raghuraman, S. (2021). Experimental analysis on density, micro-hardness, surface roughness and processing time of Acrylonitrile Butadiene Styrene (ABS) through Fused Deposition Modeling (FDM) using Box Behnken Design (BBD), Materials Today Communications, Vol. 27, Article No. 102353, doi: 10.1016/j.mtcomm.2021.102353. [38] Khan, M.S., Mishra, S.B. (2019). Minimizing surface roughness of ABS-FDM build parts: An experimental approach, Materials Today Proceedings, Vol. 26, Part 2, 1557-1566, doi: 10.1016/j.matpr.2020.02.320. [39] Kumar, R., Ranjan, N. (2021). Influences of infill percentage, bed temperature and outer perimeters on elongation of 3D printed nylon 6, Materials Today Proceedings, Vol. 48, Part 5, 1661-1665, doi: 10.1016/j.matpr.2021.09.529. [40] Chacón, J.M., Caminero, M.A., García-Plaza, E., Núñez, P.J. (2017). Additive manufacturing of PLA structures using fused deposition modelling: Effect of process parameters on mechanical properties and their optimal selection, Materials & Design, Vol. 124, 143-157, doi: 10.1016/j.matdes.2017.03.065. [41] Shubham, P., Sikidar, A., Chand, T. (2016). The influence of layer thickness on mechanical properties of the 3D printed ABS polymer by fused deposition modeling, Key Engineering Materials, Vol. 706, 63-67, doi: 10.4028/ www.scientific.net/KEM.706.63. [42] Shubham, P., Aggarwal, C., Joshi, S. (2018). Optimization of process parameter to improve dynamic mechanical properties of 3D printed ABS polymer using Taguchi method, International Journal of Mechanical and Production Engineering, Vol. 6, No. 6, 2321-2071. [43] Daminabo, S.C., Goel, S., Grammatikos, S.A., Nezhad, H.Y., Thakur, V.K. (2020). Fused deposition modeling-based additive manufacturing (3D printing): Techniques for polymer material systems, Materials Today Chemistry, Vol. 16, Article No. 100248, doi: 10.1016/j.mtchem.2020.100248. [44] Ramesh, M., Panneerselvam, K. (2020). Mechanical investigation and optimization of parameter selection for Nylon material processed by FDM, Materials Today Proceedings, Vol. 46, Part 19, 9303-9307, doi: 10.1016/j.matpr. 2020.02.697. 292 Advances in Production Engineering & Management 17(3) 2022 Effect of printing parameters on the mechanical behaviour of the thermoplastic polymer processed by FDM technique: A … [45] Pazhamannil, R.V., Govindan, P., Sooraj, P. (2020). Prediction of the tensile strength of polylactic acid fused deposition models using artificial neural network technique, Materials Today Proceedings, Vol. 46, Part 19, 9187-9193, doi: 10.1016/j.matpr.2020.01.199. [46] Yadav, D., Chhabra, D., Gupta, R.K., Phogat, A., Ahlawat, A. (2020). Modeling and analysis of significant process parameters of FDM 3D printer using ANFIS, Materials Today Proceedings, Vol. 21, Part 3, 1592-1604, doi: 10.1016/j.matpr.2019.11.227. [47] Gebisa, A.W., Lemu, H.G. (2019). Influence of 3D printing FDM process parameters on tensile property of ULTEM 9085, Procedia Manufacturing, Vol. 30, 331-338, doi: 10.1016/j.promfg.2019.02.047. [48] Wankhede, V., Jagetiya, D., Joshi, A., Chaudhari, R. (2019). Experimental investigation of FDM process parameters using Taguchi analysis, Materials Today Proceedings, Vol. 27, Part 3, 2117-2120, doi: 10.1016/j.matpr. 2019.09.078. [49] Solomon, I.J., Sevvel, P., Gunasekaran, J. (2021). A review on the various processing parameters in FDM, Materials Today Proceedings, Vol. 37, Part 2, 509-514, doi: 10.1016/j.matpr.2020.05.484. [50] Fernandez-Vicente, M., Calle, W., Ferrandiz, S., Conejero, A. (2016). Effect of infill parameters on tensile mechanical behavior in desktop 3D printing, 3D Printing and Additive Manufacturing, Vol. 3, No. 3, 183-192, doi: 10.1089/ 3dp.2015.0036. [51] Rajpurohit, S.R., Dave, H.K. (2018). Effect of process parameters on tensile strength of FDM printed PLA part, Rapid Prototyping Journal, Vol. 24, No. 8, 1317-1324, doi: 10.1108/RPJ-06-2017-0134. [52] Dawoud, M., Taha, I., Ebeid, S.J. (2016). Mechanical behaviour of ABS: An experimental study using FDM and injection moulding techniques, Journal of Manufacturing Processes, Vol. 21, 39-45, doi: 10.1016/j.jmapro.2015.11.002. [53] Wang, P., Zou, B., Xiao, H., Ding, S., Huang, C. (2019). Effects of printing parameters of fused deposition modeling on mechanical properties, surface quality, and microstructure of PEEK, Journal of Materials Processing Technology, Vol. 271, 62-74, doi: 10.1016/j.jmatprotec.2019.03.016. [54] Kaplun, B.W., Zhou, R., Jones, K.W., Dunn, M.L., Yakacki, C.M. (2020). Influence of orientation on mechanical properties for high-performance fused filament fabricated ultem 9085 and electro-statically dissipative polyetherketoneketone, Additive Manufacturing, Vol. 36, Article No. 101527, doi: 10.1016/j.addma.2020.101527. [55] Raam Kumar, S., Sridhar, S., Venkatraman, R., Venkatesan, M. (2020). Polymer additive manufacturing of ASA structure: Influence of printing parameters on mechanical properties, Materials Today Proceedings, Vol. 39, Part 4, 1316-1319, doi: 10.1016/j.matpr.2020.04.500. [56] Szykiedans, K., Credo, W., Osiński, D. (2017). Selected mechanical properties of PETG 3-D prints, Procedia Engineering, Vol. 177, 455-461, doi: 10.1016/j.proeng.2017.02.245. [57] Durgashyam, K., Indra Reddy, M., Balakrishna, A., Satyanarayana, K. (2019). Experimental investigation on mechanical properties of PETG material processed by fused deposition modeling method, Materials Today Proceedings, Vol. 18, Part 6, 2052-2059, doi: 10.1016/j.matpr.2019.06.082. [58] Gebisa, A.W., Lemu, H.G. (2018). Investigating effects of fused-deposition modeling (FDM) processing parameters on flexural properties of ULTEM 9085 using designed experiment, Materials, Vol. 11, No. 4, Article No. 500, doi: 10.3390/ma11040500. [59] Mohamed, O.A., Masood, S.H., Bhowmik, J.L., Nikzad, M., Azadmanjiri, J. (2016). Effect of process parameters on dynamic mechanical performance of FDM PC/ABS printed parts through design of experiment, Journal of Materials Engineering and Performance, Vol. 25, 2922-2935, doi: 10.1007/s11665-016-2157-6. [60] Mohamed Omar, A., Masood Syed, H., Bhowmik Jahar, L. (2016). Investigation of dynamic elastic deformation of parts processed by fused deposition modeling additive manufacturing, Advances in Production Engineering & Management, Vol. 13, No. 3, 227-238, doi: 10.14743/apem2016.3.223. [61] Ahn, S.-H., Montero, M., Odell, D., Roundy, S., Wright, P.K. (2002). Anisotropic material properties of fused deposition modeling ABS, Rapid Prototyping Journal, Vol. 8, No. 4, 248-257, doi: 10.1108/13552540210441166. [62] Deng, X., Zeng, Z., Peng, B., Yan, S., Ke, W. (2018). Mechanical properties optimization of poly-ether-ether-ketone via fused deposition modeling, Materials, Vol. 11, No. 2, Article No. 216, doi: 10.3390/ma11020216. [63] Onwubolu, G.C., Rayegani, F. (2014). Characterization, and optimization of mechanical properties of ABS parts manufactured by the fused deposition modelling process, International Journal of Manufacturing Engineering, Vol. 2014, Article ID 598531, doi: 10.1155/2014/598531. [64] Bagsik, A., Schöppner, V., Klemp, E. (2010). FDM part quality manufactured with Ultem* 9085. In: Proceedings of the 14th International Scientific Conference on Polymeric Materials, Halle (Saale), Germany, 307-315. [65] Bagsik, A., Schöppner, V. (2011). Mechanical properties of fused deposition modeling parts manufactured with Ultem 9085, In: Proceedings of ANTEC 2011: 69th Annual Technical Conference of the Society of Plastics Engineers, Boston, USA,1294-1298. [66] Motaparti, K.P., Taylor, G., Leu, M.C., Chandrashekhara, K., Castle, J., Matlack, M. (2016). Effects of build parameters on compression properties for ULTEM 9085 parts by fused deposition modeling, In: Proceedings of the 27th Annual International Solid Freeform Fabrication Symposium - An Additive Manufacturing Conference, SFF 2016, Austin, USA, 964-977. [67] Motaparti, K.P., Taylor, G., Leu, M.C., Chandrashekhara, K., Castle, J., Matlack, M. (2017). Experimental investigation of effects of build parameters on flexural properties in fused deposition modelling parts, Virtual and Physical Prototyping, Vol. 12, No. 3, 207-220, doi: 10.1080/17452759.2017.1314117. [68] Masood, S.H., Mau, K., Song, W.Q. (2010). Tensile properties of processed FDM polycarbonate material, Materials Science Forum, Vol. 654-656, 2556-2559, doi: 10.4028/www.scientific.net/MSF.654-656.2556. Advances in Production Engineering & Management 17(3) 2022 293 Tripathy, Sharma, Rattan [69] Górski, F., Wichniarek, R., Kuczko, W., Zawadzki, P., Buń, P. (2015). Strength of ABS parts produced by fused deposition modelling technology – A critical orientation problem, Advances in Science and Technology Research Journal, Vol. 9, No. 26, 12-19, doi: 10.1291322998624/2359. [70] Durgun, I., Ertan, R. (2014). Experimental investigation of FDM process for improvement of mechanical properties and production cost, Rapid Prototyping Journal, Vol. 20, No. 3, 228-235, doi: 10.1108/RPJ-10-2012-0091. [71] Lužanin, O., Movrin, D., Plančak, M. (2014). Effect of layer thickness, deposition angle, and infill on maximum flexural force in FDM-built specimens, Journal for Technology of Plasticity, Vol. 39, No. 1, 49-58. [72] Al-Ghamdi, K.A. (2019). Sustainable FDM additive manufacturing of ABS components with emphasis on energy minimized and time efficient lightweight construction, International Journal of Lightweight Materials and Manufacture, Vol. 2, No. 4, 338-345, doi: 10.1016/j.ijlmm.2019.05.004. [73] Garzon-Hernandez, S., Garcia-Gonzalez, D., Jérusalem, A., Arias, A. (2020). Design of FDM 3D printed polymers: An experimental-modeling methodology for the prediction of mechanical properties, Materials & Design, Vol. 188, Article No. 108414, doi: 10.1016/j.matdes.2019.108414. [74] Pramanik, D., Mandal, A., Kuar, A.S. (2020). An experimental investigation on improvement of surface roughness of ABS on fused deposition modelling process, Materials Today Proceedings, Vol. 26, Part 2, 860-863, doi: 10.1016/j.matpr.2020.01.054. [75] Galeja, M., Hejna, A., Kosmela, P., Kulawik, A. (2020). Static and dynamic mechanical properties of 3D printed ABS as a function of raster angle, Materials, Vol. 13, No. 2, Article No. 297, doi: 10.3390/ma13020297. [76] Divyathej, M.V., Varun, M., Rajeev, P. (2016). Analysis of mechanical behavior of 3D printed ABS parts by experiments, International Journal of Scientific & Engineering Research, Vol. 7, No. 3, 116-124. [77] Kuznetsov, V.E., Solonin, A.N., Urzhumtsev, O.D., Schilling, R., Tavitov, A.G. (2018). Strength of PLA components fabricated with fused deposition technology using a desktop 3D printer as a function of geometrical parameters of the process, Polymers, Vol. 10, No. 3, Article No. 313, doi: 10.3390/polym10030313. [78] Rodríguez-Panes, A., Claver, J., Camacho, A.M. (2018). The influence of manufacturing parameters on the mechanical behaviour of PLA and ABS pieces manufactured by FDM: A comparative analysis, Materials, Vol. 11, No. 8, Article No. 1333, doi: 10.3390/ma11081333. [79] Arif, M.F., Kumar, S., Varadarajan, K.M., Cantwell, W.J. (2018). Performance of biocompatible PEEK processed by fused deposition additive manufacturing, Materials & Design, Vol. 146, 249-259, doi: 10.1016/j.matdes.2018. 03.015. [80] Rinaldi, M., Ghidini, T., Cecchini, F., Brandao, A., Nanni, F. (2018). Additive layer manufacturing of poly (ether ether ketone) via FDM, Composites Part B: Engineering, Vol. 145, 162-172, doi: 10.1016/j.compositesb.2018.03.029. [81] Mishra, S.B., Malik, R., Mahapatra, S.S. (2017). Effect of external perimeter on flexural strength of FDM build parts, Arabian Journal for Science and Engineering, Vol. 42, 4587-4595, doi: 10.1007/s13369-017-2598-8. [82] Samykano, M. (2021). Mechanical property and prediction model for FDM-3D printed polylactic acid (PLA), Arabian Journal for Science and Engineering, Vol. 46, 7875-7892, doi: 10.1007/s13369-021-05617-4. [83] Mendricky, R., Fris, D. (2020). Analysis of the accuracy and the surface roughness of FDM/FFF technology and optimization of process parameters, Tehnički Vjesnik – Technical Gazette, Vol. 27, No. 4, 1166-1173, doi: 10.17559/ TV-20190320142210. [84] Liu, X., Zhang, M., Li, S., Si, L.,Peng, J., Hu, Y. (2017). Mechanical property parametric appraisal of fused deposition modeling parts based on the gray Taguchi method, International Journal of Advanced Manufacturing Technology, Vol. 89, 2387-2397, doi: 10.1007/s00170-016-9263-3. [85] Srivastava, M., Rathee, S., Maheshwari, S., Kundra, T.K. (2018). Multi-objective optimisation of fused deposition modelling process parameters using RSM and fuzzy logic for build time and support material, International Journal of Rapid Manufacturing, Vol. 7, No. 1, 25-42, doi: 10.1504/ijrapidm.2018.089727. [86] Sahu, R.K, Mahapatra, S.S., Sood, A.K. (2013) A study on dimensional accuracy of fused deposition modeling (FDM) processed parts using fuzzy logic, Journal for Manufacturing Science & Production, Vol. 13, No. 3, 183-197, doi: 10.1515/jmsp-2013-0010. [87] Raju, M., Gupta, M.K., Bhanot, N., Sharma, V.S. (2019). A hybrid PSO–BFO evolutionary algorithm for optimization of fused deposition modelling process parameters, Journal of Intelligent Manufacturing, Vol. 30, 2743-2758, doi: 10.1007/s10845-018-1420-0. [88] Zaman, U.K.U., Boesch, E., Siadat, A., Rivette, M., Baqai, A.A. (2019). Impact of fused deposition modeling (FDM) process parameters on strength of built parts using Taguchi’s design of experiments, International Journal of Advanced Manufacturing Technology, Vol 101, 1215-1226, doi: 10.1007/s00170-018-3014-6. [89] Torres, J., Cotelo, J., Karl, J., Gordon, A.P. (2015). Mechanical property optimization of FDM PLA in shear with multiple objectives, Journal of The Minerals, Metals & Materials Society, Vol. 67, 1183-1193, doi: 10.1007/s11837-0151367-y. [90] Deshwal, S., Kumar, A., Chhabra, D. (2020). Exercising hybrid statistical tools GA-RSM, GA-ANN and GA-ANFIS to optimize FDM process parameters for tensile strength improvement, CIRP Journal of Manufacturing Science and Technology, Vol. 31, 189-199, doi: 10.1016/j.cirpj.2020.05.009. [91] Wang, C.C., Lin, T.-W., Hu, S.-S. (2007). Optimizing the rapid prototyping process by integrating the Taguchi method with the gray relational analysis, Rapid Prototyping Journal, Vol 13, No. 5, 304-315, doi: 10.1108/ 13552540710824814. 294 Advances in Production Engineering & Management 17(3) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 3 | September 2022 | pp 295–310 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.3.437 Original scientific paper Evolutionary game analysis of company collaborative strategy in cloud manufacturing platform environment Xiao, M.a,*, Tian, Z.Y.a aShenyang University of Technology, School of Management, Shenyang, P.R. China ABSTRACT ARTICLE INFO The collaboration between manufacturing companies and demand companies is the focus of effective operation of cloud manufacturing platform. The evolutionary game model of manufacturing company, demand company and cloud platform was established, and the strategy stability of the three parties was analyzed in this paper. Based on Lyapunov discrimination method, the equilibrium points of the system were explored, and the simulation was applied to analyze the influence of key factors in the evolution process by MATLAB2021a. The results show that: (1) The evolution of company collaborative cooperation strategies in the cloud platform environment is staged; (2) The collaborative subsidy to the manufacturing company and the demand company by the cloud platform, the collaborative effort degree of the manufacturing company and the demand company, the value-added profits of the manufacturing company, the penalties and profits of the manufacturing company's speculation behavior, the loss of information leakage of demand company, and the government's subsidy for cloud platform supervision are important factors that affect the strategies of each subject; (3) The establishment of the cloud platform supervision mechanism can promote collaboration between the manufacturing company and the demand company. The results of the study can provide a beneficial strategic decision guidance for the development of the cloud manufacturing platform. Keywords: Cloud manufacturing platform; Manufacturing company; Collaborative cooperation; Evolutionary game; Simulation; MATLAB programming platform *Corresponding author: mengxiao@sut.edu.cn (Xiao, M.) Article history: Received 15 March 2022 Revised 17 August 2022 Accepted 29 August 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction With the integration of Internet of Things and Internet of services with manufacturing, the production systems of the fourth industrial revolution are undergoing renovation [1]. The cloud manufacturing is becoming a service-oriented manufacturing mode for the development of advanced manufacturing [2]. With the good communication channels and expanded communication fields, the cloud manufacturing platform transforms the companies on the platform from a relatively closed self-centered and self-organization system to an open innovation system with cooperation, which is an effective implementation of the strategy of "Internet + Manufacturing". In the cloud platform, capacity sharing changes the traditional manufacturing mode, breaks the balance of the original production system, and transforms the roles of companies and users from the traditional separation mode of producer and consumer to the co-creators of products, improving the technical performance and reducing the purchase price [3]. The relationship between supplier and demander has changed from simple value exchange to value co-creation. Shared manufacturing based on the cloud platform has attracted the attention of relevant scholars and industrialists [4], but the development of cloud platform is still in the exploratory stage, and how to develop cloud manufacturing platform is still a common concern of platform 295 Xiao, Tian operators and users. However, in the process of cloud platform application, some problems restricting companies' cloud adoption are gradually exposed [5]. While company collaboration is facilitated, large-scale resource sharing implemented in cloud platforms may widen the credibility gap [6]. In the process of cooperation, the situation of "free-riding" in which one partner only benefits and does not invest often occurs [7]. This reduces the effectiveness of the cloud platform to create value for companies and is not conducive to the promotion of shared innovative ideas in the system, which requires certain supervision. Facing the market environment in which the scale of companies entering the cloud platform is gradually expanding, it is necessary to make an in-depth analysis on the strategies to promote the collaborative cooperation of companies in the cloud platform. Therefore, from the perspective of cooperation and supervision of the cloud platform, this study systematically analyzes the promotion effect of the subsidy and penalty mechanism of the cloud platform and the efforts of manufacturing company and demand company on company collaboration with the evolutionary game method, which can provide some guidance for the prosperous sharing economy and the healthy development of cloud manufacturing platform. 2. Literature review The existing researches on cloud platform mainly focus on the business model of cloud platform, the relationship between the supply and the demand in cloud platform and the supervision of cloud platform. The cloud platform integrates sharing with the internet, expanding small-scale sharing based on strong ties to large-scale sharing based on weak ties. Therefore, the sharing based on the cloud platform breaks through the traditional sharing behavior and becomes a more macroeconomic sharing. In the sharing economy, the cloud platform plays the role of digital media to match supply and demand. Some scholars have proposed that platform services based on the network environment will gradually become the mainstream mode of the modern service industry. Compared with traditional business mode, cloud platforms can assist buyers and sellers to match and connect faster, provide a more economical mode to increase customer value, create competitive advantage and transform business processes to increase industry profits [8], which is more consistent with the concept of sustainable development. The cloud manufacturing can realize customization and modularization of resources in the cloud platform [9], and the multiuser-oriented manufacturing service distribution [2]. Many scholars have discussed the mode of cloud manufacturing. Woo et al. [10] believed that intelligent cloud manufacturing platform can improve the utilization efficiency of resources in platform network sharing and provide manufacturing services on demand. Barenji et al. [11] found that various departments in the platform can use joint design to achieve effective communication across regions and reach perfect cooperative target by using the method of the case study. Zhang et al. [12] proposed that the machine system based on cloud platform can customize the architecture of intelligent manufacturing of products. Li et al. [13] thought that industrial robots were the service objects of the internet platform deriving from the industrial mode of "government procurement and leasing". Xu et al. [14] and Wu and Zhang [15] proposed the design scheme of the comprehensive platform for information services provided by supply chain participants based on the ethereum block-chain for intelligent manufacturing. Xiao et al. [16] suggested a service resource matching method by combining the characteristics of manufacturing service task on cloud platform, such as relevance, synergy and diversity. The construction and mode of cloud manufacturing platforms have attracted more and more scholars' attention. Based on big data and artificial intelligence, the digital cloud platform focuses on the resource sharing of bilateral participants and is an effective carrier to achieve value creation of resource sharing service system. In the cloud platform, the main subject of supply and demand can give full play to the effective utilization of resources[17], form complementary advantages, reduce energy consumption[18], and play a guiding role in innovation. The services of cloud platforms have the characteristics of network externality, and integration, functionality and derivation of scientific and technological resources [19]. The researches on cloud platforms have found that 296 Advances in Production Engineering & Management 17(3) 2022 Evolutionary game analysis of company collaborative strategy in cloud manufacturing platform environment the network effects generated by cloud platforms improve the competitive advantages and profits of the platforms [20], and the active cooperation of service providers can create higher benefits for both parties. Upgrading of manufacturing networks through the cloud platform has become the mode adopted by many manufacturing companies, which is also the reason that drives them to join the cloud manufacturing platform [21]. At the same time, product design, manufacturing network [22], competitive pressures, manager's influence, compatibility and applicability all play the critical roles in the cloud platform operation [9]. Collaboration is the key to the success of cloud platforms [23]. Ren et al. [24] suggested the service composition method because of synergies in allusion to social synergy characteristics of manufacturing services, and described five relationships of service networks. Company collaboration in the cloud platform is a complex system engineering [25]. How to effectively promote this synergistic relationship is still in the exploratory stage. While the cloud manufacturing platform brings many conveniences to the development of the manufacturing industry, it also produces certain negative effects. For example, intelligent manufacturing requires the sharing of data and information, which not only leads to the risk of information exchange [26], but also brings issues such as the security of cloud platform data and information [11] and the complexity of trust relationships between cooperating subjects [27], making it difficult to ensure the credibility and responsibility of cross-company production activities [28]. Some scholars have proposed that the complexity of service upgrade would initiate cognitive bias behavior of organizational participants to jeopardize the accomplish of serviceization within the organization [29]. With the increase in the number of cloud manufacturing platform products, platform services focus more on communication and coordination between service providers and consumers, while incentive and punishment mechanisms are not well established [30]. All these make it difficult for platform supervision to promote its healthy development. Scholars have realized the necessity of effective monitoring of cloud platforms [30], and proposed some monitoring methods such as consensus mechanism of service capability proof [5]. Even if the existing supervision methods are not perfect and need to be further explored, it has been recognized by scholars that company coordination still needs to be managed, which the platform is responsible for [31, 32], and one of the autonomous cycles of the platform is believed to allow self-supervision of the coordination process [33]. 3. Model building 3.1 Model description and assumption In cloud manufacturing environment, a variety of manufacturing resources are organized by the platform to enhance the competitiveness of supply chain and realizes on-demand matching between resource demanders and suppliers based on unified management and operation, and finally completes the full life cycle of manufacturing. In this study, a collaborative cooperation multi-agent game model of cloud platform, manufacturing company and demand company is constructed. The logical relationship of the subjects in cloud manufacturing platform is shown in Fig. 1. Fig. 1 Logical relationship of game model in the cloud platform environment Advances in Production Engineering & Management 17(3) 2022 297 Xiao, Tian For the purpose of studying behavioral strategies of three-party game subjects of cloud platform, manufacturing company and demand company, the following assumptions are proposed. Assumption 1: There are three participants in the evolutionary game model, namely the cloud platform, the manufacturing company and the demand company, and they take the maximization of their respective benefits as the goal in decision-making. Due to the characteristics of bounded rational subjects, each subject achieves the optimal strategy with keeping learning in the process and adjusts the strategy based on the strategic choice of the other parties and their benefits. The game process is repeated and dynamic. The proportion of manufacturing company collaborative cooperation is indicated as 𝑥𝑥, and the proportion of general cooperation is indicated as 1 – 𝑥𝑥; the proportion of demand company collaborative cooperation is indicated as 𝑦𝑦, and the proportion of general cooperation is indicated as 1 – 𝑦𝑦; the proportion of cloud platform supervision is indicated as 𝑧𝑧, and the proportion of non-supervision is indicated as 1 – 𝑧𝑧; where 0 ≤ 𝑥𝑥 ≤ 1, 0 ≤ 𝑦𝑦 ≤ 1, 0 ≤ 𝑧𝑧 ≤ 1. Assumption 2: The government actively promotes cloud manufacturing platform, and will subsidize platform supervision and the collaborative cooperation behavior of manufacturing company and demand company. The payoff of the normal operation of the cloud platform without supervision is E. When implementing the supervision of companies on the platform, the regulatory cost of cloud platform is CP, and government subsidy for the cloud platform is SP. If both manufacturing company and demand company choose the collaborative cooperation strategy, it will bring the value-added benefits FP to the cloud platform. Assumption 3: When cloud platform chooses the supervision strategy, if manufacturing company or the demand company chooses to collaboratively cooperate, the degree of collaborative effort of the manufacturing company is set as α (0 < 𝛼𝛼 ≤ 1), and the degree of collaborative effort of the demand company is set as β (0 < 𝛽𝛽 ≤ 1). The cloud platform provides subsidies to manufacturing company and demand company on behalf of the government, and the subsidies are proportional to the effort of the company, denoted as αSM and βSC respectively. Assumption 4: When both manufacturing company and demand company choose to collaborative cooperation, they can obtain value-added collaborative profits. The value-added profit of collaborative cooperation of manufacturing company is WM, and that of demand company is WC. The amount of the collaborative cooperation profit is proportional to the effort of the company, and the value-added collaborative profits of manufacturing company is αWM and the valueadded collaborative profits of demand company is βWC. Assumption 5: When the manufacturing company chooses collaborative cooperation and the demand company chooses general cooperation, due to the hardware upgrades carried out by the manufacturing company, even if the demand company does not collaborate cooperate with it, the manufacturing company will have a certain additional profit T. The value-added profit of the manufacturing company is proportional to its effort, so it can be described as αT. At this time, the demand company cannot obtain additional profits. Assumption 6: When the manufacturing company chooses general cooperation and the demand company chooses collaborative cooperation, because of collaboratively cooperating by providing information, the information leakage loss of the demand company may occur, denoted as V. The loss of demand company is proportional to its collaborative effort, and the loss amount is expressed as βV. At this time, the general cooperation as "free-rider" behavior can bring the speculative profit Q to the manufacturing company, and the amount of the speculative profit is proportional to the effort of the demand company, which is expressed as βQ. The punishment mechanism in cooperation can effectively curb the occurrence of "free-rider" behavior. Therefore, the manufacturing company should be punished with the penalty to compensate the collaborative cooperation of the demand company, which is expressed as LM. Assumption 7: When both manufacturing company and demand company choose general cooperation, the parties can only obtain the payoffs of general cooperation, which are expressed as RM and RC respectively. 298 Advances in Production Engineering & Management 17(3) 2022 Evolutionary game analysis of company collaborative strategy in cloud manufacturing platform environment On the basis of the above descriptions and assumptions, the strategy game payoff matrix of the three-party is acquired, as illustrated in Table 1. Strategy choice Manufacturing company Collaborative cooperation (𝑥𝑥) General cooperation (1 – 𝑥𝑥) 3.2 Model analysis Table 1 Payoff matrix of three-party subjects Cloud platform Demand company Supervision Non-supervision (𝑧𝑧) (1 – 𝑧𝑧) Collaborative coo𝛼𝛼𝑊𝑊𝑀𝑀 + 𝛼𝛼𝑆𝑆𝑀𝑀 + 𝑅𝑅𝑀𝑀 𝛼𝛼𝑊𝑊𝑀𝑀 + 𝑅𝑅𝑀𝑀 peration 𝛽𝛽𝑊𝑊𝐶𝐶 + 𝛽𝛽𝑆𝑆𝐶𝐶 + 𝑅𝑅𝐶𝐶 𝛽𝛽𝑊𝑊𝐶𝐶 + 𝑅𝑅𝐶𝐶 (𝑦𝑦) 𝐸𝐸 − 𝐶𝐶𝑃𝑃 + 𝑆𝑆𝑃𝑃 + 𝐹𝐹𝑃𝑃 − 𝛼𝛼𝑆𝑆𝑀𝑀 − 𝛽𝛽𝑆𝑆𝐶𝐶 𝐸𝐸 + 𝐹𝐹𝑃𝑃 General cooperati𝛼𝛼𝑆𝑆𝑀𝑀 + 𝑅𝑅𝑀𝑀 + 𝛼𝛼𝛼𝛼 𝑅𝑅𝑀𝑀 + 𝛼𝛼𝛼𝛼 on 𝑅𝑅𝐶𝐶 𝑅𝑅𝐶𝐶 (1 – 𝑦𝑦) 𝐸𝐸 − 𝐶𝐶𝑃𝑃 + 𝑆𝑆𝑃𝑃 − 𝛼𝛼𝑆𝑆𝑀𝑀 𝐸𝐸 Collaborative coo𝑅𝑅𝑀𝑀 − 𝐿𝐿𝑀𝑀 + 𝛽𝛽𝑄𝑄 𝑅𝑅𝑀𝑀 + 𝛽𝛽𝑄𝑄 peration 𝛽𝛽𝑊𝑊𝐶𝐶 + 𝑅𝑅𝐶𝐶 − 𝛽𝛽𝛽𝛽 + 𝐿𝐿𝑀𝑀 𝑅𝑅𝐶𝐶 − 𝛽𝛽𝛽𝛽 (𝑦𝑦) 𝐸𝐸 − 𝐶𝐶𝑃𝑃 + 𝑆𝑆𝑃𝑃 − 𝛽𝛽𝑆𝑆𝐶𝐶 𝐸𝐸 General cooperati𝑅𝑅𝑀𝑀 𝑅𝑅𝑀𝑀 on 𝑅𝑅𝐶𝐶 𝑅𝑅𝐶𝐶 (1 – 𝑦𝑦) 𝐸𝐸 − 𝐶𝐶𝑃𝑃 + 𝑆𝑆𝑃𝑃 𝐸𝐸 The stability and evolution path of three subjects strategies are explored by the stability theory of differential equations, and two conditions should be satisfied for the stable point of replica𝑑𝑑𝑑𝑑(𝑥𝑥) tion dynamic equation: 𝐹𝐹(𝑥𝑥) = 0, and < 0. 𝑑𝑑𝑑𝑑 Replication dynamic analysis of manufacturing company strategy The expected payoff of manufacturing company carrying out collaborative cooperation strategy is set as U11, and the expected payoff of manufacturing company carrying out general cooperation strategy is set as U12, which are defined as follows: 𝑈𝑈11 = 𝑦𝑦𝑦𝑦(𝛼𝛼𝑊𝑊𝑀𝑀 + 𝛼𝛼𝑆𝑆𝑀𝑀 + 𝑅𝑅𝑀𝑀 ) + (1 − 𝑦𝑦)𝑧𝑧(𝛼𝛼𝑆𝑆𝑀𝑀 + 𝑅𝑅𝑀𝑀 + 𝛼𝛼𝛼𝛼) + 𝑦𝑦(1 − 𝑧𝑧)(𝛼𝛼𝑊𝑊𝑀𝑀 + 𝑅𝑅𝑀𝑀 ) + (1 − 𝑦𝑦)(1 − 𝑧𝑧)(𝑅𝑅𝑀𝑀 + 𝛼𝛼𝛼𝛼) 𝑈𝑈12 = 𝑦𝑦𝑦𝑦(𝑅𝑅𝑀𝑀 − 𝐿𝐿𝑀𝑀 + 𝛽𝛽𝑄𝑄) + (1 − 𝑦𝑦)𝑧𝑧𝑅𝑅𝑀𝑀 + 𝑦𝑦(1 − 𝑧𝑧)𝑅𝑅𝑀𝑀 + (1 − 𝑦𝑦)(1 − 𝑧𝑧)𝑅𝑅𝑀𝑀 𝑈𝑈1 = 𝑥𝑥 𝑈𝑈11 + (1 − 𝑥𝑥)𝑈𝑈12 The replication dynamic equation of manufacturing company strategy is as follows: 𝑑𝑑𝑑𝑑 𝐹𝐹(𝑥𝑥) = = 𝑥𝑥(𝑈𝑈11 − 𝑈𝑈1 ) = 𝑥𝑥(1 − 𝑥𝑥)(𝑈𝑈11 −𝑈𝑈12 ) 𝑑𝑑𝑑𝑑 = 𝑥𝑥(1 − 𝑥𝑥)(𝑦𝑦(𝛼𝛼 𝑊𝑊𝑀𝑀 − 𝛼𝛼𝛼𝛼 − 𝛽𝛽𝑄𝑄) + 𝑧𝑧𝑧𝑧𝑆𝑆𝑀𝑀 + 𝑦𝑦𝑦𝑦𝐿𝐿𝑀𝑀 + 𝛼𝛼𝛼𝛼) 𝐹𝐹 ′ (𝑥𝑥) = 𝑑𝑑𝑑𝑑(𝑥𝑥) = (1 − 2𝑥𝑥)(𝑦𝑦(𝛼𝛼𝑊𝑊𝑀𝑀 − 𝛼𝛼𝛼𝛼 − 𝛽𝛽𝑄𝑄) + 𝑧𝑧𝑧𝑧𝑆𝑆𝑀𝑀 + 𝑦𝑦𝑦𝑦𝐿𝐿𝑀𝑀 + 𝛼𝛼𝛼𝛼) 𝑑𝑑𝑑𝑑 Assume 𝑊𝑊(𝑧𝑧) = 𝑦𝑦(𝛼𝛼𝑊𝑊𝑀𝑀 − 𝛼𝛼𝛼𝛼 − 𝛽𝛽𝛽𝛽) + 𝑧𝑧𝑧𝑧𝑆𝑆𝑀𝑀 + 𝑦𝑦𝑦𝑦𝐿𝐿𝑀𝑀 + 𝛼𝛼𝛼𝛼 , when 𝑧𝑧0 = proposition 1 is established. (1) (2) (3) (4) (5) (𝑦𝑦−1)𝛼𝛼𝛼𝛼−𝑦𝑦(𝛼𝛼𝑊𝑊𝑀𝑀 −𝛽𝛽𝛽𝛽) , 𝛼𝛼𝑆𝑆𝑀𝑀 +𝑦𝑦𝐿𝐿𝑀𝑀 Proposition 1: when 0 < z < 𝑧𝑧0 < 1, the evolutionary stable state of x tends to 0, the stable strategy of the manufacturing company is general cooperation. When 0 < 𝑧𝑧0 < z < 1, the evolutionary stable state of x tends to 1, the stable strategy of the manufacturing company is collaborative cooperation. Proof: 𝑊𝑊(𝑧𝑧) increases monotonically over the interval. When 𝑧𝑧 = 𝑧𝑧0 , 𝑊𝑊(𝑧𝑧) = 0, 𝐹𝐹(𝑥𝑥) = 0, and 𝐹𝐹𝑥𝑥′ (𝑥𝑥) = 0, so 𝑥𝑥 ∈ [0,1] is in the stable state, and there is no fixed stable strategy in the interval; When 0 < 𝑧𝑧 < 𝑧𝑧0 < 1, 𝑊𝑊(𝑧𝑧) < 0, 𝐹𝐹𝑥𝑥 (0) = 0, and 𝐹𝐹𝑥𝑥′ (0) < 0, so 𝑥𝑥 = 0 has stability; When 0 < 𝑧𝑧0 < z < 1, 𝑊𝑊(𝑧𝑧) > 0, 𝐹𝐹𝑥𝑥 (1) = 0, and 𝐹𝐹𝑥𝑥′ (1) < 0, so 𝑥𝑥 = 1 has stability. The phase diagram of the manufacturing company strategy choice is obtained according to the above analysis, as illustrated in Fig. 2. Advances in Production Engineering & Management 17(3) 2022 299 Xiao, Tian Z V2 z=z z>z 0 0 V1 z 0, 𝐹𝐹𝑦𝑦 (1) = 0, and 𝐹𝐹𝑦𝑦′ (1) < 0, so 𝑦𝑦 = 1 has stability. The phase diagram of the demand company strategy choice is obtained according to the above analysis, as illustrated in Fig. 3. Z V3 V4 x=x 0 xx 0 X Y Fig. 3 Phase diagram of the demand company strategy choice Inference 2: When the values of WC, SC and LM raise while other parameters keep constant, the demand company will approach collaborative cooperation strategy. In common, when the value of V raises, the demand company will approach general cooperation strategy. 𝛽𝛽𝛽𝛽−𝑧𝑧𝑧𝑧𝑆𝑆𝐶𝐶 −𝑧𝑧𝐿𝐿𝑀𝑀 , 𝐶𝐶 +𝛽𝛽𝛽𝛽−𝑧𝑧𝐿𝐿𝑀𝑀 Proof: Since 𝑥𝑥0 = 𝛽𝛽𝑊𝑊 the value of 𝑥𝑥0 will fall with the raising of the values of SC, WC and LM, and the volume of V4 changes inversely with the value of 𝑥𝑥0 . The enlarge of V4 shows that the demand company is more inclined to the collaborative cooperation strategy. The value of x0 will raise with the raising of the value of V, and the volume of V3 changes the same as the value of 𝑥𝑥0 , The enlarge of V3 shows that the demand company is more inclined to the general cooperation strategy. It presents that the proportion of demand company implementing collaborative cooperation is directly proportional to the subsidies for the collaborative cooperation of the demand company, the value-added profits of the demand company when the two sides collaborative cooperate, and the speculative penalty for the general cooperation of the manufacturing company, inversely proportional to the loss of information leakage of the collaborative cooperation of the demand company. Replication dynamic stability analysis of the cloud platform strategy The expected payoff of cloud platform carrying out supervision strategy is set as U31, and the expected payoff of cloud platform carrying out non-supervision strategy is set as U32, which are defined as follows: 𝑈𝑈31 = 𝑥𝑥𝑥𝑥(𝐸𝐸 − 𝐶𝐶𝑃𝑃 + 𝑆𝑆𝑃𝑃 + 𝐹𝐹𝑃𝑃 − 𝛼𝛼𝑆𝑆𝑀𝑀 − 𝛽𝛽𝑆𝑆𝐶𝐶 ) + 𝑥𝑥(1 − 𝑦𝑦)(𝐸𝐸 − 𝐶𝐶𝑃𝑃 + 𝑆𝑆𝑃𝑃 − 𝛼𝛼𝑆𝑆𝑀𝑀 ) (11) + (1 − 𝑥𝑥)𝑦𝑦(𝐸𝐸 − 𝐶𝐶𝑃𝑃 + 𝑆𝑆𝑃𝑃 − 𝛽𝛽𝑆𝑆𝐶𝐶 ) + (1 − 𝑥𝑥)(1 − 𝑦𝑦)(𝐸𝐸 − 𝐶𝐶𝑃𝑃 + 𝑆𝑆𝑃𝑃 ) 𝑈𝑈32 = 𝑥𝑥𝑥𝑥(𝐸𝐸 + 𝐹𝐹𝑃𝑃 ) + 𝑥𝑥(1 − 𝑦𝑦)𝐸𝐸 + (1 − 𝑥𝑥)𝑦𝑦𝑦𝑦 + (1 − 𝑥𝑥)(1 − 𝑦𝑦)𝐸𝐸 (12) 𝑈𝑈3 = 𝑧𝑧𝑈𝑈31 + (1 − 𝑧𝑧)𝑈𝑈32 (13) The replication dynamic equation of cloud platform strategy is as follows: 𝑑𝑑𝑑𝑑 (14) 𝐹𝐹(𝑧𝑧) = = 𝑧𝑧(𝑈𝑈31 − 3) = 𝑧𝑧(1 − 𝑧𝑧)(𝑈𝑈31 −𝑈𝑈32 ) = 𝑧𝑧(1 − 𝑧𝑧)(𝑆𝑆𝑃𝑃 − 𝑦𝑦𝑦𝑦𝑆𝑆𝐶𝐶 − 𝑥𝑥𝑥𝑥𝑆𝑆𝑀𝑀 − 𝐶𝐶𝑃𝑃 ) 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑(𝑧𝑧) (15) 𝐹𝐹 ′ (𝑧𝑧) = = (1 − 2𝑧𝑧)(𝑆𝑆𝑃𝑃 − 𝑦𝑦𝑦𝑦𝑆𝑆𝐶𝐶 − 𝑥𝑥𝑥𝑥𝑆𝑆𝑀𝑀 − 𝐶𝐶𝑃𝑃 ) 𝑑𝑑𝑑𝑑 𝑆𝑆 −𝑥𝑥𝛼𝛼𝛼𝛼 −𝐶𝐶 Assume 𝑊𝑊(𝑦𝑦) = 𝑆𝑆𝑃𝑃 − 𝑦𝑦𝑦𝑦𝑆𝑆𝐶𝐶 − 𝑥𝑥𝑥𝑥𝑆𝑆𝑀𝑀 − 𝐶𝐶𝑃𝑃 , when 𝑦𝑦0 = 𝑃𝑃 𝛽𝛽𝑆𝑆 𝑀𝑀 𝑃𝑃 , proposition 3 is established. 𝐶𝐶 Advances in Production Engineering & Management 17(3) 2022 301 Xiao, Tian Proposition 3: when 0 < 𝑦𝑦 < 𝑦𝑦0 < 1, the evolutionary stable state of z tends to 1, the stable strategy of the cloud platform is supervision. When 0 < 𝑦𝑦0 < 𝑦𝑦 < 1, the evolutionary stable state of z tends to 0, the stable strategy of the cloud platform is non-supervision. Proof: 𝑊𝑊(𝑦𝑦) decreases monotonically over the interval. When 𝑦𝑦 = 𝑦𝑦0 , 𝑊𝑊(𝑦𝑦) = 0, 𝐹𝐹(𝑧𝑧) = 0, and 𝐹𝐹𝑧𝑧′ (𝑧𝑧) = 0, so 𝑧𝑧 ∈ [0,1] is in the stable state, and there is no fixed stable strategy in the interval; When 0 < 𝑦𝑦 < 𝑦𝑦0 < 1, 𝑊𝑊(𝑦𝑦) > 0, 𝐹𝐹𝑧𝑧 (1) = 0, and 𝐹𝐹𝑧𝑧′ (1) < 0, so 𝑧𝑧 = 1 has stability; When 0 < 𝑦𝑦0 < 𝑦𝑦 < 1, 𝑊𝑊(𝑦𝑦) < 0, 𝐹𝐹𝑧𝑧 (0) = 0, and 𝐹𝐹𝑧𝑧′ (0) < 0, so 𝑧𝑧 = 0 has stability. The phase diagram of the cloud platform strategy choice is obtained according to the above analysis, as illustrated in Fig. 4. Z yy 0 X Y Fig. 4 Phase diagram of the cloud platform strategy choice Inference 3: When the value of SP raises while other parameters keep constant, the cloud platform will approach supervision strategy. In common, when the values of α, β, SC, SM and CP raise, the cloud platform will approach non-supervision strategy. Proof: Since 𝑦𝑦0 = 𝑆𝑆𝑃𝑃 −𝑥𝑥𝛼𝛼𝛼𝛼𝑀𝑀 −𝐶𝐶𝑃𝑃 , 𝛽𝛽𝑆𝑆𝐶𝐶 the value of 𝑦𝑦0 will raise with the raising of the value of SP, and the volume of V5 changes the same as the value of 𝑦𝑦0 . The enlarge of V5 shows that the cloud platform is more inclined to supervision strategy. The value of 𝑦𝑦0 will fall with the raising of the values of α, β, SC, SM and CP, and the volume of V6 changes inversely with the value of 𝑦𝑦0 . The enlarge of V6 shows that the cloud platform is more inclined to non-supervision strategy increases. It presents that the proportion of cloud platform implementing collaborative cooperation is directly proportional to the government subsidy for the supervision of the cloud platform, and inversely proportional to the degree of collaborative effort of the manufacturing company and the demand company, the subsidies provided by the cloud platform for the collaborative cooperation of the manufacturing company and the demand company and the regulatory cost of the cloud platform. 4. Results and discussion 4.1 Strategy stability analysis of the strategies in evolutionary games In order to analyze the asymptotic stability of the strategies in evolutionary games, according to Lyapunov method, the eigenvalues of the Jacobian matrix are determined based on the replication dynamic equation of the subject. When the eigenvalues are negative, the equilibrium point is asymptotically stable. The Jacobian matrix of the replication dynamic system is expressed as Eq. 16. The eigenvalues of Jacobian matrix are indicated in Appendix A. 𝐹𝐹𝑥𝑥′ (𝑥𝑥) 𝐹𝐹𝑦𝑦′ (𝑥𝑥) 𝐹𝐹𝑧𝑧′ (𝑥𝑥) 𝐽𝐽 = �𝐹𝐹𝑥𝑥′ (𝑦𝑦) 𝐹𝐹𝑦𝑦′ (𝑦𝑦) 𝐹𝐹𝑧𝑧′ (𝑦𝑦)� 𝐹𝐹𝑥𝑥′ (𝑧𝑧) 𝐹𝐹𝑦𝑦′ (𝑧𝑧) 𝐹𝐹𝑧𝑧′ (𝑧𝑧) (16) The system equilibrium points of three-party evolutionary game are inditacted in Table 2. 302 Advances in Production Engineering & Management 17(3) 2022 Evolutionary game analysis of company collaborative strategy in cloud manufacturing platform environment Table 2 Strategy stability analysis of evolutionary game system Eigenvalue Symbol Stability Equilibrium point 𝛼𝛼𝛼𝛼 ,−𝛽𝛽𝛽𝛽, 𝑆𝑆𝑃𝑃 − 𝐶𝐶𝑃𝑃 E1(0,0,0) (+, -, X) unstable E2(0,0,1) 𝛼𝛼𝑆𝑆𝑀𝑀 + 𝛼𝛼𝛼𝛼, 𝛽𝛽𝑆𝑆𝐶𝐶 − 𝛽𝛽𝛽𝛽 + 𝐿𝐿𝑀𝑀 , −(𝑆𝑆𝑃𝑃 − 𝐶𝐶𝑃𝑃 ) (+, X, X) unstable 𝛼𝛼𝑊𝑊𝑀𝑀 − 𝛽𝛽𝑄𝑄, 𝛽𝛽𝛽𝛽, 𝑆𝑆𝑃𝑃 − 𝛽𝛽𝑆𝑆𝐶𝐶 − 𝐶𝐶𝑃𝑃 E3(0,1,0) (X, +, X) unstable E4(1,0,0) −𝛼𝛼𝛼𝛼, 𝛽𝛽𝑊𝑊𝐶𝐶 , 𝑆𝑆𝑃𝑃 − 𝛼𝛼𝑆𝑆𝑀𝑀 − 𝐶𝐶𝑃𝑃 (-, +, X) unstable E5(0,1,1) 𝛼𝛼𝑊𝑊𝑀𝑀 + 𝛼𝛼𝑆𝑆𝑀𝑀 + 𝐿𝐿𝑀𝑀 − 𝛽𝛽𝑄𝑄, −(𝛽𝛽𝑆𝑆𝐶𝐶 + 𝐿𝐿𝑀𝑀 − 𝛽𝛽𝛽𝛽), −(𝑆𝑆𝑃𝑃 − 𝛽𝛽𝑆𝑆𝐶𝐶 − 𝐶𝐶𝑃𝑃 ) (X, X, X) ESS in condition Ⅰ E6(1,0,1) −(𝛼𝛼𝑆𝑆𝑀𝑀 + 𝛼𝛼𝛼𝛼), 𝛽𝛽𝑊𝑊𝐶𝐶 + 𝛽𝛽𝑆𝑆𝐶𝐶 , −(𝑆𝑆𝑃𝑃 − 𝛼𝛼𝑆𝑆𝑀𝑀 − 𝐶𝐶𝑃𝑃 ) (-, +, X) unstable E7(1,1,0) −(𝛼𝛼𝑊𝑊𝑀𝑀 − 𝛽𝛽𝑄𝑄), −𝛽𝛽𝑊𝑊𝐶𝐶 , 𝑆𝑆𝑃𝑃 − 𝛽𝛽𝑆𝑆𝐶𝐶 − 𝛼𝛼𝑆𝑆𝑀𝑀 − 𝐶𝐶𝑃𝑃 (X, -, X) ESS in condition Ⅲ −(𝛼𝛼𝑊𝑊𝑀𝑀 − 𝛽𝛽𝑄𝑄 + 𝛼𝛼𝑆𝑆𝑀𝑀 + 𝐿𝐿𝑀𝑀 ), −(𝛽𝛽𝑊𝑊𝐶𝐶 + 𝛽𝛽𝑆𝑆𝐶𝐶 ), −(𝑆𝑆𝑃𝑃 − 𝛽𝛽𝑆𝑆𝐶𝐶 − 𝛼𝛼𝑆𝑆𝑀𝑀 − 𝐶𝐶𝑃𝑃 ) E8(1,1,1) (X, -, X) ESS in condition Ⅱ Note: X denotes uncertain of symbol, ESS denotes the evolutionary stable strategy. Condition Ⅰ：𝛼𝛼(𝑆𝑆𝑀𝑀 + 𝑊𝑊𝑀𝑀 ) < 𝛽𝛽𝛽𝛽 − 𝐿𝐿𝑀𝑀 , 𝛽𝛽𝑆𝑆𝐶𝐶 + 𝐿𝐿𝑀𝑀 > 𝛽𝛽𝛽𝛽, 𝑆𝑆𝑃𝑃 > 𝛽𝛽𝑆𝑆𝐶𝐶 + 𝐶𝐶𝑃𝑃 Condition Ⅱ：𝛼𝛼(𝑆𝑆𝑀𝑀 + 𝑊𝑊𝑀𝑀 ) > 𝛽𝛽𝛽𝛽 − 𝐿𝐿𝑀𝑀 , 𝑆𝑆𝑃𝑃 > 𝛽𝛽𝑆𝑆𝐶𝐶 + 𝛼𝛼𝑆𝑆𝑀𝑀 + 𝐶𝐶𝑃𝑃 Condition Ⅲ：𝛼𝛼𝑊𝑊𝑀𝑀 > 𝛽𝛽𝛽𝛽, 𝑆𝑆𝑃𝑃 < 𝛽𝛽𝑆𝑆𝐶𝐶 + 𝛼𝛼𝑆𝑆𝑀𝑀 + 𝐶𝐶𝑃𝑃 When 𝛼𝛼(𝑆𝑆𝑀𝑀 + 𝑊𝑊𝑀𝑀 ) < 𝛽𝛽𝛽𝛽 − 𝐿𝐿𝑀𝑀 , 𝛽𝛽𝑆𝑆𝐶𝐶 + 𝐿𝐿𝑀𝑀 > 𝛽𝛽𝛽𝛽, 𝑆𝑆𝑃𝑃 > 𝛽𝛽𝑆𝑆𝐶𝐶 + 𝐶𝐶𝑃𝑃 , if the difference between the speculative profit and the speculative penalty when the manufacturing company chooses general cooperation is more than the sum of the additional profit of the collaborative cooperation and the cooperative subsidy of the cloud platform, then the manufacturing company tends to choose the general cooperation strategy. When the sum of the platform subsidy for the demand company and the speculative punishment of the manufacturing company is more than the information leakage risk loss of the demand company, then the demand company tends to choose the collaborative cooperation strategy. If the government's subsidy for cloud platform supervision is more than the sum of the cloud platform regulatory cost and the subsidy for the demand company, the cloud platform tends to choose supervision strategy. As a result, the stable evolution strategy of the three-party subjects is E5(general cooperation, collaborative cooperation, supervision). When 𝛼𝛼(𝑆𝑆𝑀𝑀 + 𝑊𝑊𝑀𝑀 ) > 𝛽𝛽𝛽𝛽 − 𝐿𝐿𝑀𝑀 and 𝑆𝑆𝑃𝑃 > 𝛽𝛽𝑆𝑆𝐶𝐶 + 𝛼𝛼𝑆𝑆𝑀𝑀 + 𝐶𝐶𝑃𝑃 , on the basis of condition Ⅰ, if the sum of the synergistic subsidy and synergistic benefit of the manufacturing company is more than the difference between the speculative profit and the speculative penalty of the manufacturing company, the manufacturing company tends to choose the collaborative cooperation. If the government's subsidies for cloud platform supervision are still more than the sum of the regulatory costs of cloud platform and the subsidies for manufacturing company and demand company, the cloud platform will continue to choose the supervision strategy. When the manufacturing company chooses collaborative collaboration and the cloud platform chooses supervision, the value-added profits of the demand company's collaborative cooperation are greater, so the collaborative cooperation strategies are chosen. Therefore, the stable evolution strategy of the three-party subjects is E8 (collaborative cooperation, collaborative cooperation, supervision). When 𝛼𝛼𝑊𝑊𝑀𝑀 > 𝛽𝛽𝛽𝛽, and 𝑆𝑆𝑃𝑃 < 𝛽𝛽𝑆𝑆𝐶𝐶 + 𝛼𝛼𝑆𝑆𝑀𝑀 + 𝐶𝐶𝑃𝑃 , on the basis of condition Ⅱ, if the manufacturing company and the demand company improve their collaborative efforts, the sum of the regulatory cost and the subsidies for the manufacturing company and demand company of the cloud platform is more than the government's subsidies for cloud platform supervision, the cloud platform tends to non-supervision strategy. If the value-added profits of the manufacturing company's collaborative cooperation are more than the profits of the manufacturing company's speculative behavior, the value-added profits of the demand company are larger, and the manufacturing company and the demand company also tend to adopt the collaborative cooperation strategy. Therefore, the stable evolution strategy of the three-party subjects is E7( collaborative cooperation, collaborative cooperation, non-supervision). 4.2 Numerical simulation analysis To test strategic stability of three-party evolutionary game, the model parameters are assigned values based on the real situation, and MATLAB2021a is used for numerical simulation. Equilibrium steady state of the model When condition I is met, the model parameters are assigned as followings: CP = 30, SP = 50, WM = 30, SM = 20, α = 0.1, Q = 25, T = 15, LM = 5, WC = 30, SC = 20, β = 0.5, V = 26; when condition Ⅱ is Advances in Production Engineering & Management 17(3) 2022 303 Xiao, Tian met, SM = 40, α = 0.2, and other parameters are the same with condition I; when condition Ⅲ is met, α = 0.6, β = 0.6, SC = 40, and other parameters are the same with condition Ⅱ. The evolution results of the data simulation over time are shown in Fig. 5. According to Fig. 5, in the early stage of the establishment of the cloud platform, the profits of collaborative cooperation are less than the speculative profits of general cooperation for the manufacturing company. Therefore, driven by the interests, the manufacturing company will gradually stabilize in the general cooperation strategy. When the manufacturing company generally cooperates, if the government’s supervision subsidy is more than the supervision investment for the cloud platform, the cloud platform will stabilize in the supervision strategy. So the evolutionary game system will be stable in the strategy combination E5 (0,1,1). As the supervision mechanism of the cloud platform is gradually established, with the increase of subsidies obtained by manufacturing company for collaborative cooperation, the level of collaborative effort of company will increase, and manufacturing company will be stable in collaborative cooperation strategy, so the evolutionary game system is stable in the strategy combination E8 (1,1,1). In the improvement stage of cloud platform, with the increase of collaborative subsidies for the demand company, the degree of collaborative effort between manufacturing company and demand company is further increased, the proportion of cloud platform supervision is reduced, and finally stabilized in the non-supervision strategy, so the evolutionary game system will be stable in the strategy combination E7 (1,1,0). This means that as long as both the manufacturing company and the demand company have a long-term development concept and can recognize the benefits brought by collaboration, the cloud platform can make the two parties collaborate without supervision. E5(0,1,1) E8(1,1,1) Fig. 5 System evolution stability at equilibrium points E7(1,1,0) The influence of the subsidies and the value-added profits for the collaborative cooperation of the manufacturing company On the basis of condition I, if SM = {20, 30, 50, 60}, and the simulation results of three-party evolutionary game are indicated in Fig. 6a. If WM = {30, 45, 60, 80}, the simulation results of the three-party evolutionary game are indicated in Fig. 6b. According to Fig. 6a, with the raising of the subsidy of cloud platform for manufacturing company, the proportion of the manufacturing company to choose collaborative cooperation increases. The strategy of the manufacturing company will shift from general cooperation to collaborative cooperation, and the critical value of changing the strategy is SM = 45. Due to the change of manufacturing company's strategy, the evolution strategy combination will change from E5 (general cooperation, collaborative cooperation, supervision) to E8 (collaborative cooperation, collaborative cooperation, supervision). According to Fig. 6b, with the increase of the value-added profits of manufacturing company in collaborative cooperation, the proportion of manufacturing company choosing collaborative cooperation increases. The strategy of the manufacturing company will shift from general cooperation to collaborative cooperation, and the critical value for changing the strategy is WM = 55. Due to the change of manufacturing company's strategy, the evolution strategy combination will change from E5 (general cooperation, collaborative cooperation, supervision) to E8 (collaborative cooperation, collaborative cooperation, supervision). 304 Advances in Production Engineering & Management 17(3) 2022 Evolutionary game analysis of company collaborative strategy in cloud manufacturing platform environment (a) (b) Fig. 6 Influence of the subsidies and the value-added profits for the collaborative cooperation of manufacturing company on strategy evolution The influence of the degree of collaborative effort of the manufacturing company and the demand company On the basis of condition I, if α = {0.10, 0.13, 0.20, 0.35, 0.55, 0.65}, and the simulation results of three-party evolutionary game are indicated in Fig. 7a. If β = {0.2, 0.3, 0.41, 0.5, 0.85, 0.95}, the simulation results of three-party evolutionary game are indicated in Fig. 7b. According to Fig. 7a, with the increase of the collaborative efforts of the manufacturing company, three evolutionary stable states may appear in the system. The critical value of changing the strategy of manufacturing company is α1 = 0.15, and the critical value of changing the strategy of the cloud platform is α2 = 0.5. When 0.15 < 𝛼𝛼 < 0.5, the proportion of the manufacturing company choosing collaborative cooperation increases with the increase of α. The strategy of the manufacturing company will shift from general cooperation to collaborative cooperation, the evolution strategy combination will change from E5 (general cooperation, collaborative cooperation, supervision) to E8(collaborative cooperation, collaborative cooperation, supervision). When 𝛼𝛼 > 0.5, the proportion of the cloud platform choosing supervision decreases with the increase of α. The strategy of the cloud platform will change from supervision to nonsupervision, and the evolution strategy combination will change from E8(collaborative cooperation, collaborative cooperation, supervision) to E7 (collaborative cooperation, collaborative cooperation, non-supervision). According to Fig. 7b, with the change of the degree of collaborative effort of the demand company, two evolutionary stable states and an unstable state may appear in the system. The critical value of changing the strategy of manufacturing company is β1 = 0.4, and the critical value of changing the strategy of demand company is β2 = 0.83. When 0.4 < 𝛽𝛽 < 0.83, the proportion of manufacturing company choosing collaborative cooperation increases with the increase of β. The strategy of the manufacturing company will change from general cooperation to collaborative cooperation, and the evolution strategy combination will change from E5 (general cooperation, collaborative cooperation, supervision) to E8 (collaborative cooperation, collaborative cooperation, supervision). When 𝛽𝛽 > 0.83, the proportion of the demand company will decrease with the increase of β. The strategy of the demand company will tend to the unstable state, and the evolution strategy combination will be also in an unstable state. (a) (b) Fig. 7 The influence of the degree of collaborative effort of the manufacturing company and demand company on strategy evolution Advances in Production Engineering & Management 17(3) 2022 305 Xiao, Tian The influence of the speculative penalty and profit of the general cooperation of the manufacturing company On the basis of condition I, if LM = {5, 7, 10, 15}, and the simulation results of three-party evolutionary game are indicated in Fig. 8a. If Q = {10, 15, 21, 25}, the simulation results of three-party evolutionary game are indicated in Fig. 8b. According to Fig. 8a, with the increase of the speculative penalty of manufacturing company, the proportion of manufacturing company to choose collaborative cooperation increases. The strategy of the manufacturing company will shift from general cooperation to collaborative cooperation, and the critical value of changing the strategy is LM = 7.5. Due to the change of manufacturing company's strategy, the evolution strategy combination will change from E5 (general cooperation, collaborative cooperation, supervision) to E8 (collaborative cooperation, collaborative cooperation, supervision). According to Fig. 8b, with the decrease of the speculative profits of manufacturing company, the proportion of manufacturing company to choose collaborative cooperation increases. The strategy of the manufacturing company will shift from general cooperation to collaborative cooperation, and the critical value of changing the strategy is Q = 20. Due to the change of manufacturing company's strategy, the evolution strategy combination will change from E5 (general cooperation, collaborative cooperation, supervision) to E8 (collaborative cooperation, collaborative cooperation, supervision). (a) (b) Fig. 8 The influence of the speculative penalty and profit of the general cooperation of the manufacturing company on strategy evolution The influence of the loss of information leakage and the subsidies for the collaborative cooperation of the demand company On the basis of condition Ⅱ, if V = {15, 26, 40, 60}, and the simulation results of three-party evolutionary game are indicated in Fig. 9a. If SC = {10, 20, 30, 35}, the simulation results of threeparty evolutionary game are indicated in Fig. 9b. According to Fig. 9a, with the increase of the information leakage loss of demand company, the proportion of manufacturing company to choose collaborative cooperation increases, the proportion of cloud platform to choose supervision increases, and the proportion of demand company to choose collaborative cooperation decreases. The evolution strategy combination will tend to E8 (collaborative cooperation, collaborative cooperation, supervision). According to Fig. 9b, the strategies of the cloud platform and the manufacturing company will be affected by the collaborative subsidies of the demand company. The critical value of changing the strategy is SC = 24. When SC < 24, with the increase of collaborative subsidies of demand company, the proportion of manufacturing company and demand company to choose collaborative cooperation increases, and the proportion of cloud platform to choose supervision increases. The evolution strategy combination will tend to E8 (collaborative cooperation, collaborative cooperation, supervision). When SC > 24, with the increase of collaborative subsidies of demand company, the proportion of cloud platform supervision and the manufacturing company collaborative cooperation decreases, the cloud platform and the manufacturing company cannot evolve to a stable state, and the system cannot evolve to a stable state. 306 Advances in Production Engineering & Management 17(3) 2022 Evolutionary game analysis of company collaborative strategy in cloud manufacturing platform environment (a) (b) Fig. 9 The influence of the loss of information leakage and the subsidies for the collaborative cooperation of the demand company on strategy evolution The influence of the government subsidy for the cloud platform supervision On the basis of condition Ⅲ, if SP = {50, 70, 80, 90}, and the simulation results of three-party evolutionary game are indicated in Fig. 10. According to Fig. 10, when the government subsidies for cloud platform supervision decrease, the proportion of the platform to choose supervising decreases. The strategy of the cloud platform will shift from supervision to non-supervision, and the critical value of changing the strategy is SP = 78. Due to the change of cloud platform’s strategy, the evolution strategy combination will change from E8 (collaborative cooperation, collaborative cooperation, supervision) to E7 (collaborative cooperation, collaborative cooperation, non-supervision). Fig. 10 The influence of the government subsidy for the cloud platform supervision on strategy evolution 5. Conclusion This study constructed a three-party collaborative evolutionary game model with the cloud platform, the manufacturing company and the demand company, and the main conclusions are as follows: • The strategy combination evolution of company collaborative cooperation in the cloud platform environment is staged. In the initial stage of cloud platform, since the manufacturing company can obtain free-riding profits in the process of cooperation, it tends to general cooperation strategy. However, with the support of platform subsidies, reward and punishment, the demand company can obtain better profits by sharing information and inclined to choose collaborative cooperation, and the platform tends to supervision due to government subsidies, so the system will be stable in the strategy combination of E5 (general cooperation, collaborative cooperation, supervision). With the increase of penalty costs and synergy profits of manufacturing company, the manufacturing company also tends to choose collaborative cooperation. Therefore, in the mid stage of cloud platAdvances in Production Engineering & Management 17(3) 2022 307 Xiao, Tian form, the system will be stable in the strategy combination of E8(collaborative cooperation, collaborative cooperation, supervision) depending on the supervision measures of the platform. When the cloud platform runs smoothly, manufacturing company and demand company can take advantage of the platform to integrate resources, the degree of company collaborative effort gradually increases, and the platform tends to implement non-supervision strategy. The platform has reached mature stage, in which the spontaneous collaboration of manufacturing company and demand company can form the effective operation of the cloud platform. • The collaborative subsidy to manufacturing company, the value-added profit of the manufacturing company, the degree of collaborative effort of the manufacturing company and the demand company, and the penalty and profits of the manufacturing company's speculation are the important factors that affect the cooperation strategy of the manufacturing company. By appropriately increasing the subsidy to manufacturing company, the valueadded profit of manufacturing company, the penalty for free-riding speculation of manufacturing company, and reducing the speculative profit of manufacturing company, and promoting the degree of collaborative effort of manufacturing company, the strategy of the manufacturing company will be changed from general cooperation to collaborative cooperation. • The collaborative subsidy to demand company, the degree of collaborative efforts of demand company, the loss of information leakage of demand company, and the speculation penalty of manufacturing company are important factors that affect the cooperation strategy of demand company. With the increase of collaborative subsidy of demand company, the appropriate improvement of the level of collaborative efforts of demand company, the reduction of information leakage loss of demand company and the increase of speculative penalty of manufacturing company, the proportion of demand company to collaborative cooperation increases, and demand company gradually stabilizes in collaborative cooperation strategy. • The degree of collaborative efforts of manufacturing company and demand company and the government's subsidy for cloud platform supervision are important factors that affect the platform supervision strategy. When the degrees of collaborative effort of manufacturing company and demand company are low, raising the government's regulatory subsidy for cloud platform can gradually increase the proportion of cloud platform supervision and cloud platform stabilize in the supervision strategy. However, as the degrees of collaborative efforts of manufacturing company and demand company increase, and the government's subsidy for cloud platform supervision reduces, the strategy of cloud platform can be changed from supervision to non-supervision. Acknowledgement This study was financially supported by 2023 LiaoNing Provincial Federation Social Science Circles Project (2023lslybkt-095), Social Science Planning Fund of Liaoning Province (L19BGL029), Social Science Planning Fund of Liaoning Province (L22AJY012), 2022 Shenyang Science and Technology Innovation Think Tank Decision-making Consulting Project (No.52), Key Project Fund of Scientific Research of Shenyang University of Technology (No.ZDZRGD2020041). References [1] [2] [3] 308 Gerrikagoitia, J.K., Unamuno, G., Urkia, E., Serna, A. (2019). Digital manufacturing platforms in the Industry 4.0 from private and public perspectives, Applied Sciences, Vol. 9, No. 14, Article No. 2934, doi: 10.3390/app914 2934. Wang, T., Li, C., Yuan, Y., Liu, J., Adeleke, I.B. (2019). An evolutionary game approach for manufacturing service allocation management in cloud manufacturing, Computers & Industrial Engineering, Vol. 133, 231-240, doi: 10.1016/j.cie.2019.05.005. Gnoni, M.G., Bragatto, P.A., Milazzo, M.F., Setola, R. (2020). Integrating IoT technologies for an “intelligent” safety management in the process industry, Procedia Manufacturing, Vol. 42, 511-515, doi: 10.1016/j.promfg.2020. 02.040. Advances in Production Engineering & Management 17(3) 2022 Evolutionary game analysis of company collaborative strategy in cloud manufacturing platform environment [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] Sahu, A.K., Sahu, A.K., Sahu, N.K. (2020). A review on the research growth of Industry 4.0: IIoT business architectures benchmarking, International Journal of Business Analytics, Vol. 7, No. 1, 77-97, doi: 10.4018/IJBAN. 2020010105. Zhang, Y., Zhang, L., Liu, Y., Luo, X. (2021). Proof of service power: A blockchain consensus for cloud manufacturing, Journal of Manufacturing Systems, Vol. 59, 1-11, doi: 10.1016/j.jmsy.2021.01.006. Yu, C., Jiang, X., Yu, S., Yang, C. (2020). Blockchain-based shared manufacturing in support of cyber physical systems: Concept, framework, and operation, Robotics and Computer-Integrated Manufacturing, Vol. 64, Article No. 101931, doi: 10.1016/j.rcim.2019.101931. Hu, Y.L., Han, Q.L. (2021). Evolutionary game analysis on value co-creation of product service system, Management Review, Vol. 33, No. 6, 242-254, doi: 10.14120/j.cnki.cn11-5057/f.2021.06.021. Kumar, A.S., Iyer, E. (2019). An industrial IoT in engineering and manufacturing industries–Benefits and challenges, International Journal of Mechanical and Production Engineering Research and Development, Vol. 9, No. 2, 151160, doi: 10.24247/ijmperdapr201914. Aziz, M.H., Qamar, S., Khasawneh, M.T., Saha, C. (2020). Cloud manufacturing: A myth or future of global manufacturing, Journal of Manufacturing Technology Management, Vol. 31, No. 7, 1325-1350, doi: 10.1108/jmtm-102019-0379. Woo, J., Shin, S.-J., Seo, W., Meilanitasari, P. (2018). Developing a big data analytics platform for manufacturing systems: Architecture, method, and implementation, International Journal of Advanced Manufacturing Technology, Vol. 99, 2193-2217, doi: 10.1007/s00170-018-2416-9. Barenji, A.V., Guo, H., Wang, Y., Li, Z., Rong, Y. (2021). Toward blockchain and fog computing collaborative design and manufacturing platform: Support customer view, Robotics and Computer-Integrated Manufacturing, Vol. 67, Article No. 102043, doi: 10.1016/j.rcim.2020.102043. Zhang, Z., Wang, X., Zhu, X., Cao, Q., Tao, F. (2019). Cloud manufacturing paradigm with ubiquitous robotic system for product customization, Robotics and Computer-Integrated Manufacturing, Vol. 60, 12-22, doi: 10.1016/j.rcim.2019.05.015. Li, P., Cheng, Y., Song, W., Tao, F. (2020). Manufacturing services collaboration: Connotation, framework, key technologies, and research issues, International Journal of Advanced Manufacturing Technology, Vol. 110, 25732589, doi: 10.1007/s00170-020-06042-x. Xu, Z., Zhang, J., Song, Z., Liu, Y., Li, J., Zhou, J. (2021). A scheme for intelligent blockchain-based manufacturing industry supply chain management, Computing, Vol. 103, 1771-1790, doi: 10.1007/s00607-020-00880-z. Wu, Y., Zhang, Y. (2022). An integrated framework for blockchain-enabled supply chain trust management towards smart manufacturing, Advanced Engineering Informatics, Vol. 51, Article No. 101522, doi: 10.1016/j.aei. 2021.101522. Xiao, Y., Li, C., Song, L., Yang, J., Su, J. (2021). A multidimensional information fusion-based matching decision method for manufacturing service resource, IEEE Access, Vol. 9, 39839-39851, doi: 10.1109/access.2021.306 3277. Xu, W., Sun, H.Y., Awaga, A.L., Yan, Y., Cui, Y.J. (2022). Optimization approaches for solving production scheduling problem: A brief overview and a case study for hybrid flow shop using genetic algorithms, Advances in Production Engineering & Management, Vol. 17, No. 1, 45-56, doi: 10.14743/apem2022.1.420. Zhang, L., Yan, Y., Xu, W., Sun, J., Zhang, Y. (2022). Carbon emission calculation and influencing factor analysis based on industrial big data in the “double carbon” era, Computational Intelligence and Neuroscience, Vol. 2022, Article ID 2815940, doi: 10.1155/2022/2815940. García, K., Mendoza, S., Decouchant, D., Brézillon, P. (2018). Facilitating resource sharing and selection in ubiquitous multi-user environments, Information Systems Frontiers, Vol. 20, 1075-1095, doi: 10.1007/s10796-0169708-0. Wang, H.Q., Li, J., Li, Y. (2019). Research on the evolution mechanism of platform-based science and technology resource sharing service paradigm, China Soft Science, No. 11, 153-165, doi: 10.3969/j.issn.1002-9753.2019.11. 015. Meng, F.S., Zhao, G., Xu, Y. (2019). Research on intelligent transformation and upgrading evolution game of highend equipment manufacturing enterprises based on digitalization, Scientific Management Research, Vol 37, No. 5, 89-97, doi: 10.19445/j.cnki.15-1103/g3.2019.05.015. Lampón, J.F., Frigant, V., Cabanelas, P. (2019). Determinants in the adoption of new automobile modular platforms: What lies behind their success?, Journal of Manufacturing Technology Management, Vol. 30, No. 4, 707728, doi: 10.1108/jmtm-07-2018-0214. Meng, Z., Wu, Z., Gray, J. (2020). Architecting ubiquitous communication and collaborative-automation-based machine network systems for flexible manufacturing, IEEE Systems Journal, Vol. 14, No. 1, 113-123, doi: 10.1109/JSYST.2019.2918542. Ren, M., Ren, L., Jain, H. (2018). Manufacturing service composition model based on synergy effect: A social network analysis approach, Applied Soft Computing, Vol. 70, 288-300, doi: 10.1016/j.asoc.2018.05.039. Ayala, N.F., Gerstlberger, W., Frank, A.G. (2019). Managing servitization in product companies: The moderating role of service suppliers, International Journal of Operations & Production Management, Vol. 39, No. 1, 43-74, doi: 10.1108/IJOPM-08-2017-0484. Assaqty, M.I.S., Gao, Y., Hu, X., Ning, Z., Leung, V.C.M., Wen, Q., Chen, Y. (2020). Private-blockchain-based industrial IoT for material and product tracking in smart manufacturing, IEEE Network, Vol. 34, No. 5, 91-97, doi: 10.1109/MNET.011.1900537. Advances in Production Engineering & Management 17(3) 2022 309 Xiao, Tian [27] Wang, J., Yang, B., Zhai, L. (2022). Tripartite evolutionary game analysis of trust relationship between enterprises in a cloud manufacturing environment: A service composition perspective, Discrete Dynamics in Nature and Society, Vol. 2022, Article ID 6922627, doi: 10.1155/2022/6922627. [28] Leng, J., Liu, J., Jiang, P. (2019). Blockchain models for cyber-credits of social manufacturing, In: Jiang P. (ed.), Social Manufacturing: Fundamentals and Applications, Springer, Cham, Switzerland, 197-217, doi: 10.1007/9783-319-72986-2_9. [29] Kapoor, K., Bigdeli, A.Z., Schroeder, A., Baines, T. (2021). A platform ecosystem view of servitization in manufacturing, Technovation, Article No. 102248, doi: 10.1016/j.technovation.2021.102248. [30] Tan, W., Zhu, H., Tan, J., Zhao, Y., Xu, L.D., Guo, K. (2021). A novel service level agreement model using blockchain and smart contract for cloud manufacturing in Industry 4.0, Enterprise Information Systems, Vol. 2021, No. 9, 126, doi: 10.1080/17517575.2021.1939426. [31] Breunig, D.A., Stock, D., Bauernhansl, T. (2020). Requirements and concept for a modular and state-oriented control device architecture, Procedia Manufacturing, Vol. 42, 281-287, doi: 10.1016/j.promfg.2020.02.096. [32] Wang, B., Wang, P., Tu, Y. (2021). Customer satisfaction service match and service quality-based blockchain cloud manufacturing, International Journal of Production Economics, Vol. 240, Article No. 108220, doi: 10.1016/ j.ijpe.2021.108220. [33] Sánchez, M., Exposito, E., Aguilar, J. (2020). Implementing self-* autonomic properties in self-coordinated manufacturing processes for the Industry 4.0 context, Computers in Industry, Vol. 121, Article No. 103247, doi: 10.1016/j.compind.2020.103247. Appendix A Jacobian matrix of replicated dynamical systems: 𝐽𝐽 = � 𝑥𝑥(1 − 𝑥𝑥)(𝛼𝛼𝑊𝑊𝑀𝑀 − 𝛼𝛼𝛼𝛼 − 𝛽𝛽𝑄𝑄 + 𝑧𝑧𝐿𝐿𝑀𝑀 ) 𝑥𝑥(1 − 𝑥𝑥)(𝛼𝛼𝑆𝑆𝑀𝑀 + 𝑦𝑦𝐿𝐿𝑀𝑀 ) (1 − 2𝑥𝑥)(𝑦𝑦(𝛼𝛼𝑊𝑊𝑀𝑀 − 𝛼𝛼𝛼𝛼 − 𝛽𝛽𝑄𝑄) + 𝑧𝑧𝑧𝑧𝑆𝑆𝑀𝑀 + 𝑦𝑦𝑦𝑦𝐿𝐿𝑀𝑀 + 𝛼𝛼𝛼𝛼) 𝑦𝑦(1 − 𝑦𝑦)(𝛽𝛽𝑊𝑊𝐶𝐶 + 𝛽𝛽𝛽𝛽 − 𝑧𝑧𝐿𝐿𝑀𝑀 ) 𝑦𝑦(1 − 𝑦𝑦)(𝛽𝛽𝑆𝑆𝐶𝐶 + (1 − 𝑥𝑥)𝐿𝐿𝑀𝑀 (1 − 2𝑦𝑦)(𝑥𝑥(𝛽𝛽𝑊𝑊𝐶𝐶 + 𝛽𝛽𝛽𝛽) + 𝑧𝑧𝛽𝛽𝑆𝑆𝐶𝐶 − 𝛽𝛽𝛽𝛽 + (1 − 𝑥𝑥)𝑧𝑧𝐿𝐿𝑀𝑀 ) � 𝑧𝑧(1 − 𝑧𝑧)(−𝛼𝛼𝑆𝑆𝑀𝑀 ) 𝑧𝑧(1 − 𝑧𝑧)(−𝛽𝛽𝑆𝑆𝐶𝐶 ) (1 − 2𝑧𝑧)(𝑆𝑆𝑃𝑃 − 𝑦𝑦𝛽𝛽𝑆𝑆𝐶𝐶 − 𝑥𝑥𝛼𝛼𝑆𝑆𝑀𝑀 − 𝐶𝐶𝑃𝑃 ) 310 Advances in Production Engineering & Management 17(3) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 3 | September 2022 | pp 311–325 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.3.438 Original scientific paper Development of a flexible tooling system for sheet metal bending Stefanovska, E.a, Pepelnjak, T.a,* aUniversity of Ljubljana, Faculty of Mechanical Engineering, Slovenia ABSTRACT ARTICLE INFO This article presents the design and development of a flexible tooling system for sheet metal bending. The flexible tooling system aims to reduce manufacturing disturbances and increase the efficiency of the forming process. First and foremost, the structural behaviour of the sheet metal is investigated using the finite element method for the numerical simulation of the three-point bending process. The analysis’ findings enabled the prediction of component reaction to loads, which are essential for the further optimization and enhancement of the tooling system’s flexibility. At the initial stage of the development phase, SolidWorks, the computer-aided design software, is utilized to visualise the flexible tooling system and improve the tooling connectivity design. Furthermore, the prototype is developed by integrating mechanical and electrical components, such as the Arduino Mega microcontroller, stepper motors, and digital stepper drivers. Automation is achieved by programming the Arduino microcontroller board and controlling the stepper motors’ movement to ensure precise displacement and speed control of the forming tools. The tooling system’s major qualities are its high flexibility, achieved through the implementation of two moveable support cylinders and the possibility of being further upgraded to a closed-loop forming system. The higher level of automation and optimization of the sheet metal bending process can lead to improved processing efficiency and help achieve the desired formed products with higher quality and the required geometric tolerance. It is expected that the development of a flexible tooling system will find widespread application in sheet metal bending processes, resulting in reduced material costs, rapid equipment set-up and higher processing repeatability. Keywords: Sheet metal forming; Finite element analysis (FEM); Computer-aided design (CAD); Flexible tooling system; Cyber-physical systems; Smart manufacturing; Industry 4.0; Digital twin *Corresponding author: tomaz.pepelnjak@fs.uni-lj.si (Pepelnjak, T.) Article history: Received 25 January 2022 Revised 17 September 2022 Accepted 21 September 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Sheet metal forming processes are manufacturing processes used to deform the sheet metal plastically into desired shapes. Sheet metal forming is widely used as a mass production processing technology due to its high processing speed and low processing cost compared to other methods [1]. Metal forming processes are an important field of research since the modern industry constantly aims for advanced processing performance and product quality control [2]. For minimizing production costs and achieving desired product quality, the determination of optimal process parameters, such as tool and workpiece geometrical data, material properties, contact conditions, and other technological parameters is of critical importance [3, 4]. Complicated physical phenomena, such as tool elastic deformations, sheet metal's material non-linearities, springback occurrence caused by material elastic recovery, and dynamic friction situations, impact output product quality [5]. Better output results can be obtained by studying the relative performance of a material in a given application and considering all the influential parameters that occur throughout the 311 Stefanovska, Pepelnjak forming process. The parameters of the process, including acting stresses, strains, and temperature fields, as well as local conditions of the microstructure (e.g., damage, grain size, structural composition) and the surface (e.g., lubricant layer thickness, surface micro-geometry), are used to describe the process and its limits [6]. Finite element simulation is essential for evaluating the material response to different influential parameters, further reducing forming process uncertainties and eliminating any deviations of the finished part from the initial design [7]. Optimizing all the process parameters and controlling the process limits can be extremely challenging, though it can improve the performance of the forming process used for the manufacturing of parts with a more accurate final geometry. Applying methods for modelling, simulation and optimization of production processes leads to the generation of new and better manufacturing solutions and to the optimization of process parameters [8]. Industries have developed various advanced technologies that can contribute to the creation of autonomous operational systems and process enhancements [9]. Effective implementation of Industry 4.0 technologies [10] offers more efficient and higher-quality production processes, as well as enabling predictive and preventative maintenance, resulting in reduced downtime and decreased long-term operational costs. The advanced connectivity of the embedded systems allows collecting and exchanging real-time information to identify, locate, track, monitor, and optimize the production processes [11, 12]. This allows for improved product quality, efficiency, and flexibility in producing customized items on a wide scale while reducing resource consumption [13, 14]. Sensors that monitor the part during the manufacturing process, actuators with sufficient flexibility and adaptability to allow modifications in response to changing process conditions, and model development with sufficient speed and efficiency to allow operation under changing process conditions are just a few of the features that can be implemented to improve the sheet metal forming processes [15]. Fig. 1 shows a closed-loop concept of metal forming control system that uses multiple sensors to monitor and optimize the metal forming process. Fig. 1 A system diagram for closed-loop control of sheet metal forming process [15] 1.1 Fundamentals of sheet metal bending process The production of high-precision sheet metal components is extremely important in the automotive, electronics, and housing-utensil industries [16]. The stability of the forming process is affected by a variety of structural properties, process disturbances, and complex parameter correlations. Therefore, manufacturers must constantly evaluate their strategies and search for new methods to improve process efficiency and achieve the desired product quality. One of the most frequent forming processes used in the manufacturing of sheet metal components is bending [17]. In sheet metal bending, plastic deformation occurs when the specimen undergoes permanent deformation or a non-reversible change in shape in response to applied loads. The formability of sheet metals, which refers to the material’s capability to undergo plastic deformation to a specific shape while meeting quality requirements, is primarily influenced by the general mechanical properties, including the thickness and anisotropic features of the materials [18]. Dai et al. emphasize that during the design stage of the bending process, specific sheet material characteristics must be considered (i.e., Young’s modulus, yield stress, the ratio of yield stress to ultimate tensile stress, initial anisotropy yielding criterion, and the microstructure of the material) [19]. FEM is the main technique for predicting sheet metal forming processes and determining the distribution of stresses and strains in the material, forming forces, and possible locations of defects in advance [20, 21]. For the successful application of the FEM to predict springback, it is necessary to know and understand the influence of numerical parameters on simulation results. In the metal forming 312 Advances in Production Engineering & Management 17(3) 2022 Development of a flexible tooling system for sheet metal bending process, the bending force has to be determined so that the sheet metal can undergo plastic deformation and the desired shape can be achieved. Nevertheless, after the forming force is released, the material partially returns to its original shape due to its elastic recovery, which is known as springback [22]. Springback is expressed as the difference in dimension between the fully loaded and the unloaded configuration [23]. As a result, the springback must be considered in the metal forming process, since it decreases the bent angle of the sheet metal by a few degrees. The springback significantly influences the dimensional accuracy of the bent sheet metal; therefore, controlling and minimizing this challenging phenomenon can improve the bending process’s accuracy. 1.2 Optimization of sheet metal forming processes The fourth industrial revolution influences sheet metal forming operations with modifications, including enhanced manufacturing productivity, increased product quality, decreased technological difficulties for adapting the equipment, and reduced processing time. By developing and integrating sensing technologies for the visualization and monitoring of the forming process, production control (e.g., quality verification and traceability of the parameters) can be enhanced [24]. The expansion of smart manufacturing is enabled by innovative technologies that improve the cyber-physical systems (CPS) for better communication, process control, decision-making, and problem-solving capabilities [25]. Medić et al. [26] investigated the contribution of advanced digital technologies offering the greatest benefits to the Industry 4.0 production, considering the realtime monitoring of manufacturing processes as one of the key elements. In smart manufacturing, the digital twin (DT) technique is utilized to simulate physical entities, predicting their performance and behaviour under various scenarios [27]. The digital twin establishes the mapping and interaction between the physical and digital worlds, delivering specific information and presenting all of the influencing factors, thereby providing comprehensive technical guarantee and optimization capabilities [28]. In the event of an unplanned change or shutdown, the digital twin simulates numerous possibilities and delivers the optimal solution in real-time, allowing the real system to be constantly improved through a feedback loop. In the simulated environment, the DT of a real manufacturing activity can show, evaluate, and improve the process. The digital twin allows for process parameter identification, monitoring, and prediction, as well as comparison of the digital equivalent of the process to its recorded parameters obtained from the measured data from the physical environment. The digital twin's decision-making abilities can enable modification of the formed part's geometry by timely responding to predictions of potential process uncertainties that may occur during the forming process and by controlling the forming tool actuators to react fast to the instructions. The accuracy of the forming process, the quality of the finished product, and the processing efficiency can continuously improve with the implementation of the digital twin. Developing appropriate sensors for monitoring the material flow during the sheet metal forming processes is extremely challenging. Fig. 3 depicts an example of applicable technology using a contact-based material flow measurement sensor known as a rolling ball sensor [29]. The mechanical transmission of the sheet metal’s plane movement onto the rolling ball serves as the foundation for this sensor. The rotating motion of the ball is transmitted to two perpendicularly positioned measuring rollers. Each measuring roller has a slotted running wheel that runs inside a photoelectric barrier and converts rotation to electrical impulses without contact. With this sensor technique, the material flow direction, velocity, and path may all be monitored independently in two orthogonal directions. Fig. 3 Roller-ball sensor for material flow measurement [29] Advances in Production Engineering & Management 17(3) 2022 313 Stefanovska, Pepelnjak Sah et al. [30] created a draw-in sensor based on the mutual inductance concept, as shown in Fig. 4. Current is stimulated in the first coil, causing electromotive force or induced voltages in the secondary coil. When metal is present close to the coils, the degree of mutual inductance varies; thus, the produced signal in the secondary coil reflects how much of the coil is covered up, providing a measure for the material draw-in amount. When monitoring the material draw-in of stamping processes, the contactless sensor eliminates the difficulties of conventional sensing. For example, when measuring material draw-in in stamping operations using standard sensing techniques, the edge wrinkle may cause loss of contact and difficulties in detecting the displacement. Groche et al. [31] presented sensor fasteners that allow mechanical connections between the parts to be monitored for analysing forces and operational loads. To gather combined force and torque information in diverse regions, the sensor unit must be able to deliver and receive loads in all directions of space. The sensor fastener shown in Fig. 5 integrates a sensor component into an empty load-carrying model in the shape of a bolt. Simplified sensors are connected to the surface of the sensor body. To meet its functional requirements, the module incorporates an axial preload. A tensile load would otherwise cause the connected components to separate and interrupt the force transmission. In the sensor set-up, three strain gauges are placed on three sides of a rectangular cross-section. Individual axial forces and bending torques may be calculated by analysing each signal provided by the strain gauge. As a result, the novel concept enables a mechanical connection between the forming tools and the machine, as well as monitoring of operating loads. Hinchy et al. [32] developed a physical manufacturing testbed that bends metal into V-brackets alongside a digital twin counterpart consisting of the three elements: machine, product, and process. Finite element modelling is utilized in the digital twin to forecast product outcomes and estimate product stress throughout the bending process. As shown in Fig. 6, the bending machine moves a V-press relative to a static V-die with a pair of high-torque stepper motors, while a load cell measures load throughout the bending process. An Internet of Things (IoT) [33] enabled microcontroller is used to control the system; it is capable of wirelessly transferring sensor data. A database of product attributes, such as material type, material qualities, product geometry, and product status, form the product’s digital twin. The digital twin can be used to secure the expected results in metal forming operations, for example, the desired final bend angle. The digital twin concept contributes meaningfully to the metal forming process by predicting and optimizing the operation through the implementation of cyber-physical systems. Fig. 4 Draw-in sensor based on the mutual inductance concept [30] Fig. 5 Configuration of the sensor fastener [31] 314 Advances in Production Engineering & Management 17(3) 2022 Development of a flexible tooling system for sheet metal bending Haag et al. [34] developed a digital twin concept for a bending beam test bench to prove that the digital representation of an individual product can play an integral role in a fully digitalized product life cycle. Fig. 7 presents the entire set-up of the digital twin system. The digital twin primarily includes the bending beam’s precise computer-aided design (CAD). The following steps include a combination of finite element technique simulations to reflect the complete test bench accurately in a virtual environment. An architecture based on the message-queuing telemetry transport (MQTT) protocol links the physical and digital twins. As parameters, either the resulting force on the beam or the ultimate displacement of the beam is entered into the system. Furthermore, the parameters are sent to the broker, who sends them to the physical twin, which then goes to the predetermined position until the movement or force is obtained, and then checks the other variables. The variable is then returned to the broker, who passes it along to the digital twin and IoT network. The digital twin starts an automated FEM analysis with the real force or movement values. Via the broker, the estimated findings are also sent back to the IoT platform, where they may be evaluated to the physical outputs. The objective is to automatically produce the digital twin and establish the network connection with its physical twin to make the concept applicable to a wide variety of devices. By analysing data from prior research work in sheet metal forming, the set of scientific concepts and technologies being recently employed to improve the forming processes’ quality have been identified. This article proposes a novel perspective of increasing the flexibility of the three-point bending process by developing an innovative tooling system. The employment of two moveable support cylinders in addition to the forming punch that conducts the bending operation improves the configuration of the forming tools, resulting in higher efficiency and reduced forming time. The device is designed to provide greater opportunities for further optimization of the bending process and the capacity to be upgraded to a closed-loop forming system. Fig. 6 Integration of physical and digital bending system [32] Fig. 7 Digital twin concept for bending beam test bench [34] Advances in Production Engineering & Management 17(3) 2022 315 Stefanovska, Pepelnjak In the presented article, Section 1 reviewed the literature on topics relevant to the research undertaken, including introductory definitions related to the bending processes and the material properties of sheet metals. Also, the impact of Industry 4.0 on sheet metal forming operations, as well as several techniques for improving forming processes, were discussed. Furthermore, Section 2 describes the implemented methods using finite element analysis and computer-aided design for the visualization of the flexible tooling system. Section 3 presents the obtained results from the numerical simulations and the developed prototype of the flexible tooling system for sheet metal bending. Section 4 reviews the major findings in this article and offers recommendations for further research related to this study. 2. Materials and methods This section describes the flexible tooling system set-up in detail, as well as the methods utilized to obtain the desired results. Fig. 8 illustrates the set-up of the three-point bending system and the overbending technique used in this investigation. The direction of the arrows indicates the movement of the forming tools that perform the sheet metal bending process. The three moveable forming tools exert force on the sheet metal, causing it to bend until the desired final shape is achieved. The overbending technique is used to obtain the desired bent angle by angularly bending the sheet metal over the specified angle and achieving the chosen final shape after the occurrence of springback. Fig. 8 Set-up of the three-point bending system and springback phenomenon 2.1 Finite element analysis In the performed study, the initial findings of the three-point bending tests with flexible supports are obtained with a numerical simulation using the finite element software Abaqus. The goal of the numerical simulations was to determine the optimal process parameters for achieving a 90° bent angle of the specimen after springback. The model consists of sheet metal, forming punch and two support cylinders with precisely defined dimensions. The material properties, the design of the forming tool, the processing conditions and the tool wear are factors that influence the quality of the product, and their prediction is of great importance [35]. The thickness and material type of the sheet metal, as well as the radius of the forming tools, were the main parameters considered in the simulation. The sheet metal has a length of 140 mm, a width of 20 mm, and a thickness of 1 mm. The forming punch has a radius of 5 mm, while the moveable support cylinders have a radius of 10 mm. Geometry information and a set of material behaviour rules are contained in each of the created parts in the Abaqus simulation. Homogeneous, solid sections are used to define the section properties of the sheet metal. The specified material type is steel DC04 according to DIN EN 10130 standard [36]. The material’s mass density is 7.8 × 10-9 tonne/mm3, Young’s modulus is 210,000 MPa, and Poisson’s ratio is 0.3. The selected type of interaction is the surface-to-surface contact, which describes the contact between the sheet metal as a deformable surface and the forming tools as rigid surfaces. Considering the different surface roughness, the general contact with a Coulomb friction coefficient equal to 0.15 was selected for the interaction between the sheet metal 316 Advances in Production Engineering & Management 17(3) 2022 Development of a flexible tooling system for sheet metal bending and the forming tools. The boundary conditions are then used to specify the loading and interaction between the sheet metal’s surface and the forming tools, guaranteeing that the sheet metal deforms appropriately. The appropriate selection of finite element formulation, element size, and the number of integration points through the sheet metal’s thickness is critical for the analysis’s accuracy and prediction of the sheet metal’s behaviour. Fig. 9 shows the variable number of elements in different regions over the sheet’s metal thickness. An increased number of 5 elements through the thickness of the sheet metal is used in the region where it undergoes elasto-plastic deformation and comes into contact with the forming tools. The meshed specimen consists of a total number of 11,088 nodes and 8,700 elements. The elements consist of 1,800 linear hexahedral elements of type C3D8R and 6,900 linear hexahedral elements of type C3D8I. Considering the symmetry conditions, only a quarter of the sheet metal needs to be modelled. The FEM is simplified as a result, and the computing time is reduced. The symmetry boundary conditions are applied to the highlighted surfaces of the sheet metal, as shown in Fig. 9. During the loading phase, the forming tools move with a velocity of 30 mm/s in both vertical and horizontal directions. The displacement of the forming punch, sp, and the displacement of the support cylinders, sc, is different in each FEM simulation, as shown in Table 1. Depending on the displacement and the velocity of the forming tools, the time of forming punch, tp, the time of support cylinders, tc, and the total forming time, ttot, required for completing the bending process have different values. Fig. 9 Symmetry boundary conditions and assigned mesh on the sheet metal for the three-point bending analysis No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Table 1 Combination of process parameters used in the three-point bending FEM simulations sp (mm) sc (mm) tp (s) tc (s) ttot (s) 14 30 0.46 1 1 15 30 0.5 1 1 15.65 30 0.52 1 1 16 30 0.53 1 1 17 30 0.56 1 1 22.5 20 0.75 0.67 0.75 23.5 20 0.78 0.67 0.78 24.08 20 0.8 0.67 0.80 25.5 20 0.85 0.67 0.85 26.5 20 0.88 0.67 0.88 34 10 1.13 0.33 1.13 35 10 1.16 0.33 1.16 37 10 1.23 0.33 1.23 37.47 10 1.24 0.33 1.24 38 10 1.26 0.33 1.26 48 0 1.6 0 1.6 49 0 1.63 0 1.63 49.68 0 1.65 0 1.65 50 0 1.66 0 1.66 51 0 1.7 0 1.7 2.2 Computer-aided design The three-point bending system is designed using the computer-aided design program SolidWorks, which involves sketching and adding dimensions to specify the geometry and position of all the components. The horizontal plate at the bottom supports the two vertical plates on which the linear systems are mounted. One linear system consists of two forming tools for supporting and bending the sheet metal in a horizontal direction, whereas the second linear system only has Advances in Production Engineering & Management 17(3) 2022 317 Stefanovska, Pepelnjak one forming tool for bending the sheet metal in a vertical direction. The connected stepper motors enable the moving and positioning of the forming tools fixed on the linear systems. The sheet metal is inserted underneath the forming punch and on the movable support cylinders. The threedimensional (3D) model of the bending device with the linear systems that perform the bending of the sheet metal in the vertical and horizontal direction is shown in Fig. 10. Fig. 10 3D model of the bending device with the vertical and horizontal linear systems 3. Results and discussion This section presents the obtained results of the numerical approach and a comparative analysis for evaluating the findings’ reliability. The finite element analysis was utilized to simulate the three-point bending process numerically. The findings of the numerical simulations were used to determine all specifications and requirements for the prototype development of the flexible tooling system. 3.1 Numerical simulation results The influence of the process parameters on the sheet metal bending operation was studied by comparing the numerical results of 20 FEM simulations. The numerical simulations were conducted to identify the appropriate combination of process parameters for obtaining a 90° bent angle of the specimen after springback. The following influential process parameters were analyzed: bending angle before springback, α1, bending angle after springback, α2, angle difference before and after springback, Δα, the maximum forming force of the forming punch, Fp, the maximum forming force of the support cylinders, Fc, displacement of the forming punch, sp, displacement of the support cylinders, sc, and total forming time required for completing the bending process, ttot. In the first set of numerical simulations, the range of the forming punch displacement is from 14 mm to 17 mm, and the displacement of the support cylinders is 30 mm. The second set has a range of forming punch displacement from 22.5 mm to 26.5 mm, and the displacement of the support cylinders is 20 mm. In the third set, the range of the forming punch displacement is from 34 mm to 38 mm, and the displacement of the support cylinders is 10 mm. In the fourth set, the support cylinders are fixed in their initial position, and the distance between them is 106 mm, whereas the range of the forming punch displacement is from 48 mm to 51 mm. Fig. 11 presents the various bending angle after springback, α2, obtained for different combinations of the forming tools’ displacement. It can be seen that the bending angle after springback, α2, increases linearly by increasing the displacement of the forming punch, sp. The desired bending angle after springback is 90° ±0.05° when the displacement of the forming punch is 15.65 mm, 24.08 mm, 37.47 mm, 49.68 mm, and the displacement of the support cylinders is 30 mm, 20 mm, 10 mm, 0 mm respectively. Fig. 12 shows the relationship of the angle difference before and after springback, Δα, and the bending angle after springback, α2. The numerical data show that when the forming force is released, the sheet metal returns towards its original shape by a few degrees due to the effect of springback. The overbending method is utilized to acquire the required bent angle by angularly bending the sheet metal over the specified angle and achieving the chosen final shape after the occurrence of springback. 318 Advances in Production Engineering & Management 17(3) 2022 Development of a flexible tooling system for sheet metal bending Fig. 11 Displacement of the forming punch, sp, versus bending angle after springback, α2, for different displacement of the support cylinders, sc Fig. 12 The relationship of the angle difference before and after springback, Δα, and the bending angle after springback, α2 The total forming time, ttot, is the sum of the time of forming punch, tp, and the time of support cylinders, tc, required for completing the bending process. During the loading phase of each numerical simulation, the forming tools move with a velocity of 30 mm/s in both vertical and horizontal directions. Fig. 13 presents the total forming time, ttot, required to obtain the various bending angles after springback, α2. In addition to the forming punch that performs the bending operation, two moveable support cylinders are employed in the sets with numbers 1, 2, and 3. In the fourth set, the support cylinders are fixed in their initial position, and only the forming punch is moveable, resulting in a significantly longer total forming time necessary to complete the bending operation. In the first set, the range of the forming punch displacement is from 14 mm to 17 mm, while the displacement of the support cylinders is 30 mm in each of the numerical simulations. As a result, the support cylinders need longer time than the forming punch to reach the specified displacement, equal to the total forming time, ttot, of 1 s. It can be concluded that a reduction of the total forming time can be achieved by implementing two moveable support cylinders in addition to the forming punch that performs the bending operation simultaneously. By reducing forming time, continuous quality improvements and better production efficiency can be achieved. Fig. 13 Total forming time, ttot, required for obtaining different bending angles after springback, α2 Advances in Production Engineering & Management 17(3) 2022 319 Stefanovska, Pepelnjak The four cases of the FEM simulations for which the desired bending angle after springback is 90° ±0.05° are presented in Table 2. Fig. 14 shows the forming force evolution for different displacements of the forming tools in the cases when the bending angle after springback is 90° ±0.05°. The solid section of the curve represents the forming tools’ movement, while the dotted section of the curve shows the condition in which the forming punch has already reached the specified displacement and the moveable support cylinders are still performing the bending process (Fig. 14a), or vice versa (Fig. 14b). During the sheet metal bending operation, force is applied on the specimen in the vertical direction by the forming punch and in the horizontal direction by the support cylinders. The amount of maximum forming force required to achieve a 90° bending angle after springback has been determined. Furthermore, knowing the maximum forming force contributes to improving the design of the flexible tooling system by selecting the stepper motors with the relevant key specifications. Additionally, the forming force required to bend the sheet metal is considered to be twice as large when selecting the stepper motor used to position two movable support cylinders. Case 1 2 3 4 Table 2 Variety of cases in which the bending angle after springback is 90° ±0.05° sp (mm) sc (mm) tp (s) tc (s) ttot (s) α1 ( ̊ ) α2 ( ̊ ) Δα ( ̊ ) Fp (N) 15.65 30 0.52 1 1 95.53 90.04 5.49 157.69 24.08 20 0.8 0.66 0.8 91.82 89.98 1.84 87.79 37.47 10 1.25 0.33 1.25 100.04 90.01 10.03 65.93 49.68 0 1.66 0 1.66 100.86 89.95 10.91 50.83 Fc (N) 53.89 33.28 21.78 16.25 a) b) Fig. 14 Forming force evolution in the cases in which the bending angle after springback is 90° ±0.05°: a) force of the forming punch, Fp, versus displacement of the forming punch, sp; b) force of the support cylinders, Fc, versus displacement of the support cylinders, sc Fig. 15 shows the relationship between the angle difference before and after springback, Δα, and the total forming time, ttot, in the cases in which the bending angle after springback is 90° ±0.05°. Analysis was carried out to evaluate the angle difference before and after springback throughout the simulations to define the appropriate process parameters for reducing springback and achieving the necessary final geometry of the part. The best process parameters that minimize the springback were identified in the second case by comparing the simulations’ results in which the bending angle after springback is 90° ±0.05°. Springback is a critical challenge in metal forming, although by predicting and minimizing it using FEM simulations, it is feasible to improve the accuracy of the produced parts. Furthermore, ideal results are determined in the second case for the shortest time required to finish the bending process and obtain a bending angle of 90° ±0.05° degrees after springback. By comparing the results obtained from the FEM simulations, the impact of various process parameters on the sheet metal bending operation is investigated. The second case in Table 3 has the process parameters of the optimal three-point bending FEM simulation. The specimen is bent to the required shape at a bending angle after springback of 90° ±0.05° degrees. The simulated bending angle before springback is 91.82°, and the bending angle after springback is 89.98°, thus resulting in 1.84° of springback. 320 Advances in Production Engineering & Management 17(3) 2022 Development of a flexible tooling system for sheet metal bending Fig. 15 The relationship of the angle difference before and after springback, Δα, and the total forming time, ttot, when the bending angle after springback is 90° ±0.05° a) b) Fig. 16 Visualization of the three-point bending model: a) loading step; b) unloading step The forming punch that bends the sheet metal in a vertical direction has a specified displacement of 24.08 mm and a maximum reaction force with a value of 87.79 N. The moveable support cylinders that bend the sheet metal horizontally from the left and right sides have a specified displacement of 20 mm and a maximum horizontal reaction force of 33.28 N. The total time required for the forming tools to reach the specified displacement for obtaining the desired bending angle after springback is 0.8 seconds. The sheet metal’s behaviour at loading and unloading steps in the Abaqus simulation is shown in Fig. 16. The numerical simulation results enabled the optimization of geometrical properties of the sheet metal, reduction of springback effect, and selection of the most dependable process parameters that are utilized as a reference for the design of the flexible tooling system. The obtained results show which process parameters are suitable for achieving the required 90° bent angle of the specimen after springback. It has been concluded that the flexibility of the three-point bending process is increased by the implementation of two moveable support cylinders in addition to the forming punch that performs the bending process. The appropriate forming tools’ displacement and velocity during the bending process are identified to reduce processing time and increase process productivity. The computed maximum response force required for the forming tools to bend the sheet metal contributes to the comprehensive selection of stepper motors for a better design of the flexible tooling system for sheet metal bending. 3.2 Prototype development The developed prototype of the bending device represents a preliminary version of a flexible tooling system for sheet metal bending, as shown in Fig. 17. The findings of the numerical simulations and the computer-aided design of the 3D model for the flexible tooling system were used to determine all specifications and requirements for the prototype development. The numerical simulations contributed to the identification of the optimal process parameters necessary for the production of sheet metal components with the desired shape. Furthermore, the 3D model’s design enabled the visualization of the tooling system and the correct integration of the hardware and software components for effective system control. The prototype is created by integrating mechanical and electrical components, including Arduino Mega microcontroller, Nema 23 stepper motors, and digital stepper drivers. The stepper motors’ movement is controlled by programming Advances in Production Engineering & Management 17(3) 2022 321 Stefanovska, Pepelnjak the Arduino microcontroller board to provide accurate displacement and regulate the speed of the forming tools. The Nema 23 stepper motors are driven by DM542T digital stepper drivers, which use logical inputs to pulse the motors and are suitable for their voltage and current requirements. To adjust the position of the motor shaft, the micro-stepping technique is used, which may enhance resolution and significantly increase motion stability [37]. Micro-stepping allows the stepper drivers to position the Nema 23 stepper motor shaft accurately by generating a step angle as small as 0.014° (25,600 steps per revolution). In addition, a switching power supply model S350-24 is utilized in the prototype. The open-source Arduino Software – Integrated Development Environment (IDE) is used to write the code and upload it to the Arduino Mega 2560 microcontroller. The wiring connection of the Arduino microcontroller, the power supply, and the Nema 23 stepper motors with their micro-stepping drivers is shown in Fig. 17. The prototype’s functionality was evaluated after the development phase, and the bending method was successfully completed. To conduct an accurate comparison of numerical and experimental data, several areas for future improvement of the currently developed flexible tooling system have been identified. Closed-loop automation, which enables improved process control, and the use of appropriate sensors allowing real-time monitoring of the bending angle throughout the bending operation, are the most significant advancements. Fig. 17 Developed prototype of the flexible tooling system for sheet metal bending 4. Conclusion Sheet metal bending processes are of crucial importance because they are widely applied for the manufacturing of various products, the majority of which are used in the automotive and aerospace industries. Since industrial requirements are rapidly increasing, the development of new methods for optimizing the bending process of sheet metals is in great demand. As a result, traditional metal forming tools are continuously being upgraded with novel technologies that can capture important data to improve the forming process. In this study, a novel flexible tooling system for optimizing process parameters and enhancing the sheet metal bending operation was developed. The acquired results from the final element analysis contributed to the determination of the set-up and the geometry of the forming tools that are essential for obtaining the desired final shape of the bent sheet metal. The impact of various process parameters is evaluated by comparing simulation results, and the optimal three-point bending FEM simulation is selected. The most significant findings obtained from the performed numerical analysis are: • The performed finite element analysis enabled the accurate prediction of the springback, which is 1.84° in the optimal three-point bending simulation. • In addition to the forming punch that performs the bending process at the shortest production time with a displacement in a range from 22.5 mm to 26.5 mm, the innovative implementation of the moveable support cylinders with a displacement of 20 mm resulted in 322 Advances in Production Engineering & Management 17(3) 2022 Development of a flexible tooling system for sheet metal bending greater flexibility of the bending process. • The generated results indicate that the appropriate forming tools’ displacement for obtaining the desired bending angle of 90° ±0.05° is 24.08 mm for the forming punch and 20 mm for the support cylinders. • The determination of optimal displacement for the forming punch and the moveable support cylinders that move with a velocity of 30 mm/s during the bending process provided a reduction of processing time and improvement of process productivity for 48%, compared to the traditional three-point bending only with a movable forming punch. • The applied overbending technique helps to eliminate the effect of springback occurrence by angularly bending the sheet metal for 1.84° over the required angle and achieving the desired angle of 89.98° after the forming force is released. • The calculated maximum vertical force of 87.79 N and maximum horizontal force of 33.28 N required for the forming tools to bend the sheet metal aided in the selection of stepper motors for the design of the flexible sheet metal bending tooling system. By predicting the influence of different process parameters using the numerical method, the essential data are acquired and incorporated into the design of a flexible tooling system for sheet metal bending. The following are the key characteristics of the developed flexible tooling system: • Operating as an automated system capable of adjusting the forming tools’ position and precisely controlling the bending process. • Production of bent sheet metal parts with high quality and accuracy. • Performance of continuous, well-structured, and rule-based forming operations. • Run with high stability and dependability, reducing the occurrence of failures. • The ability to bend sheet metals at various angles and thickness levels. The expected results and the scientific contributions of the proposed research are focused to cover the most important, original, and innovative aspects of the following fields: • Developed flexible tooling system for sheet metal bending that does not yet exist. The flexible tooling system aims to increase the efficiency of the forming process and reduce manufacturing disturbances. • Significantly improved processing speed compared to the traditional three-point bending only with a movable forming punch, which is achieved by the innovative implementation of the moveable support cylinders. • Designed flexible tooling system for sheet metal bending that has the potential for further implementation of sensors and upgrade of the controlling algorithm that can be utilized to process and analyse signals in real time. Those processed data will enable the prediction of potential deviations in bending process parameters that impact the final quality of the formed product and support the corresponding reaction of the actuators connected to the forming tools to eliminate potential errors. Several areas can be recommended for potential improvement of the currently developed flexible tooling system, such as: • Closed-loop automation that will enable advanced control of the forming process variables to the desired outcome without the need of human assistance. • Implementation of appropriate sensors that will allow real-time measurement of the bending angle during the bending operation. • Improvement of the currently developed flexible tooling system that will establish a connection between the FEM tools and the physical system for smooth data transfer between the cyber-physical system enabling online process monitoring and control. Advances in Production Engineering & Management 17(3) 2022 323 Stefanovska, Pepelnjak Acknowledgement The authors acknowledge the financial support of research core funding No. P2-0248 and Young Researcher Ema Stefanovska from the Slovenian Research Agency. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] 324 Tsuruya, T., Danseko, M., Sasaki, K., Honda, S., Takeda, R. (2019). Forming state recognition in deep drawing process with machine learning, Journal of Advanced Mechanical Design, Systems and Manufacturing, Vol. 13, No. 3, 13, doi: 10.1299/jamdsm.2019jamdsm0066. Al-Tamimi, A., Darvizeh, R., Davey, K. (2018). Experimental investigation into finite similitude for metal forming processes, Journal of Materials Processing Technology, Vol. 262, 622-637, doi: 10.1016/j.jmatprotec.2018.0 7.028. Puchlerska, S., Żaba, K., Pyzik, J., Pieja, T., Trzepieciński, T. (2021). Statistical analysis and optimisation of data for the design and evaluation of the shear spinning process, Materials, Vol. 14, No. 20, Article No. 6099, doi: 10.3390/ ma14206099. Zhao, X., Liu, Y., Hua, L., Mao, H. (2020). Structural analysis and size optimization of a fine-blanking press frame based on sensitivity analysis, Strojniški Vestnik – Journal of Mechanical Engineering,, Vol. 66, No. 6, 408-417, doi: 10.5545/sv-jme.2020.6564. Tatipala, S., Pilthammar, J., Sigvant, M., Wall, J., Johansson, C.M. (2018). Introductory study of sheet metal forming simulations to evaluate process robustness, IOP Conference Series: Materials Science and Engineering, Vol. 418, Article No. 012111, doi: 10.1088/1757-899X/418/1/012111. Volk, W., Groche, P., Brosius, A., Ghiotti, A., Kinsey, B.L., Liewald, M., Madej, L., Min, J., Yanagimoto, J. (2019). Models and modelling for process limits in metal forming, CIRP Annals, Vol. 68, No. 2, 775-798, doi: 10.1016/j.cirp.2019. 05.007. Satošek, R., Valeš, M., Pepelnjak, T. (2019). Study of influential parameters of the sphere indentation used for the control function of material properties in forming operations, Strojniški vestnik – Journal of Mechanical Engineering, Vol. 65, No. 10, 585-598, doi: 10.5545/sv-jme.2019.6312. Savkovic, B., Kovac, P., Rodic, D., Strbac, B., Klancnik, S. (2020). Comparison of artificial neural network, fuzzy logic and genetic algorithm for cutting temperature and surface roughness prediction during the face milling process, Advances in Production Engineering & Management, Vol. 15, No. 2, 137-150, doi: 10.14743/apem2020.2.354. Spaić, O., Krivokapić, Z., Kramar, D. (2020). Development of family of artificial neural networks for the prediction of cutting tool condition, Advances in Production Engineering & Management, Vol. 15, No. 2, 164-178, doi: 10.14743 /apem2020.2.356. Ačko, B., Weber, H., Hutzschenreuter, D., Smith, I. (2020). Communication and validation of metrological smart data in IoT-networks, Advances in Production Engineering & Management, Vol. 15, No. 1, 107-117, doi: 10.14743/ apem2020.1.353. Rojko, A. (2017). Industry 4.0 concept: Background and overview, International Journal of Interactive Mobile Technologies, Vol. 11, No. 5, 77-90, doi: 10.3991/ijim.v11i5.7072. Buń, P., Grajewski, D., Górski, F. (2021). Using augmented reality devices for remote support in manufacturing: A case study and analysis, Advances in Production Engineering & Management, Vol. 16, No. 4, 418-430, doi: 10.14743 /apem2021.4.410. Lopes De Sousa Jabbour, A.B., Jabbour, C.J.C., Foropon, C., Godinho Filho, M. (2018). When titans meet – Can Industry 4.0 revolutionise the environmentally-sustainable manufacturing wave? The role of critical success factors, Technological Forecasting and Social Change, Vol. 132, 18-25, doi: 10.1016/j.techfore.2018.01.017. Rosin, F., Forget, P., Lamouri, S., Pellerin, R. (2021). Impact of Industry 4.0 on decision-making in an operational context, Advances in Production Engineering & Management, Vol. 16, No. 4, 500-514, doi: 10.14743/apem2021. 4.416. Polyblank, J.A., Allwood, J.M., Duncan, S.R. (2014). Closed-loop control of product properties in metal forming: A review and prospectus, Journal of Materials Processing Technology, Vol. 214, No. 11, 2333-2348, doi: 10.1016/ j.jmatprotec.2014.04.014. Thipprakmas, S., Phanitwong, W. (2011). Process parameter design of spring-back and spring-go in V-bending process using Taguchi technique, Materials & Design, Vol. 32, No. 8-9, 4430-4436, doi: 10.1016/j.matdes.2011. 03.069. Liu, J.G., Fu, M.W., Lu, J., Chan, W.L. (2011). Influence of size effect on the springback of sheet metal foils in microbending, Computational Materials Science, Vol. 50, No. 9, 2604-2614, doi: 10.1016/j.commatsci.2011.04.002. Kacar, I., Ozturk, F., Toros, S., Kılıc, S. (2020). Prediction of strain limits via the Marciniak-Kuczynski model and a novel semi-empirical forming limit diagram model for dual-phase DP600 advanced high strength steel, Strojniški Vestnik – Journal of Mechanical Engineering, Vol. 66, No. 10, 602-612, doi: 10.5545/sv-jme.2020.6755. Dai, H.-L., Jiang, H.-J., Dai, T., Xu, W.-L., Luo, A.-H. (2017). Investigation on the influence of damage to springback of U-shape HSLA steel plates, Journal of Alloys and Compounds, Vol. 708, 575-586, doi: 10.1016/j.jallcom.2017. 02.270. Trzepiecinski, T., Lemu, H.G. (2017). Effect of computational parameters on springback prediction by numerical simulation. Metals, Vol. 7, No. 9, Article No. 380, doi: 10.3390/met7090380. Szávai, S., Kovács, S., Bézi, Z., Kozak, D. (2021). Coupled numerical method for rolling contact fatigue analysis, Tehnički Vjesnik – Technical Gazette, Vol. 28, No. 5, 1560-1567, doi: 10.17559/TV-20201117124940. Advances in Production Engineering & Management 17(3) 2022 Development of a flexible tooling system for sheet metal bending [22] Sulaiman, S., Ariffin, M.K.A.M., Lai, S.Y. (2012). Springback behaviour in sheet metal forming for automotive door, AASRI Procedia, Vol. 3, 224-229, doi: 10.1016/j.aasri.2012.11.037. [23] Panthi, S.K., Ramakrishnan, N., Ahmed, M., Singh, S.S., Goel, M.D. (2010). Finite element analysis of sheet metal bending process to predict the springback, Materials & Design, Vol. 31, No. 2, 657-662, doi: 10.1016/j.matdes.2009. 08.022. [24] Yang, M. (2019). Sensing technologies for metal forming, Sensors and Materials, Vol. 31, No. 10, 3121-3128, doi: 10.18494/SAM.2019.2399. [25] Herakovič, N., Zupan, H., Pipan, M., Protner, J., Šimic, M. (2019). Distributed manufacturing systems with digital agents, Strojniški Vestnik – Journal of Mechanical Engineering, Vol. 65, No. 11-12, 650-657, doi: 10.5545/svjme.2019.6331. [26] Medić, N., Anišić, Z., Lalić, B., Marjanović, U., Brezocnik, M. (2019). Hybrid fuzzy multi‐attribute decision making model for evaluation of advanced digital technologies in manufacturing: Industry 4.0 perspective, Advances in Production Engineering & Management, Vol. 14, No. 4, 483-493, doi: 10.14743/apem2019.4.343. [27] Qi, Q., Tao, F. (2018). Digital twin and big data towards smart manufacturing and Industry 4.0: 360 degree comparison, IEEE Access, Vol. 6, 3585-3593, doi: 10.1109/ACCESS.2018.2793265. [28] Li, Y., Li, L. (2020). Enhancing the optimization of the selection of a product service system scheme: A digital twindriven framework, Strojniški Vestnik – Journal of Mechanical Engineering, Vol. 66, No. 9, 534-543, doi: 10.5545/svjme.2020.6621. [29] Doege, E., Seidel, H.-J., Griesbach, B., Yun, J.-W. (2002). Contactless on-line measurement of material flow for closed loop control of deep drawing, Journal of Materials Processing Technology, Vol. 130-131, 95-99, doi: 10.1016/ S0924-0136(02)00763-X. [30] Sah, S., Mahayotsanun, N., Peshkin, M., Cao, J., Gao, R.X. (2016). Pressure and draw-in maps for stamping process monitoring, Journal of Manufacturing Science and Engineering, Vol. 138, No. 9, Article No. 091005, doi: 10.1115/ 1.4033039. [31] Groche, P., Brenneis, M. (2014). Manufacturing and use of novel sensoric fasteners for monitoring forming processes, Measurement, Vol. 53, 136-144, doi: 10.1016/j.measurement.2014.03.042. [32] Hinchy, E.P., Carcagno, C., O’Dowd, N.P., McCarthy, C.T. (2020). Using finite element analysis to develop a digital twin of a manufacturing bending operation, Procedia CIRP, Vol. 93, 568-574, doi: 10.1016/j.procir.2020.03.031. [33] Chen, L., Ye, Z., Jin, S. (2021). A security, privacy and trust methodology for IIoT, Tehnički Vjesnik – Technical Gazette, Vol. 28, No. 3, 898-906, doi: 10.17559/TV-20210122095638. [34] Haag, S., Anderl, R. (2018). Digital twin – Proof of concept, Manufacturing Letters, Vol. 15, Part B, 64-66, doi: 10.1016/j.mfglet.2018.02.006. [35] Gomah, M., Demiral, M. (2020). An experimental and numerical investigation of an improved shearing process with different punch characteristics, Strojniški Vestnik – Journal of Mechanical Engineering, Vol. 66, No. 6, 375-384, doi: 10.5545/sv-jme.2020.6583. [36] DIN EN 10130 (2007). Cold rolled low carbon steel flat products for cold forming – Technical delivery conditions, DIN Deutsches Institut für Normung e. V., Berlin, Germany. [37] Kim, W., Shin, D., Lee, Y., Chung, C.C. (2016). Simplified torque modulated microstepping for position control of permanent magnet stepper motors, Mechatronics, Vol. 35, 162-172, doi: 10.1016/j.mechatronics.2016.02.002. Advances in Production Engineering & Management 17(3) 2022 325 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 3 | September 2022 | pp 326–338 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.3.439 Original scientific paper A new approach for quality prediction and control of multistage production and manufacturing process based on Big Data analysis and Neural Networks Tian, S.a, Zhang, Z.b, Xie, X.b,*, Yu, C.c aSchool of Basic Sciences, Shandong Institute of Petroleum and Chemical Technology, Dongying, P.R. China Jiaotong University, School of Economics and Management, Beijing, P.R. China cSchool of Information and Electronics, Beijing Institute of Technology, Beijing, P.R. China bBeijing ABSTRACT ARTICLE INFO As consumers care more and more about product quality, it is important to mine the deep correlations between production and manufacturing parameters and the evaluation of product quality through the analysis of industrial big data. The existing research of product quality prediction faces several major problems: the lack of diverse quality features, the poor tractability of abnormal parameters, the strong nonlinearity of parameters, the obvious sequential property of data, and the severe time lag of data. To solve these problems, this paper explores the quality prediction and control of multistage MP process (MPMP) based on big data analysis. Firstly, the prediction strategy and flow were specified for MPMP product quality prediction, and the features were extracted from MPMP product quality. After that, the MPMP product quality features were described in multiple dimensions, the attention mechanism was introduced to the prediction process. In addition, the recurrent neural network was improved, and an MPMP product quality prediction model was established on bidirectional long short-term memory (BiLSTM) network. Our model was compared with AdaBoost and XGBoost through experiments. The effectiveness of our model was demonstrated by the results of the appearance quality PQ1, and the area under the curve (AUC) for each process parameter. In general, our model is superior to other algorithms in the accuracy, mean accuracy, and precision of product quality prediction. Keywords: Big data analysis; Multistage production and manufacturing process (MPMP); Quality prediction; Machine learning; Artificial neural network; Recurrent neural network; Bidirectional long short-term memory (BiLSTM) *Corresponding author: xxie@bjtu.edu.cn (Xie, X.) Article history: Received 9 May 2022 Revised 16 August 2022 Accepted 20 August 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction With the continuous advancement of manufacturing intelligence, the new generation information technology (IT) has been deeply integrated with intelligent, automated production technology, providing an important driver of the industrial transformation of modern manufacturing [1-7]. As products become increasingly personalized, customized, and complex, the production and manufacturing (MP) process tends to cover multiple stages, and the consumers care more and more about product quality [8-14]. The manufacturing Internet of things (IoT) collects and stores the changing parameter data of the MP process, forming the industrial big data [15-22]. Through big data analysis, it is possible to reveal the deep connections between the parameters and the evaluation of product quality, 326 A new approach for quality prediction and control of multistage production and manufacturing process based on Big … providing support to the optimization of manufacturing technology and the prediction of product quality in modern manufacturing. In modern industries, information has been fully shared between production machines, smart subsystems, and mobile devices through advanced network technology [23, 24]. Ren et al. [25] proposed a soft measuring method for product quality prediction based on semi-supervised deep parallel factorization-machine (deepFM). Specifically, the process variables were discretized through data blocking; the deepFM was improved to extract quality information from different components, and obtain both high- and low-dimensional features. To solve the lack of process data and the strong nonlinearity and multiscale property of new intermittent processes, Chu et al. [26] presented a product quality prediction approach based on multi-scale kernel JYMKPLS (Joint-Y multi-scale kernel partial least squares) transfer learning. The merits of transfer learning and multiscale kernel learning were fully inherited by their approach. In addition, Lughofer et al. designed the strategies for online update and data removal of the model, aiming to adapt the transfer model continuous to new batch processes. Lughofer et al. [27] suggested that, in modern manufacturing facilities, high-quality production can be guaranteed through two basic stages. The first stage is to recognize the possible problems of product quality early on. The second stage is to take proper responses to the recognized problems. On this basis, Hao et al. put forward a holistic method to continuously implement the two stages under the prediction and maintenance framework of online production system, constructed a data-driven prediction model based on product quality standard, and realized the cyclic technological optimization in support of multistage functions. Hao et al. [28] developed an interaction model, which uses a linear model to characterize the influence of old production techniques and machines over quality degradation, and employs a random differential equation to capture the factors affecting quality degradation. Based on multiphase support vector regression (SVR), Zheng and Pan [29] proposed a soft measurement model for online quality prediction of liquid product concentration, and proved that the model is more efficient than the reported technologies. Melhem et al. [30] monitored the real-time quality of electronic products through the autocorrelation multivariate process, and came up with an online product quality prediction method, which forecasts the quality of products based on the correlations between product quality measurements in different steps. The existing research of product quality prediction faces several major problems: the lack of diverse quality features, the poor tractability of abnormal parameters, the strong nonlinearity of parameters, the obvious sequential property of data, and the severe time lag of data. To solve these problems, this paper explores the quality prediction and control of multistage MP process (MPMP) based on big data analysis. Section 2 specifies the prediction strategy and flow for MPMP product quality prediction. Section 3 introduces recursion to the principal component analysis (PCA) based on kernel functions, and extracts the features of MPMP product quality. Section 4 describes the MPMP product quality features in multiple dimensions, and incorporates the attention mechanism to prediction process. In addition, the recurrent neural network was improved, and an MPMP product quality prediction model was established on bidirectional long short-term memory (BiLSTM) network. Our model was compared with AdaBoost and XGBoost through experiments. The effectiveness of our model was demonstrated by the results of the appearance quality PQ1, and the area under the curve (AUC) for each process parameter. 2. Quality prediction framework Fig. 1 shows the MPMP product quality prediction strategy. Wireless sensing, industrial IoT, and big data analysis are adopted to capture and store the PM states and production technology parameters in different MP stages, aiming to facilitate the big data analysis. Fig. 2 shows the flow of MPMP product quality prediction. The specific steps of the prediction are as follows. Firstly, the historical MPMP data are combined with the data on manufacturing technology, MP experience, and abnormal product quality into a real-time MPMP and product quality database. Next, the MPMP product quality is monitored in real time, referring to the product quality indices. After that, the MPMP data in the current stage and previous stages are mined through Advances in Production Engineering & Management 17(3) 2022 327 Tian, Zhang, Xie, Yu big data analysis. On this basis, a product quality prediction model is established, and a strategy is developed to optimize abnormal production technology parameters. The data from the historical MP and product quality database are preprocessed before being used to predict whether the product is qualified, update the product quality rule library, and optimize the abnormal production technology parameters. Fig. 1 MPMP product quality prediction strategy 3. Feature extraction Fig. 2 Flow of MPMP product quality prediction MPMP product quality data contains a rich information of MP process, and many redundant factors. The variables in the data are strongly correlated, and cannot be directly used to build the MPMP product quality prediction model. To solve the problem, it is necessary to extract lowdimensional features from the data to obtain the most representative data of the MPMP, thereby reducing the modeling difficulty and computing complexity. The recursive update of principal components was introduced to the PCA based on kernel functions. In this way, the model can be updated without needing overall computing. The model 328 Advances in Production Engineering & Management 17(3) 2022 A new approach for quality prediction and control of multistage production and manufacturing process based on Big … computing becomes less complex, and satisfies the real-time online requirement of MPMP product quality prediction. Fig. 3 explains the flow of extracting MPMP product quality features. The kernel-based PCA recursive update algorithm mainly has four steps: Step 1: The original MPMP product quality data are mapped from low-dimensional feature space to high-dimensional feature space, producing the reconstructed data ψ(ai). Step 2: The kernel matrix L(ai, aj) = {ψ(ai), ψ(aj)} is constructed, and the inner product of vectors in the original data space is converted into kernel functions. Step 3: In the high-dimensional feature space, the kernel functions obtained in the previous steps are subjected to PCA, and the corresponding eigenvalues and eigenvectors are calculated. Step 4: The MPMP product quality data in the new stage are introduced to the kernel space through recursive solving. Step 5: The kernel-based PCA model of product quality is updated recursively, and the dynamic PCA features of MP product quality are extracted from the new stage. Fig. 3 Flow of MPMP product quality feature extraction Let ai be the n-dimensional MPMP product quality variable obtained through m samplings under the normal working condition; En be the original MPMP product quality data; G be the high-dimensional feature space; ψ(ai) ∈ G ⊆ En be the product quality data mapped nonlinearly from En to G. Then, we have 𝜓𝜓: 𝐸𝐸 𝑛𝑛 → 𝐺𝐺 𝑎𝑎 → 𝜓𝜓(𝑎𝑎) (1) Let λψ be the mean of the data mapped to space G from the original product quality samples. The covariance matrix DG of the MP product quality samples in the new stage after the mapping can be calculated by: 𝑚𝑚 𝑚𝑚 𝑖𝑖=1 𝑖𝑖=1 1 1 𝑇𝑇 𝐷𝐷𝐺𝐺 = ��𝜓𝜓(𝑎𝑎𝑖𝑖 ) − 𝜆𝜆𝜓𝜓 ��𝜓𝜓(𝑎𝑎𝑖𝑖 ) − 𝜆𝜆𝜓𝜓 � = � 𝜓𝜓(𝑎𝑎𝑖𝑖 )𝜓𝜓(𝑎𝑎𝑖𝑖 )𝑇𝑇 𝑚𝑚 𝑚𝑚 Advances in Production Engineering & Management 17(3) 2022 (2) 329 Tian, Zhang, Xie, Yu where, λψ can be calculated by: 𝑚𝑚 𝜆𝜆𝜓𝜓 = (1/𝑚𝑚) � 𝜓𝜓(𝑎𝑎𝑖𝑖 ) (3) 𝑖𝑖=1 Suppose the mapping values of the original product quality samples in space G are zerocentered. Then, λψ is equal to zero. To obtain the corresponding eigenvalue μ and eigenvector U, DG should go through eigenvalue decomposition in space G: 𝜇𝜇𝜇𝜇 = 𝐷𝐷𝐺𝐺 𝑈𝑈 (4) Solving the inner product of each product quality sample, i.e., pre-multiplying Eq. 4 with ψ(al), l = 1, 2, ..., m: 𝜇𝜇(𝜓𝜓(𝑎𝑎𝑙𝑙 ) ⋅ 𝑈𝑈) = (𝜓𝜓(𝑎𝑎𝑙𝑙 ) ⋅ 𝐷𝐷𝐺𝐺 𝑈𝑈) (5) According to the reproducing kernel theory, all the eigenvectors U corresponding to nonzero eigenvalues μ are all distributed in the tensor space of {ψ(a1), ψ(a2), …, ψ(am)}. Then, the coefficient vector βi(i = 1, 2, ..., m) should satisfy: 𝑚𝑚 𝑈𝑈 = � 𝛽𝛽𝑖𝑖 𝜓𝜓(𝑎𝑎𝑖𝑖 ) Combining Eqs. 5 and 6: 𝑚𝑚 𝑚𝑚 𝑖𝑖=1 𝑖𝑖=1 𝑖𝑖=1 (6) 𝑛𝑛 1 𝜇𝜇 � 𝛽𝛽𝑖𝑖 ⟨𝜓𝜓(𝑎𝑎𝑖𝑖 ), 𝜓𝜓(𝑎𝑎𝑙𝑙 )⟩ = � 𝛽𝛽𝑖𝑖 �𝜓𝜓(𝑎𝑎𝑖𝑖 ) • � 𝜓𝜓�𝑎𝑎𝑗𝑗 �� • �𝜓𝜓�𝑎𝑎𝑗𝑗 �, 𝜓𝜓(𝑎𝑎𝑖𝑖 )� 𝑚𝑚 (7) 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 𝐿𝐿2 𝛽𝛽 ⇒ 𝑚𝑚𝑚𝑚𝑚𝑚 = 𝐿𝐿𝐿𝐿 (8) 𝑗𝑗=1 Let Lij = L(ai, aj) = {ψ(ai), ψ(aj)} be an n × n-order kernel matrix. That is, the kernel functions of the two variables in the input space can characterize the inner product between the variables in the feature spaceThe specific form of ψ should be avoided in the computing process. Substituting Lij into Eq. 7, the characteristic equation can be obtained: Solving Eq. 8, it is possible to obtain nonzero eigenvalues μ2(μ1 ≥ μ2 ≥ ... μm) and the corresponding eigenvectors βl(l = 1, 2, ..., m). There exists (ul,ul) = 1 for normalizing eigenvector Ul. Thus, it can be derived from Eq. 7 that μ(βl – βl) = 1. Then, the l-th principal component pl mapped from original MPMP product quality sample a to space G can be expressed as: 𝑝𝑝𝑙𝑙 = ⟨𝑢𝑢𝑙𝑙 , 𝜓𝜓(𝑎𝑎)⟩ = 𝑚𝑚 � 𝛽𝛽𝑖𝑖𝑙𝑙 ⟨𝜓𝜓(𝑎𝑎𝑖𝑖 ) 𝑖𝑖=1 𝑚𝑚 • 𝜓𝜓(𝑎𝑎)⟩ = � 𝛽𝛽𝑖𝑖𝑙𝑙 𝐿𝐿(𝑎𝑎, 𝑎𝑎𝑖𝑖 ) 𝑖𝑖=1 (9) The principal component direction of a in space G is the projection of ψ(a) on new eigenvector U. After being added to the data window, the MP data am+1 of a new stage should be mapped to space G. Let ψ(am+1) be the nonlinearly mapped value of am+1 from low-dimensional feature space to high-dimensional feature space. Then, the mapped mean eigenvalue v'ψ can be recursively computed by: 1 𝑚𝑚 1 (10) 𝜆𝜆′𝜓𝜓 = 𝜓𝜓([𝐴𝐴, 𝑎𝑎𝑚𝑚+1 ])𝑆𝑆𝑚𝑚+1 = 𝜆𝜆𝜓𝜓 + 𝜓𝜓(𝑎𝑎𝑚𝑚+1 ) 𝑚𝑚 + 1 𝑚𝑚 + 1 𝑚𝑚 + 1 where, S = [1, 1, ..., 1] ∈ Em+1. The covariance matrix D'G can be recursively solved by: 𝐷𝐷𝐺𝐺′ = 1 𝜓𝜓([𝐴𝐴, 𝑎𝑎𝑚𝑚+1 ])𝜓𝜓([𝐴𝐴, 𝑎𝑎𝑚𝑚+1 ])𝑇𝑇 𝑚𝑚 𝑚𝑚 𝑚𝑚 1 1 𝑇𝑇 𝑇𝑇 = ��𝜓𝜓(𝑎𝑎𝑖𝑖 ) − 𝜆𝜆′𝜓𝜓 ��𝜓𝜓(𝑎𝑎𝑖𝑖 ) − 𝜆𝜆′𝜓𝜓 � + ��𝜓𝜓(𝑎𝑎𝑚𝑚+1 ) − 𝜆𝜆′𝜓𝜓 ��𝜓𝜓(𝑎𝑎𝑚𝑚+1 ) − 𝜆𝜆′𝜓𝜓 � 𝑚𝑚 𝑚𝑚 𝑖𝑖=1 𝑚𝑚 𝑖𝑖=1 𝑇𝑇 1 1 1 1 1 = � �𝜓𝜓(𝑎𝑎𝑖𝑖 ) − 𝜆𝜆𝜓𝜓 + 𝜆𝜆𝜓𝜓 + 𝜓𝜓(𝑎𝑎𝑚𝑚+1 )� × �𝜓𝜓(𝑎𝑎𝑖𝑖 ) − 𝜆𝜆𝜓𝜓 + 𝜆𝜆𝜓𝜓 + 𝜓𝜓(𝑎𝑎𝑚𝑚+1 )� 𝑚𝑚 𝑚𝑚 + 1 𝑚𝑚 + 1 𝑚𝑚 + 1 𝑚𝑚 + 1 𝑖𝑖=1 𝑇𝑇 1 𝑚𝑚 𝑚𝑚 𝑚𝑚 𝑚𝑚 + � 𝜓𝜓(𝑎𝑎𝑚𝑚+1 ) − 𝜆𝜆 � × � 𝜓𝜓(𝑎𝑎𝑚𝑚+1 ) − 𝜆𝜆 � 𝑚𝑚 𝑚𝑚 + 1 𝑚𝑚 + 1 𝜓𝜓 𝑚𝑚 + 1 𝑚𝑚 + 1 𝜓𝜓 330 (11) Advances in Production Engineering & Management 17(3) 2022 A new approach for quality prediction and control of multistage production and manufacturing process based on Big … 𝑚𝑚 𝑚𝑚 1 1 𝑇𝑇 𝑇𝑇 ��𝜓𝜓(𝑎𝑎𝑖𝑖 ) − 𝜆𝜆𝜓𝜓 ��𝜓𝜓(𝑎𝑎𝑖𝑖 ) − 𝜆𝜆𝜓𝜓 � + ��𝜓𝜓(𝑎𝑎𝑚𝑚+1 ) − 𝜆𝜆𝜓𝜓 ��𝜓𝜓(𝑎𝑎𝑚𝑚+1 ) − 𝜆𝜆𝜓𝜓 � 𝑚𝑚 𝑚𝑚 + 1 𝑖𝑖=1 𝑖𝑖=1 𝑚𝑚 − 1 1 𝑇𝑇 = 𝐷𝐷𝐺𝐺 + �𝜓𝜓(𝑎𝑎𝑚𝑚+1 ) − 𝜆𝜆𝜓𝜓 ��𝜓𝜓(𝑎𝑎𝑚𝑚+1 ) − 𝜆𝜆𝜓𝜓 � 𝑚𝑚 𝑚𝑚 + 1 = 𝑚𝑚 − 1 𝑚𝑚 − 1 𝑚𝑚 𝑚𝑚 − 1 𝑚𝑚 = �� 𝜓𝜓(𝑎𝑎)� 2 �𝜓𝜓(𝑎𝑎𝑚𝑚+1 ) − 𝜆𝜆𝜓𝜓 �� × �� 𝜓𝜓(𝑎𝑎)� 2 �𝜓𝜓(𝑎𝑎𝑚𝑚+1 ) − 𝜆𝜆𝜓𝜓 �� 𝑚𝑚 𝑚𝑚 𝑚𝑚 − 1 𝑚𝑚 𝑚𝑚 − 1 𝑇𝑇 To complete the eigenvalue decomposition of v'ψ and D'G, linear PCA should be employed to extract the principal component features of the MP product quality in the new stage. Therefore, this paper introduces the recursive algorithm to the kernel-based PCA, eliminating the need to compute the entire principal component model again after the input of the MP product quality data of the new stage. In this way, our model can effectively reduce the computing load of realtime prediction. 4. Methodology 4.1 Multidimensional description of quality variables and attention mechanism Fig. 4 describes MPMP product quality features in multiple dimensions. To illustrate the timevariation of product quality data, this paper evaluates product quality from three dimensions: production technology, product quality, and time. The production technology dimension examines the level of production technology from the accuracy of dimensions, shape, and position. The product quality dimension evaluates product quality from appearance quality, performance index, and life index. The time dimension is generated from the real-time MPMP product quality dataset. The global decision-making of production control is underpinned by the online detection of key processes of each MP stage, and the information interaction and sharing of the time dimension. This paper extracts the samples from the time series of MPMP product quality, and constructs a multidimensional MPMP product quality prediction model, which is capable of tracing and optimizing the abnormal production technology parameters. Fig. 5 shows the flow of realtime tracking and optimization of abnormal production technology parameters. Under the different features of production technology parameters, the product quality features of different MP processes are affected to different degrees. To this end, the attention mechanism was innovatively introduced to MPMP product quality prediction. Firstly, the MP product quality of the new stage was analyzed against the quality evaluation criteria. Then, the similarity between product quality features of adjacent stages was calculated. After that, the authors computed the correlation of the product quality features in the current MP stage with the change law of different production technology parameters, and obtained the corresponding similarity score. On this basis, the abnormal technology parameters were valued for the new MP stage, thereby completing the prediction of MPMP product quality. The core parameters of the attention mechanism include Key, Query, and Value. Among them, Key corresponds to Value, and is used to query for and compute the similarity of product quality features between adjacent stages. Query is the query during the execution of the attention mechanism. Value is the MPMP product quality data receiving attention and being selected. The attention mechanism can be defined by: 𝐴𝐴𝐴𝐴𝐴𝐴(𝐾𝐾𝐾𝐾𝐾𝐾, 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄, 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉) = 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆�𝑆𝑆𝑆𝑆𝑆𝑆(𝐾𝐾𝐾𝐾𝐾𝐾, 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄)� ∗ 𝑉𝑉𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 (12) 𝑢𝑢𝑖𝑖 = 𝑡𝑡𝑡𝑡𝑡𝑡(𝜔𝜔𝑞𝑞𝑖𝑖 + 𝑟𝑟) (13) Let qi be the output tensor of the upper layer series at position i. If the upper layer is a bidirectional neural network in the model, then the Key at position i can be denoted by ui: Advances in Production Engineering & Management 17(3) 2022 331 Tian, Zhang, Xie, Yu Fig. 4 Multidimensional description of MPMP product quality features Fig. 5 Real-time tracking and optimization of abnormal production technology parameters Eq. 13 shows that ui can be derived from Value via the fully-connected layer. The attention weight βi can be calculated by: 𝑜𝑜 𝑢𝑢𝑖𝑖𝑇𝑇 𝑑𝑑 (14) 𝛽𝛽𝑖𝑖 = ∑𝑖𝑖 𝑜𝑜 𝑢𝑢𝑖𝑖𝑇𝑇 𝑑𝑑 The output of the attention layer can be calculated by: 𝑆𝑆𝑆𝑆 = � 𝛽𝛽𝑖𝑖 (𝑎𝑎)𝑢𝑢𝑖𝑖 (𝑎𝑎) (15) 𝑖𝑖 The Query of that attention layer can be adjusted and updated through random initialization and model training: 𝜔𝜔𝑝𝑝 (𝑖𝑖) = 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑚𝑚𝑚𝑚𝑚𝑚 �𝛾𝛾𝑝𝑝 𝑆𝑆𝑆𝑆𝑆𝑆 �𝑎𝑎𝑝𝑝 , 𝑁𝑁𝑝𝑝 (𝑖𝑖)�� 𝛼𝛼𝑝𝑝 𝜔𝜔𝑝𝑝 (𝑖𝑖) = 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑚𝑚𝑚𝑚𝑚𝑚 ��� 𝜔𝜔𝑝𝑝 (𝑙𝑙)𝑡𝑡𝑝𝑝 (𝑖𝑖 + 𝑙𝑙)� � The output tensor fi can be expressed as: 𝑙𝑙 𝑞𝑞𝑖𝑖 = 𝐶𝐶𝐶𝐶𝐶𝐶(𝑞𝑞⃗𝑖𝑖 , 𝑞𝑞⃖𝑖𝑖 ) 332 (16) (17) (18) Advances in Production Engineering & Management 17(3) 2022 A new approach for quality prediction and control of multistage production and manufacturing process based on Big … 4.2 Construction of product quality prediction model The LSTM network, as a variant of recurrent neural network, can prevent the common problems of recurrent neural network: exploding gradients and vanishing gradients. Each LSTM network consists of an input gate SRp, a forget gate LEp, an output gate EXp, and a memory cell dp. Let Ap be the input vector of stage 𝑝𝑝; fp-1 be the hidden layer state of stage p – 1. Then, the forget gate can be calculated by: 𝐴𝐴𝑝𝑝 𝐴𝐴 = � � (19) 𝑓𝑓𝑝𝑝−1 𝐿𝐿𝐸𝐸𝑝𝑝 = 𝜀𝜀�𝜔𝜔𝐿𝐿𝐿𝐿 ⋅ �𝑓𝑓𝑝𝑝−1 , 𝐴𝐴𝑝𝑝 � + 𝑟𝑟𝐿𝐿𝐿𝐿 � (20) 𝑆𝑆𝑅𝑅𝑝𝑝 = 𝜀𝜀�𝜔𝜔𝑖𝑖 ⋅ �𝑓𝑓𝑝𝑝−1 , 𝐴𝐴𝑝𝑝 � + 𝑟𝑟𝑖𝑖 � (21) The forget gate determines whether the MPMP product quality information should be preserved or discarded. Let Dp* be the candidate cell state used to determine the new cell state Dp. The input gate can be calculated by: 𝐷𝐷𝑝𝑝 ∗ = 𝑡𝑡𝑡𝑡𝑡𝑡�𝜔𝜔𝑑𝑑 ⋅ �𝑓𝑓𝑝𝑝−1 , 𝐴𝐴𝑝𝑝 � + 𝑟𝑟𝑑𝑑 � (22) The input gate determines how to update information. The training parameters of our model are configured as follows: the weight of LSTM network, θ; bias, r; activation function sigmoid, s; point-by-point product, ⊙. The output gate can be calculated by: 𝐷𝐷𝑝𝑝 = 𝐿𝐿𝐸𝐸𝑝𝑝 ∗ 𝐷𝐷𝑝𝑝 + 𝑆𝑆𝑅𝑅𝑝𝑝 ∗ 𝐷𝐷𝑝𝑝 ∗ (23) 𝐸𝐸𝑋𝑋𝑝𝑝 = 𝜀𝜀�𝜃𝜃𝐸𝐸𝐸𝐸 ⋅ �𝑓𝑓𝑝𝑝−1 , 𝐴𝐴𝑝𝑝 � + 𝑟𝑟𝐸𝐸𝐸𝐸 � The memory cell can be expressed as: 𝑑𝑑𝑝𝑝 = 𝐿𝐿𝐸𝐸𝑝𝑝 ⊗ 𝑑𝑑𝑝𝑝−1 + 𝑆𝑆𝑅𝑅𝑝𝑝 ⊗ 𝑡𝑡𝑡𝑡𝑡𝑡(𝜃𝜃𝑑𝑑 ⋅ 𝐴𝐴 + 𝑟𝑟𝑑𝑑 ) The hidden layer state of stage 𝑝𝑝 can be calculated by: 𝑓𝑓𝑝𝑝 = 𝐸𝐸𝑋𝑋𝑝𝑝 ⊗ 𝑡𝑡𝑡𝑡𝑡𝑡�𝑑𝑑𝑝𝑝 � The activation function can be defined as: (24) (25) (26) 1 (27) 1 + 𝑜𝑜 −𝑎𝑎 𝑜𝑜 𝑎𝑎 − 𝑜𝑜 −𝑎𝑎 (28) 𝑡𝑡𝑡𝑡𝑡𝑡(𝑎𝑎) = 𝑎𝑎 𝑜𝑜 + 𝑜𝑜 −𝑎𝑎 The LSTM network can effectively handle product quality data with a strong sequential property and correlations. However, the network is unable to mine the information of future product quality data. This defect can be solved by combining forward LSTM with inverse LSTM into a BiLSTM. Let δ be the length of a data series; ML be the processing of a single LSTM. Then, the BiLSTM can obtain the forward and inverse information of product quality data from input vectors fp: → (29) 𝑓𝑓⃗𝑝𝑝 = 𝑀𝑀𝑀𝑀�𝑓𝑓⃗𝑝𝑝−1 , 𝑎𝑎𝑝𝑝 , 𝑑𝑑𝑝𝑝−1 �, 𝑝𝑝 ∈ [1, 𝛿𝛿] 𝜀𝜀(𝑎𝑎) = ← 𝑓𝑓⃖𝑝𝑝 = 𝑀𝑀𝑀𝑀�𝑓𝑓⃖𝑝𝑝−1 , 𝑎𝑎𝑝𝑝 , 𝑑𝑑𝑝𝑝+1 �, 𝑝𝑝 ∈ [1, 𝛿𝛿] (30) 𝑏𝑏𝑝𝑝 = ℎ �𝜔𝜔𝑓𝑓⃗𝑏𝑏 𝑓𝑓⃗𝑝𝑝 + 𝑊𝑊𝑓𝑓𝑏𝑏⃖� 𝑓𝑓⃖𝑝𝑝 + 𝑟𝑟𝑏𝑏 � (31) The information in the two directions (Eqs. 29 and 30) is combined into the final output of BiLSTM. The output of stage 𝑝𝑝 can be expressed as: Let Ap-m and fp-m be the state input and hidden layer output of the previous n MP stages, respectively; Ap be the input of production technology parameters in the current stage; fp be the output through the hidden layer; Ap+m be the input of production technology parameters in the m MP stages in future; fp+m be the hidden layer output. Then, we have: Advances in Production Engineering & Management 17(3) 2022 333 Tian, Zhang, Xie, Yu 𝑓𝑓𝑝𝑝 = 𝑔𝑔�𝜔𝜔3 𝐴𝐴𝑝𝑝 + 𝜔𝜔4 𝑓𝑓𝑝𝑝−1 � (32) 𝐸𝐸𝑋𝑋𝑝𝑝 = 𝑏𝑏𝑝𝑝 = ℎ�𝜔𝜔5 𝑓𝑓𝑝𝑝 + 𝜔𝜔6 𝑓𝑓𝑝𝑝′ � (34) 𝑓𝑓𝑝𝑝′ = 𝐿𝐿𝐿𝐿�𝜔𝜔1 𝐴𝐴𝑝𝑝 + ′ 𝜔𝜔2 𝑓𝑓𝑝𝑝−1 � (33) The dynamic memory network capable of retaining time dependence can be established by: 𝑝𝑝 𝑝𝑝 𝑝𝑝 𝑝𝑝 𝑝𝑝 𝑓𝑓𝑖𝑖 = ℎ𝑖𝑖 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵�𝑑𝑑𝑖𝑖 , 𝑓𝑓𝑖𝑖−1 � + �1 − ℎ𝑖𝑖 �𝑓𝑓𝑖𝑖−1 (35) Considering the sequential property and strong correlations between production technology parameters, as well as the dynamic nonlinearity of product quality features, this paper assigns weights to different production technology parameters according to the correlations between the two variables, following the attention mechanism of quality variables, and takes the weighed parameters as the input of BiLSTM. Firstly, the key parameters that induce the abnormal product quality were identified for each MP stage. Next, a product quality prediction model was established based on BiLSTM. To improve the prediction accuracy, the product quality states of stages p + 1, ..., p + m were predicted in real time in stage 𝑝𝑝. Then, the key technology parameters were further optimized. The production technology parameters of historical MPMP and those Zij of the current stage were converted into time series stage by stage. Let Zmi(p – 1) be production technology parameter i of MP process m in stage p – 1, and F(p) be the corresponding product quality feature. Then, we have: 𝑍𝑍11 (𝑝𝑝 − 1) ⋯ 𝑍𝑍1𝑛𝑛 (𝑝𝑝) 𝐹𝐹(𝑝𝑝) 𝑍𝑍 (𝑝𝑝 − 1) ⋯ 𝑍𝑍2𝑛𝑛 (𝑝𝑝) 𝐹𝐹(𝑝𝑝 + 1) �𝑍𝑍𝑖𝑖𝑖𝑖 = � 21 �� ⇒ � � (36) ⋮ ⋱ ⋮ ⋮ 𝑍𝑍𝑚𝑚1 (𝑝𝑝 − 1) ⋯ 𝑍𝑍𝑚𝑚𝑚𝑚 (𝑝𝑝) 𝐹𝐹(𝑝𝑝 + 𝑚𝑚) Let ξij(l + 1) be the observation of stage l + 1; ξmax and ξmin be the maximum and minimum of a parameter in that stage, respectively. Then, the normalization can be expressed as: 𝜉𝜉𝑖𝑖𝑖𝑖 (𝑙𝑙 + 1) − 𝜉𝜉𝑚𝑚𝑚𝑚𝑚𝑚 (37) 𝑍𝑍𝑖𝑖𝑖𝑖 (𝑙𝑙 + 1) = 𝜉𝜉𝑚𝑚𝑚𝑚𝑚𝑚 − 𝜉𝜉𝑚𝑚𝑚𝑚𝑚𝑚 Let F*(l + 1) be the prediction for stage l + 1; γk be the weight of the similarity between the parameter and product quality features; χk(l + 1) be the corresponding attention weight. Then, we have: 𝐹𝐹 ∗ (𝑙𝑙 𝐾𝐾 + 1) = � 𝜒𝜒𝑘𝑘 (𝑙𝑙 + 1) 𝛾𝛾𝑘𝑘 ∗ 𝑎𝑎𝑖𝑖𝑖𝑖 (𝑙𝑙 + 1) 𝑘𝑘=1 The prediction can be expanded as: 𝐹𝐹 ∗ (𝑙𝑙 + 1) = 𝐿𝐿𝐿𝐿[𝐹𝐹(𝑙𝑙), 𝐹𝐹(𝑙𝑙 − 1), . . . , 𝐹𝐹(𝑙𝑙 − 𝑚𝑚 + 1); 𝑍𝑍(𝑙𝑙 + 1), 𝑍𝑍(𝑙𝑙), 𝑍𝑍(𝑙𝑙 − 𝑛𝑛 + 1); 𝜎𝜎(𝑙𝑙 + 1)] (38) (39) Eq. 39 shows that the output of product quality features in stage l + 1 depends on Z(l + 1), ((Z(l), ..., Z(l – n + 1)), (F(l), F(l – 1), . . . , F(l – m + 1)) and an unpredictable error σ. Let Fi1 and Fi1* be the actual value and predicted value of a quality feature, respectively; τ||Φ||2 be the regularization term of the loss function. During model training, the loss function of product quality prediction can be expressed as: 𝑚𝑚 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙(𝛷𝛷) = − � 𝐹𝐹𝑖𝑖1 ∗ 𝑙𝑙𝑙𝑙𝑙𝑙(𝐹𝐹𝑖𝑖1 ) + 𝐹𝐹𝑖𝑖2 ∗ 𝑙𝑙𝑙𝑙𝑙𝑙(𝐹𝐹𝑖𝑖2 )+, . . . , 𝐹𝐹𝑖𝑖𝑖𝑖 ∗ 𝑙𝑙𝑙𝑙𝑙𝑙(𝐹𝐹𝑖𝑖𝑖𝑖 ) + 𝜏𝜏‖𝛷𝛷‖2 𝑖𝑖=1 (40) The fully-connected layer of the model was activated by Softmax function. The final output of the product quality prediction model can be given by: 𝑜𝑜 𝑖𝑖 (41) 𝑏𝑏� = 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆(𝑎𝑎𝑖𝑖 ) = 𝑛𝑛 ∑𝑛𝑛=1 𝑜𝑜 𝑖𝑖 334 Advances in Production Engineering & Management 17(3) 2022 A new approach for quality prediction and control of multistage production and manufacturing process based on Big … 5. Experiments and results analysis Fig. 6 compares the PCA results before and after the introduction of recursion. In Fig. 6a, the quality samples of 1,200 products were not recursively processed, but statically analyzed. Many PCA results surpassed the control line, indicating that the model could not effectively extract the principal component features of product quality in the latest MP stage. In Fig. 6b, the quality samples of 500 out of the 1,200 samples were recursively processed. It can be observed that the real-time performance of the analysis on samples collected by sliding time windows was effectively enhanced, as the results above the control line were reduced by more than 8 %. In our prediction model, the MPMP production technology parameters and MPMP product quality variables being collected and stored were preprocessed and normalized, so that the product quality prediction accuracy will not be undermined by dimensional disunity. After that, the product quality variation of stage 𝑝𝑝 was predicted based on the samples of stage p – 1. The specific data are given in Tables 1 and 2, where the product quality indices include appearance quality PQ1, performance index PQ2, and life index PQ3. Specifically, PQ1 covers cleanness PQ11, style PQ12, color PQ13, and packaging PQ14; PQ2 covers dimension parameter PQ21, motion parameter PQ22, and power parameter PQ23; PQ3 covers reliability PQ31, failure rate PQ32, and use cycle PQ33. (a) Before (b) After Fig. 6 PCA results before and after the introduction of recursion PQ11 PQ12 PQ13 PQ14 PQ21 PQ22 PQ23 PQ31 PQ32 PQ33 0.9625 0.1658 0.0241 0.9638 0.6521 0.3583 0.5382 0.1574 0.5271 0.3122 Table 1 Normalized values of samples in stage p – 1 0.9657 0.9686 0.9628 0.9639 0.9583 0.9655 0.1534 0.1643 0.1725 0.1848 0.1538 0.1342 0.0325 0.0521 0.0375 0.0265 0.0164 0.0335 0.9254 0.9587 0.9352 0.9583 0.9285 0.9428 0.6358 0.6149 0.6823 0.6951 0.6214 0.6725 0.3869 0.3763 0.3242 0.3629 0.4233 0.4126 0.6353 0.5876 0.6764 0.5372 0.6857 0.5728 0.1758 0.1635 0.1634 0.1725 0.1838 0.1524 0.3525 0.5241 0.3672 0.4258 0.3581 0.7868 0.2174 0.2563 0.3727 0.1631 0.2836 0.2751 0.9662 0.1658 0.0276 0.9647 0.6353 0.3584 0.6241 0.1326 0.5127 0.2675 0.9675 0.1546 0.0215 0.9562 0.6438 0.3217 0.6834 0.1532 0.4136 0.3123 PQ11 PQ12 PQ13 PQ14 PQ21 PQ22 PQ23 PQ31 PQ32 PQ33 0.9584 0.1546 0.0124 0.9258 0.6382 0.3581 0.4968 0.1538 0.2514 0.2386 0.9625 0.1346 0.0135 0.9342 0.6426 0.3684 0.5326 0.1627 0.3012 0.2485 0.9742 0.1347 0.0175 0.9346 0.3751 0.3926 0.5147 0.1825 0.2534 0.2358 0.9641 0.1527 0.0182 0.9504 0.3624 0.4257 0.4826 0.1926 0.2816 0.2719 Table 2 Normalized values of samples in stage p 0.9359 0.9433 0.9352 0.9375 0.1738 0.1826 0.1628 0.1435 0.0183 0.0175 0.0163 0.0157 0.9328 0.9626 0.9731 0.9539 0.6375 0.6832 0.6284 0.3505 0.4213 0.3825 0.3862 0.4135 0.4867 0.5315 0.4835 0.5327 0.1628 0.1824 0.1736 0.1524 0.2810 0.2624 0.2519 0.2746 0.2104 0.2517 0.2825 0.2431 Advances in Production Engineering & Management 17(3) 2022 0.9537 0.1628 0.0130 0.9582 0.3628 0.4253 0.4932 0.1438 0.2413 0.2042 335 Tian, Zhang, Xie, Yu This paper adopts two typical ensemble algorithms of machine learning, namely, AdaBoost and XGBoost, as well as our model to predict the product quality in terms of PQ1-3. The prediction results (Table 3) show that our model surpassed the other algorithms in terms of accuracy, mean accuracy, and precision. Fig. 7 compares the AUCs of PQ1 predicted by AdaBoost, XGBoost, and our model. Our model achieved desirable prediction performance, despite the large difference of MPMP in product quality. Besides, XGBoost algorithm also demonstrated a good classification ability of various product quality features. XGBoost and our model were separately adopted to predict PQ2 and PQ3 of 60 products with known production technology parameters. The results (Figs. 8 and 9) show that XGBoost incorrectly predicted 5 qualified products as unqualified in terms of PQ2, and incorrectly predicted 2 qualified products as unqualified in terms of PQ3. By contrast, our model successfully predicted all unqualified products. This means our model has a strong ability to predict product quality. Product quality features PQ1 PQ2 PQ3 Table 3 Production quality prediction results Indices Accuracy Mean accuracy Precision Accuracy Mean accuracy Precision Accuracy Mean accuracy Precision AdaBoost 0.862 0.85243 0.842678 0.834 0.868457 0.863758 0.814 0.823758 0.825712 XGBoost 0.87 0.884672 0.875689 0.846 0.885674 0.883758 0.827 0.863074 0.862875 Our model 0.89 0.953281 0.925768 0.86 0.896725 0.895235 0.851 0.875426 0.886425 Fig. 7 Area under the curve (AUC) of PQ1 336 Fig. 8 Predicted PQ2 vs. true PQ2 Advances in Production Engineering & Management 17(3) 2022 A new approach for quality prediction and control of multistage production and manufacturing process based on Big … 6. Conclusion Fig. 9 Predicted PQ3 vs. true PQ3 This paper analyzes the MPMP quality prediction and control based on big data analysis. Firstly, the MPMP product quality prediction strategy and flow were detailed, followed by the extraction of MPMP product quality features. Then, the MPMP product quality features were described in multiple dimensions. Next, the attention mechanism was introduced to the prediction process, and a product quality prediction model was established based on BiLSTM. Through experiments, the PCA results before and after the introduction of recursion were compared, revealing the effectiveness of our feature extraction algorithm. After that, our model and several state-of-thearts were separately adopted to predict product quality in terms of PQ1-3. The results show that our model achieved better accuracy, mean accuracy, and precision of product quality than other algorithms. This paper innovatively introduces the attention mechanism to establish a quality prediction model. But many details are worthy of further study. For example, the future research could try to optimize the product quality classification rules, and apply reinforcement learning to adaptively optimize various process parameters and the manufacturing quality features collected by sensors. In addition, it is an urgent need to develop a real-time system that can automatically perceive abnormal parameters, and decide on how to optimize these parameters, in the light of the manufacturing state. The product quality prediction model can be embedded into the system to manufacture high-quality products. References [1] [2] [3] [4] [5] [6] Liukkonen, M., Tsai, T.-N. (2016). Toward decentralized intelligence in manufacturing: Recent trends in automatic identification of things, International Journal of Advanced Manufacturing Technology, Vol. 87, No. 9, 2509-2531, doi: 10.1007/s00170-016-8628-y. Nazifa, T.H., Ramachandran, K.K. (2019). Information sharing in supply chain management: A case study between the cooperative partners in manufacturing industry, Journal of System and Management Sciences, Vol. 9, No. 1, 19-47, doi: 10.33168/JSMS.2019.0102. Li, B.-H., Hou, B.-C., Yu, W.-T., Lu, X.-B., Yang, C.-W. (2017). Applications of artificial intelligence in intelligent manufacturing: A review, Frontiers of Information Technology & Electronic Engineering, Vol. 18, No. 1, 86-96, doi: 10.1631/FITEE.1601885. Istokovic, D., Perinic, M., Vlatkovic, M., Brezocnik, M. (2020). Minimizing total production cost in a hybrid flow shop: A simulation-optimization approach, International Journal of Simulation Modelling, Vol. 19, No. 4, 559-570, doi: 10.2507/IJSIMM19-4-525. Shafiq, S.I., Sanin, C., Szczerbicki, E., Toro, C. (2017). Towards an experience based collective computational intelligence for manufacturing, Future Generation Computer Systems, Vol. 66, 89-99, doi: 10.1016/j.future.2016. 04.022. Wang, C., Yang, B., Wang, H.Q. (2020). Multi-objective master production schedule for balanced production of manufacturers, International Journal of Simulation Modelling, Vol. 19, No. 4, 678-688, doi: 10.2507/IJSIMM19-4CO17. Advances in Production Engineering & Management 17(3) 2022 337 Tian, Zhang, Xie, Yu [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] 338 Liang, Q. (2020). Production logistics management of industrial enterprises based on wavelet neural network, Journal Européen des Systèmes Automatisés, Vol. 53, No. 4, 581-588, doi: 10.18280/jesa.530418. Stasiak-Betlejewska, R. (2015). Construction product quality improvement with applying production problems analysis, Manufacturing Technology, Vol. 15, No. 5, 756-761, doi: 10.21062/ujep/x.2015/a/1213-2489/MT/15/ 5/756. Zhao, Z., Yuan, Q. (2022). Integrated multi-objective optimization of predictive maintenance and production scheduling: perspective from lead time constraints, Journal of Intelligent Management Decision, Vol. 1, No. 1, 6777, doi: 10.56578/jimd010108. Ben-Ammar, O., Bettayeb, B., Dolgui, A. (2020). Integrated production planning and quality control for linear production systems under uncertainties of cycle time and finished product quality, International Journal of Production Research, Vol. 58, No. 4, 1144-1160, doi: 10.1080/00207543.2019.1613580. Amar, H., Ghodbane, H., Amir, M., Zidane, M.A., Hamouda, C., Rouane, A. (2020). Microstrip sensor for product quality monitoring, Journal of Computational Electronics, Vol. 19, 1329-1336, doi: 10.1007/s10825-020-01517-2. Schiermeyer, A. (2020). Optimizing product quality in molecular farming, Current Opinion in Biotechnology, Vol. 61, 15-20, doi: 10.1016/j.copbio.2019.08.012. Poth, A., Riel, A. (2020). Quality requirements elicitation by ideation of product quality risks with design thinking, In: Proceedings of 2020 IEEE 28th International Requirements Engineering Conference (RE), Zurich, Switzerland, 238-249, doi: 10.1109/RE48521.2020.00034. Hou, Y., Cao, Z.J., Yang, S.L. (2019). Cloud intelligent logistics service selection based on combinatorial optimization algorithm, Journal Européen des Systèmes Automatisés, Vol. 52, No. 1, 73-78, doi: 10.18280/jesa.520110. Xu, M., Cai, H., Liang, S. (2015). Big data and industrial ecology, Journal of Industrial Ecology, Vol. 19, No. 2, 205210, doi: 10.1111/jiec.12241. Chen, D. (2020). Multiple linear regression of multi-class images in devices of internet of things, Traitement du Signal, Vol. 37, No. 6, 965-973, doi: 10.18280/ts.370609. Wang, Y., Jan, M.N., Chu, S., Zhu, Y. (2020). Use of big data tools and industrial internet of things: An overview, Scientific Programming, Vol. 2020, Article ID 8810634, doi: 10.1155/2020/8810634. Song, Y.-J., Lee, J.-K. (2020). A blockchain and internet of things based architecture design for energy transaction, Journal of System and Management Sciences, Vol. 10, No. 2, 122-140. Yin, B., Wei, X., Wang, J., Xiong, N., Gu, K. (2019). An industrial dynamic skyline based similarity joins for multidimensional big data applications, IEEE Transactions on Industrial Informatics, Vol. 16, No. 4, 2520-2532, doi: 10.1109/TII.2019.2933534. Gupta, A.K., Chakraborty, C., Gupta, B. (2019). Monitoring of epileptical patients using cloud-enabled health-IoT system, Traitement du Signal, Vol. 36, No. 5, 425-431, doi: 10.18280/ts.360507. Lu, J. (2020). Industrial pollution governance efficiency and big data environmental controlling measures: A case study on Jiangsu province, China, Nature Environment and Pollution Technology, Vol. 19, No. 4, 1743-1748, doi: 10.46488/NEPT.2020.v19i04.046. Zhang, X., Ge, Z. (2020). Local parameter optimization of LSSVM for industrial soft sensing with big data and cloud implementation, IEEE Transactions on Industrial Informatics, Vol. 16, No. 5, 2917-2928, doi: 10.1109/ TII.2019.2900479. Rosin, F., Forget, P., Lamouri, S., Pellerin, R. (2021). Impact of Industry 4.0 on decision-making in an operational context, Advances in Production Engineering & Management, Vol. 16, No. 4, 500-514, doi: 10.14743/apem2021. 4.416. Nowakowska, M., Pajecki, M. (2021). Latent class analysis for identification of occupational accident casualty profiles in the selected Polish manufacturing sector, Advances in Production Engineering & Management, Vol. 16, No. 4, 485-499, doi: 10.14743/apem2021.4.415. Ren, L., Meng, Z., Wang, X., Zhang, L., Yang, L.T. (2020). A data-driven approach of product quality prediction for complex production systems, IEEE Transactions on Industrial Informatics, Vol. 17, No. 9, 6457-6465, doi: 10.1109 /TII.2020.3001054. Chu, F., Peng, C., Jia, R., Chen, T., Lu, N. (2021). Online prediction method of batch process product quality based on multi-scale kernel JYMKPLS transfer model, CIESC Journal, Vol. 72, No. 4, 2178-2189, doi: 10.11949/04381157.20200995. Lughofer, E., Zavoianu, A.-C., Pollak, R., Pratama, M., Meyer-Heye, P., Zörrer, H., Eitzinger, C., Radauer, T. (2019). Autonomous supervision and optimization of product quality in a multi-stage manufacturing process based on self-adaptive prediction models, Journal of Process Control, Vol. 76, 27-45, doi: 10.1016/j.jprocont.2019.02.005. Hao, L., Bian, L., Gebraeel, N., Shi, J. (2016). Residual life prediction of multistage manufacturing processes with interaction between tool wear and product quality degradation, IEEE Transactions on Automation Science and Engineering, Vol. 14, No. 2, 1211-1224, doi: 10.1109/TASE.2015.2513208. Zheng, R., Pan, F. (2017). Multi-phase support vector regression soft sensor for online product quality prediction in glutamate fermentation process, American Journal of Biochemistry and Biotechnology, Vol. 13, No. 2, 90-98, doi: 10.3844/ajbbsp.2017.90.98. Melhem, M., Ananou, B., Ouladsine, M., Pinaton, J. (2016). Regularized regression models to predict the product quality in multistep manufacturing, In: Proceedings of 2016 5th International Conference on Systems and Control (ICSC), Marrakesh, Morocco, 31-36, doi: 10.1109/ICoSC.2016.7507067. Advances in Production Engineering & Management 17(3) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 3 | September 2022 | pp 339–349 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.3.440 Original scientific paper Experimental determination of influences on a gauge block’s stack length Lipus, L.C.a, Acko, B.a,*, Tompa, J.a aUniversity of Maribor, Faculty of Mechanical Engineering, Slovenia ABSTRACT ARTICLE INFO Gauge blocks are an important basis for maintaining traceability in dimensional metrology, used for calibrating length measuring instruments and for adjustments in all branches of manufacturing. Their important feature is that they can be wrung with small dimensional uncertainty. An overview of the factors influencing the accuracy of a stack length, such as the quality of the gauge blocks (grade, wear), surface preparation (cleaning and usage of a lubricant), wringing (way and time, temperature of hands and gloves) is given in the paper. Experiments for determining these influences were performed with a highly precise gauge block comparator. Proper selection of gauge blocks, preparation of their surfaces and oiling improve the accuracy of a stack length. Application of a lubricant, wiped with a dry cloth or paper towel, helps to wring them more easily, but its contribution to the stack length in the experiment was 0.1 µm for oil and 0.2 µm for grease. Temperature changes of gauge blocks were estimated by holding them, and, during wringing in well controlled air conditions, monitoring them to yield the empirical coefficients of their warming up. The results showed that usage of gloves reduces the warming up by approximately half, but still the stack must be stabilised in well controlled conditions for at least one hour if it is used for micrometre-level precise measurements. Keywords: Gauge blocks; Wringing; Measurement uncertainty; Dimensional metrology *Corresponding author: bojan.acko@um.si (Acko, B.) Article history: Received 7 April 2022 Revised 25 September 2022 Accepted 28 September 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Gauge blocks (GBs) are one of the most accurate standards of length, an important basis of industrial length measurements, as well as commonly used measurement standards for maintaining traceability in dimensional metrology. They are made of wear-resistant material (hardened steel, ceramics, or tungsten carbide), and their length is defined by two parallel measuring surfaces. An important feature of gauge blocks is that they can be joined together with very little dimensional uncertainty. They are used as a reference, either as single blocks, or two or more joined strongly together by wringing, or wrung onto plates with a similar high-quality surface. The four grades of GBs available on the market are defined by the Standard SIST EN ISO 3650. The reference standard sets of grade K are calibrated by laser interferometry, performed almost exclusively by national laboratories. Lower-level grade sets are calibrated by mechanical comparison to the reference GBs, performed widely in calibration laboratories throughout the engineering industry. Calibration uncertainty with a comparator is inferior to interferometric calibration, but the instrumentation is less expensive and the procedure much simpler. Generally, GBs of grade zero are used for inspections and calibrations in measurement laboratories, GBs of grade 1 are used for precise adjustments, e.g., for sin bars, GBs of grade 2, having the smallest accuracy, are used for adjusting machine tools. 339 Lipus, Acko, Tompa In micrometre-precise laboratory and production measurements, grade zero is generally used as a reference. Along with length deviation and the uncertainty of GBs, known from their calibration certificate, the uncertainty of wringing film thickness and thermal contributions to the mutual uncertainty of the reference, must be taken into consideration. In the present paper, these uncertainty contributions are analysed and presented by in-situ measurements of different GBs (ceramic, steel; single or wrung), performed with a gauge block comparator and precise temperature sensors in well controlled air conditions. The experiments were performed in the Laboratory for Production Measurement (University of Maribor, Slovenia). The applied mechanical comparison procedure is accredited, and the calibration and measurement capability (CMC) is included into the key comparison database at BIPM [1, 2]. The laboratory, as a holder of the National Standard for length, is accredited for lengthcalibrations of standards and measuring equipment, with the primary purpose to assure dimensional traceability in Slovenian industry. For maintaining high level measurement capability, the laboratory develops measurement procedures steadily with novel equipment and laser interferometry, and, periodically, joins international comparisons for their verification [3-6]. Reliable measurement systems are especially important in complex geometrical measurements, as well as in precise machine tool monitoring and verification, in the sense of optimising production processes, and for controlling product quality. The secondary task of the laboratory is focused on the development of sustainable manufacturing systems and advanced automated integration of data, including calibration results, up to the global information level [7, 8]. 2. Materials, methods and execution of expaeriments 2.1 Gauge blocks as a length standard Standard SIST EN ISO 3650 defines the geometrical characteristics of gauge blocks and tolerances precisely for four grades, at the standard temperature 20 °C. Some are represented here (Fig. 1 and Table 1) for the purpose of interpretation of the experimental results. The limit deviation, te, is the maximal permitted deviation of the length from the nominal length ln at any point of the measuring face. The recommended points to measure are the five points presented in Fig. 1. The tolerance tv is defined for variation ν = lmax – lmin. The central deviation is ec = lc – ln, while the limit deviations are defined as fo = lmax – lc and fu = lc – lmin. Fig. 1 Geometrical characteristics of GB length Table 1 Limit deviation, te, of the length at any point of the measuring face from the nominal length and tolerance, tv, for the variation in length Ln / mm 0.5 ≤ Ln ≤ 10 10 ˂ Ln ≤ 25 25 ˂ Ln ≤ 50 50 ˂ Ln ≤ 75 340 Grade K te / µm tv / µm 0.2 0.05 0.3 0.05 0.4 0.06 0.5 0.06 Grade 0 te / µm tv / µm 0.12 0.1 0.14 0.1 0.20 0.1 0.25 0.12 Grade 1 te / µm tv / µm 0.2 0.16 0.3 0.16 0.4 0.18 0.5 0.18 Grade 2 te / µm tv / µm 0.45 0.3 0.6 0.3 0.8 0.3 1.0 0.35 Advances in Production Engineering & Management 17(3) 2022 Experimental determination of influences on a gauge block’s stack length Although the materials chosen for producing GBs have very stable crystal structures, on the level of the required reliability (of grade K and 0) the material structure stability is still temporal, even with proper handling and storage. Therefore, periodical calibration of GB sets is recommended, once per year up to three years, depending on the frequency and required dimensional accuracy of their use. The measuring surfaces are polished to such a degree that can be joined easily by sliding, and they can get so strongly adhered that can be separated only by tangential pulling apart. The wringing film is small, with very little dimensional uncertainty, if the gauge blocks are treated properly. Considering the fact that GBs are used either as a single block wrung onto a plate with similar surface quality, or as a stack of blocks, the wringing film is included into the calibration results of the block length, as defined by the ISO 3650 standard (Fig. 1 and Table 1). In the case of calibrating Grade K with laser interferometry, the wringing film on the plate contributes to a length uncertainty of less than 6 nm [9]. The roughness of a well-polished surface varies from 15 nm to 30 nm [10, 11]. The wringing film thickness varies with the surface quality and lubricant fluid used. Blocks are cleaned with alcohol or petrol ether, while steel blocks also need protection against corrosion with special oil wetting. Before usage, the blocks are wiped with a lint-free cloth to make sure they are free from dust. By sliding the blocks air is squeezed out, and the surfaces get adhered together by vacuum and molecular interaction. The strong adherence can be explained by the surface tension of the liquid film (of oil, or water vapour from the air): The cohesive forces between molecules in a liquid and with a solid surface are stronger than those on its surface in contact with the air, therefore, when we try to separate the blocks, the liquid tries to minimise its surface. Fig. 2 presents the high ability of oil to wet the surface of a gauge block. Additionally, the fine roughness observed on the measuring surfaces could enhance the adhesion, due to the phenomenon of liquid bridge splitting, since mobile wetting bridges can naturally migrate to narrower gaps [12]. The stacks should be disassembled after usage, even in daily use. Leaving them together for a few days can cause that they become difficult to separate, or even to get permanently fused. We need to make sure that the blocks to be wrung are clean, free from dust, nicks and burs. If the surface is not clean, for instance, due to fingerprints, they get wrung more easily, but the uncertainty of the wringing film is higher. The presence of nicks or burs was inspected visually and with an optical flat (Figs. 3a-c). We place the glass on the measuring surface of the block to check for a rainbow by sliding it slightly. If the rainbow disappears when we press harder, it means there are no asperities present. If the rainbow stays in the same place when we slide the glass over the block, it means that the asperity is on the block. If the rainbow moves, the asperity is attached to the glass surface, or too much oil was applied. Fig. 2 Wetting of a GB surface with anti-corrosion oil (goniometrical observation of the contact angle) Fig. 3 The surface inspection with plane-parallel glass and wringing of thin blocks Advances in Production Engineering & Management 17(3) 2022 341 Lipus, Acko, Tompa Wringing should be done by sliding without much pressure. Two ways of wringing of thin blocks are presented in Fig. 3. By repeatedly sliding the upper block on the lower at a cross position (with slight pressure of the finger downward at the central point, Fig. 3d), the air is squeezed out and the surfacesstick together . Then, we align the blocks by rotating the upper block (with lateral pressure of another finger keeping the vertical pressure on the centre). Another way is by direct sliding of the upper block along the lower one (with slight pressure of the finger downward, Fig. 3e). If possible, blocks should be held on their side surfaces, otherwise the measuring surface that has been touched must be cleaned with petroleum ether, either to perform the measurement properly, or to continue with wringing of an additional block. When wringing, excessive force shall not be used, because the contact might be weaker (with greater thickness and variability), also some damage might occur on the edges or scratches on the measuring surfaces. Before storing a steel block, clean it with petroleum ether (or ethanol) and coat it with oil, to protect it from corrosion, especially if it has been touched it with bare hands. When reused, they shall be wiped with a dry cloth or petroleum ether. As a new block is wrung repeatedly, the film thickness might shrink due to wear of the asperities of surface roughness. If a block becomes worn and scratched, its ability to wring decreases and the film thickness increases, so it is better to replace it with a new one, or to repair it, because even using it as a single may give erratic results. A block with a corroded measuring surface must be replaced immediately, because it will damage any other block it is wrung onto. In some cases, we can repair a scratched surface with a special stone (Fig. 4). Again, we need to make sure that both surfaces, of the GB and of the stone, are clean and free from dust, before and after polishing. While a scratch remains visible, austerities are removed, and the GB has an improved ability to wring. Gauge blocks are available in sets enabling them to be stacked to the desired length in a wide range. With GBs from the conventional set presented in Tab. 2, we can make any length up to three decimal places. For instance, 15.63 mm is a combination of four blocks (1.03 + 1.6 + 3 + 10) mm. We try to assemble the desired length with as few blocks as possible to avoid accumulation of size errors. Single blocks with specific nominal lengths are available for this purpose. There are sets with which we can compose any measure in three decimal places. Depending on the desired minimum number of contacts in the assembly, individual blocks can be purchased, with which the same length can be assembled with one or two blocks less than in the conventional way of assembling. From Table 3, lengths up to 27.50 mm can be assembled only by two blocks, also in regions like (31.00 to 32.50) mm, for instance, 31.11 mm from 30 mm and 1.11 mm, while from Table 2 four blocks would be needed: (1.01 + 1.1 + 9 + 20) mm. In ranges like (27.51 to 29.99) mm we need three blocks from Table 3, for instance 27.51 mm is (1.51 + 1 + 25) mm, and 29.99 mm is (1.49 + 3.5 + 25) mm, a block less than from Table 2. Fig. 4 Polishing with GB stone: (a) Petrol ether for cleaning and anti-corrosion oil, (b) Scratches, (c) Polishing with low pressure along the stone, (d-f) Accessory for a thin GBs 1.001 1.01 1.1 1 10 342 1.002 1.02 1.2 2 20 Table 2 Conventional set of gauge blocks (all in mm) 1.003 1.03 1.3 3 30 1.004 1.04 1.4 4 40 1.005 1.05 1.5 5 50 1.006 1.06 1.6 6 60 1.007 1.07 1.7 7 70 1.008 1.08 1.8 8 80 1.009 1.09 19 9 90 Advances in Production Engineering & Management 17(3) 2022 Experimental determination of influences on a gauge block’s stack length 1.00 1.01 1.02 3 25 3.5 30 4 35 2.00 2.01 2.02 Table 3 Individual gauge blocks (all in mm) 1.03 1.04 … 1.45 1.46 1.5 1.6 1.7 1.8 1.9 2.03 2.04 … 2.45 2.46 2.5 2.6 2.7 2.8 2.9 4.5 5 … 22.5 23 40 45 50 60 70 1.47 1.48 1.49 23.5 80 24 90 24.5 100 2.47 2.48 2.49 Standard grade blocks are made of a hardened steel alloy, while calibration grade blocks are often made of carbide or ceramic, because they are harder and wear less. The results of measurements should be given at the standard temperature 20 °C, which can be achieved by well-controlled air conditions in measuring rooms or chambers. When the measuring systems and measurands are made of steel and steel blocks are used, the thermal expansion coefficients of the materials, 𝛼𝛼, are similar, and the length errors, ∆𝐿𝐿, at temperature deviations, 𝛥𝛥𝛥𝛥, might be negligible (Eq. 2). The thermal expansion coefficient of steel blocks is approximately 11.5⋅10-6 K-1, of ceramic 9.4⋅10-6 K-1 and of carbide 4.4⋅10-6 K-1. In the case of ceramic or carbide blocks, due to the significant difference of their coefficients compared to steel, it is necessary to pay more attention to the thermal stabilisation and to temperature correction of the measured length. ∆𝐿𝐿 = 𝛼𝛼𝛼𝛼𝛼𝛼T ∆𝐿𝐿 = 𝛥𝛥𝛥𝛥𝛥𝛥𝛥𝛥T (1) (2) Among other influences, a change in a gauge block’s temperature may be caused by touching it by hand. Gloves are recommended for handling them, tweezers could also be used to transfer individual gauge blocks, but, when assembling them, the blocks warm up noticeably, even if we manage to wring them in a very short time by using gloves. Therefore, we need to wait some time for the stack to be cooled. The cooling time depends on the required accuracy of measurement for which it is going to be applied. 2.2 Measurement of gauge block stack length The purpose of the experiments was to determine the time of temperature stabilisation after assembling the blocks, and the repeatability of the residual contact. The deviation was observed with a precision GB comparator (Fig. 5), which is used in our laboratory for calibrating GB sets [1, 2]. The air temperature in the chamber was maintained at (20 ± 0.3) °C and monitored by a sensor calibrated with a measurement uncertainty of 0.05 K, installed near to the blocks. The GBs’ temperature was measured with sensors with a 0.015 K measurement uncertainty (Fig. 6a). Immediately after wringing (Fig. 6b), the stack was inserted under the comparator’s probe (Fig. 6c). During its temperature stabilisation, the deviation was measured periodically in comparison with the reference (Figs. 6c-e) until the temperature difference of the assembly and the reference became negligible. The length difference ec was measured at the central points, and corrected for the length deviation of the reference eref (taken from the calibration certificate). The measurement uncertainty for the length of 50 mm, evaluated as our CMC in the accredited calibration procedure, is 0.055 µm for steel and 0.07 µm for ceramic GBs. Fig. 5 Mechanical comparator for GB calibration Advances in Production Engineering & Management 17(3) 2022 343 Lipus, Acko, Tompa Fig. 6 Measurement of stack length by mechanical comparison: (a) Temperature stabilisation of GBs, (b) Wringing, (c) Comparison of the ceramic stack to the ceramic ref., (d) Ceramic stack to the steel, (e) Steel stack to the steel reference 3. Experimental results and discussion The measurements were performed for three combinations (presented in Fig. 6). The stack of steel blocks S1 and S2, and the stack of ceramic blocks (C1 and C2) were compared with the (S) steel reference 50 mm from the master set (Grade K). The measurement with the ceramic stack was repeated also in comparison with the (C) ceramic reference 50 mm (Grade 0), in order to eliminate the difference in the thermal expansion coefficient. The blocks used for the wringing test were previously calibrated on the comparator. Their geometrical characteristics, derived from five points (as presented in Fig. 1) are given in Table 4 for five repeated measurements. ec -0.05 -0.05 -0.05 -0.05 -0.05 ec -0.04 -0.05 -0.04 -0.03 -0.04 Table 4 Geometrical characteristics of the gauge blocks used in the experiments (all in µm) (S1) steel 25 mm (Grade K) fu ec v fo 0.00 0.01 0.02 0.00 0.00 0.02 0.02 0.00 0.00 0.02 0.03 0.00 0.01 0.01 0.02 0.00 0.00 0.01 0.02 0.00 (C1) ceramic 25 mm (Grade 0) v fo 0.10 0.10 0.09 0.09 0.07 0.07 0.09 0.08 008 0.08 (C2) ceramic 25 mm (Grade 0) v fo 0.06 0.06 0.07 0.07 0.08 0.08 0.06 0.06 0.08 0.08 fu 0.00 0.00 0.00 0.00 0.00 ec 0.00 0.00 -0.01 0.00 0.00 (S2) steel 25 mm (Grade 0) v fo 0.04 0.00 0.04 0.01 0.05 0.01 0.05 0.01 0.05 0.01 fu 0.02 0.02 0.03 0.02 0.02 fu 0.04 0.03 0.04 0.04 0.04 By precise observation of these characteristics, taking into account that the lower contact layer is already included into the given central deviation ec for both blocks in the stack, the additional geometrical contribution to the central deviation of the stack can be estimated from the characteristics given for the upper surface of the lower block, and the means of C2 in the ceramic stack and S2 in the steel stack (Fig. 6), respectively. From Table 4, the block S1 has fo = 0.00 µm and the centre, as the highest level, has the deviation ec = 0.014 µm (higher than the nominal value 25 mm); the block S2 has ec = 0.00 µm and fo = 0.01 µm. So, we can estimate the mutual geometrical contribution to be 0.024 µm. The C1 block has fo = 0.084 µm (some asperity around the centre, which does not affect the length of the stack, because this block is on the top) and central deviation ec = -0.05 µm (lower than the nominal value 25 mm). Similarly, C2 has ec = -0.04 µm and fo = 0.07 µm (some asperity around the centre, which could affect the length of the stack). So, we can estimate the mutual geometrical contribution to be -0.02 µm. Both estimated values are smaller than the measurement accuracy. To determine the influencing factors, the repeatability of stack length was observed at different conditions, such as temperature of the hand, GB material and the addition of lubricant. Firstly, the single blocks were held in the hand (in a similar way as when assembling them) for 5 min and 344 Advances in Production Engineering & Management 17(3) 2022 Experimental determination of influences on a gauge block’s stack length then cooled in air in the chamber, to estimate the heat transmission coefficient and time for stabilisation back to a standard temperature. The graphs in Fig. 7 show the heating of 25 mm long blocks, ceramic or steel, with a bare hand or with gloves, respectively (Fig. 7). It should be emphasised here that the general recommendation is to hold the blocks on their side faces. Surfaces touched by bare fingers should be cleaned with alcohol or petroleum ether, and coated with oil before being stored, as contact with the skin promotes corrosion. Fig. 7 Heating blocks by holding: (a) With gloves, (b) With bare hands, (c) Stabilisation for 45 min Fig. 8 Heating of 25 mm long blocks: (a) J.T. experimenter with plasticised gloves, (b) M.M. with cotton gloves Fig. 8 presents the graphs of heating performed by two persons (a J.T. experimenter and an M.M. experimenter). In Fig. 8a the blocks were held with relatively cold hands and plasticised cotton gloves were used, while, in Fig. 8b, held with relatively warm hands and cotton gloves which were not plasticised. We can see that warming up depends strongly on the temperature of the hand (Table 5) and time of holding (Table 6). In the case of the higher temperature of the hand, warming was significantly faster. The heat transfer rates are higher at the beginning, due to the larger temperature differences in the hand-block contact. Also, the cooling rate was initially higher, depending on the temperature difference between the block and the air. Within one hour, the temperature of the blocks returned to room temperature, regardless of the height of the temperature peak and the material, because the cooling rate depends more on the air convection than on the conductivity of the material. Bare hand With gloves Table 5 Variation in the hand’s temperature during the experimentation (all in °C) J.T. experimenter M.M. experimenter 20.8 21.5 22.5 29.8 32.5 20.5 21.1 21.8 27.4 30.5 Steel (bare hand) Ceramic (bare hand) Steel (gloves) Ceramic (gloves) 32.7 31.0 Table 6 The slope of heating at the first 30 sec (K/10 sec) J.T. experimenter M.M. experimenter First 30 sec During 5 min First 30 sec During 5 min 0.23 0.08 0.55 0.40 0.13 0.06 0.50 0.34 0.07 0.06 0.37 0.23 0.04 0.03 0.25 0.22 Advances in Production Engineering & Management 17(3) 2022 345 Lipus, Acko, Tompa Fig. 9 Deviation of stack length after wringing: (a) Steel stack (J2 + J1) by J.T. with plasticised gloves (at conventional or extra oil application) and M.M. with cotton gloves, (b) Ceramic stack (K2 + K1) by J.T. with plasticised gloves Some measurements of the stack length were performed on the comparator within 30 seconds of cooling, starting immediately after wringing. The length deviations of the stack in comparison to the reference block are presented in Fig. 9. The time needed for wringing is given in the legend for each repetition. The major cause of the wide range of deviations was the difference in temperature of the hands, time of wringing, while the residual deviations depend on oil application, wear of the gauge blocks and wringing skills. The ceramic blocks were more difficult to wring and easier to separate in comparison to the steel blocks, where traces of oil contributed to stronger adhesion. The major reason for the increased length was warming by hands. (a) Ceramic stack wrung by J.T. (30 sec) (c) Steel stack wrung by M.M. (28 sec) 346 (b) Ceramic stack wrung by J.T. (18 sec) (d) Steel stack by J.T. (18 sec) with anticorrosive grease Fig. 10 Temperatures and length deviation of the stacks Advances in Production Engineering & Management 17(3) 2022 Experimental determination of influences on a gauge block’s stack length Table 7 The residual length deviations (all in µm) Residual length deviation After one hour Ceramic stack (Fig. 10a) 0.15 Ceramic stack (Fig. 10b) 0.39 Steel stack (Fig. 10c) 0.13 Steel stack with grease (Fig. 10d) 0.32 After 16 hours 0.15 0.40 0.12 0.31 The precise observations on the comparator were repeated with the temperature of all blocks and the air monitored in well controlled conditions in the laboratory chamber (Fig. 6). Different cases are collected on Fig. 10. We can see that the temperature of the stack stabilised within one hour. Some fluctuation of the air temperature appeared, due to the experimenter’s presence, at the beginning (during wringing and installation of the stack onto the comparator), and periodically during performance of the measurement on the comparator, but this didn’t affect the residual deviation of the stack significantly (because both the stack and the reference block had the same temperature of the air at the end), as well it decreased very little the initial length deviation of the stack, maximally 5 % (because the reference block responded slowly, with the quotient between the temperature of refence and the air approximately 0.2). The residual deviations were checked the next day and remained almost the same (Table 7). The measured deviation is the sum of the residual deviation and the deviation due to the temperature difference between the assembly and the reference block, which can be calculated by Eq. 1. Taking from Fig. 10 the time of wringing and the initial temperature change, the slope of heating is around 0.55 K/10 sec by the M.M. experimenter, 0.15 K/10 sec for the ceramic and 0.25 K/10 sec for the steel by the J.T. experimenter, which is higher than when the blocks were just held (Table 6), i.e. without active work of the hands. It is known that friction between surfaces can heat the material significantly [13, 14], depending on load, friction coefficient and lubrication [15]. In cases of blocks’ wringing, these contributions are rather negligible. Fig. 11 presents repetitions of the sliding of blocks similarly to the previous wringing (Fig. 10), but in this observation the blocks were held with thick insulation material to prevent the heat transfer from the hands, and the sensors were attached to the side surfaces of the blocks just at the edge, to monitor the temperature close to the sliding surfaces. From the temperature rise for both blocks, corrected for other possible influences from Fig. 11d, the contribution of friction was around 0.03 K/10 sec. Fig. 11 Temperature rise at the estimated force (perpendicular to the surface) 10 N during 35 sec of sliding Advances in Production Engineering & Management 17(3) 2022 347 Lipus, Acko, Tompa 4. Conclusion Gauge blocks used as a reference, either as single blocks wrung onto a plate or assembled together, have some deviation in length due to inter-surface contact thickness, which depends on many factors: the quality of the blocks (grade, geometric characteristics, roughness, and wear), surface preparation (cleaning and use of a lubricant), the method of assembly, time and wringing skills, hand temperature and insulating protection of gloves. To determine the quality of blocks, it is recommended to calibrate gauge blocks periodically. In the calibration certificate, the given length of a block already includes the thickness of the contact of the lower measuring surface (when wrung onto an ideal base), and the geometric contribution to the upper contact can be estimated from the given variance of the upper measuring surface. Depending on the length of the gauge blocks and their grade, a tolerance of 0.1 µm variance is allowed up to 25 mm, 0.16 µm for grade 1 and 0.3 µm for grade 2. In our experiment, gauge blocks (grade 0) with such geometric characteristics were selected that the final geometric contribution was negligible compared to the reliability of the measurement procedure on the comparator. The main contribution in this article are precise insitu measurements with length comparator and temperature sensors in well air controlled laboratory environment to determine the length uncertainty of stacks due to wringing process. The results that initial deviations due to heating by hands are not negligible in comparison to the geometrical deviations (that are determined by quality of blocks used for assembly). They vary with time, way of wringing and temperature of hands. The results in the article are given for the range of cold and extremely warm hands. The use of plasticised gloves is highly recommended to reduce the temperature contribution, as the heating rate was slowed by about half in both cases. The observations regarding the preparation of bloks’ surface showed that in the case of oil traces (after oil application the surface is wiped with petrolether) the adhesion increased, the contact is smaller and with better repeatability. Additional application of oil (wiped just with a dry cloth or paper towel) is useful for lower quality surfaces, this makes the blocks easier to wring, but the contribution of the contact is greater. In our experiments, the oil layer contributed 0.1 µm and the grease 0.2 µm. After wringing, the stacks shall be allowed to cool to operating temperature before using them, depending on the required reliability of the measurements, where they are use as a reference. Our experiments have shown that one hour is enough at well controlled air conditions. The residual deviations after one hour were the same as after one day of stabilization. The residual value can be estimated from the geometrical quality of used blocks (depending on wear and grade determined from calibration certificate) and slightly varying with application of a lubricant, as was proved in the case of grade 0. Acknowledgement The authors acknowledge the financial support from the Slovenian Research Agency (Research Core Funding No. P20190), as well as from the Metrology Institute of the Republic of Slovenia (funding of the National Standard of length; Contract No. C3212-10-000072). References [1] [2] [3] [4] 348 Godina, A., Acko, B., Druzovec, M. (2007). New approach to uncertainty evaluation in the calibration of gauge block comparators, Measurement, Vol. 40, No. 6, 607-614, doi: 10.1016/j.measurement.2006.09.010. Godina, A., Vuherer, T., Acko, B. (2012). Possibilities for minimizing uncertainty of dissimilar materials gauge blocks calibration by mechanical comparison, Measurement, Vol. 45, No. 3, 517-524, doi: 10.1016/j.measurement.2011.10.018. Šafarič, J., Klobučar, R., Ačko, B. (2021). Measurement setup and procedure for precise step gauge calibration, IEEE Transactions on Instrumentation and Measurement, Vol. 70, Article No. 1009610, doi: 10.1109/TIM.2021.3115579. Klobucar, R., McCarthy, M., Acko, B. (2019). Metrological set-up for calibrating 2-dimensional grid plates with submicrometre precision, Measurement, Vol. 132, 60-67, doi: 10.1016/j.measurement.2018.09.035. Advances in Production Engineering & Management 17(3) 2022 Experimental determination of influences on a gauge block’s stack length [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] Klobucar, R., Acko, B. (2017). Automatic high resolution measurement set-up for calibrating precise line scales, Advances in Production Engineering & Management, Vol. 12, No. 1, 88-96, doi: 10.14743/apem2017.1.242. Lipus, L.C., Budzyn, G., Acko, B. (2021). Analysis of laser interferometer measurement uncertainty by simulating error sources, International Journal of Simulation Modelling, Vol. 20, No. 2, 339-350, doi: 10.2507/IJSIMM20-2563. Acko, B., Weber, H., Hutzschenreuter, D., Smith, I. (2020). Communication and validation of metrological smart data in IoT-networks, Advances in Production Engineering & Management, Vol. 15, No. 1, 107-117, doi: 10.14743/apem2020.1.353. Ojstersek, R., Acko, B., Buchmeister, B. (2020). Simulation study of a flexible manufacturing system regarding sustainability, International Journal of Simulation Modelling, Vol. 19, No. 1, 65-76, doi: 10.2507/IJSIMM19-1-502. Mudronja, V., Katić, M., Šimunović, V. (2014). Realization of the highest level of traceability in Croatian national laboratory for length, Transactions of Famena, Vol. 38, No. 1, 37-44. Ali, S.H.R., Naeim, I.H. (2014). Surface imperfection and wringing thickness in uncertainty estimation of end standards calibration, Optics and Lasers in Engineering, Vol. 60, 25-31, doi: 10.1016/j.optlaseng.2014.03.012. Buchta, Z., Šarbort, M., Čížek, M., Hucl, V., Řeřucha, S., Pikálek, T., Dvořáčková, S., Dvořáček, F., Kůr, J., Konečný, P., Weigl, M., Lazar, J. Číp, O. (2017). System for automatic gauge block length measurement optimized for secondary length metrology, Precision Engineering, Vol. 49, 322-331, doi: 10.1016/j.precisioneng.2017.03.002. Butler, M.D., Vella, D. (2022). Liquid bridge splitting enhances normal capillary adhesion and resistance to shear on rough surfaces, Journal of Colloid and Interface Science, Vol. 607, Part 1, 514-529, doi: 10.1016/j.jcis. 2021.08.133. Fan, W.G., Zhang, S., Wang, J.D., Wang, X.H., Wang, W.X. (2020). Temperature field of open-structured abrasive belt rail grinding using FEM, International Journal of Simulation Modelling, Vol. 19, No. 2, 346-356, doi: 10.2507/ IJSIMM19-2-CO10. Khawaja, A.H., Jahanzaib, M., Cheema, T.A. (2020). High-speed machining parametric optimization of 15CDV6 HSLA steel under minimum quantity and flood lubrication, Advances in Production Engineering & Management, Vol. 15, No. 4, 403-415, doi: 10.14743/apem2020.4.374. Hsu, S.M., Gates, R.S. (2005). Boundary lubricating films: Formation and lubrication mechanism, Tribology International, Vol. 38, No. 3, 305-312, doi: 10.1016/j.triboint.2004.08.021. Advances in Production Engineering & Management 17(3) 2022 349 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 3 | September 2022 | pp 350–366 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.3.441 Original scientific paper Last-mile delivery optimization considering the demand of market distribution methods: A case studies using Adaptive Large Neighborhood Search algorithm Huang, Q.L.a,b,*, Wang, W.J.b, Liang, X.J.b, Xu, L.b, Niu, X.Y.a, Yang, X.Y.b aBeijing bChina Jiaotong University, Shangyuan Village, Haidian District, Beijing, P.R. China Academy of Transportation Sciences, Chaoyang District, Beijing, P.R. China ABSTRACT ARTICLE INFO Based on the current situation and problems of transportation "last mile" transportation distribution, this paper establishes a path optimization model based on user distribution methods from the perspective of market preference for transportation distribution methods, designs an Adaptive Large Neighborhood Search (ALNS) algorithm, and builds a user portrait based on the solution algorithm and the construction method. Based on the solution algorithm and the user portrait construction method, the solution scenario is established, and the distribution route and transportation distribution method are planned based on five real location data. Through the analysis of the solution scenarios, it can be obtained that after the optimization of the model, the transportation distribution cost of enterprises can be reduced, and the satisfaction of the transportation distribution service quality can be improved. The higher the complaint cost, the lower the total transportation and distribution cost, and the higher the satisfaction rate; the higher the time window penalty cost, the higher the total distribution cost, and the lower the satisfaction rate. Through several model comparisons, it is found that the optimized model has obvious advantages in transportation cost and good performance in transportation service satisfaction. To further strengthen the promotion and application of the distribution path optimization model, countermeasures are proposed in three aspects: establishing a unified end transportation information service platform, increasing the investment in end transportation path optimization, and strengthening the formulation of supporting policies to realize the optimization of end distribution services. Keywords: Transportation; Last mile; Adaptive Large Neighborhood Search (ALNS); Market demand; Logistics; Distribution; Optimization; Heuristic algorithms *Corresponding author: (Huang, Q.L.) 16113127@bjtu.edu.cn Article history: Received 19 February 2022 Revised 27 August 2022 Accepted 31 August 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction In recent years, with the gradual acceleration of China's economic development, people's living standards greatly improved, the demand for all kinds of commodities also gradually increased. With the popularity of the Internet, online shopping, live shopping and other business models have gradually emerged, which has brought new growth points to China's economy and put forward new requirements for the development of China's transportation. With the issuance of the Outline for The Construction of a Transport Power, the development of transport has gradually changed from high-speed development to high-quality development, putting forward higher requirements for the distribution path at the end of the transport logistics supply chain [1]. The distribution path at the end of transportation is the "last mile" link of the development of logistics supply chain in China. It is a direct link between the transportation operator and the har350 Last-mile delivery optimization considering the demand of market distribution methods: A case studies using Adaptive … vester, and also an important embodiment of the development level of transportation system in cities and regions. It has high requirements for transportation efficiency and service quality. For the development of the transportation industry, optimizing the distribution path of the city transportation terminal and getting through the "last mile" of logistics can further meet the needs of the people. It is an important starting point for the transportation industry to grasp the new development stage, implement the new development concept and construct the new development pattern. For the development of transportation enterprises, scientific and accurate calculation of the optimal distribution path at the end of city transportation can further do a good job in cost control, improve distribution efficiency, enhance the competitiveness of enterprises, and achieve development of enterprises. Pointed in this paper, the proposed path, not just the actual path and distance, but to the goods which are transported to the user in the city or regional distribution site, which is transported from the distribution site to the user to specify locations after submitting orders by the users, and contained in the process of route optimization, cost control, customer satisfaction, etc., by optimizing the path, so as to further meet the needs of user diversity [2]. 1.1 Problem definition In China's city end transportation distribution field, the user's high difficulty in matching the time window has been one of the difficulties of end transportation distribution. User demand is scattered, and the average daily transportation distribution volume of many communities is more than 150 pieces, and there are no less than 500 such communities in each city in China. As China's transportation and distribution platform is gradually bigger, the implementation of city transportation and distribution of goods and cargo types gradually increased, so the diversity of user demand for the end of the goods transportation methods further increased. At present, users for the end distribution mainly includes door-to-door transportation distribution and selfpickup, due to different user needs, the enterprises also need to consider their own costs, so there are often poor communication and coordination between the transporters and users, affecting the consumer experience and satisfaction. The main problems include the following aspects. Firstly, the distribution path selection and demand mismatch. Due to the diversity of users' demands for transportation distribution modes, sometimes the transportation distribution personnel cannot fully match users' demands when both parties communicate and coordinate, such as the need to wait, etc. Moreover, since the agreed time with the transportation distribution personnel cannot be precise to the minute, and even if users agree to face-to-face transportation distribution, they may be out of the office or in other situations, so they cannot complete the handover and inspection of goods at the first time when the goods arrive. Affecting the efficiency of transportation distribution, sometimes also due to poor communication and coordination between the two sides, resulting in complaints. In the promotion of the use of unmanned intelligent cabinets, as some communities are lack of regular maintenance of some intelligent cabinets leads to a high rate of damage, so it may further lead to transportation distribution personnel and users need to increase the additional transportation distribution distance to complete the transportation distribution. Secondly, the transportation path selection randomness is strong. From the viewpoint of the implementation status of China's transport enterprises, the implementation path of the "last mile" of urban transportation and distribution is often determined by the subjective experience and awareness of the distribution personnel. In different scenarios, facing different cargo conditions and external environment, the distribution personnel make judgments based on their own subjective experience and determine the final transportation distribution method on their own, even without communicating with users. In addition, influenced by the environment and income treatment, distribution personnel generally have lower education in China, so most of them are "empirical" when choosing the transportation distribution route, which leads to a large randomness of transportation distribution methods and affects the service experience of users is affected. Thirdly, the depth of the transportation enterprises' awareness of the distribution cost is insufficient. The enterprises' cognition of cost mainly focuses on the cost accounting of labor and Advances in Production Engineering & Management 17(3) 2022 351 Huang, Wang, Liang, Xu, Niu, Yang vehicles, ignoring the attention to intangible costs. Since the selection of end distribution mode mainly relies on the experience judgment of distribution personnel, which leads to the distribution personnel always being under pressure in the process of distribution, and when there is a change of distribution time, it may have an impact on the overall distribution time of the distribution personnel on that day. It is difficult for the relevant personnel to choose the best way to deliver through their own decision, and the resulting poor communication and coordination will lead to dissatisfaction and complaints from both sides, which will also affect the experience and satisfaction of the parties concerned with the transportation service. 1.2 Literature review The end distribution methods include home transportation distribution and goods pickup. The first one is door-to-door distribution, which refers to the transportation distribution method of delivering goods to users on time and at the agreed time and place. Han et al. [3] proposed that door-to-door distribution is the transportation distribution of goods to users by short-distance vehicle transportation, and it is one of the most important methods of end transportation. Howe [4] was the first to propose crowdsourcing service, which is the use of "rush order" mode to provide transportation distribution services for users, and this approach has been widely used in end transportation distribution. Bühler et al. [5] argued that logistics providers aim at the lowest cost for end transportation distribution, and constructed four new linear mixed integer programming models to portray the service situation of door-to-door transportation distribution. Chen et al. [6] constructed the M/D/1 queuing system to portray the specific utility of doorto-door transportation distribution to users, and argued that although door-to-door distribution can bring greater convenience, there are disadvantages such as high cost and low timeliness. The second one is goods self-pickup, which refers to the transportation distribution method in which goods no longer continue to be delivered door-to-door but are delivered to the user's surrounding logistics terminals and the user picks up the goods by himself, is also the most common way of end logistic supply chain. Guo [7] focused on the end transportation time mismatch problem to alleviate the problem of time conflict between users and distribution personnel. Song et al. [8] used the collected end transportation information to study cargo self-pickup, which effectively solved the time mismatch of cargo distribution, and at the same time greatly improved the efficiency of cargo distribution. Zhou et al. [9], Li et al. [10], and Xu et al. [11] analyzed the impact of self-pickup courier services on users' usage, the spatial distribution pattern of cargo self-pickup terminals, and users' willingness to choose self-pickup parcels through example verification. Guo [12] and others summarized cargo font points into different modes, such as: retail stores, subway stations, communities, and 24-hour public smart parcel stations for collection and transportation distribution; cargo self-pickup also includes Jing Dong pickup cabinets, Feng Chao Express provided by SF, CaiNiao post, and ShouHuobao. In terms of research methods, there are three main algorithms: exact algorithm, traditional metaheuristic algorithm, and ALNS algorithm. Lee et al. [13] analyzed the route optimization problem of multiple vehicles and optimized the exact algorithm based on the shortest path search algorithm using the minimum number of vehicles as the optimization goal. Ozbaygin and Savelsberg [14] proposed an iterative branch pricing method based on the solution based on the branch pricing method and used the algorithm to solve the optimization problem of distribution routes. Zhao et al. [15] assembled genetic algorithm and forbidden search algorithm to solve a joint optimization scheme for end distribution, taking urban distribution in the core area of Su Ning in Chongqing as an example. Zhou et al. [16] portrayed the scenario of multiple users picking up at the same intermediate pickup facility, with the objective of minimizing the total distribution cost. Goeke et al. [17] conducted a comparative analysis of the cross-sectional and longitudinal computing performance between the large neighborhood search algorithm and other algorithms through a comparative analysis, and concluded that the large neighborhood search algorithm has higher and better computing efficiency and computing performance. Rohmer et al. [18] aimed at cost optimization, and on the basis of fully considering the costs incurred by distribution improved the adaptive large-neighborhood search metaheuristic algorithm with the goal of cost optimization, and verified the effectiveness of the algorithm. Jin et al. [19] used heu352 Advances in Production Engineering & Management 17(3) 2022 Last-mile delivery optimization considering the demand of market distribution methods: A case studies using Adaptive … ristic approach to optimize the trucks transportation route to reduce travel cost. In the application of other methods, Ocampo et al. [20] constructed an integrated multiple criteria decisionmaking approach to locate the locations of last-mile delivery facilities. Wang et al. [21] discussed optimization model of joint distribution system including warehousing, transportation and logistics business to optimize logistic solution. 2. Model construction and validation Focusing on the problems faced by "last mile" path of transportation, the fundamental solution lies in understanding the needs of different users and providing exclusive transportation distribution services for users on the basis of good enterprise cost control. Combining the current situation of research and the application of related methods, this paper intends to use the ALNS algorithm to establish a model design to optimize the end transportation path considering users' preferences for transportation distribution methods and users' tendency to complain, and to determine the appropriate strategy to reduce transportation distribution costs and improve users’ satisfaction. 2.1 Model construction Consider the following transportation distribution situation. There is an end distribution terminal which offers service for 𝑚𝑚 users. Every user 𝑖𝑖 has a request 𝑞𝑞𝑖𝑖 and the earliest time window and latest time window 𝐸𝐸𝑖𝑖 , 𝐿𝐿𝑖𝑖 . each user has a preferred transportation distribution method which is represented by 𝑝𝑝𝑖𝑖 . 𝑝𝑝𝑖𝑖 = 1 represents user preferred door-to-door transportation distribution, 𝑝𝑝𝑖𝑖 = 0 respresents user preferred self-pickup transportation distribution. If the vehicle does not deliver according to the user's preference, there may be two results, the user who is easy to complain will complain to the relevant departments, and thus the transportation distribution company has to accept a certain penalty; while another part of the users are more talkative and suffer this result silently, without taking any complaint behavior. Users can be divided into four categories, based on their preferences and complaint behavior, and each category is represented by 𝑛𝑛 (𝑛𝑛 = 1, 2, 3, 4), including preferring door-to-door transportation distribution and easier to complain (𝑛𝑛 = 1), preferring self-pickup transportation distribution and easier to complain (𝑛𝑛 = 2), preferring door-to-door transportation distribution with no complain(𝑛𝑛 = 3), preferring self-pickup transportation distribution with no complain (𝑛𝑛 = 4). The cost of complaint for category 𝑛𝑛 users is 𝑝𝑝𝑛𝑛1 . Each user point can be accessed once and only once. The number of vehicles available at the distribution station is 𝑘𝑘. Each vehicle departs from the distribution station to serve the user point and returns to the station. The capacity of the vehicle is 𝑄𝑄𝑘𝑘 . The running distance 𝑑𝑑𝑖𝑖𝑖𝑖 between user points 𝑖𝑖 and 𝑗𝑗, the running time is 𝑡𝑡𝑖𝑖𝑖𝑖 , and the running cost is 𝑐𝑐𝑖𝑖𝑖𝑖 . Vehicles can arrive earlier than the earliest time window of user 𝑖𝑖 or later than the latest time window, but incur a corresponding penalty cost, the size of which is related to the user type and is denoted by 𝑝𝑝𝑛𝑛2 . The distribution starts immediately after the vehicle arrives at the user's point 𝑖𝑖. The service time is 𝑠𝑠𝑖𝑖 (the case of self-pickup applies to loading and unloading time, door-to-door applies to waiting + transportation distribution time) and leaves immediately after serving the point. The vehicles are homogeneous. The model symbols are shown in Table 1. Constraint Eq. 1 is an objective function with three components: transportation distribution cost, complaint cost, and time window penalty cost. Constraint Eq. 2 limits the number of vehicles used. Constraint Eq. 3 expresses the relationship between and. Constraint Eq. 4 guarantees that each user can be served only once. Constraint Eq. 5 expresses the flow balance. Constraint Eq. 6 expresses that the total demand of user points delivered by a transportation distribution vehicle cannot exceed the capacity of that vehicle. Constraint Eq. 7 expresses the relationship between the starting service moments of two neighboring user points visited by the vehicle. Constraints Eq. 8 to Eq. 9 are the initial values of the vehicle when it stops at the distribution station. Constraints Eq. 10 to Eq. 12 are the decision variable definition fields. Advances in Production Engineering & Management 17(3) 2022 353 Huang, Wang, Liang, Xu, Niu, Yang Symbol 0 𝐶𝐶 𝑉𝑉 𝐾𝐾 𝑎𝑎𝑖𝑖𝑛𝑛 𝑝𝑝𝑛𝑛1 𝑝𝑝𝑛𝑛2 𝑑𝑑𝑖𝑖𝑖𝑖 𝑡𝑡𝑖𝑖𝑖𝑖 𝑐𝑐𝑖𝑖𝑖𝑖 𝑠𝑠𝑖𝑖 𝑞𝑞𝑖𝑖 𝑒𝑒𝑖𝑖 , 𝑙𝑙𝑖𝑖 𝑄𝑄 𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 𝑦𝑦𝑖𝑖𝑖𝑖 𝑧𝑧𝑖𝑖 𝑟𝑟𝑖𝑖𝑖𝑖 Table 1 End distribution mode model symbol description Instruction Distribution terminal User collection, 𝐶𝐶 = {1,2, . . . , 𝑚𝑚} Terminal collection, 𝑉𝑉 = 𝐶𝐶 ∪ {0} Cars collection, 𝐾𝐾 = {1,2, . . . , 𝑘𝑘} If the user point 𝑖𝑖 belongs to category 𝑛𝑛, if so, 𝑎𝑎𝑖𝑖𝑛𝑛 = 1; or 0 Cost of complaints for category 𝑛𝑛 users Cost per unit penalty for violating the time window of 𝑛𝑛 class a user Distance between arcs (𝑖𝑖, 𝑗𝑗) Operating time between arcs (𝑖𝑖, 𝑗𝑗) Operating cost between arcs (𝑖𝑖, 𝑗𝑗) Service time of user 𝑖𝑖 Demand quantity of user 𝑖𝑖 Time window of user 𝑖𝑖 Capacity of the vehicle If the car 𝑘𝑘 go through arcs (𝑖𝑖, 𝑗𝑗), and it is 1; or 0 If the car 𝑘𝑘 service user 𝑖𝑖, and it is 1；or 0 If the distribution method is same with preference of user 𝑖𝑖, it is 0; or 1 The starting time of service of the car 𝑘𝑘 to user point 𝑖𝑖 𝑚𝑚𝑚𝑚𝑚𝑚 � � � 𝑐𝑐𝑖𝑖𝑖𝑖 𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 + � � 𝑝𝑝𝑛𝑛1 𝑎𝑎𝑖𝑖𝑛𝑛 𝑧𝑧𝑖𝑖 + � � � 𝑝𝑝𝑛𝑛2 𝑎𝑎𝑖𝑖𝑛𝑛 (1 − 𝑧𝑧𝑖𝑖 )𝑦𝑦𝑖𝑖𝑖𝑖 [(𝐸𝐸𝑖𝑖 − 𝑟𝑟𝑖𝑖𝑖𝑖 )+ + (𝑟𝑟𝑖𝑖𝑖𝑖 − 𝐿𝐿𝑖𝑖 )+ ] 𝑖𝑖∈𝑉𝑉 𝑗𝑗∈𝑉𝑉 𝑘𝑘∈𝐾𝐾 𝑛𝑛∈{1,2} 𝑖𝑖∈𝐶𝐶 𝑛𝑛∈{1,2} 𝑘𝑘∈𝐾𝐾 𝑖𝑖∈𝐶𝐶 (1) ∑𝑘𝑘∈𝐾𝐾 ∑𝑗𝑗∈𝐶𝐶 𝑥𝑥0𝑗𝑗𝑗𝑗 ≤ 𝐾𝐾 (2) ∑𝑘𝑘∈𝐾𝐾 ∑𝑗𝑗∈𝐶𝐶 𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 = 1∀𝑖𝑖 ∈ 𝐶𝐶 (4) ∑𝑖𝑖∈𝐶𝐶 𝑦𝑦𝑖𝑖𝑖𝑖 𝑞𝑞𝑖𝑖 ≤ 𝑄𝑄𝑘𝑘 ∀𝑘𝑘 ∈ 𝐾𝐾 (6) ∑𝑖𝑖∈𝑉𝑉 𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑦𝑦𝑗𝑗𝑗𝑗 ∀𝑗𝑗 ∈ 𝐶𝐶, 𝑘𝑘 ∈ 𝐾𝐾 ∑𝑖𝑖∈𝑉𝑉 𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 = ∑𝑖𝑖∈𝑉𝑉 𝑥𝑥𝑗𝑗𝑗𝑗𝑗𝑗 ∀𝑗𝑗 ∈ 𝐶𝐶, 𝑘𝑘 ∈ 𝐾𝐾 𝑟𝑟𝑖𝑖𝑖𝑖 + 𝑠𝑠𝑖𝑖 + 𝑡𝑡𝑖𝑖𝑖𝑖 − 𝑟𝑟𝑗𝑗𝑗𝑗 ≤ 𝑀𝑀(1 − 𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 ) 𝑟𝑟0𝑘𝑘 = 0 ∀𝑖𝑖 ∈ 𝑉𝑉, 𝑗𝑗 ∈ 𝑉𝑉, 𝑘𝑘 ∈ 𝐾𝐾 𝑠𝑠0 = 0 𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 = {0,1}∀𝑖𝑖 ∈ 𝑉𝑉, 𝑗𝑗 ∈ 𝑉𝑉, 𝑘𝑘 ∈ 𝐾𝐾 𝑦𝑦𝑖𝑖𝑖𝑖 = {0,1} ∀𝑖𝑖 ∈ 𝐶𝐶, 𝑘𝑘 ∈ 𝐾𝐾 𝑧𝑧𝑖𝑖 ∈ {0,1} ∀𝑖𝑖 ∈ 𝐶𝐶 (3) (5) (7) (8) (9) (10) (11) (12) To verify the effectiveness of the model proposed in this paper for large-scale cases, we also use this algorithm to solve the Vehicle Routing Problems with Time Windows (VRPTW) problem. Based on numerical examples from Solomon and Desrosiers [22] (100 consumers) and Homberger and Gehring [23] (200 and 400 consumers), the applicability of the proposed algorithm is obtained. Tables 2, 3 and 4 show the 100, 200 and 400 consumer scenarios, respectively. According to the results, the algorithm proposed in this paper has strong adaptability and can solve other similar problems well. In addition, we also verified the efficiency of the proposed algorithm compared with the genetic algorithm based on the calculation example in this paper, the algorithm effect is shown in Table 5. Compared with the Genetic Algorithm, the proposed algorithm is more efficient, so it can better find the optimal solution, and when the data is larger, the efficiency of the proposed algorithm is higher. 354 Advances in Production Engineering & Management 17(3) 2022 Last-mile delivery optimization considering the demand of market distribution methods: A case studies using Adaptive … Numerical example 1 2 3 4 5 6 Total Numerical example 1 2 3 4 5 6 Total Numerical example 1 2 3 4 5 6 Total Numerical example 100 200 436 Table 2 Solomon 100 consumers numerical example HGA (best 6 result) 828.38 589.86 1210.69 951.51 1384.17 1119.24 57196 Table 3 200 consumers numerical example HGA (best 6 result) 2718.41 1831.59 3613.16 2929.41 3180.48 2536.2 168092 Table 4 400 consumers numerical example HGA (best 6 result) 7170.47 3952.95 8402.57 6152.92 7907.14 5215.21 388013 Table 5 Comparison of algorithm efficiency Genetic algorithm LNS 256.22 254.38 292.49 287.66 313.57 303.23 2.2 Example adoption and algorithm analysis LNS (best 6 result) 828.38 589.86 1209.2 956 1384.17 1123.17 57259 LNS (best 6 result) 2720.12 1831.65 3605.09 2921.85 3204.41 2547.84 168809 LNS (best 6 result) 7188.35 3877.18 8538.45 6238.56 8145.91 5233 392214 Comparison 0.7 % 1.6 % 3.2 % Combining the model calculation results, the model of user transportation distribution method preference is further validated and analyzed by using examples. Example adoption As shown in Fig. 1, this paper uses five neighborhoods in Haidian District of Beijing as the basis for calculation example analysis, including Gangyan neighborhood, Jiaodajiayuan neighborhood, Mingguangcun neighborhood, Tianzhaojiayuan neighborhood, and Changhewan neighborhood as the community transportation distribution area, and the number of transportation distribution users in each neighborhood is 89, 87, 99, 85, and 75. In order to simplify the analysis and better display the results, the transportation distribution points of users in each district are simplified to 5. According to the actual research of the relevant company, the distribution center is selected at the bottom of Yixi Business Hotel, No. 33, Xueyuannan Road, Haidian District. To get the data of the users in the district, this paper designed questionnaires around basic information, preference of transportation distribution methods and complaint behavior, and the questionnaires were mainly obtained by posting the questionnaire links in the property groups, and 436 valid data were finally collected. Other model calculation parameters are set as follows: 𝑘𝑘 = 8, 𝑄𝑄𝑘𝑘 = 350, 𝐸𝐸𝑖𝑖 and 𝐿𝐿𝑖𝑖 are obtained from the questionnaires filled out by users, 𝑑𝑑𝑖𝑖𝑖𝑖 is calculated from latitude and longitude, 𝑐𝑐𝑖𝑖𝑖𝑖 = 10, 𝑠𝑠𝑖𝑖 and 𝑞𝑞𝑖𝑖 are randomly generated, 𝑝𝑝𝑛𝑛1 = 1, 𝑝𝑝𝑛𝑛2 = 8. Advances in Production Engineering & Management 17(3) 2022 355 Huang, Wang, Liang, Xu, Niu, Yang Algorithm analysis Fig. 1 Community distribution district selection figure Initial setting Since the objective function is profit maximization, we need to deal with the objective function first. Since 𝑚𝑚𝑚𝑚𝑚𝑚 𝑓𝑓𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 = 𝑚𝑚𝑚𝑚𝑚𝑚 (−𝑓𝑓𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 ), we let the cost of any feasible solution 𝑂𝑂(𝑆𝑆) = −𝑓𝑓𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 . So the initial solution 𝑆𝑆 0 corresponds to the expression of the temperature function as: 𝑇𝑇 = 𝑂𝑂(𝑆𝑆 0 ) × 𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (13) Neighborhood structure Since the distribution method of users who have checked the value-added service will no longer change, we add new removal and insertion policies to improve the feasibility of the path based on the original removal and insertion policies. For the convenience of description, we refer to the users who have checked the value-added service as value users. The basic idea of these two strategies is that the higher the proportion of value users included in a path, the lower the number of solutions generated by adjusting the user distribution method for that path, and the less favorable it is to generate feasible solutions in the early stage of the algorithm. Therefore, our two strategies operate mainly on such paths to ensure the convergence speed of the algorithm. Path removal strategy Step1: Count the proportion of each path containing value users in a certain solution 𝑆𝑆, and then sort them in descending order. Step2: Remove the paths until the number of removed is 𝑛𝑛𝑟𝑟 . Distribution method factor insertion strategy The distribution mode factor insertion strategy is to determine whether the user point is allowed to be inserted based on the distribution mode. Step1: Calculate the distribution mode correlation between the arc and the user point to be inserted. Since it is assumed that arc (𝑖𝑖, 𝑗𝑗) is an arc on path 𝑝𝑝, 𝑘𝑘 is the target insertion point, and 𝐸𝐸𝑖𝑖 ≤ 𝐸𝐸𝑘𝑘 ≤ 𝐸𝐸𝑗𝑗 . Arc (𝑖𝑖, 𝑗𝑗) is associated with the distribution method of the user point𝑘𝑘, the calculation method is as follows: 𝑚𝑚𝑚𝑚𝑚𝑚{ 𝐿𝐿𝑖𝑖 − 𝐸𝐸𝑘𝑘 , 0} 𝐸𝐸𝑖𝑖 ≤ 𝐸𝐸𝑘𝑘 𝜎𝜎𝑖𝑖𝑖𝑖 = �𝑚𝑚𝑚𝑚𝑚𝑚{ 𝐿𝐿𝑖𝑖 , 𝐿𝐿𝑘𝑘 } − 𝐸𝐸𝑖𝑖 𝐸𝐸𝑘𝑘 < 𝐸𝐸𝑖𝑖 ≤ 𝐿𝐿𝑘𝑘 (14) 𝑚𝑚𝑚𝑚𝑚𝑚{ 𝐿𝐿𝑘𝑘 − 𝐸𝐸𝑖𝑖 , 0} 𝐸𝐸𝑖𝑖 > 𝐿𝐿𝑘𝑘 356 Advances in Production Engineering & Management 17(3) 2022 Last-mile delivery optimization considering the demand of market distribution methods: A case studies using Adaptive … 𝜎𝜎𝑘𝑘𝑘𝑘 𝑚𝑚𝑚𝑚𝑚𝑚{ 𝐿𝐿𝑘𝑘 − 𝐸𝐸𝑗𝑗 , 0} 𝐸𝐸𝑘𝑘 ≤ 𝐸𝐸𝑗𝑗 𝑚𝑚𝑚𝑚𝑚𝑚{ 𝐿𝐿𝑘𝑘 , 𝐿𝐿𝑗𝑗 } − 𝐸𝐸𝑘𝑘 𝐸𝐸𝑗𝑗 < 𝐸𝐸𝑘𝑘 ≤ 𝐿𝐿𝑗𝑗 =� 𝑚𝑚𝑚𝑚𝑚𝑚{ 𝐿𝐿𝑗𝑗 − 𝐸𝐸𝑘𝑘 , 0} 𝐸𝐸𝑘𝑘 > 𝐿𝐿𝑗𝑗 𝜎𝜎𝑖𝑖𝑖𝑖 = 𝜎𝜎𝑖𝑖𝑖𝑖 + 𝜎𝜎𝑘𝑘𝑘𝑘 (15) (16) Step2: According to the distribution mode association degree, user point 𝑘𝑘 is inserted into the arc (𝑖𝑖, 𝑗𝑗) with the largest association degree. By analyzing the distribution mode correlation here, due to the existence of value users in the later stage of the algorithm, the basic constraints such as vehicle capacity can be easily satisfied, but it is more difficult to satisfy the distribution mode constraint, and the penalty cost incurred is larger, which needs to be handled specifically for the distribution method. The increased cost of considering the insertion of arc (𝑖𝑖, 𝑗𝑗) into user point 𝑘𝑘 does not need much consideration. Therefore, we need to recalculate the correlation degree. 3. Case studies: Results and discussion Combining the model results and the arithmetic results, the optimal path is further analyzed, including the selection of routes and transportation distribution methods, etc., and its sensitivity is further analyzed. 3.1 Optimal path and transportation distribution method Optimal route Because of the large number of points in the example, each path is shown separately in this paper to clearly demonstrate the path of the vehicle driving, and the specific vehicle route scheme is shown in Table 6. As can be seen from the Table 6, due to the time window constraints, the transportation distribution paths are not based on the distance to choose aggregated transportation distribution. Most of the vehicles will deliver to 4 or 5 neighborhoods. But in reality, the transportation distribution companies often distribute the cargo to a neighborhood by a special transporter, but after taking into account the cost of time window, user preferences for transportation distribution services and the cost of complaints, the distribution of vehicles will show a more decentralized form. No. 1 2 3 4 5 6 7 8 Table 6 Optimal route display Path [0,50,115,259,293,309,424,427,436,21,30,142,152,246,264,287,315,347,349,402,8,9,44,71,87,102,110,114,120, 136,141,166,169,178,207,209,247,255,279,283,308,321,325,350,385,421,93,155,223,379,387,98,122,180,183, 314,274,0] [0,337,390,403,82,83,224,228,268,304,2,15,124,129,131,149,162,168,206,213,225,226,230,328,215,280,281,2 43,417,46,150,194,273,307,327,352,368,391,404,20,37,184,195,201,222,244,305,330,432,109,116,143,164,27 7,284,326,419,153,361,19,63,130,170,0] [0,270,285,289,316,324,331,338,346,397,400,426,428,429,431,27,42,57,74,75,112,172,396,58,154,182,62,92,1 99,359,411,23,101,145,176,250,251,290,317,334,358,383,103,237,261,265,345,348,353,167,375,137,146,212, 332,344,418,11,18,81,156,187,231,256,303,398,125,235,16,29,86,105,119,135,138,147,245,249,340,73,0] [0,173,272,298,393,10,77,84,186,288,370,197,39,48,61,89,96,128,157,258,271,323,372,1,41,51,132,214,282,39 9,433,4,181,216,266,292,364,435,3,36,165,335,177,218,275,286,320,384,388,76,106,161,210,310,378,185,196, 200,236,241,252,254,291,311,322,336,339,357,416,99,0] [0,14,204,229,232,28,72,160,260,371,140,238,253,354,413,423,425,5,7,17,22,24,26,31,47,60,64,90,111,123,17 9,188,198,203,217,221,234,239,257,269,278,297,301,333,366,367,94,97,107,267,318,356,362,373,374,394,40 9,25,45,49,70,329,377,0] [0,32,38,43,52,56,65,69,78,88,95,104,133,139,190,211,220,242,342,351,360,363,380,386,392,401,406,414,434, 53,233,422,34,55,66,68,80,91,117,118,174,208,227,248,276,295,355,365,382,405,67,296,300,306,319,13,144,1 48,158,313,381,408,59,151,171,412,299,369,0] [0,12,33,35,54,191,193,240,263,40,126,134,189,192,202,205,341,343,395,415,430,302,407,312,100,219,0] [0,79,85,121,127,159,163,175,262,389,6,108,113,294,376,410,420,0] Advances in Production Engineering & Management 17(3) 2022 357 Huang, Wang, Liang, Xu, Niu, Yang This section first checks the distribution of users in the different routes and the characteristics of user types. • Distribution of users in Route 1 and characteristics of user types. Fig. 2 shows the distribution of users as well as the path. Each point represents the number of users delivered at that point. The users in Route 1 are mainly distributed in Mingguangcun and Tianzhaojiayuan neighborhoods, and a small number of Jiaodajiayuan users. The distance between Mingguangcunand Tianzhaojiayuan neighborhoods is relatively close to each other, so they will deliver together to gain the advantage of distance. In Route 1, the transportation distribution method for Mingguangcun users is mostly door-to-door method, while the transportation distribution method for Tianzhaojiayuan and Jiaodajiayuan users is mostly selfpickup. To satisfy more users within a certain time, the transportation company can intersperse a certain number of self-pickup users among the door-to-door users, so as not to waste waiting time but also to satisfy the needs of self-pickup users. According to the time window data in Route 1, in order to reduce the waiting time, the distribution company should first transport to users with similar time window together. The time window of users who deliver to Mingguangcun neighborhood in Route 1 are mostly concentrated in the afternoon, and some of them are self-pickup users. Since the time window of self-pickup users are very flexible, they can be satisfied together. Fig. 2 The user distribution and the route of Route 1 • Distribution of users in Route 2 and characteristics of user types. Fig. 3 shows the distribution of users in Route 2 and the relevant situation. The distribution of users in Route 2 is similar to Route 1, distributed in Mingguangcun and Tianzhaojiayuan neighborhoods, with the difference that there are also users in Changhewan neighborhood in Route 2. However, the number of users in Changhewan neighborhood is very small, and they are basically self-pickup users, which means that the self-pickup users in Changhewan neighborhood are dispatched by the way because there is still spare capacity in the second vehicle. In route 2, the transportation distribution method of users in Mingguangcun and Tianzhaojiayuan neighborhoods is mostly door-to-door transportation distribution method, while the transportation distribution method of users in Jiaodajiayuan and Changhewan is mostly self-pickup. 358 Advances in Production Engineering & Management 17(3) 2022 Last-mile delivery optimization considering the demand of market distribution methods: A case studies using Adaptive … Fig. 3 The user distribution and the route of Route 2 • The distribution of users in Route 3 and the characteristics of user types. Fig. 4 shows the transportation and distribution of users in Route 3 and the paths. The distribution of users in Route 3 is relatively wide, within all five neighborhoods. However, the number of users in Changhewan and Gangyan neighborhoods are small, and they are basically users of self-pickup method. In Route 3, the transportation distribution methods of users in Mingguangcun, Tianzhaojiayuan, and Jiaodajiayuan neighborhoods are mostly door-to-door method, but the time window of users in Mingguangcun and Tianzhaojiayuan neighborhoods are concentrated in the morning, while the time window of users in Jiaodajiayuan are concentrated in the afternoon. The transportation distribution method for users in Changhewan and Gangyan neighborhoods are mostly self-pickup. Fig. 4 The user distribution and the route of Route 3 • The distribution of users in Route 4 and the characteristics of user types. As shown in Fig. 5, in Route 4, the transportation distribution paths are spread across every neighborhood, but users are more concentrated in Tianzhaojiayuan, Jiaodajiayuan, and Changhewan neighborhoods. In route 4, the transportation distribution method of users is door-to-door transportation distribution method. However, the users are more concentrated in Tianzhaojiayuan, Jiaodajiayuan, and Changhewan neighborhoods. The time window of the users in Mingguangcun and Tianzhaojiayuan neighborhoods are concentrated in the morning, while the users in Jiaodajiayuan and Changhewan neighborhoods are concentrated in the afternoon. Advances in Production Engineering & Management 17(3) 2022 359 Huang, Wang, Liang, Xu, Niu, Yang Fig. 5 The user distribution and the route of Route 4 • Distribution of users and the characteristics of user types in Route 5 As shown in Fig. 6, in Route 5, the users are distributed in Tianzhaojiayuan, Jiaodajiayuan, Changhewan, and Gangyan neighborhoods. Among them, the number of users in Changhewan and Gangyan neighborhoods are the largest. In Route 5, the most users' transportation distribution method is door-to-door method. However, there are some self-pickup method users in Changhewan neighborhood. The time window of users in Tianzhaojiayuan and Jiaodajiayuan neighborhoods are concentrated in the morning, while the users in Jiaodajiayuan and Changhewan neighborhoods are concentrated in the afternoon. Fig. 6 The user distribution and the route of Route 5 • Distribution of users and the characteristics of user types in Route 6 As shown in Fig. 7, in Route 6, the transportation distribution users are distributed in Jiaodajiayuan, Changhewan, and Gangyan neighborhoods, among which the number of users in Gangyan neighborhood is the largest. In Route 6, the transportation distribution method of users in Jiaodajiayuan and Changhewan neighborhoods are door-to-door distribution method. However, there are more self-pickup method users in Gangyan neighborhood. The time window of users in Jiaodajiayuan and Changhewan neighborhoods are concentrated in the morning, while the users in Gangyan neighborhood are concentrated in the afternoon. 360 Advances in Production Engineering & Management 17(3) 2022 Last-mile delivery optimization considering the demand of market distribution methods: A case studies using Adaptive … Fig. 7 The user distribution and the route of Route 6 • Distribution of users and the characteristics of user types in Route 7 and 8. As shown in Fig. 8, in both Route 7 and Route 8, the delivered users are distributed in Gangyan neighborhood. In both Route 7 and Route 8, the transportation distribution method of users is door-to-door transportation distribution method. Among them, the time window of users of Route 7 are all concentrated in the morning, while the time window of users of Route 8 are all concentrated in the afternoon. Therefore, although the Route 7 and 8 have spare capacity, they are not delivered together because the time window of the two paths are so different that it would take a long waiting time if they are delivered together, and it is better to deliver separately. Fig. 8 The user distribution and the route of Route 7 and Route 8 By analyzing the characteristics of the users of each route, it can be found that the users in the same route show the following pattern: Type 1: Each path has major distribution cells; Type 2: Users in the same neighborhood have relatively close time window; Type 3: Self-pickup users are interspersed with door-to-door method users, which can realize interpolated transportation distribution in the gaps of discontinuous time window of two users. Advances in Production Engineering & Management 17(3) 2022 361 Huang, Wang, Liang, Xu, Niu, Yang Transportation distribution method According to the calculation results, the final decision of the transportation distribution method with different user preferences is: Route 1: 337 Route 2: 225 Route 3: 150 Route 4: 428 Route 5: 181 Route 6: 267 Route 7: 117 390 321 250 192 58 435 275 47 359 157 251 317 395 298 182 28 253 55 300 320 235 12 59 85 193 217 360 407 365 306 219 This section examines the points where transportation distribution methods do not match user preferences, and finds that these user points are characterized by: a lower percentage of Type 1 users changing transportation distribution methods than Type 3 users; fewer users with a large earliest time window changing transportation distribution methods than those with a small earliest time window; a greater tendency for deliverers to concentrate on those users with the same transportation distribution methods; and priority for Type 1 and Type 3 users with smaller earliest time window transportation distribution. This is mainly determined by the complaint cost and time window violation cost, which are analyzed as follows: • The complaint cost of Type 1 users is higher. Under the condition of the same time window violation cost, compared with Type 3 users, changing the transportation distribution method of Type 1 users will increase the higher complaint cost, while the reduced time window penalty cost is insignificant, therefore, the deliverers will tend to change the transportation distribution method of Type 3 users. • Users with larger earliest time window are generally placed at the end of the path for transportation distribution, and the arrival time of the deliverer is more likely to be smaller than these users. If the transportation distribution method is changed, not only the complaint cost will increase, but also the arrival time of subsequent user points is advanced, and the time window penalty cost increases accordingly. Therefore, the transportation distribution person prefers not to change the transportation distribution method for this type of users. • For users whose transportation distribution method is door-to-door method, the transportation distribution method of the dispatcher can choose door-to-door or self-pickup method, which has higher flexibility. The dispatcher can freely adjust the transportation distribution method according to the actual situation to achieve the purpose of reducing the time window penalty cost and thus reducing the total cost. • If a transportation distribution path has both users who prefer door-to-door and self-pickup methods, the transportation distribution time window of self-pickup users is more relaxed and will not violate the time window of such users. Therefore, the transportation distribution agent will give priority to the door-to-door method users. Users satisfaction This section first conducts a comparative study of user satisfaction rates. To show the value of optimizing the user's transportation distribution method, the total cost 𝐶𝐶𝑎𝑎𝑎𝑎𝑎𝑎 when the satisfaction rate is 100 % (i.e., the transportation distribution is made exactly according to the user's preference for self-pickup and door-to-door transportation distribution) is first calculated. Then, the optimal solution 𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜 in the example problem of this paper and the number of user points 𝑛𝑛𝑜𝑜𝑜𝑜𝑡𝑡 = 38, which change the transportation distribution method can be obtained. In reality, the transporters also do not adopt the self-pickup method exactly for the users. Some users' packages are directly delivered to the pickup point, while some users' parcels are delivered to their homes. There is a certain degree of randomness in whether users are delivered by self-pickup or door-to-door transportation distribution, without considering the users' own preferences and complaint behavior. Therefore, 38 users are randomly selected to deliver according to the trans′ . To anaportation distribution method opposite to their preferences and get the total cost 𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜 362 Advances in Production Engineering & Management 17(3) 2022 Last-mile delivery optimization considering the demand of market distribution methods: A case studies using Adaptive … lyse the effect of changing the number of users' transportation distribution method preferences by considering the cost, 142 users are also randomly selected to deliver according to the transportation distribution method opposite to their preferences and get the total cost 𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 . The cost corresponding to each satisfaction and the parameters are shown in Table 7. As can be seen in Table 7, the higher the satisfaction rate, the greater the transportation distribution cost, meaning that the transportation vehicle needs to drive longer distances to meet the user's transportation distribution method preference. When the satisfaction rate is 100 %, no complaint cost is incurred, but the time window penalty cost is high because one vehicle often has to transport to many users, so it is inevitable that users' time conflicts will occur, but at this time, the transportation distribution mode preference of door-to-door method users cannot be violated, thus the time window of many users will be violated, so the time window penalty cost of users is high. The total cost 𝐶𝐶𝑎𝑎𝑎𝑎𝑎𝑎 = 329.09, the optimal solution 𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜 = 303.23 is obtained after optimizing the distribution method, which saves 25.86. The number of distribution methods changed after optimization, 𝑛𝑛𝑜𝑜𝑜𝑜𝑜𝑜 = 38 , which has the optimal satisfaction rate which is 91.28 %. Keeping the satisfaction rate constant and randomly violating the user's transportation distribution method preference, the time window violation cost will increase at this time, and the complaint cost will also increase, and the path cost will instead have a small decrease, and the total cost will increase by 17.36. With a satisfaction rate of 67.43 %, the complaint cost is much higher than the complaint cost of the optimal solution, and the time window penalty cost is not much different. From the overall trend, as the satisfaction rate decreases, the complaint cost increases and the time window penalty cost decreases. However, when the satisfaction rates are the same, the complaint costs will differ, which is mainly determined by the percentage of the first category of users among the user points that change the transportation distribution method. When the satisfaction rates are the same, the complaint cost will be higher for the paths with a high percentage of first category users, so the complaint cost in the optimal solution will be higher than the com′ plaint cost in 𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜 . On the other hand, the position of user points in the path that change the transportation distribution method affects the time window penalty cost. When increasing the number of user points that change the transportation distribution method in a small range, the change of the time window penalty cost is unpredictable. When the number of user points to be added to change the transportation distribution method is in a larger range, the time window penalty cost decreases, and the decrease changes according to the location of the user points. Satisfaction Distribution Costs Complaint Costs Time window penalty cost Total Cost 3.2 Sensitivity analysis Table 7 Impact of user satisfaction rate on cost 100 % 219.55 0 91.28 % 184.75 82 91.28 %; 𝑛𝑛𝑜𝑜𝑜𝑜𝑜𝑜 = 38 181.37 94 67.43 %; 𝑛𝑛𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 142 166.94 386 329.09 303.23 320.59 599.37 109.54 36.48 45.22 46.43 This section analyses the time window penalty cost. Holding the complaint cost constant, and change the unit time window penalty cost 𝛼𝛼 gradually from 1 to 6 to observe the changes in total cost, complaint cost, transportation cost and time window penalty cost. As seen in Figs. 9 and 10, the total cost rises rapidly and remains constant when 𝛼𝛼 = 5, when the penalty factor increases. The complaint cost shows the same trend as the total cost, indicating that the increase in the total cost is mainly caused by the increase in the complaint cost, and the change of α has little effect on the transportation cost and the time window penalty cost. As seen in Fig. 9, this is mainly because as the time window penalty cost 𝛼𝛼 increases, the transportation distribution personnel choose to put the goods into the self-pickup counter, and the complaint cost increases but reduces the amount of time window violation (time window penalty cost = 𝛼𝛼* time window violation). At this point, the total cost still increases, but slows down the growth of the total cost. As 𝛼𝛼 continues to increase, the time window violation volume Advances in Production Engineering & Management 17(3) 2022 363 Huang, Wang, Liang, Xu, Niu, Yang gradually decreases to 0, and the time window penalty cost will also be 0. No matter how it increases, it has no effect on the time window penalty cost. If we continue to change the transportation distribution method of the first and third category of users, i.e., the goods are put into the self-pickup cabinet, it can only increase the complaint cost and make the total cost not optimal. Fig. 10 gives the effect of the complaint cost coefficient on the total cost. It can be seen that the larger the complaint cost coefficient is, the lower the total complaint cost is instead, indicating that due to the larger complaint cost, the transport companies choose the way of preference for users to reduce the transportation distribution cost. The higher the complaint cost, instead, the higher the time window penalty cost, because changing the transportation distribution method will require a higher time window, thus increasing the time window penalty cost. In terms of total cost, the complaint cost coefficient can reduce the total cost of the company in general, but it causes a transient increase in total cost because in the first period, it may lead to an increase in time window penalty cost, and the increased penalty cost will be higher than the reduced complaint cost. The essence of this model lies in the trade-off between the cost of complaints and the cost of time window violation. For users, the unit time window violation cost is the same, but the complaint cost is different, and the heterogeneous and homogeneous costs of users can be transformed by vehicle route planning with the decision of user's transportation distribution method. In the transformation, the cost saving can then be achieved by the route change to form a favorable distribution method for users with high complaint cost. Fig. 9 The effect of penalty cost per unit time window on total cost Fig. 10 The influence of complaint cost coefficient on total cost 364 Advances in Production Engineering & Management 17(3) 2022 Last-mile delivery optimization considering the demand of market distribution methods: A case studies using Adaptive … 4. Conclusion remarks and suggestions for policy and measures In this paper, a path optimization model considering user's transportation distribution mode preference is established to optimize the driving path of end transportation vehicles as well as the transportation distribution methods, and the algorithm of ALNS is designed. Firstly, the initial solution is obtained by greedy algorithm and set as the optimal solution and the current solution, then the current solution is destroyed and repaired to obtain the neighborhood solution 𝑆𝑆 𝑡𝑡 . Based on the improved algorithm, the solution scenario is established, and the distribution paths and methods are planned based on the data of five neighborhoods, and the path optimization direction of the distribution methods is clarified. The analysis of the algorithm solution shows that the optimization of the model further satisfies the diversified needs of users for transportation distribution methods, and the satisfaction of the transportation distribution service can be improved while the cost of the terminal transportation distribution enterprises is reduced. The higher the complaint cost is, the total distribution cost first decreases slightly then increases and finally decreases again; the higher the time window penalty cost is, the higher the total distribution cost is. The calculation methods and results can provide some reference for the optimization of transportation end transportation routes based on users' preferences for transportation distribution methods. In order to ensure the smooth implementation of relevant optimization methods and improve the quality of urban transportation and distribution services, it is necessary to provide policy guarantee and measure guarantee for urban transportation and distribution path optimization from multiple angles and aspects, and strengthen the promotion and application of relevant supporting policies, measures and methods from different levels and angles to achieve highquality development of urban transportation and distribution market. First, establish a unified terminal transportation information service platform, strengthen the integration of data related to enterprise information, user information and industry information, establish a large database and realize the integration of data resources. Combined with the information on the service scale of distribution enterprises, user demand, and user service feedback, the industry management department further strengthens the research and judgment on the development of the transportation distribution market, forms industry development reports, and evaluates, analyzes and researches the market; enterprises collect information related to the distribution mode preference of users in the end distribution link through the platform, and constantly makes dynamic corrections to the end distribution habit preference characteristics of this user. Thus, the transportation and distribution paths can be further optimized dynamically. Second, increase the investment in the optimization of the end distribution path. Taking policy as a guide, from the height of the industry, guide all places to increase the policy and regulation guarantee for urban transportation and distribution path optimization, so as to realize the scientific and rationalization of end distribution path layout design. To industrial layout optimization, tax relief and other preferential means to guide the relevant enterprises to use scientific and efficient methods to optimize and adjust the path, and open up the transportation distribution "last mile". Enterprises to further increase the investment in path optimization program research, strengthen the science of transport and distribution route selection, control their own costs at the same time, to further meet the diversity of user needs. Third, strengthen the development of supporting policies. At present, urban transportation and distribution "last mile" vehicles are mainly tricycles, motorcycles, often crowding the motorway, sidewalk phenomenon, therefore, it is recommended that through policy guidance, in areas where conditions are ripe to pilot the opening of urban transportation and distribution of special channels, and motorway, non-motorized lanes, sidewalks to distinguish. Further ensure road traffic safety, while improving the efficiency of transportation distribution, and promote the opening of special parking spaces for distribution vehicles to solve the key problem of difficult parking for logistics and distribution vehicles. Establish a negative list in the field of urban transportation and distribution, promote the application of "double random a public" regulatory means, focus on the end of urban transportation and distribution of regulatory priorities, difficulties and weak links, the development of specific regulatory rules to reduce unnecessary costs for enterprises and promote a virtuous cycle of the market. Advances in Production Engineering & Management 17(3) 2022 365 Huang, Wang, Liang, Xu, Niu, Yang References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] 366 Liu, Z., Yuan, Q. (2021). Carry forward the spirit of "two roads" towards strong transportation country, People's Daily, Vol. 2021, No. 7, doi: 10.28655/n.cnki.nrmrb.2021.012208. Sun, H., Gao, H. (2021). Research on the last-mile distribution of rural express logistics based on cost reduction and efficiency enhancement, Logistics Technology, Vol. 44, No. 11, 41-44, doi: 10.13714/j.cnki.1002-3100.2021. 11.017. Han, S., Zhao, L., Chen, K., Luo, Z.-W., Mishra, D. (2017). Appointment scheduling and routing optimization of attended home delivery system with random customer behavior, European Journal of Operational Research, Vol. 262, No. 3, 966-980, doi: 10.1016/j.ejor.2017.03.060. Howe, J. (2006). The rise of crowdsourcing, Wired Magazine, Vol. 149, No. 6, 176-183. Bühler, D., Klein, R., Neugebauer, M. (2016). Model-based transportation distribution cost approximation in attended home services, Computers & Industrial Engineering, Vol. 98, 78-90, doi: 10.1016/j.cie.2016.05.014. Chen, Y.Y., Zhang, J., Luo, J.Q., Jian, P. (2020). Impacts of customer bounded rationality on last-mile transportation distribution service systems, Journal of Systems Management, Vol. 29, No. 2, 389-399, doi: 10.3969/j.issn.10052542.2020.02.020. Guo, L. (2021). Research on "last mile" distribution strategy of express transportation distribution industry, China Storage and Transport, Vol. 8, 133-134, doi: 10.16301/j.cnki.cn12-1204/f.2021.08.062. Song, L., Cherrett, T., Guan, W. (2011). Implications of collection/delivery points for transport and logistics, OR Insight, Vol. 24, 231-255, doi: 10.1057/ori.2011.9. Zhou, M., Zhao, L., Kong, N., Campy, K.S., Xu, G., Zhu, G., Cao, X., Wang, S. (2020). Understanding consumers’ behavior to adopt self-service parcel services for last-mile delivery, Journal of Retailing and Consumer Services, Vol. 52, Article No. 101911, doi: 10.1016/j.jretconser.2019.101911. Li, G., Chen, W., Yang, L., Liu, Q., Chen, X. (2019). Spatial pattern and agglomeration mode of parcel collection and delivery points in Wuhan City, Progress in Geography, Vol. 38, No. 3, 407-416, doi: 10.18306/dlkxjz.2019.03.010. Xu, J., Jiang, L., Li, Y. (2014). Research on consumers' willingness to choose self-picked packages based on service driven hypothesis, Journal of Management, Vol. 11, No. 12, 1850-1857, doi: 10.3969/j.issn.1672-884x.2014.12. 016. Guo, L. (2015). Research on the "last mile" problem and new mode of express transportation distribution in colleges and universities – A case study of Fujian commercial college, Journal of Fujian Commercial College, Vol. 5, 34-38, doi: 10.19473/j.cnki.1008-4940.2015.05.007. Lee, C.-G., Epelman, M.A., White, C.C., Bozer, Y.A. (2006). A shortest path approach to the multiple-vehicle routing problem with split pick-ups, Transportation Research Part B, Vol. 40, No. 4, 265-284, doi: 10.1016/j.trb.2004.11. 004. Ozbaygin, G., Savelsbergh, M. (2019). An iterative re-optimization framework for the dynamic vehicle routing problem with roaming delivery locations, Transportation Research Part B: Methodological, Vol. 128, 207-235, doi: 10.1016/j.trb.2019.08.004. Zhao, Q., Zhao, J., Lin, Y. (2017). Research on urban distribution network optimization of large retail enterprises based on O2O, Chinese Journal of Management Science, Vol. 25, No. 9, 159-167, doi: 10.16381/j.cnki.issn1003207x.2017.09.018. Zhou, L., Baldacci, R., Vigo, D., Wang, X. (2018). A multi-depot two-echelon vehicle routing problem with transportation distribution options arising in the last mile distribution, European Journal of Operational Research,, Vol. 265, No. 2, 765-778, doi: 10.1016/j.ejor.2017.08.011. Goeke, D., Roberti, R., Schneider, M. (2019). Exact and heuristic solution of the consistent vehicle-routing problem, Transportation Science, Vol. 53, No. 4, 1023-1042, doi: 10.1287/trsc.2018.0864. Rohmer, S.U.K, Claassen, G.D.H, Laporte, G. (2019). A two-echelon inventory routing problem for perishable products, Computers & Operations Research, Vol. 107, 156-172, doi: 10.1016/j.cor.2019.03.015. Jin, C., Lu, L.J., Min, J.N. (2022). A two-stage construction heuristic approach for vehicle routing problem with split deliveries and pickups: Case studies and performance comparison, Advances in Production Engineering & Management, Vol. 17, No. 1, 121-133, doi: 10.14743/apem2022.1.425. Ocampo, L.A., Himang, C.M., Kumar, A., Brezocnik, M. (2019). A novel multiple criteria decision-making approach based on fuzzy DEMATEL, fuzzy ANP and fuzzy AHP for mapping collection and distribution centers in reverse logistics, Advances in Production Engineering & Management, Vol. 14, No. 3, 297-322, doi: 10.14743/apem2019.3. 329. Wang, L., Chen, X.Y., Zhang, H. (2021). Joint distribution models in fast-moving consumer goods wholesale enterprise：Comparative analysis and a case study, Advances in Production Engineering & Management, Vol. 16, No. 2, 212-222, doi: 10.14743/apem2021.2.395. Solomon, M.M., Desrosiers, J. (1988). Survey paper – Time window constrained routing and scheduling problems, Transportation Science, Vol. 22, No. 1, 1-13, doi: 10.1287/trsc.22.1.1. Homberger, J., Gehring, H. (1999). Two evolutionary metaheuristics for the vehicle routing problem with time windows, INFOR: Information Systems and Operational Research, Vol. 37, No. 3, 297-318, doi: 10.1080/03155986. 1999.11732386. Advances in Production Engineering & Management 17(3) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 17 | September 2022 | pp 367–380 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.3.442 Original scientific paper Modelling surface roughness in finish turning as a function of cutting tool geometry using the response surface method, Gaussian process regression and decision tree regression Vukelic, D.a,*, Simunovic, K.b, Kanovic, Z.a, Saric, T.b, Doroslovacki, K.a, Prica, M.a, Simunovic, G.b aUniversity bUniversity of Novi Sad, Faculty of Technical Sciences, Novi Sad, Serbia of Slavonski Brod, Mechanical Engineering Faculty in Slavonski Brod, Slavonski Brod, Croatia ABSTRACT ARTICLE INFO In this study, the modelling of arithmetical mean roughness after turning of C45 steel was performed. Four parameters of cutting tool geometry were varied, i.e.: corner radius r, approach angle κ, rake angle γ and inclination angle λ. After turning, the arithmetical mean roughness Ra was measured. The obtained values of Ra ranged from 0.13 μm to 4.39 μm. The results of the experiments showed that surface roughness improves with increasing corner radius, increasing approach angle, increasing rake angle, and decreasing inclination angle. Based on the experimental results, models were developed to predict the distribution of the arithmetical mean roughness using the response surface method (RSM), Gaussian process regression with two kernel functions, the sequential exponential function (GPR-SE) and Mattern (GPR-Mat), and decision tree regression (DTR). The maximum percentage errors of the developed models were 3.898 %, 1.192 %, 1.364 %, and 0.960 % for DTR, GPR-SE, GPR-Mat, and RSM, respectively. In the worst case, the maximum absolute errors were 0.106 μm, 0.017 μm, 0.019 μm, and 0.011 μm for DTR, GPR-SE, GPR-Mat, and RSM, respectively. The results and the obtained errors show that the developed models can be successfully used for surface roughness prediction. Keywords: Turning; Tool geometry; Modelling; Surface roughness; Response surface method; Decision tree regression; Gaussian process regression *Corresponding author: vukelic@uns.ac.rs (Vukelic, D.) Article history: Received 13 June 2022 Revised 19 September 2022 Accepted 21 September 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Turning plays an important role in machining. It can be achieved in several ways. The steps that need to be taken must be carefully defined to achieve the desired quality, lower cost and shorter production time. Roughness is an important quality indicator of the machining surface, as it affects the performance of the product, but also the production costs [1]. Numerous factors affect the quality of the machining surface: machining conditions (machine tool rigidity, vibrations, use of cutting fluid, type of cutting fluid, etc.), machining parameters (cutting speed, feed rate and depth of cut), material properties of the workpiece (chemical composition, mechanical properties, physical properties, thermal properties, etc.), and cutting tool parameters (geometry, material, coating, etc.) [2-4]. Cutting tool geometry has a great influence on dimensional accuracy, shape accuracy, tool wear, residual stress, chip shape, cutting force, heat distribution, hardness variation, vibration, and surface roughness. 367 Vukelic, Simunovic, Kanovic, Saric, Doroslovacki, Prica, Simunovic Various methods have been proposed in the literature that have investigated the effects of tool geometry on surface roughness during turning. For example, Zerti et al. [5] studied the effects of corner radius, approach angle, and machining parameters on surface topography. Davoudinejad and Noordin [6] presented the effect of chamfer and honed edge geometry on surface finish. Zhao et al. [7] presented the effect of edge radius on surface roughness. Duc et al. [8] investigated the effect of cutting edge angle, rake angle, and inclination angle on surface roughness. Neseli et al. [9] investigated the influence of corner radius, approach angle and rake angle on surface roughness. Ashish and Lokesha [10] presented the effect of rake angle, approach angle, and process parameters on surface roughness. Karim et al. [11] studied the effects of different rake angles on surface roughness. Kumar et al. [12] determined the effect of corner radius and approach angle, as well as turning parameters on the surface roughness. Cui et al. [13] performed an optimization of corner radius, rake angle and approach angle. Sung et al. [14] studied the effect of corner radius micro deviation on surface roughness. Ponugoti et al. [15] studied the surface roughness after turning with variable cutting speed, feed, depth of cut, corner radius and negative rake angle. Senthilkumar and Tamizharasan [16] analyzed the influence of insert shape, relief angle, and corner radius on surface roughness. Tauhiduzzaman and Veldhuis [17] investigated the role of tool geometry on roughness using a tool with a rounded primary cutting edge and a flat secondary cutting edge. Abainia and Ouelaa [18] studied the effect of rake angle, approach angle, and inclination angle on surface roughness. Mohammad et al. [19] studied the effects of approach angle, rake angle, and inclination angle on surface roughness. Hai et al. [20] studied the surface quality with different corner radii, cutting speeds, and feeds. Khellaf et al. [21] presented a comparison of surface roughness with coated and uncoated mixed ceramics. Ozdemir [22] investigated the influence of turning parameters and corner radius on surface roughness. Kuntoglu et al. [23] investigated the influence of turning parameters and approach angle on surface roughness. In addition, some studies compared the machined surface quality of conventional and wiper inserts after turning operations [24, 25]. The results showed that the wiper insert had better surface roughness performance compared to conventional inserts. In analyzing the previous research in this field, which investigates the effects of tool geometry on surface roughness, experimental research dominates. The results obtained can only be applied to the conditions under which the experiments were conducted, and the associated cost and time cannot be neglected. To streamline this process, it is possible to model it. Response surface methodology, Taguchi method, artificial neural networks and fuzzy logic are most commonly used to model the turning process [26-28]. Most of the previous research dealt with the effects of machining parameters (cutting speed, feed rate, depth of cut) on the output parameters of the process [29-32]. Soft computing methods were predominantly used for modelling the turning process. When the turning process is properly modelled and the errors in predicting surface roughness are within acceptable limits, the cost and time of experimental investigations are reduced and the subjective influence of the technologist on the results obtained is diminished. There is also greater universality and thus the possibility of practical application. The most important question is which method should be used and when, because each of them has advantages, but also disadvantages. Despite some existing guidelines, it is still not possible to define an algorithm for selecting an appropriate method for specific production conditions. The error between the predicted and experimental values must be within acceptable limits for the prediction model to be used in practice. Finally, the results of all surface roughness prediction methods should converge with increasing accuracy, leading to an integration that accounts for all possible variables. All prediction methods require significant resources to achieve the desired goals. Therefore, it is critical to select an appropriate modelling method and formulate a sufficiently accurate model. In contrast to previous studies, the objective of this study is to evaluate the influence of four cutting tool geometry parameters, which have not been extensively studied in the literature, on surface roughness. The input parameters were the corner radius r, the approach angle κ, the rake angle γ and the inclination angle λ, while the output parameter was the arithmetical mean roughness Ra. For the obtained results, the modelling of the finish turning was performed with DTR, GPR-SE and GPR-Mat, which were also not previously used for modelling the turning process. 368 Advances in Production Engineering & Management 17(3) 2022 Modelling surface roughness in finish turning as a function of cutting tool geometry using the response surface method … 2. Materials and methods The methodological framework used in the research is shown in Fig. 1. The experimental studies were carried out on a DMG Mori CTX 510 Ecoline CNC lathe. Dry external longitudinal turning was performed on a workpiece with dimensions Ø50 × 600 mm. The workpiece was fixed and clamped by means of the chuck and rotating centre. The tests were carried out on workpieces made of medium-carbon steel C45, whose chemical composition is 0.42-0.50 % C, 0.50-0.80 % Mn, ≤ 0.4 % Si, ≤ 0.045 % P, ≤ 0.045 % S, ≤ 0.4 % Cr, ≤ 0.4 % Ni, ≤ 0.1 % Mo, and ≤ 0.63 % Cr+Mo+Ni. In addition, the mechanical and physical properties were as follows: density 7.87 g/cm3, hardness 163 HB, tensile strength 565 MPa, modulus of elasticity 200 GPa, and Poisson's ratio 0.29. Turning parameters were set for all tests: cutting speed vc = 440 m/min, feed rate f = 0.10 mm/rev, and depth of cut ap = 1.5 mm. The parameters were chosen in accordance with the recommendations of the manufacturers of the turning inserts. CVD-coated (TiCN+Al2O3+TiN) turning inserts were used for the experiments. All inserts had the same parameters: effective cutting edge length 10.34 mm, insert thickness 3.175 mm, inscribed circle diameter 6.35 mm, and clearance angle 7°. A new turning insert was used for each experiment. The geometrical parameters of the inserts varied during the experiments are listed in Table 1. The study was conducted in accordance with the randomized full factorial experiment, which allows the analysis of all combinations of input quantity levels. A total of 34 = 81 experiments were performed. Fig. 1 Methodological framework Table 1 Turning insert geometry levels (input variables) Level Input parameters Low Medium High Corner radius, r (mm) 0.4 0.8 1.2 Approach angle, κ (°) 60 75 90 Rake angle, γ (°) 3 6 9 Inclination angle, λ (°) -3 0 3 Advances in Production Engineering & Management 17(3) 2022 Table 2 Measurement conditions Parameter Value Sampling length 0.8 mm Cut-off wavelength 0.8 mm Evaluation length 4 mm Stylus tip diamond ball Stylus radius 2 μm Stylus force 1 mN 369 Vukelic, Simunovic, Kanovic, Saric, Doroslovacki, Prica, Simunovic After each experiment, the surface roughness Ra was measured. The measurement was performed using a Talysurf 6 measuring instrument, under the conditions listed in Table 2. The surface roughness was measured at six evenly spaced locations along the cut length. The average value from these measurements was taken as the mean value of the surface roughness. After the experiments were conducted, process modelling was performed based on the obtained results, i.e., prediction of surface roughness with: RSM, DTR, GPR-SE and GPR Mat. 3. Results 3.1 Results of experimental research The results of experimental research, i.e. the measured values of Ra for different combinations of input parameters, are presented in Table 3. Run ord. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 r (mm) 0.8 0.8 0.4 0.4 1.2 0.8 1.2 0.8 0.4 0.4 0.4 0.4 1.2 0.4 1.2 1.2 0.4 0.8 0.8 1.2 0.4 0.4 0.4 1.2 0.8 0.8 0.4 κ (°) 60 60 90 90 90 90 75 75 90 60 90 75 75 90 60 60 75 75 90 90 75 75 60 60 60 60 75 γ (°) 3 6 6 6 9 3 6 6 9 3 9 9 9 3 3 6 6 9 6 3 3 3 9 3 9 9 6 λ (°) -3 3 3 -3 -3 3 0 0 0 3 3 -3 3 -3 0 3 -3 -3 -3 -3 0 3 0 -3 0 3 3 Ra (μm) 1.38 1.39 2.65 2.61 0.81 1.33 0.86 1.33 2.58 2.91 2.60 2.64 0.85 2.68 0.91 0.91 2.69 1.29 1.28 0.85 2.77 2.80 2.75 0.89 1.35 1.36 2.73 3.2 Response surface method Table 3 Results of experimental research Run ord. 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 r (mm) 0.4 1.2 0.4 1.2 1.2 0.4 0.4 1.2 0.4 1.2 0.8 1.2 1.2 0.8 1.2 1.2 0.8 0.8 0.4 0.8 0.8 0.8 0.4 0.4 0.8 1.2 0.8 κ (°) 60 75 60 75 90 90 90 90 75 60 60 75 90 90 60 75 60 90 75 90 75 90 90 75 75 75 75 γ (°) 6 9 6 9 6 3 6 6 6 9 9 6 3 9 6 3 6 3 9 9 3 6 3 9 6 6 3 λ (°) -3 0 3 -3 0 3 0 -3 0 -3 -3 3 0 -3 -3 -3 -3 0 0 3 3 3 0 3 -3 -3 -3 Ra (μm) 2.76 0.84 2.84 0.84 0.84 2.72 2.63 0.83 2.71 0.87 1.34 0.87 0.86 1.26 0.87 0.87 1.35 1.32 2.66 1.28 1.37 1.30 2.69 2.68 1.32 0.85 1.35 Run ord. 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 r (mm) 0.4 0.4 1.2 1.2 0.4 0.8 0.8 1.2 0.8 0.8 1.2 0.8 0.8 1.2 1.2 0.8 0.8 1.2 0.8 1.2 1.2 0.8 0.4 0.4 0.4 1.2 0.4 κ (°) 60 75 60 75 60 90 75 90 75 75 90 60 90 90 60 90 60 60 60 90 60 75 60 60 90 75 60 γ (°) 3 3 9 3 6 9 9 6 9 3 9 6 6 3 3 3 3 9 3 9 6 6 9 3 9 3 9 λ (°) 0 -3 3 0 0 0 0 3 3 0 0 0 0 3 3 -3 3 0 0 3 0 3 3 -3 -3 3 -3 Ra (μm) 2.86 2.74 0.88 0.88 2.80 1.27 1.30 0.84 1.31 1.36 0.82 1.37 1.29 0.86 0.93 1.31 1.42 0.87 1.40 0.83 0.89 1.34 2.78 2.81 2.56 0.89 2.72 The experimental data (Table 3) were statistically processed using Design Expert software (version DX8, 8.0.7.1) and a regression model was derived to predict the surface roughness. Fig. 2 shows the response surface plots of surface roughness resulting from the regression model. Fig. 2 shows that changing the approach angle κ, rake angle γ, and inclination angle λ does not significantly change the surface roughness (Figs. 2a and 2c), while increasing the corner radius r significantly affects the reduction in surface roughness (Figs. 2b and 2d). Table 4 shows the ANOVA for the reduced quadratic regression model. The nonsignificant interaction terms AD, BC, BD, CD, and the quadratic term A2 as well as the terms related to interactions between the three factors and higher-order interactions have been removed. Below is the regression model in terms of the coded (Eq. 1) and the natural (actual) (Eq. 2) input variables. ln 𝑅𝑅𝑅𝑅 = 0.28 + 0.010 ∙ 𝐴𝐴 − 0.021 ∙ 𝐵𝐵 − 0.031 ∙ 𝐶𝐶 − 0.57 ∙ 𝐷𝐷 − 1.731 ∙ 10−3 ∙ 𝐴𝐴 ∙ 𝐵𝐵 − 3.286 ∙ 10−3 ∙ 𝐴𝐴 ∙ 𝐶𝐶 + 2.03 ∙ 10−3 ∙ 𝐵𝐵2 + 2.395 ∙ 10−3 ∙ 𝐶𝐶 2 + 0.14 ∙ 𝐷𝐷2 370 (1) Advances in Production Engineering & Management 17(3) 2022 Modelling surface roughness in finish turning as a function of cutting tool geometry using the response surface method … ln 𝑅𝑅𝑅𝑅 = 2.24998 + 0.010042 ∙ λ − 9.5811 ∙ 10−3 ∙ γ − 3.63354 ∙ 10−3 ∙ κ − 2.82799 ∙ 𝑟𝑟 − 1.92283 ∙ (2) 10−4 ∙ λ ∙ γ − 7.30217 ∙ 10−5 ∙ λ ∙ κ + 2.25531 ∙ 10−4 ∙ γ2 + 1.06423 ∙ 10−5 ∙ κ2 + 0.87167 ∙ 𝑟𝑟 2 Fig. 2 Response surface plots of surface roughness, a) with approach angle κ and corner radius r at the intermediate levels, b) with rake angle γ and approach angle κ at the intermediate levels, c) with rake angle γ and corner radius r at the intermediate levels, d) with inclination angle λ and rake angle γ at the intermediate levels Source Model A – inclination angle λ B – rake angle γ C – approach angle κ D – corner radius r AB AC B2 C2 D2 Residual Cor Total Table 4 ANOVA for response surface reduced quadratic model Sum of Squares 18.18 0.005657 0.023 0.050 17.75 0.0001078 0.0003887 7.416 ⋅ 10-5 0.0001032 0.35 0.0008709 18.18 DF 9 1 1 1 1 1 1 1 1 1 71 80 Mean Square 2.02 0.005657 0.023 0.050 17.75 0.0001078 0.0003887 7.416 ⋅ 10-5 0.0001032 0.35 1.227 ⋅ 10-5 F Value 164684.3 461.19 1872.60 4110.92 1447116 8.79 31.69 6.05 8.41 28543.75 p-value, Prob > F < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 0.0041 < 0.0001 0.0164 0.0050 < 0.0001 Table 5 lists the regression coefficient for each model term, their standard errors, and 95 percent confidence intervals (95 % CI). Confidence intervals are ranges within which the true regression coefficients must fall. In the table, these ranges are low for the intercept, the regression coefficients of A, B, C, D, and D2, while they are high for AB, AC, B2, and C2. However, it is important that the regression coefficients do not span zero, because that would mean that a single regression coefficient can be zero, i.e., that a particular factor has no effect. Residual analysis follows as an important technique for analyzing regression models. Fig. 3 shows the constructed normal probability plot of the internally studentized residuals to check the assumption of normality of the residuals or errors. From Fig. 3, it can be seen that the error distribution is approximately normal as the graph resembles the straight line. There are small deviations from the straight line at the extremes, but this is not the case for most of the intermediate values. It is also clear that all internally studentized residuals are within ±3 standard deviations from zero (studentized residuals have unit variance), which means that there are no outliers. This is also evident from Fig. 4, which shows the plot of internally studentized residuals against four Advances in Production Engineering & Management 17(3) 2022 371 Vukelic, Simunovic, Kanovic, Saric, Doroslovacki, Prica, Simunovic factors. Fig. 4 also shows that for the factor D (corner radius r), there is some rule for the dependence of the residuals on this factor, i.e. some pattern. Although both positive and negative internally studentized residuals occur (which is fine), there is still smaller scatter for the smaller corner radius and larger for the larger corner radius, which means that it is not a completely constant variance. This is mainly affected by only four internally studentized residuals, i.e., for the experiments labelled 5 and 42 (Run ord.) in Table 3 (the internally studentized residuals are -2.59 and 2.53, respectively) and for experiments 37 and 16 (the internally studentized residuals are 2.68 and 2.95, respectively). These samples were rechecked and it was found that there were no possible errors in the measurement or recording of the results. Table 5 Standard errors and confidence intervals for regression coefficients Coefficient Estimate DF Standard Error 95 % CI Low Intercept 0.28 1 0.281 1.030 ⋅ 10-3 A – inclination angle (λ) 0.010 1 0.00928 4.766 ⋅ 10-4 B – rake angle (γ) –0.021 1 –0.0216 4.766 ⋅ 10-4 C – approach angle (κ) –0.031 1 –0.0315 4.766 ⋅ 10-4 D – corner radius (r) –0.57 1 –0.574 4.766 ⋅ 10-4 AB 1 –1.731 ⋅ 10-3 5.837 ⋅ 10-4 –2.89 ⋅ 10-3 AC 1 –3.286 ⋅ 10-3 5.837 ⋅ 10-4 –4.45 ⋅ 10-3 B2 1 2.030 ⋅ 10-3 8.255 ⋅ 10-4 3.84 ⋅ 10-4 C2 1 2.395 ⋅ 10-3 8.255 ⋅ 10-4 7.485 ⋅ 10-4 D2 0.14 1 0.138 8.255 ⋅ 10-4 Term 95 % CI High 0.285 0.011 –0.01967 –0.0296 –0.572 –5.67 ⋅ 10-4 –2.12 ⋅ 10-3 3.68 ⋅ 10-3 4.04 ⋅ 10-3 0.141 Fig. 3 Normal probability plot of internally studentized residuals Fig. 4 Residuals versus factors, a) Residuals versus inclination angle λ, b) Residuals versus rake angle γ, c) Residuals versus approach angle κ, d) Residuals versus corner radius r 372 Advances in Production Engineering & Management 17(3) 2022 Modelling surface roughness in finish turning as a function of cutting tool geometry using the response surface method … 3.3 Decision tree regression A decision tree is a machine learning algorithm that can be used for both classification and regression. It is one of the most commonly used practical approaches for supervised learning [33]. In regression, the goal of a decision tree-based model is to predict a continuous output value for a given multivariate input data instance. The model is trained on the given training dataset 𝑚𝑚 {(𝑥𝑥𝑖𝑖 , 𝑦𝑦𝑖𝑖 )}𝑁𝑁 𝑖𝑖=1 ∈ 𝑅𝑅 × 𝑅𝑅, where 𝑥𝑥𝑖𝑖 is an m-dimensional input vector and 𝑦𝑦𝑖𝑖 is the corresponding output value. Based on this dataset, a tree-structured regression model is built, as shown in Fig. 1, which consists of three types of nodes. The root node is the initial node which represents the whole dataset. It is split into additional nodes according to the decision (or division) rules contained in both the root node and all subsequent nodes. The interior nodes represent the features of the dataset, and the branches represent the decision (i.e., division) rules. Finally, the leaf nodes represent terminal parts and provide the output results. The basic idea is to split the entire dataset into groups of "similar" samples, using decision rules contained in interior nodes, applied to input variables 𝑥𝑥𝑖𝑖 [34]. In the decision tree regression problems, the criterion for dataset splitting is the variance of the output value 𝑦𝑦𝑖𝑖 : 1 𝑣𝑣𝑣𝑣𝑣𝑣 = 𝑛𝑛 ∑𝑛𝑛1=1(𝑦𝑦𝑖𝑖 − 𝑦𝑦�)2 (3) where n is the total number of samples in the node and 𝑦𝑦� is the mean of the output values of all samples in the node. Each "parent" node is divided into two "child" nodes. All possible ways of splitting the dataset in a given node are considered, and the one that provides the greatest variance reduction defined as follows: (4) 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 = 𝑣𝑣𝑣𝑣𝑣𝑣(𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝) − ∑2𝑖𝑖=1 𝑤𝑤𝑖𝑖 𝑣𝑣𝑣𝑣𝑣𝑣(𝑐𝑐ℎ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ) is adopted. In the Eq. 4, 𝑤𝑤𝑖𝑖 is the ratio between the number of elements in the child node and the total number of elements in the parent node. In other words, we split the dataset each time into two new sets, each containing “similar” data, while at the same time the obtained sets differ as much as possible. The described process of node splitting is performed until the desired depth of the tree is reached, which depends on the complexity of the problem. Once the tree model is trained, it can be used to obtain the predicted value for each new data sample. Following the division rules for the input values xi, starting from the root node through all the interior nodes, the data sample can be grouped to one of the terminal nodes. The predicted value for that data sample is calculated as the average value of the output values yi of all the data samples from the training dataset that were grouped to that particular terminal node. In this study, the following turning process parameters were used as inputs 𝑥𝑥1 to 𝑥𝑥4: corner radius r, approach angle κ, rake angle γ, and inclination angle λ. The value of the surface roughness Ra was taken as the output parameter y. The tree model was built using Matlab and the application Regression learner, which has three variants for the tree depth according to the maximum number of splits: low, medium and fine tree. All variants were tested, and the fine tree variant, which allows a maximum of 100 splits, was adopted based on the mean square error (MSE) value in the 5fold cross-validation training procedure. The minimum number of samples per node was set at five, which was determined by a trial-and-error procedure. The cross-validation procedure was also used to remove unnecessary branches to avoid overfitting. 3.4 Gaussian process regression A Gaussian processes regression is a powerful machine learning technique that can be used to solve a wide variety of supervised learning problems, even when only a small amount of training data is available. It is a probability distribution over possible functions matching a set of points, 𝑚𝑚 given with the training dataset {(𝑥𝑥𝑖𝑖 , 𝑦𝑦𝑖𝑖 )}𝑁𝑁 𝑖𝑖=1 ∈ 𝑅𝑅 × 𝑅𝑅, as described previously. The Gaussian process regression is not given in the form of a function, but in a nonparametric form. Thus, instead of computing the probability distribution of the parameters of a specific function, GPR calculates the probability distribution over all admissible functions that fit the data in the dataset. The regression function modelled by Gaussian process regression has the following form: Advances in Production Engineering & Management 17(3) 2022 373 Vukelic, Simunovic, Kanovic, Saric, Doroslovacki, Prica, Simunovic 𝑃𝑃(𝑓𝑓|𝑋𝑋) = 𝒩𝒩(𝑓𝑓|𝜇𝜇, 𝐾𝐾) (5) [𝑚𝑚(𝑥𝑥 ], [𝑓𝑓(𝑥𝑥 [𝑥𝑥 ), ), )], ), ), )] 𝜇𝜇 = and 𝐾𝐾𝑖𝑖𝑖𝑖 = where 𝑋𝑋 = 1 , 𝑥𝑥2 , … , 𝑥𝑥𝑁𝑁 𝑓𝑓 = 1 𝑓𝑓(𝑥𝑥2 … , 𝑓𝑓(𝑥𝑥𝑁𝑁 1 𝑚𝑚(𝑥𝑥2 … , 𝑚𝑚(𝑥𝑥𝑁𝑁 𝑘𝑘�𝑥𝑥𝑖𝑖 , 𝑥𝑥𝑗𝑗 �. X are the observed input data, m represents the mean function, and K represents a positive definite kernel function, that defines the smoothness of the function, i.e., if the points 𝑥𝑥𝑖𝑖 and 𝑥𝑥𝑗𝑗 are considered similar by the kernel, the function outputs of the two points, 𝑓𝑓(𝑥𝑥𝑖𝑖 ) and 𝑓𝑓�𝑥𝑥𝑗𝑗 � are expected to be similar. Given the points of the training dataset and a mean function f estimated by these points, one can make predictions for each new dataset 𝑋𝑋∗ as 𝑓𝑓(𝑋𝑋∗ ) with a certain confidence interval depending on the values and distribution of the training dataset. The simple one-dimensional GPR regression is shown in Fig. 1. Based on the training data (black dots), the mean function is determined (green line), and it gives predictions for all new data points 𝑋𝑋∗ with the confidence interval marked in grey. If we introduce 𝑓𝑓∗ as a prediction for a new dataset 𝑋𝑋∗ , we can express the joint distribution of 𝑓𝑓 and 𝑓𝑓∗ as follows: 𝐾𝐾 𝐾𝐾∗ 𝑓𝑓 𝑚𝑚(𝑋𝑋) � � ∼ 𝒩𝒩 �� � , � 𝑇𝑇 �� (6) 𝑓𝑓∗ 𝑚𝑚(𝑋𝑋∗ ) 𝐾𝐾∗ 𝐾𝐾∗∗ where 𝐾𝐾 = 𝐾𝐾(𝑋𝑋, 𝑋𝑋), 𝐾𝐾∗ = 𝐾𝐾(𝑋𝑋, 𝑋𝑋∗ ) and 𝐾𝐾∗∗ = 𝐾𝐾(𝑋𝑋∗ , 𝑋𝑋∗ ). To be able to make a prediction, we need to derive the conditional distribution 𝑃𝑃(𝑓𝑓∗|𝑓𝑓, 𝑋𝑋, 𝑋𝑋∗ ) = 𝒩𝒩(𝑓𝑓|𝜇𝜇, 𝐾𝐾). This derivation is given in detail in [35], obtaining: (7) 𝑓𝑓∗ |𝑓𝑓, 𝑋𝑋, 𝑋𝑋∗ ∼ 𝒩𝒩(𝐾𝐾∗𝑇𝑇 𝐾𝐾 𝑓𝑓, 𝐾𝐾∗∗ − 𝐾𝐾∗𝑇𝑇 𝐾𝐾 −1 𝐾𝐾∗ ) In real applications, however, we do not need exact function values, but rather the noisy version of the data, 𝑦𝑦 = 𝑓𝑓(𝑥𝑥) + 𝜀𝜀, where we assume that 𝜀𝜀 is an additive independent and identically distributed (i.i.d.) Gaussian noise with a variance 𝜎𝜎𝑛𝑛2 that can be determined from the training dataset. The variance function then becomes cov(𝑦𝑦) = 𝐾𝐾 + 𝜎𝜎𝑛𝑛2 𝐼𝐼, and the joint distribution of the observed points (training dataset) and the function values at new dataset points: 𝑦𝑦 𝑚𝑚(𝑋𝑋) 𝐾𝐾 + 𝜎𝜎𝑛𝑛2 I 𝐾𝐾∗ �𝑓𝑓 � ∼ 𝒩𝒩 �� �,� �� 𝑚𝑚(𝑋𝑋∗ ) ∗ 𝐾𝐾∗𝑇𝑇 𝐾𝐾∗∗ (8) 𝑓𝑓∗̅ |𝑦𝑦, 𝑋𝑋, 𝑋𝑋∗ ∼ 𝒩𝒩 �𝑓𝑓∗̅ , cov(𝑓𝑓∗ )� (9) By deriving the conditional distribution, we get the predictive equations for Gaussian processes regression as follows: 𝑓𝑓∗̅ ≜ 𝔼𝔼�𝑓𝑓∗̅ |𝑦𝑦, 𝑋𝑋, 𝑋𝑋∗ � = 𝐾𝐾∗𝑇𝑇 [𝐾𝐾 + 𝜎𝜎𝑛𝑛2 𝐼𝐼]−1 𝑦𝑦 cov(𝑓𝑓∗ ) = 𝐾𝐾∗∗ − 𝐾𝐾∗𝑇𝑇 [𝐾𝐾 + 𝜎𝜎𝑛𝑛2 𝐼𝐼]−1 𝐾𝐾∗ (10) The practical implementation algorithm for Eqs. 8 to 10 is described in [35]. The best results were obtained with the quadratic exponential kernel (SE) and Matern kernel. The values of kernel parameters were optimized using marginal likelihood as the objective function [35]. 3.5 The results of the prediction Of the total 81 experiments, 72 were used for training and 9 for confirmation. Table 6 shows the results of the training dataset, and Table 7 shows the modelling results of the confirmation dataset. The strength of the modelling, i.e., the deviation between the measured Ra value (Raimv) and the predicted Ra value (Raipv), was estimated by the absolute error (AE) and the percentage error (PE) as follows: 𝐴𝐴𝐴𝐴 = �𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖𝑖𝑖 − 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖𝑖𝑖 � 𝑃𝑃𝑃𝑃 = 374 �𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖𝑖𝑖 − 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖𝑖𝑖 � ∙ 100 % 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖𝑖𝑖 (11) (12) Advances in Production Engineering & Management 17(3) 2022 1.368 1.368 2.625 2.625 0.832 1.294 0.866 1.335 2.625 2.804 2.625 0.832 2.625 0.894 0.894 2.723 1.294 0.848 2.723 2.723 2.804 0.894 1.368 1.368 2.723 2.804 0.832 2.804 0.832 2.625 0.848 2.723 1.368 0.866 0.848 1.294 0.894 0.866 1.368 1.294 2.723 1.294 1.335 1.294 2.625 2.723 1.335 0.866 1.335 2.804 2.723 0.894 0.866 1.294 1.335 0.848 1.335 1.335 0.832 1.368 0.848 0.894 1.294 0.894 1.368 0.832 0.894 1.335 2.804 2.804 2.625 2.804 1.378 1.396 2.650 2.612 0.812 1.328 0.859 1.327 2.581 2.906 2.600 0.848 2.674 0.909 0.904 2.686 1.281 0.851 2.771 2.799 2.748 0.888 1.349 1.364 2.735 2.760 0.843 2.837 0.839 2.631 0.828 2.710 1.338 0.867 0.856 1.257 0.873 0.871 1.353 1.321 2.660 1.276 1.374 1.298 2.692 2.680 1.317 0.852 1.347 2.858 2.743 0.880 0.880 1.266 1.303 0.844 1.311 1.359 0.822 1.373 0.861 0.932 1.315 0.870 1.406 0.832 0.887 1.338 2.778 2.812 2.563 2.721 1.382 1.391 2.651 2.615 0.817 1.332 0.860 1.328 2.584 2.907 2.598 0.852 2.670 0.910 0.901 2.680 1.282 0.848 2.770 2.803 2.747 0.896 1.347 1.363 2.736 2.761 0.844 2.837 0.837 2.633 0.831 2.708 1.331 0.869 0.856 1.260 0.877 0.870 1.354 1.320 2.658 1.274 1.374 1.300 2.693 2.681 1.314 0.852 1.342 2.863 2.737 0.883 0.880 1.267 1.303 0.842 1.314 1.358 0.821 1.372 0.863 0.924 1.309 0.873 1.404 0.825 0.889 1.341 2.780 2.820 2.571 2.715 0.906 1.619 0.943 0.575 2.675 2.726 0.698 0.376 1.744 3.651 0.962 2.157 2.052 1.786 1.786 1.208 1.074 0.235 1.715 2.768 1.955 0.421 1.296 0.551 0.275 1.585 0.992 1.276 0.992 0.190 2.169 0.461 2.052 0.460 1.395 2.679 2.730 0.460 1.296 1.989 2.350 1.074 2.555 0.481 2.416 1.586 1.136 1.882 1.111 1.967 0.639 1.562 1.591 1.870 2.692 0.952 1.908 1.838 1.423 0.182 1.395 3.898 1.240 2.730 2.321 0.201 0.421 0.373 0.854 0.222 2.539 3.079 Advances in Production Engineering & Management 17(3) 2022 0.139 0.464 0.001 0.077 0.191 0.149 0.072 0.263 0.043 0.135 0.017 0.191 0.224 0.117 0.628 0.139 0.070 0.116 0.023 0.025 0.064 0.229 0.105 0.286 0.181 0.015 0.364 0.091 0.144 0.032 0.220 0.001 0.180 0.327 0.450 0.223 0.313 0.122 0.188 0.086 0.004 0.318 0.278 0.172 0.067 0.009 0.240 0.240 0.229 0.079 0.109 0.009 0.012 0.344 0.202 0.520 0.068 0.054 0.203 0.192 0.074 0.210 0.417 0.043 0.403 0.215 0.283 0.120 0.063 0.063 0.108 0.047 0.170 0.060 0.046 0.177 0.835 0.142 0.039 0.175 0.168 0.107 0.082 0.200 0.377 0.052 0.960 0.354 0.146 0.210 0.004 0.123 0.101 0.648 0.231 0.210 0.217 0.043 0.534 0.110 0.317 0.108 0.078 0.072 0.665 0.093 0.511 0.034 0.830 0.048 0.276 0.029 0.069 0.496 0.325 0.015 0.118 0.032 0.443 0.185 0.597 0.101 0.104 0.356 0.005 0.234 0.248 0.271 0.332 0.140 0.126 0.157 0.357 0.698 0.078 0.319 0.257 0.563 0.095 0.100 0.007 0.341 0.425 0.183 0.013 0.023 0.025 0.015 0.022 0.036 0.006 0.005 0.045 0.106 0.025 0.018 0.055 0.016 0.016 0.033 0.014 0.002 0.047 0.077 0.054 0.004 0.017 0.007 0.007 0.044 0.008 0.036 0.008 0.005 0.018 0.013 0.027 0.004 0.012 0.034 0.024 0.004 0.017 0.026 0.063 0.014 0.035 0.006 0.065 0.043 0.015 0.016 0.015 0.056 0.018 0.014 0.014 0.024 0.035 0.008 0.025 0.025 0.012 0.003 0.012 0.036 0.016 0.024 0.033 0.002 0.004 0.005 0.024 0.006 0.065 0.084 AE (μm) 0.002 0.006 0.000 0.002 0.002 0.002 0.001 0.003 0.001 0.004 0.000 0.002 0.006 0.001 0.006 0.004 0.001 0.001 0.001 0.001 0.002 0.002 0.001 0.004 0.005 0.000 0.003 0.003 0.001 0.001 0.002 0.000 0.002 0.003 0.004 0.003 0.003 0.001 0.003 0.001 0.000 0.004 0.004 0.002 0.002 0.000 0.003 0.002 0.003 0.002 0.003 0.000 0.000 0.004 0.003 0.004 0.001 0.001 0.002 0.003 0.001 0.002 0.005 0.000 0.006 0.002 0.003 0.002 0.002 0.002 0.003 0.001 0.000 0.005 0.000 0.003 0.003 0.001 0.000 0.002 0.001 0.002 0.001 0.001 0.005 0.002 0.005 0.003 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.003 0.003 0.000 0.003 0.003 0.002 0.001 0.001 0.001 0.002 0.002 0.003 0.004 0.001 0.000 0.003 0.001 0.000 0.004 0.004 0.001 0.002 0.000 0.002 0.002 0.003 0.003 0.003 0.001 0.000 0.003 0.003 0.003 0.001 0.001 0.002 0.001 0.000 0.001 0.003 0.000 0.006 0.000 0.003 0.002 0.001 0.001 0.002 0.001 RSM GPRMat GPR-SE RSM GPRMat 0.025 0.391 0.004 0.110 0.318 0.084 0.047 0.185 0.049 0.061 0.039 0.120 0.180 0.171 0.543 0.103 0.047 0.062 0.024 0.027 0.043 0.168 0.117 0.230 0.117 0.008 0.307 0.111 0.215 0.028 0.102 0.021 0.139 0.214 0.300 0.349 0.160 0.024 0.203 0.073 0.007 0.306 0.283 0.103 0.062 0.007 0.128 0.181 0.206 0.101 0.093 0.089 0.001 0.268 0.232 0.394 0.058 0.078 0.224 0.098 0.021 0.130 0.255 0.015 0.399 0.012 0.284 0.134 0.037 0.047 0.074 0.041 DTR PE (%) GPR-SE RSM GPRMat 1.380 1.395 2.650 2.613 0.813 1.329 0.860 1.328 2.581 2.908 2.601 0.849 2.675 0.908 0.905 2.687 1.281 0.851 2.769 2.799 2.749 0.889 1.348 1.363 2.733 2.760 0.843 2.837 0.838 2.631 0.829 2.709 1.338 0.868 0.857 1.256 0.871 0.870 1.353 1.321 2.660 1.276 1.374 1.299 2.692 2.680 1.318 0.852 1.347 2.857 2.743 0.881 0.880 1.267 1.303 0.843 1.311 1.359 0.822 1.371 0.860 0.931 1.313 0.870 1.406 0.830 0.887 1.338 2.779 2.811 2.562 2.721 DTR Ra (μm) GPR-SE -3 3 3 -3 -3 3 0 0 0 3 3 3 -3 0 3 -3 -3 -3 0 3 0 -3 0 3 3 -3 0 3 -3 0 -3 0 -3 3 0 -3 -3 -3 -3 0 0 3 3 3 0 3 -3 -3 -3 0 -3 3 0 0 0 3 3 0 0 0 3 3 -3 0 0 3 0 3 3 -3 -3 -3 3 6 6 6 9 3 6 6 9 3 9 9 3 3 6 6 6 3 3 3 9 3 9 9 6 6 9 6 9 6 6 6 9 6 3 9 6 3 6 3 9 9 3 6 3 9 6 6 3 3 3 9 3 9 9 6 9 3 9 6 3 3 3 9 3 9 6 6 9 3 9 9 Table 6 Modelling results of the training dataset DTR λ (°) 60 60 90 90 90 90 75 75 90 60 90 75 90 60 60 75 90 90 75 75 60 60 60 60 75 60 75 60 75 90 90 75 60 75 90 90 60 75 60 90 75 90 75 90 90 75 75 75 75 60 75 60 75 90 75 90 75 75 90 60 90 60 90 60 60 90 60 75 60 60 90 60 0.8 0.8 0.4 0.4 1.2 0.8 1.2 0.8 0.4 0.4 0.4 1.2 0.4 1.2 1.2 0.4 0.8 1.2 0.4 0.4 0.4 1.2 0.8 0.8 0.4 0.4 1.2 0.4 1.2 0.4 1.2 0.4 0.8 1.2 1.2 0.8 1.2 1.2 0.8 0.8 0.4 0.8 0.8 0.8 0.4 0.4 0.8 1.2 0.8 0.4 0.4 1.2 1.2 0.8 0.8 1.2 0.8 0.8 1.2 0.8 1.2 1.2 0.8 1.2 0.8 1.2 1.2 0.8 0.4 0.4 0.4 0.4 γ (°) κ (°) 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 19 20 21 22 23 24 25 26 27 28 29 30 31 34 35 36 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 60 61 62 63 64 65 66 68 69 70 72 73 74 75 76 77 78 79 81 r (mm) Run ord. Modelling surface roughness in finish turning as a function of cutting tool geometry using the response surface method … 0.002 0.001 0.001 0.005 0.007 0.002 0.000 0.002 0.004 0.003 0.002 0.002 0.010 0.000 0.009 0.010 0.002 0.002 0.000 0.003 0.003 0.006 0.003 0.003 0.006 0.001 0.004 0.003 0.003 0.003 0.001 0.002 0.009 0.001 0.004 0.000 0.007 0.000 0.004 0.000 0.002 0.006 0.004 0.000 0.003 0.001 0.006 0.002 0.008 0.003 0.003 0.003 0.000 0.003 0.003 0.002 0.004 0.002 0.001 0.002 0.003 0.006 0.001 0.003 0.004 0.005 0.001 0.001 0.000 0.010 0.011 0.005 375 2.723 1.335 0.848 2.625 0.894 2.804 1.294 1.368 0.866 2.642 1.297 0.837 2.710 0.863 2.798 1.289 1.437 0.889 2.642 1.298 0.838 2.711 0.863 2.797 1.290 1.439 0.888 2.636 1.292 0.836 2.717 0.863 2.799 1.291 1.425 0.891 3.125 3.488 0.952 3.493 2.730 0.134 0.291 3.697 2.697 0.065 0.557 0.407 0.374 0.749 0.082 0.100 1.192 0.097 0.065 0.581 0.244 0.325 0.859 0.121 0.025 1.364 0.186 0.165 0.169 0.423 0.123 0.857 0.044 0.063 0.364 0.072 0.083 0.045 0.008 0.095 0.024 0.004 0.004 0.053 0.024 0.002 0.007 0.003 0.010 0.007 0.002 0.001 0.017 0.001 0.002 0.008 0.002 0.009 0.007 0.003 0.000 0.019 0.002 RSM GPR-Mat AE (μm) GPR-SE DTR RSM GPR-Mat PE (%) GPR-SE DTR RSM GPR-Mat -3 -3 0 3 -3 0 0 3 3 9 9 6 3 9 6 6 3 3 Ra (μm) GPR-SE λ (°) 75 75 90 90 60 60 90 60 75 Table 7 Modelling results of the confirmation dataset DTR κ (°) 12 18 32 33 37 59 67 71 80 0.4 0.8 1.2 0.4 1.2 0.4 0.8 0.8 1.2 γ (°) Run r (mm) Vukelic, Simunovic, Kanovic, Saric, Doroslovacki, Prica, Simunovic 0.004 0.002 0.004 0.003 0.007 0.001 0.001 0.005 0.001 4. Discussion The descriptive parameters of surface roughness for the experimental tests performed are listed in Table 8. The surface roughness ranges from 0.81 μm to 2.91 μm, with an average value of 1.64 μm and a standard deviation of 0.795 μm. The lowest roughness value (Ra = Ramin = 0.81 μm) was obtained when machining with the largest values for the corner radius (r = rmax = 1.2 mm), the largest approach angle (κ = κmax = 90°), the largest rake angle (γ = γmax = 9°), and the smallest inclination angle (λ = λmin = -3°) of the turning insert. The highest roughness value (Ra = Ramax = 2.91 μm) was obtained when machining with the smallest values of corner radius (r = rmin = 0.4 mm), the smallest approach angle (κ = κmin = 60°), the smallest rake angle (γ = γmin = 3°) and the largest inclination angle (λ = λmax = 3°) of the turning insert. The ratio values show that the arithmetical mean roughness changes in a wide range for suitable geometrical parameters, which ensures good process control. In other words, the desired quality of the machined surface can be achieved by a suitable choice of input parameters. The identified trends of the dependence of Ra on the input variables are consistent with some previous studies. Feed rate and corner radius have the greatest effect on surface roughness. The roughness of the machined surface decreases (improves) in the following cases: with increasing corner radius [5, 11, 12, 16, 20, 21]; with an increase in positive values of the rake angle [8, 11, 18, 19]; with an increase in the approach angle [5, 8-10, 18], and with the reduction of inclination angle [18], although to varying degrees with different combinations. The results are different, but the trend is identical. Some of the studies also reported the opposite. Surface roughness can also deteriorate (increase) under certain experimental conditions with increasing corner radius [9], smaller approach angle [9, 19], with smaller rake angle [10], and with increasing positive values of inclination angle [19]. Under certain machining conditions, roughness first increases and then decreases with increasing inclination angle [8] and in some cases it first decreases and then increases with increasing inclination angle [12]. Parameter Minimum value Maximum value Mean value Standard deviation Ratio Table 8 Descriptive parameters of the surface roughness Ra Training Ra (μm) Confirmation Ra (μm) 0.810 0.848 2.910 2.804 1.637 1.639 0.795 0.834 3.593 3.306 The reduction in roughness at a larger corner radius is a result of the lower and shallower peak height and the lower and shallower valley depth of the machined surface. Higher values of approach angle and positive inclination angle result in lower susceptibility to vibration and thus better quality of the machined surface. Increasing the rake angle improves the sharpness of the cutting edge and thus reduces the roughness of the machined surface. When the approach angle decreases, the contact length of the chip increases, the chip thickness decreases and the chip width increases. The cutting forces are distributed over the longer cutting edge and chip breaking is more difficult. Larger approach angles are characterized by an increase in resistance to auxiliary 376 Advances in Production Engineering & Management 17(3) 2022 Modelling surface roughness in finish turning as a function of cutting tool geometry using the response surface method … movements and a decrease in penetration resistance, as well as a lower tendency to vibration. In the present study, increasing the approach angle resulted in a reduction in roughness, mainly due to minimization of vibration. Reducing the cutting forces reduces the possibility of vibration and thus improving the surface roughness. A negative value of the inclination angle directs chips in the direction of workpiece (in the direction of auxiliary motion) and a positive value directs them in the opposite direction (in the direction opposite to the direction of auxiliary motion). A negative inclination angle increases the cutting edge strength, but also the back force of the cutting resistance, which can lead to chattering. In the present study, negative values of the inclination angle improved surface roughness by increasing cutting edge strength (and reducing the occurrence of various wear mechanisms) and did not affect vibration induction. During turning, the tool tip is exposed to high contact pressures and temperatures in the machining zone, which can increase various wear mechanisms. The smaller corner radius is characterized by lower strength and the larger one by higher strength. The poorest surface finish was obtained with the smallest corner radius. This is due to the low strength of the tool tip and the resulting higher wear rate. The shorter contact length between the tool tip and the workpiece results in less heat dissipation from the shear zone and a higher concentration of heat and stress in this zone. This increases the possibility of tool wear and even thermoplastic deformation of the tool tip. The visual interpretation of the absolute and percentage errors for all experiments performed (for the training dataset and the confirmation dataset) is shown in Fig. 5, and the minimum, maximum, and mean values for both datasets are shown in Table 9. Fig. 5 Visual representation of absolute and percentage errors Table 9 The percentage and absolute errors of the training and confirmation datasets DTR GPR-SE GPR-Mat RSM Experiment Value PE AE PE AE PE AE PE AE (%) (μm) (%) (μm) (%) (μm) (%) (μm) Minimum 0.182 0.002 0.001 0.000 0.001 0.000 0.004 0.000 Training Maximum 3.898 0.106 0.628 0.006 0.543 0.006 0.960 0.011 Mean 1.491 0.025 0.168 0.002 0.137 0.002 0.241 0.003 Minimum 0.134 0.004 0.065 0.001 0.025 0.000 0.044 0.001 Confirmation Maximum 3.697 0.095 1.192 0.017 1.364 0.019 0.857 0.007 Mean 2.290 0.038 0.403 0.006 0.419 0.006 0.253 0.003 • Based on Fig. 5 and Table 9, the following can be concluded: The DTR model had a PE of less than 1 % for 28 predictions, a PE of between 1% and 2 % for 28 predictions, a PE of between 2 % and 3 % for 18 predictions, and a PE of between 3 % and Advances in Production Engineering & Management 17(3) 2022 377 Vukelic, Simunovic, Kanovic, Saric, Doroslovacki, Prica, Simunovic • • • 4 % for 7 predictions. The absolute error for all predictions except one (AEmax = 0.106 μm) was less than 0.1 μm. The maximum error values occur during training. The minimum and mean error values also occur during training. The model GPR-SE had a PE of less than 1 % and an AE of less than 0.02 μm (AEmax = 0.017 μm) for all predictions except one (PEmax = 1.192 %). The maximum error values occur at confirmation. The minimum and mean error values occur during training. The GPR-Mat model had a PE of less than 1 % and an AE of less than 0.02 μm (AEmax = 0.019 μm) for all predictions except one (PEmax = 1.364 %). The maximum error values occur at confirmation. The minimum and mean error values occur during training. The RSM model had a PE of less than 1 % (PEmax = 0.960 %) and an AE of less than 0.02 μm (AEmax = 0.011 μm) for all predictions. The maximum error values occur during training. The minimum and average error values also occur during training. The GPR-SE, GPR-Mat, and RSM models conditionally gave slightly better results, while the DTR model gave slightly worse results. Moreover, the errors in the confirmation experiments are consistent with those of PE during the training phase, indicating that the modelling was performed correctly. The extremely low values of the maximum PE errors and, most importantly, the correspondingly small values of AE (which give a real deviation from the desired value of the surface roughness) show the real possibilities of practical application of all four models in practice. 5. Conclusion In this study, the integral influence of four parameters of CVD coated cutting tool geometry (corner radius r, approach angle κ, rake angle γ and inclination angle λ on surface roughness of C45 steel workpiece during finish turning was evaluated. Four models were developed based on the experimental results. Confirmation experiments were conducted to validate the model. The experimental results show that the surface roughness improves with a simultaneous increase in corner radius r, approach angle κ, and rake angle γ, and a decrease in inclination angle λ. The corner radius r has a dominant effect on roughness, followed by the approach angle κ with less effect on surface roughness, the rake angle γ even less and the inclination angle λ with the least. Based on the experimental results, the modelling of the finish turning process was performed using DTR, GPR-SE, GPR-Mat and RSM. The maximum percentage errors of the developed models were 3.898 %, 1.192 %, 1.364 % and 0.960 % for DTR, GPR-SE, GPR-Mat and RSM, respectively. In the worst case, the maximum absolute errors were 0.106 μm, 0.017 μm, 0.019 μm, and 0.011 μm for DTR, GPR-SE, GPR-Mat, and RSM, respectively. The obtained errors are in the order of tenths and hundredths of micrometers, and in most cases are many times smaller than the allowable processing tolerances in production. Based on the above, all four models can be considered acceptable. Therefore, the developed models can be used in practice as an aid for engineers in selecting the geometrical parameters of the cutting tool during the process planning in order to obtain the required surface roughness. Future research will focus on studying the influence of various cutting tool geometry factors on surface roughness, inclusion and analysis of other output parameters, and multi-objective optimization of the finish turning process. In addition, future research will consider the other parameters that also affect surface roughness. The integration of a larger number of factors in the model will increase the universality of its application and the accuracy, which is very important in the finish turning, where the influence of all variables is particularly pronounced. One of the future research directions will also be the modelling of surface roughness in finish turning as a function of the geometry of the cutting tool using other methods, as well as the comparison of the results obtained in order to choose the most suitable method for specific machining conditions. 378 Advances in Production Engineering & Management 17(3) 2022 Modelling surface roughness in finish turning as a function of cutting tool geometry using the response surface method … Acknowledgement This research was funded by the University of Slavonski Brod, Mechanical Engineering Faculty in Slavonski Brod, Republic of Croatia (grant number SV001) and by the Ministry of Education, Science and Technological Development of Republic of Serbia (grant number 451-03-68/2022-14/200156). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] Kramar, D., Cica, D. (2021). Modeling and optimization of finish diamond turning of spherical surfaces based on response surface methodology and cuckoo search algorithm, Advances in Production Engineering & Management, Vol. 16, No. 3, 326-334, doi: 10.14743/apem2021.3.403. Sterpin Valic, G., Cukor, G., Jurkovic, Z., Brezocnik, M. (2019). Multi-criteria optimization of turning of martensitic stainless steel for sustainability, International Journal of Simulation Modelling, Vol. 18, No. 4, 632-642, doi: 10.2507/IJSIMM18(4)495. Ratnam, M.M. (2017). 1.1 Factors affecting surface roughness in finish turning, In: Hashmi, M.S.J. (ed.), Comprehensive materials finishing, Elsevier, Oxford, United Kingdom, 1-25, doi: 10.1016/B978-0-12-803581-8.09147-5. Kang, W.T., Derani, M.N., Ratnam, M.M. (2020). Effect of vibration on surface roughness in finish turning: Simulation study, International Journal of Simulation Modelling, Vol. 19, No. 4, 595-606, doi: 10.2507/IJSIMM19-4-531. Zerti, O., Yallese, M.A., Khettabi, R., Chaoui, K., Mabrouki, T. (2017). Design optimization for minimum technological parameters when dry turning of AISI D3 steel using Taguchi method, International Journal of Advanced Manufacturing Technology, Vol. 89, 1915-1934, doi: 10.1007/s00170-016-9162-7. Davoudinejad, A., Noordin, M.Y. (2014). Effect of cutting edge preparation on tool performance in hard-turning of DF-3 tool steel with ceramic tools, Journal of Mechanical Science and Technology, Vol. 28, 4727-4736, doi: 10.1007/s12206-014-1039-9. Zhao, T., Zhou, J.M., Bushlya, V., Ståhl, J.E. (2017). Effect of cutting edge radius on surface roughness and tool wear in hard turning of AISI 52100 steel, International Journal of Advanced Manufacturing Technology, Vol. 91, 36113618, doi: 10.1007/s00170-017-0065-z. Duc, P.M., Giang, L.H., Dai, M.D., Sy, D.T. (2020). An experimental study on the effect of tool geometry on tool wear and surface roughness in hard turning, Advances in Mechanical Engineering, Vol. 12, No. 9, 1-11, doi: 10.1177/1687814020959885. Neşeli, S., Yaldız, S., Türkeş, E. (2011). Optimization of tool geometry parameters for turning operations based on the response surface methodology, Measurement, Vol. 44, No. 3, 580-587, doi: 10.1016/j.measurement.2010.11. 018. Ashish George, J., Lokesha, K. (2019). Optimisation and effect of tool rake and approach angle on surface roughness and cutting tool vibration, SN Applied Sciences, Vol. 1, Article No. 1133, doi: 10.1007/s42452-019-1175-z. Karim, Z., Azuan, S.A.S., Yasir, A. (2013). A study on tool wear and surface finish by applying positive and negative rake angle during machining, Australian Journal of Basic and Applied Sciences, Vol. 7, No. 10, 46-51. Kumar, S., Singh, D., Kalsi, N.S. (2019). Investigating the effect of approach angle and nose radius on surface quality of Inconel 718, Journal of The Institution of Engineers (India): Series C, Vol. 100, 121-128, doi: 10.1007/s40032017-0411-9. Cui, X., Guo, J., Zheng, J. (2016). Optimization of geometry parameters for ceramic cutting tools in intermittent turning of hardened steel, Materials & Design, Vol. 92, 424-437, doi: 10.1016/j.matdes.2015.12.089. Sung, A.N., Loh, W.P., Ratnam, M.M. (2016). Simulation approach for surface roughness interval prediction in finish turning, International Journal of Simulation Modelling, Vol. 15, No. 1, 42-55, doi: 10.2507/IJSIMM15(1)4.320. Ponugoti, U., Dantuluri, R.R., Koka, N.S.S., Bhuvanagiri, R.S. (2020). Experimental investigations on the influence of cutting and tool geometry parameters over the machinability of AISI 52100 steel in hard turning, International Journal of Modern Manufacturing Technologies, Vol. 12, No. 1, 144-156. Senthilkumar, N., Tamizharasan, T. (2014). Effect of tool geometry in turning AISI 1045 steel: experimental investigation and FEM analysis, Arabian Journal for Science and Engineering, Vol. 39, 4963-4975, doi: 10.1007/s13369014-1054-2. Tauhiduzzaman, M., Veldhuis, S.C. (2014). Effect of material microstructure and tool geometry on surface generation in single point diamond turning, Precision Engineering, Vol. 38, No. 3, 481-491, doi: 10.1016/j.precisioneng.2014.01.002. Abainia, S., Ouelaa, N. (2015). Experimental study of the combined influence of the tool geometry parameters on the cutting forces and tool vibrations, International Journal of Advanced Manufacturing Technology, Vol. 79, 11271138, doi: 10.1007/s00170-015-6885-9. Mohammad, R., Ariffin, M.K.A.M., Baharuddin, B.T.H.T., Mustapha, F., Aoyama, H. (2017). The effects of single cutting tool geometry on surface roughness, Journal of Mechanical Engineering, Vol. 3, No. 1, 45-54. Hai, S., Jung, H.-C., Shim, W.-H., Shin, H.-G. (2021). Investigation of surface quality for minor scale diameter of biodegradable magnesium alloys during the turning process using a different tool nose radius, Metals, Vol. 11, No. 8, Article No. 1174, doi: 10.3390/met11081174. Khellaf, A., Aouici, H., Smaiah, S., Boutabba, S., Yallese, M.A., Elbah, M. (2017). Comparative assessment of two ceramic cutting tools on surface roughness in hard turning of AISI H11 steel: Including 2D and 3D surface topography, International Journal of Advanced Manufacturing Technology, Vol. 89, 333-354, doi: 10.1007/s00170-0169077-3. Advances in Production Engineering & Management 17(3) 2022 379 Vukelic, Simunovic, Kanovic, Saric, Doroslovacki, Prica, Simunovic [22] Özdemir, M. (2020). Modelling and prediction of effect of machining parameters on surface roughness in turning operations, Tehnički Vjesnik – Technical Gazette, Vol. 27, No. 3, 751-760, doi: 10.17559/TV-20190320104114. [23] Kuntoğlu, M., Aslan, A., Pimenov, D.Y., Giasin, K., Mikolajczyk, T., Sharma, S. (2020). Modeling of cutting parameters and tool geometry for multi-criteria optimization of surface roughness and vibration via response surface methodology in turning of AISI 5140 steel, Materials, Vol. 13, No. 19, Article No. 4242, doi: 10.3390/ma13194242. [24] Šarić, T., Vukelić, D., Šimunović, K., Svalina, I., Tadić, B., Prica, M., Šimunović, G. (2020). Modelling and prediction of surface roughness in CNC turning process using neural networks, Tehnički Vjesnik – Technical Gazette, Vol. 27, No. 6, 1923-1930, doi: 10.17559/TV-20200818114207. [25] Zhang, P., Liu, Z. (2016). Modeling and prediction for 3D surface topography in finish turning with conventional and wiper inserts, Measurement, Vol. 94, 37-45, doi: 10.1016/j.measurement.2016.07.080. [26] Benardos, P.G., Vosniakos, G.-C. (2003). Predicting surface roughness in machining: A review, International Journal of Machine Tools and Manufacture, Vol. 43, No. 8, 833-844, doi: 10.1016/S0890-6955(03)00059-2. [27] Sousa, V.F.C., Silva, F.J.G. (2020). Recent advances in turning processes using coated tools –A comprehensive review, Metals, Vol. 10, No. 2, Article No. 170, doi: 10.3390/met10020170. [28] Dureja, J.S., Gupta, V.K., Sharma, V.S., Dogra, M., Bhatti, M.S. (2016). A review of empirical modeling techniques to optimize machining parameters for hard turning applications, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, Vol. 230, No. 3, 389-404, doi: 10.1177/0954405414558731. [29] He, C.L., Zong, W.J., Zhang, J.J. (2018). Influencing factors and theoretical modeling methods of surface roughness in turning process: State-of-the-art, International Journal of Machine Tools and Manufacture, Vol. 129, 15-26, doi: 10.1016/j.ijmachtools.2018.02.001. [30] Puh, F., Jurkovic, Z., Perinic, M., Brezocnik, M., Buljan, S. (2016). Optimization of machining parameters for turning operation with multiple quality characteristics using Grey relational analysis, Tehnički Vjesnik – Technical Gazette, Vol. 23, No. 2, 377-382, doi: 10.17559/TV-20150526131717. [31] Trung, D.D., Thinh, H.X. (2021). A multi-criteria decision-making in turning process using the MAIRCA, EAMR, MARCOS and TOPSIS methods: A comparative study, Advances in Production Engineering & Management, Vol. 16, No. 4, 443-456, doi: 10.14743/apem2021.4.412. [32] Savićević, S., Vukćević, M., Klimenko, S.A., Tanović, L. (2017). Impact of cutting elements on forces and roughness of surface during turning hard steel X160 CrMo V12 with CBN tool, Tehnički Vjesnik – Technical Gazette, Vol. 24, No. 4, 1001-1006, doi: 10.17559/TV-20161013100743. [33] Ortuño, F.M., Valenzuela, O., Prieto, B., Saez-Lara, M.J., Torres, C., Pomares, H., Rojas, I. (2015). Comparing different machine learning and mathematical regression models to evaluate multiple sequence alignments, Neurocomputing, Vol. 164, 123-136, doi: 10.1016/j.neucom.2015.01.080. [34] Breiman, L., Friedman, J., Olshen, R.A., Stone, C.J (1984). Classification and regression trees, First edition, CRC Press, Boca Raton, Florida, USA, doi: 10.1201/9781315139470. [35] Rasmussen, C.E., Williams, C.K.I. (2006). Gaussian processes for machine learning, MIT Press, Cambridge, United Kingdom, doi: 10.7551/mitpress/3206.001.0001. 380 Advances in Production Engineering & Management 17(3) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 3 | September 2022 | pp 381–393 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.3.443 Original scientific paper Multi-objective Intuitionistic Fuzzy Linear Programming model for optimization of industrial closed-loop supply chain network Kousar, S.a, Batool, M.a, Kausar, N.b, Pamucar, D.c, Ozbilge, E.d,*, Tantay, B.d aInternational Islamic University Islamabad, Department of Mathematics and Statistics, Pakistan Technical University, Faculty of Arts and Sciences, Department of Mathematics, Istanbul, Turkey cUniversity of Belgrade, Faculty of Organizational Sciences, Belgrade, Serbia dAmerican University of the Middle East, Department of Mathematics and Statistics, Egaila, Kuwait bYildiz ABSTRACT ARTICLE INFO The urge to remanufacture and address environmental concerns in various industrial processes has drawn the attention of academics as well as practitioners towards Closed-loop Supply Chain Networks (CLSC). Although everchanging and complex external factors including social and economic ones, adversely impact the sustainable development of closed-loop supply chain networks. The basic aim of the research is to optimize the functioning of CLSC networks. For the above-said, two objective functions are made. The first objective is to minimize the cost of production and assembly expenses of the forward and reverse logistics. Secondly, an endeavour has been made to reduce the fixed costs associated with plants and retailers. For the sake of achieving two objective functions, two methods are employed: triangular fuzzy numbers and triangular intuitionistic fuzzy numbers. Among the two methods, triangular intuitionistic fuzzy numbers achieved the said objectives with greater optimization substantiated by statistics. This method can deal with uncertain external factors without undermining the optimization of the CLSC networks. Keywords: Supply chain; Closed-loop supply chain; Multi-objective linear programming; Modelling; Optimization; Fuzzy logic; Intuitionistic fuzzy numbers *Corresponding author: ebru.kahveci@aum.edu.kw (Ozbilge, E.) Article history: Received 7 March 2022 Revised 12 September 2022 Accepted 17 September 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction In human surroundings have a significant impact on daily routines. Environmental policies are associated with sustainable development. Clean environments have positive effects on mental and physical health. Technically and logically, policies are necessary to address environmental challenges. Currently, the reduction of pollution generated by industrial activities is under significant environmental and political pressure [1]. All developed and underdeveloped countries are developing strategies and modifying their plans of action so that their surplus can be recycled. Developing countries face challenges in finding ways out of poverty for their poorest citizens to provide better standards of living for their people. This necessitates providing opportunities for all by increasing industrial output through a series of changes, including the use of by-products 381 Kousar, Batool, Kausar, Pamucar, Ozbilge, Tantay [2]. Most large corporations use their waste materials as raw materials for other processes rather than considering their residues as waste products. Waste management is key in any economy, but as the world shifts toward a more sustainable and circular economy, end-of-life options are begin enhanced [3]. The recognition that all wastes are resources and perhaps more appropriately referred to as by-products or non-product outputs is also notable [4]. Excessive return of product flow from consumers to suppliers over a wide range becomes a concern. A supply chain (SC) network is introduced to bring in raw materials and inventory of end products, and transform these materials for the utilisation of retailers. Returns have been viewed as annoyance for manufacturers, suppliers, and distributors. Successful policies and systems for inventory returns result in higher sales, reduced prices, better profitability, and improved consumer service levels [5]. Designing a supply chain network has become a necessity. Owing to government policies and societal appetites for environmental awareness, the supply chain network has acquired enormous importance. With the ongoing pressure to cut prices, environmental issues, high levels of uncertainty, and many other challenges can be successfully controlled by supply chains. The creation of a commodity delivery strategy for supply chain (SC) networks is also a dynamic activity [6]. The primary goal of the supply chain is to reduce costs and improve the efficiency of supply chain enterprises to maximise economic benefits. The traditional supply chain starts with the supplier and ends with users. Closed-loop Supply Chain (CLSC) pattern is divided into two main parts: (a) Forward flow and (b) Reverse Flow. Integrating forward and reverse logistics delivers strong outcomes such as increasing customer loyalty and boosting revenue through change [7]. Internally, companies analyse logistics services on interest discernment using an appropriate model. Aleksic et al. [8] proposed a model which illustrates the failure mode and effects analysis (FMEA) and a case study technique to analyse the productivity of fuzzy logic, and many interdependent challenges related to the reverse supply chain (RSC) were resolved by implementing analysis for long-range production. Many successful organisations have realised that an effective product return strategy significantly enhances costs which is a major aspect of reverse logistics. Reverse logistics covers returns and various other operations pertaining to "backward" products in the supply chain [9]. Many countries have become increasingly aware of the role of handling reverse flows in supply chains along with forward flows. Multi-objective supply chain models are requisite variations of numerous objectives. Optimal supply chain models are essential for the success of industrial network [10]. The stock flow is circular and reversible throughout the closed-loop, and all goods are handled over the entire life cycle [11, 12]. The business environment is continuously changing because the diversification of returned products. This diversification of commodities is related to an increase in operating expenses and a reduction in revenue. Therefore, ensuring the profitability and long-term sustainability of the company, the proper use of returned goods is a key strategic decision [13]. For the competency and proper management of returned products, companies try their best to reduce production costs while keeping customer satisfaction in mind. Sustainable supply chain networks are used to address broad range of economic issues to overcome uncertainty. Fuzzy multi-objective models are ideally suited to solving supply chains [14]. A careful assessment is needed for plants and refurbishing centers that can maintain a CLSC process in a timely manner. Most of the time, supplier strengths and weaknesses vary, which highly affects the closed-loop supply chain process. Many studies on the closed-loop supply chain process have used mathematical programming under uncertain situations owing to societal demands for environmental consciousness [15]. Closed-loop supply chain viability aimed at promoting product circulation flow from production to marketing and then reutilisation and remanufacturing. Duan et al. [16] discussed that a large amount of waste material has a considerable impact on production. In pandemic Covid-19 the closed-loop supply chain models lead the entrepreneur to a more valuable and relatively well-balanced economic state. A smooth method of return is better for companies. Thus, returned products are productive for various purposes. In the real world, we deal with vagueness at a certain level, and the uncertainty of the remanufacturing system plays a strategic role in directing a product [17]. Therefore, we deal with such uncertainties using a fuzzy set, which was first introduced by Zadeh [18]. The fuzzy set is defined by the membership degree for all its intactness. The IFS is characterised by a member382 Advances in Production Engineering & Management 17(3) 2022 Multi-objective Intuitionistic Fuzzy Linear Programming model for optimization of industrial closed-loop supply chain … ship function and a non-membership function, such that the sum of both values lies between zero and one. Any model parameter can only be approximately calculated in real-world problems. Fuzzy models have the ability to model the subjective imagination of a maker as accurately as a decision-maker would describe them. Moreover, fuzzy models help to reduce information costs. The general model for fuzzy linear programming problems includes fuzziness in the coefficients and the accomplishment of the constraints. It is possible to reformulate fuzzy constraints in such a way that they can be solved as a normal linear programming problem. The concept of an intuitionist fuzzy set [19] was explored and introduced in various areas. The intuitionistic fuzzy set/number has also recently been applied in fuzzy optimization, and measures of possibility, precondition, and integrity have a significant role in the optimization of fuzzy theory [20]. Fuzzy linear programming was further examined in decision-making and management problems under uncertain circumstances to obtain an optimal solution [21]. The remaining paper is organised as follows. Section 2 presents all the basic and essential concepts used to develop the optimisation of fuzzy multi-objective linear programming. In Section 3, we formulate the general model of multi-objective fuzzy closed-loop supply chain network, and an interactive fuzzy approach to solve the problem is outlined in Section 4. Finally, concluding remarks and suggestions for further research are presented in Section 5. 2. Preliminaries 2.1 Fuzzy set According to Zadeh [18], a fuzzy set presents a convenient point for the construction of a logical framework which might be parallel with respect to an ordinary set. In particular, the fuzzy framework provides a natural way to deal with uncertain situations. A fuzzy set 𝜇𝜇 of 𝑋𝑋 is a function of 𝑋𝑋 in the interval [0,1], that is, for each 𝑥𝑥 ∈ 𝑋𝑋, 𝜇𝜇(𝑥𝑥) is a real number ranging between 0 and 1. Function 𝜇𝜇(𝑥𝑥) is a membership function. Mathematically, the fuzzy subset 𝜇𝜇 of 𝑋𝑋 is expressed as 𝜇𝜇 = {(𝑥𝑥, 𝜇𝜇(𝑥𝑥)) ∶ 𝑥𝑥 ∈ 𝑋𝑋}. 2.2 Triangular fuzzy number The fuzzy number is a function in which the domain is any specified set, and whose range is the real number lies between 0 and 1, both inclusive. Generally, a triangular fuzzy number [22] is expressed as 𝑇𝑇𝐹𝐹𝜇𝜇 = (𝑞𝑞1 , 𝑞𝑞2 , 𝑞𝑞3 ) with the respective membership function defined as 𝑥𝑥−𝑞𝑞2 𝜇𝜇(𝑥𝑥) = 2.3 Intuitionistic fuzzy set ⎧𝑞𝑞2 −𝑞𝑞1 ⎪1, 𝑞𝑞 −𝑥𝑥 ⎨𝑞𝑞 3−𝑞𝑞 ⎪ 3 2 ⎩0, 𝑞𝑞1 ≤ 𝑥𝑥 < 𝑞𝑞2 𝑥𝑥 = 𝑞𝑞2 𝑞𝑞2 < 𝑥𝑥 ≤ 𝑞𝑞3 otherwise. (1) An intuitionistic fuzzy set [19] (IFS) 𝒩𝒩 of 𝑋𝑋 can be described in set form as 𝒩𝒩 = {〈𝑥𝑥, 𝜇𝜇𝒩𝒩 (𝑥𝑥), 𝜈𝜈𝒩𝒩 (𝑥𝑥)〉: 𝑥𝑥 ∈ 𝑋𝑋} where the functions: 𝜇𝜇𝒩𝒩 : 𝑋𝑋 → [0,1] and 𝜈𝜈𝒩𝒩 : 𝑋𝑋 → [0,1] represents the degrees of membership and non-membership of each 𝑥𝑥 ∈ 𝑋𝑋 respectively with 0 ≤ 𝜇𝜇𝑁𝑁 (𝑥𝑥) + 𝜈𝜈𝒩𝒩 (𝑥𝑥) ≤ 1. 2.4 Triangular intuitionistic fuzzy number A triangular intuitionistic fuzzy number (TrIFN) [23] 𝑋𝑋� 𝐼𝐼 is a pair of triplets written as (𝑥𝑥1 , 𝑥𝑥2 , 𝑥𝑥3 ; 𝑥𝑥1′ , 𝑥𝑥2′ , 𝑥𝑥3′ ) where 𝑥𝑥1′ ≤ 𝑥𝑥1 ≤ 𝑥𝑥2 = 𝑥𝑥2′ ≤ 𝑥𝑥3 ≤ 𝑥𝑥3′ having membership and nonmembership functions in the following manner: Advances in Production Engineering & Management 17(3) 2022 383 Kousar, Batool, Kausar, Pamucar, Ozbilge, Tantay 𝑥𝑥−𝑥𝑥1 As 𝑥𝑥2 = ⎧𝑥𝑥2 −𝑥𝑥1 ⎪1 𝜇𝜇𝑋𝑋� 𝐼𝐼 (𝑥𝑥) = 𝑥𝑥3 −𝑥𝑥 ⎨𝑥𝑥 −𝑥𝑥 ⎪ 3 2 ⎩0 𝑥𝑥2′ 𝑥𝑥2 −𝑥𝑥 , 𝑥𝑥1 ≤ 𝑥𝑥 ≤ 𝑥𝑥2 ⎧𝑥𝑥2 −𝑥𝑥1′ ⎪0 𝜈𝜈𝑋𝑋� 𝐼𝐼 (𝑥𝑥) = 𝑥𝑥−𝑥𝑥2 ⎨𝑥𝑥 ′ −𝑥𝑥 ⎪ 3 2 ⎩1 , 𝑥𝑥 = 𝑥𝑥2 , 𝑥𝑥2 ≤ 𝑥𝑥 ≤ 𝑥𝑥3 , otherwise so we can write TrIFN Arithmetic operations on TrIFN (𝑥𝑥1 , 𝑥𝑥2 , 𝑥𝑥3 ; 𝑥𝑥1′ , 𝑥𝑥2′ , 𝑥𝑥3′ ) as , 𝑥𝑥1′ ≤ 𝑥𝑥 ≤ 𝑥𝑥2 , 𝑥𝑥 = 𝑥𝑥2 , 𝑥𝑥2 ≤ 𝑥𝑥 ≤ 𝑥𝑥3′ , otherwise (2) (𝑥𝑥1 , 𝑥𝑥2 , 𝑥𝑥3 ; 𝑥𝑥1′ , 𝑥𝑥3′ ). Similar to numbers, several antiemetic operations can be defined on the TrIFNs [24]. Let 𝑋𝑋� 𝐼𝐼 = (𝑥𝑥1 , 𝑥𝑥2 , 𝑥𝑥3 ; 𝑥𝑥1′ , 𝑥𝑥3′ ) and 𝑌𝑌� 𝐼𝐼 = (𝑦𝑦1 , 𝑦𝑦2 , 𝑦𝑦3 ; 𝑦𝑦1′ , 𝑦𝑦3′ ) be any two TrIFNs and 𝑘𝑘 be a real number. Then 1. 2. 3. 4. 5. 𝑋𝑋� 𝐼𝐼 + 𝑌𝑌� 𝐼𝐼 = (𝑥𝑥1 + 𝑦𝑦1 , 𝑥𝑥2 + 𝑦𝑦2 , 𝑥𝑥3 + 𝑦𝑦3 ; 𝑥𝑥1′ + 𝑦𝑦1′ , 𝑥𝑥3′ + 𝑦𝑦3′ ). 𝑋𝑋� 𝐼𝐼 − 𝑌𝑌� 𝐼𝐼 = (𝑥𝑥1 − 𝑦𝑦3 , 𝑥𝑥2 − 𝑦𝑦2 , 𝑥𝑥3 − 𝑦𝑦1 ; 𝑥𝑥1′ − 𝑦𝑦3′ , 𝑥𝑥3′ − 𝑦𝑦1′ ). 𝑘𝑘. 𝑋𝑋� 𝐼𝐼 = 𝑘𝑘. (𝑥𝑥1 , 𝑥𝑥2 , 𝑥𝑥3 ; 𝑥𝑥1′ , 𝑥𝑥3′ ) = (𝑘𝑘𝑥𝑥1 , 𝑘𝑘𝑥𝑥2 , 𝑘𝑘𝑥𝑥3 ; 𝑘𝑘𝑥𝑥1′ , 𝑘𝑘𝑥𝑥3′ ) if 𝑘𝑘 ≥ 0. 𝑘𝑘. 𝑋𝑋� 𝐼𝐼 = 𝑘𝑘. (𝑥𝑥1 , 𝑥𝑥2 , 𝑥𝑥3 ; 𝑥𝑥1′ , 𝑥𝑥3′ ) = (𝑘𝑘𝑥𝑥3 , 𝑘𝑘𝑥𝑥2 , 𝑘𝑘𝑥𝑥1 ; 𝑘𝑘𝑥𝑥3′ , 𝑘𝑘𝑥𝑥1′ ) if 𝑘𝑘 < 0. 𝑋𝑋� 𝐼𝐼 × 𝑌𝑌� 𝐼𝐼 = (𝑥𝑥1 𝑦𝑦1 , 𝑥𝑥2 𝑦𝑦2 , 𝑥𝑥3 𝑦𝑦3 ; 𝑥𝑥1′ 𝑦𝑦1′ , 𝑥𝑥3′ 𝑦𝑦3′ ). 2.5 Linear programming Linear programming problems [25] include the optimization of real-world problems, in which the quantity of the objective function must be maximized or minimized with some constraints. Constraints are linear equalities or inequalities. It consists of the following parts. • Decision variables set 𝑋𝑋; • Objective Function: A linear function 𝑓𝑓(𝑥𝑥) is maximized(minimized); • Constraints: 𝑔𝑔𝑖𝑖 (𝑥𝑥) ≤ 𝑏𝑏𝑖𝑖 . 2.6 Multi-objective linear programming In multi-objective linear programming [26], we have variations in the objective function as well as in the constraints. The mathematical representation of multi-objective linear programming is as follows: Maximize 𝑓𝑓𝑠𝑠 (𝑥𝑥) = 𝑎𝑎𝑠𝑠1 . 𝑥𝑥1 + 𝑎𝑎𝑠𝑠2 . 𝑥𝑥2 +. . . +𝑎𝑎𝑠𝑠𝑠𝑠 . 𝑥𝑥𝑛𝑛 for all 𝑠𝑠. such that 𝑎𝑎𝑡𝑡1 . 𝑥𝑥1 + 𝑎𝑎𝑡𝑡1 . 𝑥𝑥1 +. . . +𝑎𝑎𝑡𝑡1 . 𝑥𝑥1 ⪌ 𝑏𝑏𝑡𝑡 In general, there is no single point (𝑥𝑥) = (𝑥𝑥1 , 𝑥𝑥2 , . . . , 𝑥𝑥𝑛𝑛 ) which optimizes each objective function individually. Many real-world problems can be modelled as multi-objective linear programming problems. A linear program with more than one objective function is known as a multi-objective linear program (MOLP). 2.7 Fuzzy linear programming Fuzzy linear programming [27] represented as: subject to ∑𝑛𝑛𝑗𝑗=1 Max 𝑍𝑍�. 𝑥𝑥 � � 𝑋𝑋𝑖𝑖𝑖𝑖 . 𝑥𝑥𝑗𝑗 ≥ 𝑌𝑌𝑖𝑖 , 𝑖𝑖 = 1,2, . . . 𝑚𝑚 𝑥𝑥𝑗𝑗 ≥ 0, 𝑗𝑗 = 1,2, . . . 𝑛𝑛 (3) where 𝑋𝑋𝑖𝑖𝑖𝑖 are decision variables in the constraints and 𝑥𝑥𝑗𝑗 are non-negative fuzzy numbers. Fuzzy linear programming problems with decision variables and parameters play an important role in several applications in different areas, such as mathematical modelling, manufacturing and production, environment management, supply chain management, and transportation management. In fuzzy linear programming, fuzziness considers either the objective function or the constraint equations. 384 Advances in Production Engineering & Management 17(3) 2022 Multi-objective Intuitionistic Fuzzy Linear Programming model for optimization of industrial closed-loop supply chain … 2.8 Linear programming with triangular intuitionistic fuzzy number The linear programming model with triangular intuitionistic fuzzy numbers [21] can be expressed as ∑𝑛𝑛𝑗𝑗=1 𝑍𝑍�𝑗𝑗𝐼𝐼 . 𝑥𝑥𝑗𝑗 Minimize 𝐼𝐼 ∑𝑛𝑛𝑗𝑗=1 𝑋𝑋�𝑖𝑖𝑖𝑖 . 𝑥𝑥𝑗𝑗 ≥ 𝑌𝑌�𝑖𝑖𝐼𝐼 , 𝑖𝑖 = 1,2, . . . 𝑚𝑚 (4) subject to 𝑥𝑥𝑗𝑗 ≥ 0, 𝑗𝑗 = 1,2, . . . 𝑛𝑛 ′ ′ ′ ′ ′ ′ where, 𝑍𝑍�𝑗𝑗𝐼𝐼 = (𝑧𝑧𝑗𝑗,1 , 𝑧𝑧𝑗𝑗,2 , 𝑧𝑧𝑗𝑗,3 ; 𝑧𝑧𝑗𝑗,1 , 𝑧𝑧𝑗𝑗,2 , 𝑧𝑧𝑗𝑗,3 ), 𝑌𝑌�𝑖𝑖𝐼𝐼 = (𝑦𝑦𝑖𝑖,1 , 𝑦𝑦𝑖𝑖,2 , 𝑦𝑦𝑖𝑖,3 ; 𝑦𝑦𝑖𝑖,1 𝑦𝑦𝑖𝑖,2 , 𝑦𝑦𝑖𝑖,3 ) 𝐼𝐼 ′ ′ ′ and 𝑋𝑋�𝑖𝑖𝑖𝑖 = (𝑋𝑋𝑖𝑖𝑖𝑖,1 , 𝑋𝑋𝑖𝑖𝑖𝑖,2 , 𝑋𝑋𝑖𝑖𝑖𝑖,3 ; 𝑋𝑋𝑖𝑖𝑖𝑖,1 , 𝑋𝑋𝑖𝑖𝑖𝑖,2 , 𝑋𝑋𝑖𝑖𝑖𝑖,3 ); 𝑖𝑖 = 1,2. . . , 𝑚𝑚 and 𝑗𝑗 = 1,2, . . . , 𝑛𝑛 are TrIFN’S. 3. Model formulation In a closed-loop supply chain network problem, our main purpose is to minimize overall costs, distribution time, or maximize profit; in general, objectives are usually uncertain due to unpredictable conditions in an evolving environment. In the proposed model, we first consider the raw materials and collect the initial parts. Suppliers send raw materials to the plants; in plants, the number of machines is working for proceeding with the products. These raw forms were further transformed into their final shapes. Retailers rack up commodities from plants and delivered them to customers. Collection centers collect customer previously purchased merchandise and returned goods. Further dispatch of these products to the disassembly center. The model is formulated as follows: after inspection, the reusable and manufacturable products are processed into refurbishing centers, and useless products of bad quality are disposed of. Refurbishing centers sent used parts to the plants to be used in the next period. Consequently, the CLSC problem was contrived, as shown in Fig. 1. The time and cost can be reduced by reducing the overall emissions. End-of-life vehicle (ELV) treatment is an example of a CLSC. Most European countries have had an existing ELV recycling system for decades. Parts of vehicles that are expected to have high re-sale value are first disassembled, and collection centers collect some parts in car accident and others from customers. Metal recycling and other components provide valuable product recovery which fulfils recycling targets at minimal cost [28]. Fig. 1 depicts the closedloop supply chain network, forward flow from suppliers to plants, plants to retailers, and retailers to customers, and backward flow from customer to collection center, collection center to plant, collection center to disassembly center, disassembly center to refurbishing center, and refurbishing center to plant. Fig. 1 Closed-loop supply chain network Advances in Production Engineering & Management 17(3) 2022 385 Kousar, Batool, Kausar, Pamucar, Ozbilge, Tantay Index sets 𝑥𝑥 suppliers 𝑦𝑦 plants 𝑧𝑧 retailers 𝑢𝑢 customers 𝑣𝑣 collection centers 𝑤𝑤 disassembly centers ℎ refurbishing centers 𝑡𝑡 number of parts 𝑞𝑞 number of periods Decision variables 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥 supplier 𝑥𝑥 shipped amount to plant 𝑦𝑦 for part 𝑡𝑡 in period 𝑞𝑞 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦 plant 𝑦𝑦 shipped amount to retailer 𝑧𝑧 for part 𝑡𝑡 in period 𝑞𝑞 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧 retailer 𝑧𝑧 shipped amount to customer 𝑢𝑢 for part 𝑡𝑡 in period 𝑞𝑞 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢 customer 𝑢𝑢 shipped amount to collection center 𝑣𝑣 for part 𝑡𝑡 in period 𝑞𝑞 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣 collection center 𝑣𝑣 shipped amount to plant 𝑦𝑦 for part 𝑡𝑡 in period 𝑞𝑞 𝐾𝐾𝐸𝐸𝐸𝐸 collection center 𝑣𝑣 shipped amount to disassembly center 𝑤𝑤 for part 𝑡𝑡 in period 𝑞𝑞 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤 disassembly center 𝑤𝑤 shipped amount to disposal for part 𝑡𝑡 in period 𝑞𝑞 𝐸𝐸𝑇𝑇𝑇𝑇 disassembly center 𝑤𝑤 shipped amount to refurbishing center ℎ for 𝑡𝑡 in period 𝑞𝑞 𝐹𝐹𝐼𝐼𝐼𝐼 refurbishing center ℎ shipped amount to plant 𝑦𝑦 for part 𝑡𝑡 in period 𝑞𝑞 𝐴𝐴𝑦𝑦𝑦𝑦 if plant 𝑦𝑦 is open ,1 ; else 0. 𝐵𝐵𝑧𝑧𝑧𝑧 if retailer 𝑧𝑧 is open ,1 ; else 0. Parameters 𝑙𝑙̃𝑥𝑥𝑥𝑥𝑥𝑥 fuzzy capacity in supplier 𝑥𝑥 for part 𝑡𝑡 in period 𝑞𝑞(ton) 𝑚𝑚 � 𝑦𝑦𝑦𝑦 fuzzy capacity in plant 𝑦𝑦 in period 𝑞𝑞(ton) 𝑛𝑛�𝑧𝑧𝑧𝑧 fuzzy capacity in retailer 𝑧𝑧 in period 𝑞𝑞(ton) 𝑝𝑝�𝑣𝑣𝑣𝑣 fuzzy capacity in collection center 𝑣𝑣 in period 𝑞𝑞(ton) 𝑞𝑞�𝑤𝑤𝑤𝑤𝑤𝑤 fuzzy capacity in disassembly center 𝑤𝑤 for part 𝑡𝑡 for period 𝑞𝑞(ton) 𝑟𝑟̃ℎ𝑡𝑡𝑡𝑡 fuzzy capacity in refurbishing center ℎ for part 𝑡𝑡 for period 𝑞𝑞(ton) 𝑜𝑜�𝑢𝑢𝑢𝑢 fuzzy demand of customer 𝑢𝑢 for period 𝑞𝑞 𝐴𝐴̃𝑞𝑞 maximum availability in plants for period 𝑞𝑞 � 𝐵𝐵𝑞𝑞 maximum availability in retailers for period 𝑞𝑞 𝑡𝑡 unit cost of shipping 𝑛𝑛𝑡𝑡 number of parts for the part 𝑡𝑡 from disassembling one unit of product 𝑙𝑙𝑥𝑥𝑥𝑥 unit cost of purchasing of supplier 𝑥𝑥 for part 𝑡𝑡 𝑚𝑚ℎ𝑡𝑡 unit cost of refurbishing of refurbishing center ℎ for part 𝑡𝑡 𝜇𝜇𝑦𝑦𝑦𝑦 fixed opening cost for plant 𝑦𝑦 in period 𝑞𝑞 𝜈𝜈𝑧𝑧𝑧𝑧 fixed opening cost for retailer 𝑧𝑧 in period 𝑞𝑞 𝛼𝛼� demand of fuzzy percentage that is composed by collection centers. 𝛽𝛽� fuzzy percentage for collection of amount that is resent to plants � 𝜃𝜃 fuzzy percentage for disassembled amount that is disposed Distances 𝑑𝑑𝑥𝑥𝑥𝑥 distance in the supplier 𝑥𝑥 to plant 𝑦𝑦 (kilometer) 𝑑𝑑𝑦𝑦𝑦𝑦 distance in the plant 𝑦𝑦 to retailer 𝑧𝑧 (kilometer) 𝑑𝑑𝑧𝑧𝑢𝑢 distance in the retailer 𝑧𝑧 to customer 𝑢𝑢 (kilometer) 𝑑𝑑𝑢𝑢𝑢𝑢 distance in the customer 𝑢𝑢 to collection center 𝑣𝑣 (kilometer) 𝑑𝑑𝑣𝑣𝑣𝑣 distance in the collection center 𝑣𝑣 and plant 𝑦𝑦 (kilometer) 𝑑𝑑𝑣𝑣𝑣𝑣 distance in the collection center 𝑣𝑣 and disassembly center 𝑤𝑤 (kilometer) 𝑑𝑑𝑤𝑤ℎ distance in disassembly center 𝑤𝑤 to refurbishing center ℎ (kilometer) 𝑑𝑑ℎ𝑦𝑦 distance in the refurbishing center ℎ to plant 𝑦𝑦 (kilometer) 𝑑𝑑𝑠𝑠𝑝𝑝 distance between disassembly center 𝑤𝑤 and disposal 386 Advances in Production Engineering & Management 17(3) 2022 Multi-objective Intuitionistic Fuzzy Linear Programming model for optimization of industrial closed-loop supply chain … 3.1 Objective functions Our main objectives ere to minimize the total costs. The first objective is to minimize the cost of production and assembly expenses for forward and reverse logistics, including transport system, buying, and renovation costs. The second goal is to reduce the fixed costs associated with the plants and retailers. 𝐼𝐼 𝐼𝐼 𝐼𝐼 𝑧𝑧1 ≅ 𝑡𝑡(� � � � 𝑋𝑋�𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥 . 𝑑𝑑𝑠𝑠𝑥𝑥𝑥𝑥 + � � � 𝑌𝑌�𝑦𝑦𝑦𝑦𝑦𝑦 . 𝑑𝑑𝑠𝑠𝑦𝑦𝑦𝑦 + � � � 𝑍𝑍�𝑧𝑧𝑧𝑧𝑧𝑧 . 𝑑𝑑𝑠𝑠𝑧𝑧𝑧𝑧 𝑥𝑥 𝑦𝑦 𝑡𝑡 𝑢𝑢 𝑣𝑣 𝑞𝑞 𝑞𝑞 𝑦𝑦 𝑧𝑧 𝑞𝑞 𝑧𝑧 𝑢𝑢 𝑤𝑤 𝑞𝑞 𝑞𝑞 𝐼𝐼 𝐼𝐼 𝐼𝐼 �𝑢𝑢𝑢𝑢𝑢𝑢 �𝑣𝑣𝑣𝑣𝑣𝑣 �𝑣𝑣𝑣𝑣𝑣𝑣 . 𝑑𝑑𝑠𝑠𝑢𝑢𝑢𝑢 + � � � 𝑀𝑀 . 𝑑𝑑𝑠𝑠𝑣𝑣𝑣𝑣 + � � � 𝐾𝐾 . 𝑑𝑑𝑠𝑠𝑣𝑣𝑣𝑣 + � � � 𝑊𝑊 𝑣𝑣 𝑦𝑦 𝑞𝑞 𝑣𝑣 𝐼𝐼 𝐼𝐼 𝐼𝐼 �𝑤𝑤𝑤𝑤𝑤𝑤 . 𝑑𝑑𝑠𝑠𝑝𝑝 + ∑𝑤𝑤 ∑ℎ ∑𝑡𝑡 ∑𝑞𝑞 𝐸𝐸�𝑤𝑤ℎ𝑡𝑡𝑡𝑡 . 𝑑𝑑𝑠𝑠𝑤𝑤ℎ + ∑ℎ ∑𝑦𝑦 ∑𝑡𝑡 ∑𝑞𝑞 𝐹𝐹�ℎ𝑦𝑦𝑦𝑦𝑦𝑦 . 𝑑𝑑𝑠𝑠ℎ𝑦𝑦 ) + ∑𝑤𝑤 ∑𝑡𝑡 ∑𝑞𝑞 𝐷𝐷 𝐼𝐼 𝐼𝐼 + ∑𝑥𝑥 ∑𝑦𝑦 ∑𝑡𝑡 ∑𝑞𝑞 𝑋𝑋�𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥 . 𝑙𝑙𝑥𝑥𝑥𝑥 + ∑ℎ ∑𝑦𝑦 ∑𝑡𝑡 ∑𝑞𝑞 𝐹𝐹�ℎ𝑦𝑦𝑦𝑦𝑦𝑦 . 𝑚𝑚ℎ𝑡𝑡 3.2 Constraints 𝐼𝐼 𝑧𝑧2 ≅ ∑𝑦𝑦 ∑𝑞𝑞 𝐴𝐴̃𝐼𝐼𝑦𝑦𝑦𝑦 . 𝜇𝜇𝑦𝑦𝑦𝑦 + ∑𝑧𝑧 ∑𝑞𝑞 𝐵𝐵�𝑧𝑧𝑧𝑧 . 𝜈𝜈𝑧𝑧𝑧𝑧 (5) (6) Supplier constraints The shipped amount of plant 𝑦𝑦 to supplier 𝑥𝑥 in part 𝑡𝑡 for 𝑞𝑞 is less than or equal to the fuzzy space of supplier 𝑥𝑥 in part 𝑡𝑡 for period 𝑞𝑞. The supplier constraints converted into fuzzy triangular intuitionistic numbers (see Eq. 7) show that the supplier shipped amount is less than the fuzzy supplier capacities. ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,2 ≤ 𝑙𝑙̃𝑥𝑥𝑥𝑥𝑥𝑥,2 ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,1 ≤ 𝑙𝑙̃𝑥𝑥𝑥𝑥𝑥𝑥,1 , ′ ′ ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,3 ≤ 𝑙𝑙̃𝑥𝑥𝑥𝑥𝑥𝑥,3 , ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,1 ≤ 𝑙𝑙̃𝑥𝑥𝑥𝑥𝑥𝑥,1 (7) ′ ′ ′ ′ ̃ ̃ ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,2 ≤ 𝑙𝑙𝑥𝑥𝑥𝑥𝑥𝑥,2 , ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,3 ≤ 𝑙𝑙𝑥𝑥𝑥𝑥𝑥𝑥,3 Plant constraints: The shipped amount of retailer 𝑧𝑧 to plant 𝑦𝑦 in period 𝑞𝑞 is less than or equal to the fuzzy capacity of plant 𝑦𝑦 in period 𝑞𝑞(ton). The plant constraints converted into fuzzy triangular intuitionistic numbers (see Eq. 8) show that the shipped amount to the retailer is less than the fuzzy plant capacities. ∑𝑧𝑧 𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌, 1 ≤ 𝑚𝑚 � 𝑦𝑦𝑦𝑦,1 . 𝐴𝐴𝑦𝑦𝑦𝑦,1 , ∑𝑧𝑧 𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌, 2 ≤ 𝑚𝑚 � 𝑦𝑦𝑦𝑦,2 . 𝐴𝐴𝑦𝑦𝑦𝑦,2 ′ ′ ∑𝑧𝑧 𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌, 3 ≤ 𝑚𝑚 � 𝑦𝑦𝑦𝑦,3 . 𝐴𝐴𝑦𝑦𝑦𝑦,3 , ∑𝑧𝑧 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,1 ≤ 𝑚𝑚 � 𝑦𝑦𝑦𝑦,1 . 𝐴𝐴𝑦𝑦𝑦𝑦,1 (8) ′ ′ ′ ′ ∑𝑧𝑧 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,2 ∑ ≤ 𝑚𝑚 � 𝑦𝑦𝑦𝑦,2 . 𝐴𝐴𝑦𝑦𝑦𝑦,2 , � 𝑦𝑦𝑦𝑦,3 . 𝐴𝐴𝑦𝑦𝑦𝑦,3 𝑧𝑧 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,3 ≤ 𝑚𝑚 Retailer constraints The shipped amount of customer 𝑢𝑢 to retailer 𝑧𝑧 in period 𝑞𝑞 is less than or equal to the fuzzy space of retailer 𝑧𝑧 for period 𝑞𝑞. The retailer constraints converted into fuzzy triangular intuitionistic numbers (see Eq. 9) show that the shipped amount to the customer is less than the fuzzy retailer capacities. ∑𝑢𝑢 𝑧𝑧𝑧𝑧𝑧𝑧𝑧𝑧,1 ≤ 𝑛𝑛�𝑧𝑧𝑧𝑧,1 . 𝐵𝐵𝑧𝑧𝑧𝑧,1 , ∑𝑢𝑢 𝑧𝑧𝑧𝑧𝑧𝑧𝑧𝑧,2 ≤ 𝑛𝑛�𝑧𝑧𝑧𝑧,2 . 𝐵𝐵𝑧𝑧𝑧𝑧,2 ′ ′ ∑𝑢𝑢 𝑧𝑧𝑧𝑧𝑧𝑧𝑧𝑧,3 ≤ 𝑛𝑛�𝑧𝑧𝑧𝑧,3 . 𝐵𝐵𝑧𝑧𝑧𝑧,3 , ∑𝑢𝑢 𝑧𝑧𝑧𝑧𝑧𝑧𝑧𝑧,1 ≤ 𝑛𝑛�𝑧𝑧𝑧𝑧,1 . 𝐵𝐵𝑧𝑧𝑧𝑧,1 (9) ′ ′ ′ ′ ∑𝑢𝑢 𝑧𝑧𝑧𝑧𝑧𝑧𝑧𝑧,2 ≤ 𝑛𝑛�𝑧𝑧𝑧𝑧,2 . 𝐵𝐵𝑧𝑧𝑧𝑧,2 , ∑𝑢𝑢 𝑧𝑧𝑧𝑧𝑧𝑧𝑧𝑧,1 ≤ 𝑛𝑛�𝑧𝑧𝑧𝑧,1 . 𝐵𝐵𝑧𝑧𝑧𝑧,1 Collection center The shipped amount of plant 𝑦𝑦 and disassembly center 𝑤𝑤 to collection center 𝑣𝑣 for period 𝑞𝑞 is less than or equal to the fuzzy space of collection center 𝑣𝑣 for period 𝑞𝑞. The collection center constraints converted into fuzzy triangular intuitionistic numbers (see Eq. 10) show that the shipped amount to the plant and disassembly center is less than the fuzzy capacities of the collection center. Advances in Production Engineering & Management 17(3) 2022 387 Kousar, Batool, Kausar, Pamucar, Ozbilge, Tantay Disassembly center ∑𝑦𝑦 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣,1 + ∑𝑤𝑤 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,1 ≤ 𝑃𝑃�𝑣𝑣𝑣𝑣,1 , ∑𝑦𝑦 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣,2 + ∑𝑤𝑤 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,2 ≤ 𝑃𝑃�𝑣𝑣𝑣𝑣,2 ′ ′ ∑𝑦𝑦 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣,3 + ∑𝑤𝑤 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,3 ≤ 𝑃𝑃�𝑣𝑣𝑣𝑣,3 , ∑𝑦𝑦 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣,1 + ∑𝑤𝑤 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,1 ≤ 𝑃𝑃�𝑣𝑣𝑣𝑣,1 ′ ′ ′ ′ ∑𝑦𝑦 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣,2 + ∑𝑤𝑤 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,2 ≤ 𝑃𝑃�𝑣𝑣𝑣𝑣,2 , ∑𝑦𝑦 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣,3 + ∑𝑤𝑤 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,3 ≤ 𝑃𝑃�𝑣𝑣𝑣𝑣,3 (10) The shipped amount disposal 𝑝𝑝 to disassembly center 𝑤𝑤 and refurbishing center ℎ of part 𝑡𝑡 for period 𝑞𝑞 is less than or equal to the fuzzy space for disassembly center 𝑤𝑤 of part 𝑡𝑡 in period 𝑞𝑞. The disassembly center constraints converted into fuzzy triangular intuitionistic numbers (see Eq. 11) show that the shipped amount to the disposal and refurbishing center is less than the fuzzy capacities of disassembly center. 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤,1 + ∑ℎ 𝐸𝐸𝑤𝑤ℎ𝑡𝑡𝑡𝑡,1 ≤ 𝑞𝑞�𝑤𝑤𝑤𝑤𝑤𝑤,1 , 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤,2 + ∑ℎ 𝐸𝐸𝑤𝑤ℎ𝑡𝑡𝑡𝑡,2 ≤ 𝑞𝑞�𝑤𝑤𝑤𝑤𝑤𝑤,2 ′ ′ ′ + ∑ℎ 𝐸𝐸𝑤𝑤ℎ𝑡𝑡𝑡𝑡,1 ≤ 𝑞𝑞�𝑤𝑤𝑤𝑤𝑤𝑤,1 (11) 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤,3 + ∑ℎ 𝐸𝐸𝑤𝑤ℎ𝑡𝑡𝑡𝑡,3 ≤ 𝑞𝑞�𝑤𝑤𝑤𝑤𝑤𝑤,3 , 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤,1 ′ ′ ′ ′ ′ ′ 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤,2 + ∑ℎ 𝐸𝐸𝑤𝑤ℎ𝑡𝑡𝑡𝑡,2 ≤ 𝑞𝑞�𝑤𝑤𝑤𝑤𝑤𝑤,2 , 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤,3 + ∑ℎ 𝐸𝐸𝑤𝑤ℎ𝑡𝑡𝑡𝑡,3 ≤ 𝑞𝑞�𝑤𝑤𝑤𝑤𝑤𝑤,3 Refurbishing center The shipped amount of plant 𝑦𝑦 to refurbishing center ℎ of part 𝑡𝑡 for period 𝑞𝑞 is less than or equal to the fuzzy capacity of refurbishing center ℎ of part 𝑡𝑡 for period 𝑞𝑞. The refurbishing center constraints converted into fuzzy triangular intuitionistic numbers (see Eq. 12) shows the shipped amount to the plant is less than the fuzzy capacities of the refurbishing center. Retailers ∑𝑦𝑦 𝐹𝐹ℎ𝑦𝑦𝑦𝑦𝑦𝑦,1 ≤ 𝑟𝑟̃ℎ𝑡𝑡𝑡𝑡,1 , ∑𝑦𝑦 𝐹𝐹ℎ𝑦𝑦𝑦𝑦𝑦𝑦,2 ≤ 𝑟𝑟̃ℎ𝑡𝑡𝑡𝑡,2 ′ ′ ∑𝑦𝑦 𝐹𝐹ℎ𝑦𝑦𝑦𝑦𝑦𝑦,3 ≤ 𝑟𝑟̃ℎ𝑡𝑡𝑡𝑡,3 , ∑𝑦𝑦 𝐹𝐹ℎ𝑦𝑦𝑦𝑦𝑦𝑦,1 ≤ 𝑟𝑟̃ℎ𝑡𝑡𝑡𝑡,1 ′ ′ ′ ′ ∑𝑦𝑦 𝐹𝐹ℎ𝑦𝑦𝑦𝑦𝑦𝑦,2 ≤ 𝑟𝑟̃ℎ𝑡𝑡𝑡𝑡,2 , ∑𝑦𝑦 𝐹𝐹ℎ𝑦𝑦𝑦𝑦𝑦𝑦,3 ≤ 𝑟𝑟̃ℎ𝑡𝑡𝑡𝑡,3 (12) ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,1 ≥ 𝑂𝑂�𝑢𝑢𝑢𝑢,1 , ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,2 ≥ 𝑂𝑂�𝑢𝑢𝑢𝑢,2 ′ ′ ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,3 ≥ 𝑂𝑂�𝑢𝑢𝑢𝑢,3, ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,1 ≥ 𝑂𝑂�𝑢𝑢𝑢𝑢,1 ′ ′ ′ ′ ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,2 ≥ 𝑂𝑂�𝑢𝑢𝑢𝑢,2 , ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,3 ≥ 𝑂𝑂�𝑢𝑢𝑢𝑢,3 (13) ∑𝑦𝑦 𝐻𝐻𝑦𝑦𝑦𝑦,1 ≤ 𝐴𝐴̃𝑞𝑞,1 , ∑𝑦𝑦 𝐻𝐻𝑦𝑦𝑦𝑦,2 ≤ 𝐴𝐴̃𝑞𝑞,2 ′ ∑𝑦𝑦 𝐻𝐻𝑦𝑦𝑦𝑦,3 ≤ 𝐴𝐴̃𝑞𝑞,3 , ∑𝑦𝑦 𝐻𝐻𝑦𝑦𝑦𝑦,1 ≤ 𝐴𝐴̃′𝑞𝑞,1 ′ ′ ∑𝑦𝑦 𝐻𝐻𝑦𝑦𝑦𝑦,2 ≤ 𝐴𝐴̃′𝑞𝑞,2 , ∑𝑦𝑦 𝐻𝐻𝑦𝑦𝑦𝑦,3 ≤ 𝐴𝐴̃′𝑞𝑞,3 (14) ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧,1 ≤ 𝐵𝐵�𝑞𝑞,1 , ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧,2 ≤ 𝐵𝐵�𝑞𝑞,2 ′ ′ ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧,3 ≤ 𝐵𝐵�𝑞𝑞,3 , ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧,1 ≤ 𝐵𝐵�𝑞𝑞,1 ′ ′ ′ ′ ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧,2 ≤ 𝐵𝐵�𝑞𝑞,2 , ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧,3 ≤ 𝐵𝐵�𝑞𝑞,3 (15) The shipped quantity of customer 𝑢𝑢 to retailers 𝑧𝑧 for period 𝑞𝑞 is greater than or equal to the fuzzy demand for customer 𝑢𝑢 of period 𝑞𝑞. The retailer constraints converted into fuzzy triangular intuitionistic numbers (see Eq. 13) show that the shipped quantity from the retailer is greater than the fuzzy customer demand. Plant opening constraints If plant 𝑦𝑦 is open during period 𝑞𝑞 the value is 1; otherwise, 0 is less than or equal to the maximum available set of plants for period 𝑞𝑞 (see Eq. 14). Retailer opening constraints If retailer 𝑧𝑧 is open during period 𝑞𝑞 the value is 1; otherwise, 0 is less than or equal to the maximum available set of retailers 𝑧𝑧 for period 𝑞𝑞 (see Eq. 15). Balance equations Balance equations (see Eqs. 16 to 61) show that the shipped amounts that enter these capacities must be equal to the number of products that leave the places for forward and reverse flow, and Eq. 62 incites the non-negativity of the decision variables. 388 ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,1 + ∑𝑛𝑛 𝐹𝐹ℎ𝑦𝑦𝑦𝑦(𝑞𝑞−1),1 + 𝑛𝑛𝑡𝑡 ∑𝑣𝑣 𝑀𝑀𝑣𝑣𝑣𝑣(𝑞𝑞−1),1 − 𝑛𝑛𝑡𝑡 ∑𝑧𝑧 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,1 = 0 ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,2 + ∑𝑛𝑛 𝐹𝐹ℎ𝑦𝑦𝑦𝑦(𝑞𝑞−1),2 + 𝑛𝑛𝑡𝑡 ∑𝑣𝑣 𝑀𝑀𝑣𝑣𝑣𝑣(𝑞𝑞−1),2 − 𝑛𝑛𝑡𝑡 ∑𝑧𝑧 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,2 = 0 (16) (17) Advances in Production Engineering & Management 17(3) 2022 Multi-objective Intuitionistic Fuzzy Linear Programming model for optimization of industrial closed-loop supply chain … ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,3 + ∑𝑛𝑛 𝐹𝐹ℎ𝑦𝑦𝑦𝑦(𝑞𝑞−1),3 + 𝑛𝑛𝑡𝑡 ∑𝑣𝑣 𝑀𝑀𝑣𝑣𝑣𝑣(𝑞𝑞−1),3 − 𝑛𝑛𝑡𝑡 ∑𝑧𝑧 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,3 ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,1 + ∑𝑛𝑛 𝐹𝐹ℎ𝑦𝑦𝑦𝑦(𝑞𝑞−1),1 + 𝑛𝑛𝑡𝑡 ∑𝑣𝑣 𝑀𝑀𝑣𝑣𝑣𝑣(𝑞𝑞−1),1 − 𝑛𝑛𝑡𝑡 ∑𝑧𝑧 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,1 ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,2 + ∑𝑛𝑛 𝐹𝐹ℎ𝑦𝑦𝑦𝑦(𝑞𝑞−1),2 + 𝑛𝑛𝑡𝑡 ∑𝑣𝑣 𝑀𝑀𝑣𝑣𝑣𝑣(𝑞𝑞−1),2 − 𝑛𝑛𝑡𝑡 ∑𝑧𝑧 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,2 ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,3 + ∑𝑛𝑛 𝐹𝐹ℎ𝑦𝑦𝑦𝑦(𝑞𝑞−1),3 + 𝑛𝑛𝑡𝑡 ∑𝑣𝑣 𝑀𝑀𝑣𝑣𝑣𝑣(𝑞𝑞−1),3 − 𝑛𝑛𝑡𝑡 ∑𝑧𝑧 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,3 ∑𝑦𝑦 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,1 − ∑𝑢𝑢 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,1 = 0, ∑𝑦𝑦 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,2 − ∑𝑢𝑢 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,2 = 0 ′ ′ ∑𝑦𝑦 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,3 − ∑𝑢𝑢 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,3 = 0, ∑𝑦𝑦 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,1 − ∑𝑢𝑢 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,1 =0 ′ ′ ∑𝑦𝑦 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,2 − ∑𝑢𝑢 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,2 = 0 ′ ′ ∑𝑦𝑦 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦,3 − ∑𝑢𝑢 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,3 =0 𝛼𝛼� ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,1 − ∑𝑣𝑣 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,1 = 0 𝛼𝛼� ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,2 − ∑𝑣𝑣 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,2 = 0 𝛼𝛼� ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,3 − ∑𝑣𝑣 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,3 = 0 ′ ′ − ∑𝑣𝑣 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,1 =0 𝛼𝛼� ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,1 ′ ′ =0 𝛼𝛼� ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,2 − ∑𝑣𝑣 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,2 ′ ′ 𝛼𝛼� ∑𝑧𝑧 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧,3 − ∑𝑣𝑣 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,3 = 0 𝛽𝛽� ∑𝑢𝑢 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,1 − ∑𝑦𝑦 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣,1 = 0 𝛽𝛽� ∑𝑢𝑢 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,2 − ∑𝑦𝑦 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣,2 = 0 𝛽𝛽� ∑𝑢𝑢 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,3 − ∑𝑦𝑦 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣,3 = 0 ′ ′ − ∑𝑦𝑦 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣,1 =0 𝛽𝛽� ∑𝑢𝑢 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,1 ′ ′ =0 𝛽𝛽� ∑𝑢𝑢 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,2 − ∑𝑦𝑦 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣,2 ′ ′ 𝛽𝛽� ∑𝑢𝑢 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,3 − ∑𝑦𝑦 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣,3 = 0 �1 − 𝛽𝛽� � ∑𝑢𝑢 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,1 − ∑𝑤𝑤 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,1 = 0 �1 − 𝛽𝛽� � ∑𝑢𝑢 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,2 − ∑𝑤𝑤 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,2 = 0 (1 − 𝛽𝛽� ) ∑𝑢𝑢 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,3 − ∑𝑤𝑤 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,3 = 0 ′ ′ − ∑𝑤𝑤 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,1 =0 (1 − 𝛽𝛽� ) ∑𝑢𝑢 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,1 ′ ′ � (1 − 𝛽𝛽 ) ∑𝑢𝑢 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,2 − ∑𝑤𝑤 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,2 = 0 ′ ′ − ∑𝑤𝑤 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,3 =0 (1 − 𝛽𝛽� ) ∑𝑢𝑢 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢,3 𝑛𝑛𝑡𝑡 (𝜃𝜃�) ∑𝑣𝑣 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,1 − 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤,1 = 0 𝑛𝑛𝑡𝑡 (𝜃𝜃�) ∑𝑣𝑣 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,2 − 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤,2 = 0 𝑛𝑛 𝑡𝑡 (𝜃𝜃�) ∑𝑣𝑣 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,3 − 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤,3 = 0 ′ ′ − 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤,1 =0 𝑛𝑛𝑡𝑡 (𝜃𝜃�) ∑𝑣𝑣 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,1 ′ ′ 𝑛𝑛𝑡𝑡 (𝜃𝜃�) ∑𝑣𝑣 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,2 − 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤,2 = 0 ′ ′ − 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤,3 =0 𝑛𝑛𝑡𝑡 (𝜃𝜃�) ∑𝑣𝑣 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,3 � ∑ ∑ 𝑛𝑛𝑡𝑡 �1 − 𝜃𝜃 � 𝑣𝑣 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,1 − ℎ 𝐸𝐸𝑤𝑤𝑤𝑤𝑤𝑤,1 = 0 𝑛𝑛𝑛𝑛(1 − 𝜃𝜃� ) ∑𝑣𝑣 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,2 − ∑ℎ 𝐸𝐸𝑤𝑤𝑤𝑤𝑤𝑤,2 = 0 𝑛𝑛𝑡𝑡 �1 − 𝜃𝜃� � ∑𝑣𝑣 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,3 − ∑ℎ 𝐸𝐸𝑤𝑤𝑤𝑤𝑤𝑤,3 = 0 ′ ′ − ∑ℎ 𝐸𝐸𝑤𝑤𝑤𝑤𝑤𝑤,1 =0 𝑛𝑛𝑛𝑛(1 − 𝜃𝜃� ) ∑𝑣𝑣 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,1 ′ ′ =0 𝑛𝑛𝑡𝑡 (1 − 𝜃𝜃� ) ∑𝑣𝑣 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,2 − ∑ℎ 𝐸𝐸𝑤𝑤𝑤𝑤𝑤𝑤,2 ′ ′ 𝑛𝑛𝑡𝑡 (1 − 𝜃𝜃� ) ∑𝑣𝑣 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣,3 − ∑ℎ 𝐸𝐸𝑤𝑤𝑤𝑤𝑤𝑤,3 = 0 ∑𝑤𝑤 𝐸𝐸𝑤𝑤ℎ𝑡𝑡𝑡𝑡,1 − ∑𝑦𝑦 𝐹𝐹ℎ𝑦𝑦𝑦𝑦𝑦𝑦,1 = 0 ∑𝑤𝑤 𝐸𝐸𝑤𝑤ℎ𝑡𝑡𝑡𝑡,2 − ∑𝑦𝑦 𝐹𝐹ℎ𝑦𝑦𝑦𝑦𝑦𝑦,2 = 0 ∑𝑤𝑤 𝐸𝐸𝑤𝑤ℎ𝑡𝑡𝑡𝑡,3 − ∑𝑦𝑦 𝐹𝐹ℎ𝑦𝑦𝑦𝑦𝑦𝑦,3 = 0 ′ ′ ∑𝑤𝑤 𝐸𝐸𝑤𝑤ℎ𝑡𝑡𝑡𝑡,1 − ∑𝑦𝑦 𝐹𝐹ℎ𝑦𝑦𝑦𝑦𝑦𝑦,1 =0 ′ ′ ∑𝑤𝑤 𝐸𝐸𝑤𝑤ℎ𝑡𝑡𝑡𝑡,2 − ∑𝑦𝑦 𝐹𝐹ℎ𝑦𝑦𝑦𝑦𝑦𝑦,2 = 0 ′ ′ ∑𝑤𝑤 𝐸𝐸𝑤𝑤ℎ𝑡𝑡𝑡𝑡,3 − ∑𝑦𝑦 𝐹𝐹ℎ𝑦𝑦𝑦𝑦𝑦𝑦,3 =0 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥 , 𝑌𝑌𝑦𝑦𝑦𝑦𝑦𝑦 , 𝑍𝑍𝑧𝑧𝑧𝑧𝑧𝑧 , 𝑊𝑊𝑢𝑢𝑢𝑢𝑢𝑢 , 𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣 , 𝐾𝐾𝑣𝑣𝑣𝑣𝑣𝑣 , 𝐷𝐷𝑤𝑤𝑤𝑤𝑤𝑤 , 𝐸𝐸𝑤𝑤ℎ𝑡𝑡𝑡𝑡 , 𝐹𝐹ℎ𝑦𝑦𝑦𝑦𝑦𝑦 ≥ 0. =0 =0 =0 =0 (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) (45) (46) (47) (48) (49) (50) (51) (52) (53) (54) (55) (56) (57) (58) (59) (60) (61) (62) Binary variables 𝐼𝐼 If plant y and retailer z in period q are open 1, then the binary variables 𝐴𝐴̃𝐼𝐼𝑦𝑦𝑦𝑦 𝑎𝑎𝑎𝑎𝑎𝑎 𝐵𝐵�𝑧𝑧𝑧𝑧 are 1; otherwise 0. Advances in Production Engineering & Management 17(3) 2022 389 Kousar, Batool, Kausar, Pamucar, Ozbilge, Tantay 4. Application: Results and discussion Closed-loop supply chain networks are primarily expressed as forward and reverse logistics. In this study the forward flow of the industrial CLSC contains five suppliers, four plants, four retailers, and five customers, as shown in Fig. 2. It is assumed that each supplier has three different components for the six periods, and each component has different rates depending upon its quality and demand. In this study, reverse flow incorporates two collection centers which collect used products from customers. Two disassembly centers assemble the returned products, whether they are further recycled. If the product cannot be recycled, it is sent to one disposal center to be discarded, and the remaining items are further forwarded into two refurbishing centers, as shown in reverse logistic Fig. 3. Fig. 2 Forward flow in closed-loop supply chain network Fig. 3 Reverse flow in closed-loop supply chain network Transportation cost 𝑡𝑡 per unit is taken as 4.21 USD of one tonne goods over a distance of one kilometer for general loading vehicle. Purchasing and refurbishing unit costs named as 𝑙𝑙𝑥𝑥𝑥𝑥 and 𝑚𝑚ℎ𝑡𝑡 for all the three components are set as 15 USD per ton and 10 USD per ton respectively. Fixed cost for each plant 𝜇𝜇𝑦𝑦𝑦𝑦 and retailer 𝜈𝜈𝑧𝑧𝑧𝑧 taken as 500 USD and 300 USD respectively for all the six periods. Maximum available plants 𝐴𝐴𝑦𝑦𝑦𝑦 and retailers 𝐵𝐵𝑧𝑧𝑧𝑧 both are four. The multi objective closed-loop supply chain model is used for transportation plan to control the expenses and maximize the profit. For optimising the model in fuzzy scenario, we apply the hypothetical values in proposed model in Section 3. The proposed model of closed-loop supply chain centralizes the envision to minimize total and fixed distribution cost on available capacities. Now we generate some scenarios to get the optimum result. Consider the hypothetical values for amount shipped from one stage to the next and capacities according to the storage of products. Firstly, convert the data into triangular intuitionistic fuzzy numbers to maximize the profit in industrial closed-loop supply chain. Maximization of profit by using triangular intuitionistic fuzzy numbers is highly dependent upon the constraints and objective function. In this research we covert our constraints into fuzzy constraint by using weighted average method which minimize the total and fixed cost. For instance, the supplier constraints in Eq. 7 are modified as: ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,1 ≤ 𝑤𝑤1 . 𝑙𝑙̃𝑥𝑥𝑥𝑥𝑥𝑥,1 , ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,2 ≤ 𝑤𝑤2 . 𝑙𝑙̃𝑥𝑥𝑥𝑥𝑥𝑥,2 ′ ′ ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,3 ≤ 𝑤𝑤3 . 𝑙𝑙̃𝑥𝑥𝑥𝑥𝑥𝑥,3 , ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,1 ≤ 𝑤𝑤4 . 𝑙𝑙̃𝑥𝑥𝑥𝑥𝑥𝑥,1 (63) ′ ′ ′ ′ ̃ ̃ ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,2 ≤ 𝑤𝑤5 . 𝑙𝑙𝑥𝑥𝑥𝑥𝑥𝑥,2 , ∑𝑥𝑥 𝑋𝑋𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥,3 ≤ 𝑤𝑤6 . 𝑙𝑙𝑥𝑥𝑥𝑥𝑥𝑥,3 390 Advances in Production Engineering & Management 17(3) 2022 Multi-objective Intuitionistic Fuzzy Linear Programming model for optimization of industrial closed-loop supply chain … where 𝑤𝑤1 = 0.16 , 𝑤𝑤2 = 0.18 , 𝑤𝑤3 = 0.16 , 𝑤𝑤4 = 0.16 , 𝑤𝑤5 = 0.18, 𝑤𝑤6 = 0.16 with 𝑤𝑤1 + 𝑤𝑤2 + 𝑤𝑤3 + 𝑤𝑤4 + 𝑤𝑤5 + 𝑤𝑤6 = 1. For the application of presented model hypothetical numeric values are taken in Tables 1-5. The Table 4 and 5 shows the converted values in triangular intuitionistic fuzzy number by weighted sum method which provides the significant finding. Due to recognition of ecological challenges, authorizing legislation closed-loop supply chain is highly adoptable for industrial production. However, results from complex projects show that the proposed model can find an effective, adaptable, and suitable method for industrial closed-loop supply chain network. The formulated problem is solved through MATLAB2018a fuzzy technique gives the optimality result of total cost 2020800, in which the fuzziness and ambiguity of data is absorbed by using triangular fuzzy number. Second scenario generated by using triangular intuitionistic fuzzy concept and the modelling yields more accurate and flexible result 1012400, which depicts the cost is minimized with the noticeable difference of 1008400. Therefore, the triangular intuitionistic method is much appropriate for given closed-loop supply chain problem. Table 1 Distance from suppliers to plants, plants to retailers and collection centers in km Stages Plant 1 Plant 2 1st supplier 150 200 150 150 2nd supplier 3rd supplier 160 110 80 90 1st Retailer 150 100 2nd Retailer 70 90 3rd Retailer 40 55 1st collection center 70 50 2nd collection center 50 70 3rd collection center Table 2 Distance from retailers to customers and customers to collection centers in km Stage Customer A Customer B Customer C Customer D 1st Retailer 100 60 150 80 2nd Retailer 150 90 90 60 3rd Retailer 100 80 80 30 1st collection center 150 60 30 90 2nd collection center 70 50 35 80 3rd collection center 30 80 40 50 Table 3 Distance from collection centers to disassembly centers and disassembly centers to refurbishing centers in km Disassembly Collection Collection Collection Disposal Refurbishing Refurbishing Refurbishing center center 1 center 2 center 3 center 1 center 2 center 3 1 90 60 50 70 40 70 50 2 100 95 30 50 50 60 90 3 150 80 40 80 40 30 70 Table 4 Triangular intuitionistic fuzzy supplier capacity Advances in Production Engineering & Management 17(3) 2022 391 Kousar, Batool, Kausar, Pamucar, Ozbilge, Tantay TIFNC Stage Plant1 Plant2 150 160 160 170 Retailer1 Retailer2 Retailer3 160 150 120 170 160 130 Plant1 Plant2 Retailer1 Retailer2 Retailer3 Customer1 Customer2 Customer3 Customer4 Customer1 Customer2 Customer3 Customer4 𝑎𝑎1 100 140 250 160 200 200 170 120 120 260 210 150 230 5. Conclusion 𝑎𝑎2 110 150 260 170 220 210 180 130 140 270 240 170 240 Table 5 Triangular intitionistic fuzzy capacity 𝑎𝑎3 Period 1 170 180 Period 4 120 170 Period 1 180 170 140 Period 4 270 180 230 Period 1 220 190 140 150 Period 4 280 250 200 250 𝑎𝑎1′ 𝑎𝑎3′ 𝑎𝑎1 𝑎𝑎2 130 150 180 200 310 300 320 310 150 130 110 190 180 150 140 80 100 160 900 110 90 130 240 130 180 190 160 110 100 230 200 220 210 130 180 280 190 250 230 200 150 170 290 260 210 280 120 150 230 190 210 260 210 270 310 340 350 360 420 130 170 270 200 220 270 220 280 330 350 370 370 430 𝑎𝑎3 Period 2 350 380 Period 5 140 180 Period 2 170 100 130 Period 5 280 210 230 Period 2 280 230 290 340 Period 5 360 380 380 440 𝑎𝑎1′ 𝑎𝑎3′ 𝑎𝑎1 𝑎𝑎2 300 350 380 400 270 250 280 260 130 70 80 180 110 150 350 270 250 370 280 260 100 140 200 180 200 250 200 250 300 330 340 350 410 150 190 300 220 240 290 240 300 360 370 390 400 450 370 410 230 220 260 370 400 370 220 230 200 240 230 380 420 260 230 280 380 410 380 230 240 220 250 240 𝑎𝑎3 Period 3 290 270 Period 6 390 430 Period 3 380 290 280 Period 6 270 240 300 Period 3 400 420 390 250 Period 6 250 230 260 250 𝑎𝑎1′ 𝑎𝑎3′ 250 230 300 280 330 260 220 390 300 290 360 400 210 200 240 350 380 360 200 220 200 230 210 400 450 280 250 310 410 440 400 290 300 250 270 260 Developing countries are striving to fight poverty and achieve sustainable development goals to improve the masses. In the current era, effective management of supply chain networks is imperative for reducing costs and maximizing optimization, thus contributing to the achievement of human capital development. This study chooses closed-loop supply chain (CLSC) networks for various industrial processes, as it integrates forward and backward logistics. The study relies on the triangular intuitionistic fuzzy number model to improve the output of CLSC networks in terms of reduced costs. This study contributes to the existing literature by using the chosen closed-loop supply chain model that comprehensively discusses forward and backward logistics in a systematic manner to address pricing issues more effectively under uncertain circumstances. Second, the employed method of triangular intuitionistic fuzzy numbers helped us to deal with a large dataset in a systematic and coordinated fashion, thus producing the desired results. Accounting for the catastrophes of Covid-19, and the ongoing financial turmoil in developing countries, the usage and implementation of CLSC networks alongside the employment of triangular intuitionistic fuzzy numbers for optimization of the linear programming model will effectively improve the efficiency of various supply chain networks, thus adding to human evolution. Moreover, the enhancement in software solutions would lead to more sustainable and efficient findings for further research. References [1] [2] [3] [4] [5] 392 Zhang, H., Ren, Y., Sui, Y., Qi, J., Wei, F. (2020). Recycle of industrial waste: A new method of applying the paint residue to supercapacitors, Journal of Materials Science: Materials in Electronics, Vol. 31, 274-285, doi: 10.1007/s10854-019-02488-2. Rubinos, D.A., Spagnoli, G. (2018). Utilization of waste products as alternative landfill liner and cover materials– A critical review, Critical Reviews in Environmental Science and Technology, Vol. 48, No. 4, 376-438, doi: 10.1080/10643389.2018.1461495. Wu, J., Zhu, Q., Chu, J., Liang, L. (2015). Two-stage network structures with undesirable intermediate outputs reused: A DEA based approach, Computational Economics, Vol. 46, 455-477, doi: 10.1007/s10614-015-9498-3. Sarkar, B., Ullah, M., Sarkar, M. (2022). Environmental and economic sustainability through innovative green products by remanufacturing, Journal of Cleaner Production, Vol. 332, Article No. 129813, doi: 10.1016/j.jclepro. 2021.129813. Savaskan, R.C., Bhattacharya, S., Van Wassenhove, L.N. (2004). Closed-loop supply chain models with product remanufacturing, Management Science, Vol. 50, No. 2, 239-252, doi: 10.1287/mnsc.1030.0186. Advances in Production Engineering & Management 17(3) 2022 Multi-objective Intuitionistic Fuzzy Linear Programming model for optimization of industrial closed-loop supply chain … [5] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] Hugos, M. (2018). Essentials of supply chain management, Fourth edition, John Wiley & Sons, Hoboken, New Jersey, USA, doi: 10.1002/9781119464495. Özceylan, E., Paksoy, T. (2013). A mixed integer programming model for a closed-loop supply-chain network, International Journal of Production Research, Vol. 5, No. 3, 718-734, doi: 10.1080/00207543.2012.661090. Aleksić, A., Runić Ristić, M., Komatina, N., Tadić, D. (2019). Advanced risk assessment in reverse supply chain processes: A case study in Republic of Serbia, Advances in Production Engineering & Management, Vol. 14, No. 4, 421-434, doi: 10.14743/apem2019.4.338. Jindal, A., Sangwan, K.S. (2014). Closed loop supply chain network design and optimisation using fuzzy mixed integer linear programming model, International Journal of Production Research, Vol. 52, No. 14, 4156-4173, doi: 10.1080/00207543.2013.861948. Garcia, D.J., You, F. (2015). Supply chain design and optimization: Challenges and opportunities, Computers & Chemical Engineering, Vol. 81, 153-170, doi: 10.1016/j.compchemeng.2015.03.015. Fang, I.W., Lin, W.-T. (2021). A multi-objective optimal decision model for a green closed-loop supply chain under uncertainty: A real industrial case study, Advances in Production Engineering & Management, Vol. 16, No. 2, 161-172, doi: 10.14743/apem2021.2.391. Özceylan, E., Paksoy, T. (2013). Fuzzy multi-objective linear programming approach for optimising a closed-loop supply chain network, International Journal of Production Research, Vol. 51, No. 8, 2443-2461, doi: 10.1080/ 00207543.2012.740579. Liu, Z., Li, K.W., Li, B.-Y., Huang, J., Tang, J. (2019). Impact of product-design strategies on the operations of a closed-loop supply chain, Transportation Research Part E: Logistics and Transportation Review, Vol. 124, 75-91, doi: 10.1016/j.tre.2019.02.007. Tsao, Y.-C., Thanh, V.-V., Lu, J.-C., Yu, V. (2018). Designing sustainable supply chain networks under uncertain environments: Fuzzy multi-objective programming, Journal of Cleaner Production, Vol. 174, 1550-1565, doi: 10.1016/j.jclepro.2017.10.272. Govindan, K., Darbari, J.D., Agarwal, V., Jha, P.C. (2017). Fuzzy multi-objective approach for optimal selection of suppliers and transportation decisions in an eco-efficient closed loop supply chain network, Journal of Cleaner Production, Vol. 165, 1598-1619, doi: 10.1016/j.jclepro.2017.06.180. Duan, W., Ma, H., Xu, D.S. (2021). Analysis of the impact of COVID-19 on the coupling of the material flow and capital flow in a closed-loop supply chain, Advances in Production Engineering & Management, Vol. 16, No. 1, 522, doi: 10.14743/apem2021.1.381. Zhou, L., Xie, J., Gu, X., Lin, Y., Ieromonachou, P., Zhang, X. (2016). Forecasting return of used products for remanufacturing using Graphical Evaluation and Review Technique (GERT), International Journal of Production Economics, Vol. 181, Part B, 315-324, doi: 10.1016/j.ijpe.2016.04.016. Zadeh, L.A. (1965). Fuzzy sets, Information and Control, Vol. 8, No. 3, 338-353, doi: 10.1016/S0019-9958(65)90 241-X. Atanassov, K.T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 20, No. 1, 87-96, doi: 10.1016/ S0165-0114(86)80034-3. Zimmermann, H.-J. (1975). Description and optimization of fuzzy systems, International Journal of General Systems, Vol. 2, No. 1, 209-215, doi: 10.1080/03081077508960870. Ghanbari, R., Ghorbani-Moghadam, K., Mahdavi-Amiri, N., De Baets, B. (2020). Fuzzy linear programming problems: Models and solutions, Soft Computing, Vol. 24, 10043-10073, doi: 10.1007/s00500-019-04519-w. Seikh, M.R., Nayak, P.K., Pal, M. (2012). Generalized triangular fuzzy numbers in intuitionistic fuzzy environment, International Journal of Engineering Research and Development, Vol. 5, No. 1, 8-13. Fullér, R. (1991). On product-sum of triangular fuzzy number, Fuzzy Sets and Systems, Vol. 41, No. 1, 83-87, doi: 10.1016/0165-0114(91)90158-M. Shaw, A.K., Roy, T.K. (2012). Some arithmetic operations on triangular intuitionistic fuzzy number and its application on reliability evaluation, International Journal of Fuzzy Mathematics and Systems, Vol. 2, No. 4, 363-382. Eiselt, H.A., Sandblom, C.-L. (2007). Linear programming and its applications, Springer-Verlag, Berlin, Germany, doi: 10.1007/978-3-540-73671-4. Chanas, S. (1989). Fuzzy programming in multiobjective linear programming – A parametric approach, Fuzzy Sets and Systems, Vol. 29, No. 3, 303-313, doi: 10.1016/0165-0114(89)90042-0. Zimmermann, H.-J. (1978). Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, Vol. 1, No. 1, 45-55, doi: 10.1016/0165-0114(78)90031-3. Schultmann, F., Zumkeller, M., Rentz, O. (2006). Modeling reverse logistic tasks within closed-loop supply chains: An example from the automotive industry, European Journal of Operational Research, Vol. 171, No. 3, 1033-1050, doi: 10.1016/j.ejor.2005.01.016. Appendix A List of abbreviations SC Supply chain RSC Reverse supply chain CLSC Closed-loop supply chain IFS Intuitionistic fuzzy set ELV End of life vehicle IFS Intuitionistic fuzzy Advances in Production Engineering & Management 17(3) 2022 393 Calendar of events • 16th International Conference on Micromachining Technology, October 17-18, 2022, Dubai, United Arab Emirates. • 36th Annual European Simulation and Modelling Conference, October 26-28, 2022, Porto, Portugal. • 33rd DAAAM International Symposium, Virtual Online Edition, hosted by Vienna University of Technology, October 27-28, 2022, Vienna, Austria. • 7th International Conference of Computational Methods in Engineering Science, November 24-26, 2022, Zamosc, Poland. • 14th International Conference on Mechatronics and Manufacturing, February 10-12, 2023, Royal Princess Larn Luang, Bangkok, Thailand. • 7th International Conference on Material Engineering and Manufacturing, April 7-10, 2023, Chiba University, Japan. • 51th North American Manufacturing Research Conference, June 12-16, 2023, Rutgers University, New Brunswick, New Jersey, USA. 394 Advances in Production Engineering & Management 17(3) 2022 Notes for contributors General Articles submitted to the APEM journal should be original and unpublished contributions and should not be under consideration for any other publication at the same time. 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APEM Advances in Production Engineering & Management journal Chair of Production Engineering (CPE) University of Maribor APEM homepage: apem-journal.org Volume 17 | Number 3 | September 2022 | pp 259-396 Contents Scope and topics 262 Financing and information sharing in capital-constrained supply chain Duan, H.W.; Wang, M.T.; Ye, Y.S. 263 Effect of printing parameters on the mechanical behaviour of the thermoplastic polymer processed by FDM technique: A research review Tripathy, C.R.; Sharma, R.K.; Rattan, V.K. 279 Evolutionary game analysis of company collaborative strategy in cloud manufacturing platform environment Xiao, M.; Tian, Z.Y. 295 Development of a flexible tooling system for sheet metal bending Stefanovska, E.; Pepelnjak, T. 311 A new approach for quality prediction and control of multistage production and manufacturing process based on Big Data analysis and Neural Networks Tian, S.; Zhang, Z.; Xie, X.; Yu, C. 326 Experimental determination of influences on a gauge block’s stack length Lipus, L.C.; Acko, B.; Tompa, J. 339 Last-mile delivery optimization considering the demand of market distribution methods: A case studies using Adaptive Large Neighborhood Search algorithm Huang, Q.L.; Wang, W.J.; Liang, X.J.; Xu, L.; Niu, X.Y.; Yang, X.Y. 350 Modelling surface roughness in finish turning as a function of cutting tool geometry using the response surface method, Gaussian process regression and decision tree regression Vukelic, D.; Simunovic, K.; Kanovic, Z.; Saric, T.; Doroslovacki, K.; Prica, M.; Simunovic, G. 367 Multi-objective Intuitionistic Fuzzy Linear Programming model for optimization of industrial closed-loop supply chain network Kousar, S.; Batool, M.; Kausar, N.; Pamucar, D.; Ozbilge, E.; Tantay, B. 381 Calendar of events 394 Notes for contributors 395 Published by CPE, University of Maribor ISSN 1854-6250 9 771854 625008 apem-journal.org