ISSN 1854-6250 APEM journal Advances in Production Engineering & Management Volume 14 | Number 1 | March 2019 Published by CPE apem-journal.org University of Maribor Advances in Production Engineering & Management Identification Statement APEM 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 UniversityofMaribor 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 Smetanova ulica 17, SI - 2000 Maribor, Slovenia, EU Desk Editor Martina Meh deski@apem-journal.org Janez Gotlih desk2@apem-journal.org Website Technical Editor Lucija Brezocnik lucija.brezocnik@um.si 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 Franci Cus, University of Maribor, Slovenia 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. 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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 journal University of Maribor Chair of Production Engineering (CPE) Advances in Production Engineering & Management Volume 14 | Number 1 | March 2019 | pp 1-138 Contents 4 5 15 27 39 51 65 80 93 112 125 136 137 Journal homepage: apem-journal.org ISSN 1854-6250 (print) ISSN 1855-6531 (on-line) ©2019 CPE, University of Maribor. All rights reserved. Scope and topics An integrated optimization of quality control chart parameters and preventive maintenance using Markov chain Farahani, A.; Tohidi, H.; Shoja, A. Determination of nano-roughness for micro-objects by measuring the van der Waals force Bratina, B.; Safaric, J.; Uran, S.; Safaric, R. Cutting performance of solid ceramic and carbide end milling tools in machining of nickel based alloy Inconel 718 and stainless steel 316L Grguras, D.; Kern, M.; Pusavec, F. Two-stage product design selection by using PROMETHEE and Taguchi method: A case study Crnjac, M.; Aljinovic, A.; Gjeldum, N.; Mladineo, M. Productivity improvement with parallel adjacent U-shaped assembly lines Chutima, P.; Suchanun, T. Achieving sustainable transport through resource scheduling: A case study for electric vehicle charging stations Gong, D.; Tang, M.; Liu, S.; Xue, G.; Wang, L. Product quality improvement and air pollutant emission reduction in a mining metal three-stage supply chain under cap-and-trade regulation Homaei, H.; Mahdavi, I.; Tajdin, A.; Khorram, E. Inventory control model based on multi-attribute material classification: An integrated grey-rough set and probabilistic neural network approach Zhang, Z.L.; Wang, Y.F.; Li, Y. A multi-product pricing and inventory model with production rate proportional to power demand rate Keshavarzfard, R.; Makui, A.; Tavakkoli-Moghaddam, R. Maximum-minimum distance clustering method for split-delivery vehicle-routing problem: Case studies and performance comparisons Min, J.N.; Jin, C.; Lu, L.J. Calendar of events Notes for contributors Scope and topics Advances in Production Engineering & Management (APEM journal) is an interdisciplinary refer-eed 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 Computer-Integrate d M anufacturing 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 Machine Learning in Production 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 Statistical Methods Supply Chain Management Virtual Reality in Production 4 APEM jowatal Advances in Production Engineering & Management Volume 14 | Number 1 | March 2019 | pp 5-14 https://doi.Org/10.14743/apem2019.1.307 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper An integrated optimization of quality control chart parameters and preventive maintenance using Markov chain Farahani, A.a, Tohidi, H.b*, Shoja, A.c department of Industrial Engineering, Roudehen Branch, Islamic Azad University, Roudehen, Iran department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran department of Mathematics and Statistic, Roudehen Branch, Islamic Azad University, Roudehen, Iran A B S T R A C T A R T I C L E I N F O Manufacturing costs are reduced significantly with the integrated optimization of preventive maintenance and quality control. In this paper, a new mixed integer non-linear programming model is presented. This model determines the optimal preventive maintenance interval and the optimal parameters of the (?) control chart, including the sampling interval and the sample size and the control limit. The production system is considered in the form of a continuous time Markov chain. Formulation of the production process of a machine in the form of a continuous time Markov chain is a breakthrough in the integrated modeling of repair and quality. The goal is to reduce costs per unit time. It is assumed that preventive maintenance can be carried out at several levels either perfect or imperfect. The duration of corrective and preventive maintenance is not negligible. Considering the length of time for maintenance, this model is closer to the real production environment. A numerical example is used to illustrate this new model. Sensitivity analysis was performed to determine the effect of the model parameters on optimal decisions. This analysis further shows the relationship between preventive maintenance and statistical quality control as well as the performance of the new model. © 2019 CPE, University of Maribor. All rights reserved. Keywords: Maintenance; Optimization; Chart control; Non-linear model; Markov chain *Corresponding author: H_tohidi@azad.ac.ir (Tohidi, H.) Article history: Received 10 December 2017 Revised 22 November 2018 Accepted 3 December 2018 1. Introduction The performance of a production system essentially depends on the performance of the floor of the workshop. The operating policies of the floor of the workshop include maintenance scheduling, quality control and production scheduling. These three aspects of operational planning are mutually reinforcing. Therefore, their integrated optimization considerably improves the performance of the system [1]. Production planning, quality and maintenance are the main elements of a production system. Many researchers believe that models that optimize each of these elements independently do not provide an optimal global solution for the whole production system. Accordingly, the literature has grown in the field of integrated models [2]. Pandey et al. [3] review articles that optimize quality and maintenances simultaneously. Hadidi et al. [2] referred to the list of articles that optimize integrated the maintenances and quality control. Pandey et al. [4] present an article on simultaneous optimization of maintenance planning, quality control and production planning. In this study, a model was first developed to integrate maintenance planning and decision-making related to quality control of the process. Then, with 5 Farahani, Tohidi, Shoja attention to the preventive maintenance interval, the sequence of production batches with minimization of the production schedule delay was performed. In another paper, Pandey et al. [5] present an integrated model for optimizing the preventive maintenance interval and control chart parameters using the Taguchi loss function. Liu et al. [6] consider a X control chart for a two-unit production system that operates in series. This system is described using the continuous time Markov chain. In this paper, it is assumed that the system is controlled by a X control chart to avoid cost of failure and an optimization model has been developed to obtain optimal control chart parameters for minimizing maintenance costs. When the control chart gives an out-of-control signal, a complete inspection is performed if this inspection indicates the partial failure of each system unit, it should immediately be replaced as a part of preventive maintenance, and if the system stops, that is, a unit of the system is in a state of failure. In this paper, the length of maintenance is considered negligible. Xiang [7] provide an article on determining the optimal parameters of the X control chart and preventive maintenance in the form of a discrete time Markov chain. In this model, the length of time for preventive and corrective maintenance is negligible. Zhang et al. [8] integrated a X control chart with a repair plan. This paper proposes a delayed maintenance policy. This policy takes a delay time to detect after an alarm from the control chart. Yin et al. [9] provide an integrated model for statistical quality control and maintenance decisions based on a delay control policy. This mathematical model is solved to minimize the expected cost. Tambe and Kulkarni [1] have provided an article to optimize the maintenance and quality program with the constraint on schedule, availability, and repair time and detection time for a single-machine production system and a Simulated Annealing algorithm and a Genetic algorithm are used to solve the model. Bouslah et al. [10] propose an integrated production, preventive maintenance, and quality control system for a production system, which is subject to deterioration in quality and reliability. The main objective of this study is to optimize the production, inventory level, parameters of the sampling plan and the overall repair level, minimizing the total cost imposed simultaneously. Tambe and Kulkarni [11] have presented an approach to integrate planning of repairs, quality control and production planning. The purpose of this study is to examine the benefits of the integration of these three issues with regard to the overall expected cost of the system. Lu et al. [12] presented an integrated model in which the process improvement with PM decisions in a single-machine production system was performed simultaneously. Nourelfath et al. [13] optimize production, maintenance and quality policies for a complete process in a multi-period multi-product production system with limited production size. Shrivastava et al. [14] presented an integrated model for optimizing preventive maintenance and quality control policies with CUSUM chart. Zhong et al. [15] provide an integrated model for optimizing control chart parameters and maintenance times in the supply chain. Ardakan et al. [16] presented a hybrid model for combining control charts and preventive maintenance (PM) systems to quickly diagnose out-of-control modes and this model reduces system control costs. In this paper a multivariate control chart (MEWMA) is used to control process changes. Khrueasom and Pongpullponsak [17] provide an integrated model for determining the parameters of the control charts of EWMA and Kolmogorov-Smirnov, with regard to repair management. Salmasnia et al. [18] provide an integrated model for determining the size of economic production, statistical process control, and repair, in a system, with a number of reasonable causes for failure and Particle Mass Optimization algorithms are used to minimize the total cost expected for each production cycle, according to the limitations of statistical quality. Zhong and Ma [19] provide an integrated model for statistical process control and maintenance. This paper optimizes Shewhart individual-residual (Zx —Ze) control chart and repair parameters for two-step dependent processes, with the goal of minimizing the total cost of repair, inspection and quality. In an article, Beheshti Fakher et al. [20] propose integrated production planning, incomplete repairs and process inspection in a multi-machine system. Rasay et al. [21] presented an integrated model that coordinates the decisions on designing the chi-square chart and the planning 6 Advances in Production Engineering & Management 14(1) 2019 An integrated optimization of quality control chart parameters and preventive maintenance using Markov chain of maintenance, and an independent maintenance model is also presented for assessing the integrated model, and the performance of these two the model is compared with each other. The purpose of this paper is to consider a mixed integer nonlinear programming model for simultaneous optimization of preventive maintenance and quality policies in a jobshop system in the form of a continuous time Markov chain. In this model, the process has an in control state and several out of control modes which are invisible. In out of control states, the percentage of manufactured parts is inconsistent. The failure mode is directly visible and detected immediately. Preventive maintenance is carried out at several levels, which can be perfect such that the process is turned into a state of in control or can be performed imperfect, in which case the process is converted with a probability to a state that is not worse before, but corrective maintenance is perfect and the process is then turned into a state of in control. Different modes of machine and sampling and various levels of preventive maintenance and corrective maintenance and false alarm are considered as nodes of a continuous time Markov chain. It is assumed that the duration of stay in various machine modes and the various levels of preventive maintenance and corrective maintenance and inspection for false alarm is an exponential random variable. However, the duration of stay in different modes of the machine until entering sampling mode and the duration of stay in sampling mode is a hyper exponential random variable. This model determines the optimal preventive maintenance interval and X control chart parameters for each machine at the time of production of each product, so that the cost per unit time is minimized. This paper is close to article [7]. In that paper, a discrete-time Markov chain is proposed for the integrated optimization of X control chart and preventive maintenance. In [7], the length of time for preventive and corrective maintenance is negligible and, as stated in the article itself, such a hypothesis is not feasible in practical situations. In the present study, the length of time for corrective and preventive maintenance is considered, so that the proposed model is closer to the reality of production systems. According to review articles by Pandey et al. [3] and Hadidi et al. [2], as well as reviewing the literature presented in this paper and the search, the following points can be cited as the innovation of this research. (1) All process modes including in control mode and out-of-control modes, and sampling mode and preventive maintenance at various levels, and corrective maintenance and inspection for false alarm, are considered as a continuous time Markov chain. (2) The duration of preventive and corrective repairs is not zero and the duration of their execution is exponential random variable. The rest of the article is presented as follows. Section 2 describes the problem and provides an integrated planning model for preventive maintenance and X control chart. In section 3, a numerical example is solved and sensitivity analysis is performed. In the end, section 4 will present a summary of the paper and conclusions and future suggestions. 2. Description of proposed non-linear model A jobshop system is considered. In this system, several machines work in series at the stations. In order for the production line machines to work together on balance, at some workstations several machines work in parallel to provide a specific production rate. The failure of each of the machines reduces a certain percentage of line production. A component of each machine is considered as one piece that must be preventive maintenance done on it. The length of time until the failure of each machine follows exponential distribution. Two failure modes are considered for each machine. The first one is that the machine breaks down, and the production of the same moment stops, and the machine cannot continue to work. The second is that machine failure can reduce the process quality of the machine, which is due to a change in the average of the process. Therefore, the cost of a breakdown of the first mode includes the cost of stopping the line, the cost of repair work and the fixed cost of repair and the cost of set up. The second failure mode affects the product in terms of quality and increases the production rate of the defective product until the failure has been discovered and the production is stopped, so the cost of defect product includes quality costs. Advances in Production Engineering & Management 14(1) 2019 7 Farahani, Tohidi, Shoja In this paper, it is assumed that the quality of each process can be assessed by measuring a qualitative key characteristic of the output of that process. It is also assumed that this qualitative characteristic is a random variable with a certain mean and standard deviation. When the process is in control, the average of this variable is within the control limit. This average can be out of limit due to machine failure or some other external causes such as environmental effects, operator error, use the wrong tool, etc. After this happens, the process is considered out of control. In this case, it is assumed that the inspection of the machine is carried out without stopping the process and the cause of the failure is determined. If the cause is due to machine failure, the machine will be stopped and repairs will be done. From the above, it is obvious that machine failure and repair affects the quality of the process. Therefore, the optimization of preventive maintenance and the economic design of the control chart should be carried out simultaneously. The operation of each machine on each product is considered as a process. For each process, a controlled state (mode 1) and several (f — 1) modes out of the control i = 2,3,..,/ — 1 are considered. Mode f is a failure mode. A X control chart is used to evaluate and control the process. The distribution of the qualitative feature of the process is supposed to follow the normal distribution. When the process is in control, the mean of the process is ^ = and the standard deviation of the process is a = aQ. The occurrence of the assignable cause causes the change in the mean of the process, but the process variance does not change. In this case fa + and 2 mp)(A.ISmp) J \Qmpnmp Now, Eq. 10, which is necessary to obtain the percentage of process time remaining in each of the modes. /"I L ^niimp + ^ nkmp +nfmp + ™insmv + nsmp = 1 VmeM, V pep (10) i=l 1=1 Eq. 11 calculates the probability of type I error. amp = 20(—kmp) VmeM, VpeP (11) 0(x) is the cumulative distribution function of normal distribution. Eq. 12 calculates the probability of type II error. ßmp —Qik-mp fi-mp lnmp) 0( ^mp ^mp lnmp) Vm£M, V p£P (12) Jmp f \"-mp '-'mp ¡"-mpj ,vmp '-'mp "-mp It should be noted that the duration of stay in different modes of the machine (process) up to entering the sampling mode, f — 1 type hyper exponential random variable, is considered. Because of failure mode, there is no input for sampling mode. The duration until the exit from the sampling mode is also considered to be a hyper exponential random variable of type 4. Because after the sampling, the process is detected either in-control or out-of- control, then the probability of entering the in control mode is 0.5 and the probability of entering the out-of-control modes is 0.5. Also, with the probability a, the process enters the false alarm state, and with the probability ft, it is not specified out-of-control of the process, and enters from the sampling mode into out-of-control modes. In addition, with the probability 1 — a, enters the in-control state and, with the probability 1 — ft, enters the preventive maintenance state. The duration of stay in each machine mode (process), as well as the duration of stay in a failure mode, and preventive maintenance and inspection for false alarm, is an exponential random variable. 3. Results and discussion: Case studies and sensitivity analysis In order to validate and evaluate the proposed model, a numerical example is presented here, and then a sensitivity analysis is performed to examine the effect of model parameters on optimal solutions. Consider a manufacturing system that includes a machine that produces a product by the machine. The process of controlling the machine is performed by the X control chart. The process of this machine involves various machine (process) modes and failure mode, which, if the process Advances in Production Engineering & Management 14(1) 2019 11 Farahani, Tohidi, Shoja is in a state of failure, corrective maintenance transform the process into a in control state. All modes of the machine (process) and failure mode, preventive maintenance mode, and sampling mode and false alarm mode are considered in the form of a continuous time Markov chain. In the jobshop production system, for each machine and product, a format of the continuous time Markov chain should be considered and solved. In the numerical example presented, a machine is considered to produce a product. . The machine has four modes: the in control mode (mode 1), the out of control modes (mode 2 and 3) and the mode of failure (mode 4). We know that the process state, in the absence of maintenance, only goes to worse condition. A preventive maintenance level is considered. The costs, the arrival rates and the probability of transfers and other assumed parameters, for this example, are presented in Tables 1-4. To solve the nonlinear model presented in section 2, taking into account the above parameters, a program is written in GAMS software (version 24.9.1). The optimal solution obtained using the BARON solver is Z* = 94.108, h*ii = 134, t^ = 2014, n^ = 5, k**i = 2.3. It should be noted that the unit of time in this example is in minutes. Sensitivity analysis was performed to observe the effect of model parameters on an optimal solution. The parameters we are interested in examining their impact are the cost of preventive maintenance, the cost of corrective maintenance and the magnitude of the changes. The sensitivity analysis parameters are presented in Table 5. The results of the sensitivity analysis are summarized in Table 6. As we see, the change in magnitude affects the value k11. As increases, k11 also increases. And it is logical that larger process changes necessarily require a larger control limit. Table 1 The exit rates between each mode (node) oui fáj 0211 ^0311 ^1211 ^¡/1311 ^¡/2311 ^'lll ¿fu Àins11 0.00025 0.000166 0.000125 0.0002 0.00011 0.000222 0.0222 0.00555 0.05 Table 2 The probability of transition between each mode (node) aisnl1 Q,ÍS ■]■]■] ttSim 1111 a'il211 0.0001 0.2999 0.7 0.3 0.3 0.4 0.6 0.3 0.1 Table 3 The costs "on_ci 111 ci?At ccmn_ctuj_cfn cvu cinsu_cstopu 0 100 200 2000 200 20 5 50 1000 Table 4 Other parameters 1.5 20 _ëËn. Table 5 Changes ccm11 and cl111 and 5 for sensitivity analysis Different states_ccm11_cl111_ State1 1000 State2 4000 State3 100 State4 400 State5 1 State6 3 Table 6 Sensitivity analysis results Different states Z1 fc11 State1 71.220 143 2023 3 1.85 State2 139.748 119 1999 5 2.25 State3 92.610 126 2006 3 1.67 State4 96.983 150 2030 4 2.3 State5 108.999 130 1930 3 1.98 State6 82.409 156 1680 3 2.9 12 Advances in Production Engineering & Management 14(1) 2019 An integrated optimization of quality control chart parameters and preventive maintenance using Markov chain As shown in Table 6, the cost of preventive maintenance affects both the sampling interval and the preventive maintenance interval and the sample size. As the cost of preventive maintenance is reduced, the sampling interval and the preventive maintenance interval and the sample size increases to ensure the performance of the production system. When the cost of corrective maintenance increases, the sampling interval and the preventive maintenance interval decreases, but the sample size increases. From Table 6, we can see that the relationship between the cost changes of model parameters and the optimal cost derived from the integrated model is not linear. By changing the cost parameters, the model variables that are related to repair and statistical quality control are changed so that the total cost of the integrated model is minimized. Therefore, this analysis shows that a potential cost reduction is done by applying an integrated model for determining repair and quality control policies. In today's competitive environments, cost reduction plays an important role in the performance of the production system. Changing non-cost parameters of the model also affected the optimal cost of the integrated model. This is also due to changes in the model variables, which simultaneously changed the variables related to repairs and quality control. The analysis results show that the change in input parameters affects both the preventive maintenance policy and the statistical process control policy, and simultaneously optimizes repair and quality control policies by minimizing the total cost of both policies. Moreover, these results indicate the dependence between these two policies. 4. Conclusion This paper presents an integrated model for optimizing statistical process control policies (sampling interval, sample size and control limit) and preventive maintenance (the preventive maintenance interval). The information obtained from the quality control charts was used to decide on the preventive maintenance interval. The proposed model was modeled in the form of a continuous time Markov chain, and the model was optimized with the cost-per-unit time scale. A numerical example is done to clarify the problem, and the sensitivity analysis shows the dependence between preventive maintenance and statistical process control. The contribution of this paper was to develop an integrated model to optimize preventive maintenance policy and statistical process control policy, which was modeled in the form of a continuous time Markov chain considering the length of time for preventive maintenance and corrective maintenance. The goal was to reduce costs per unit time. In this model, the duration of preventive maintenance and duration of corrective maintenance are not zero. Considering the length of time for corrective and preventive maintenance, this model is consistent with the reality of the production system. In addition, this assumption makes this model applicable to industrial environments, because in most cases, the duration of corrective and preventive maintenance is not negligible. This issue has not been considered in the literature on the integrated consideration of preventive maintenance and quality control of the process in the form of a Markov chain. This research gap was considered in this article. According to the results and findings of this research, it is possible in future researches to introduce production planning policies in this model. Considering the simultaneous optimization of production planning, preventive maintenance and statistical quality control is an interesting topic for future research. References [1] Tambe, P.P., Kulkarni, M.S. (2015). A superimposition based approach for maintenance and quality plan optimization with production schedule, availability, repair time and detection time constraints for a single machine, Journal of Manufacturing Systems, Vol. 37, Part 1, 17-32, doi: 10.1016/i.imsy.2015.09.009. [2] Hadidi, L.A., Al-Turki, U.M., Rahim, A. (2011). 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An integrated model for economic design of chi-square control chart and maintenance planning, Communications in Statistics - Theory and Methods, Vol. 47, No. 12, 2892-2907, doi: 10.1080/03610926.2017.1343848. 14 Advances in Production Engineering & Management 14(1) 2019 APEM jowatal Advances in Production Engineering & Management Volume 14 | Number 1 | March 2019 | pp 15-26 https://doi.Org/10.14743/apem2019.1.308 ISSN 1854-625G Journal home: apem-journal.org Original scientific paper Determination of nano-roughness for micro-objects by measuring the van der Waals force Bratina, B.a*, Šafarič, J.a, Uran, S.a, Šafarič, R.a aFaculty of Electrical Engineering and Computer Science, University of Maribor, Maribor, Slovenia A B S T R A C T A R T I C L E I N F O 3D printing or assembly techniques in the micro/nano-world enable production of micro-parts for building small machines or structures for biomedicine applications, such as cultivation of living cells in the field of Tissue Engineering. Micro-sized assembly requires automated manipulation procedures and methods for determination of suitable objects for assembly. The latter is possible by van der Waals force measurement and determination of distance at the van der Waals peak between two objects in contact. They are dependent not only on the Hamaker coefficients of the materials in contact and their geometries, but also on the nano-roughness asperities and crystal structure asperities of the contact surfaces. A method is presented for measuring van der Waals" force and determining micro-objects' (sizes between 10-100 |m) distances between materials in contact at the van der Waals peak in the presence of nano-roughness and crystal structure roughness. The proposed model was validated by experimental lab results between various materials and shapes (glass and polystyrene beads, metallic wires). © 2019 CPE, University of Maribor. All rights reserved. Keywords: Micro-object; Surface roughness; Nano-roughness; Van der Waals force; Distance at van der Waals peak *Corresponding author: bozidar.bratina@um.si (Bratina, B.) Article history: Received 14 September 2018 Revised 18 February 2019 Accepted 24 February 2019 1. Introduction 3D printing is becoming an essential part of rapid prototyping in Research and Development Departments. Today, classic and novel printing technologies enable printing of almost everything that can be designed. Also, the variety of printing materials and composites is increasing on the market (plastics, imitation wood, metals, etc.), which also makes possible prototyping of high end industrial products (jet engine blades, high-temperature and high-pressure rocket engine combustion chambers [1], airplane parts, etc.). However, additive manufacturing on a small scale, such as micro/ nano level 3D printing, presents one of the challenges. Scientists have developed many different deposition and hardening techniques (electron beam lithography, multiphoton polymerization, etc.), which enable printing of small objects to a micron level [2]. These 3D printing technologies have in common operating with light sensitive materials, resins, powders as an additive material which can later be treated for hardening On the other hand, 3D printing can also be managed by using micro/nano-objects assembled into a microstructure layer by layer [3, 4] (micro-machines, gearbox, motor, etc.), or structures with living cells, which could boost the field of Tissue Engineering. To be able to assemble given micro-objects into a structure, it is essential to have adequate equipment and to master the manipulation of material. Automated assembly procedures with micro/nano-manipulators include sensors to control the assembly process, hence detecting micro-objects for assembly, which are too small for machine vision applications. Therefore, a 15 Bratina, Šafarič, Uran, Šafarič method is needed to be able to determine if the object for assembly is adequate or not (dust particle, micro-object not adequate in size or material). In the paper such a method is presented, where micro-object' properties are measured by van der Waals force, and distances at van der Waals peak are determined between materials in contact. Similar measuring methods (atomic force microscope measurements, X-ray method etc.), are performed very rarely due to the expensive equipment used, whereas the presented method is quite simple, and gives similar accuracy results. Van der Waals force and distance at van der Waals peak Even on fine polished solid surfaces of materials (glass or polystyrene microbeads, metal wires, etc.), asperities are large in comparison with the size of the crystal structure (atoms or molecules) of the solid materials placed in contact. Most materials used in engineering practice have surface asperities (so-called nano-roughness) greater than few decades of a nano-metre. If two such solid materials are placed in contact, because of the mentioned asperities, the great areas of surfaces will be separated by a distance much greater than the molecular range of action [5]. Previously developed models of van der Waals forces [3] for a one-finger gripper, based on the van der Waals force, demand an accurate calculation of the van der Waals force at the point of contact. The van der Waals force between two objects in contact is dependent on the geometry of the objects, their materials (Hamaker coefficients), and the distance between the objects in contact. This paper focuses on the determination of the distances between objects in contact, with the presence of nano-roughness asperities and crystal structure asperities on both the contact surfaces (distance at van der Waals peak, Fig. 1). An assembly application of micro structures from micro/nano-objects [3] demands characterization of material properties, the identification and manipulation of micro-objects, and assembly techniques. For identification of the geometric features of a micro-sized object (size, diameter in the case of spherical or cylindrical shapes ...), measurements of the van der Waals contact forces are necessary, and demand an accurate measurement of the surface roughness of the micro-object. Determining the surface roughness of a micro-object has been proven to be problematic, whereas present methods can only give an inaccurate estimation or calculation of the roughness and, consequently, the van der Waals contact force. Three methods exist for measuring or determining the roughness of micro-sized objects. The first one, originally described by Rowland and Taylor [6], and later used by Alvarez [7], calculates the distances at van der Waals peak statistically from the distribution of intermolecular distances (Fig. 1) between most of the elements in the periodic system against a so-called oxygen probe. This method is based on the statistical analysis of the intermolecular contacts in X-ray crystal structures for determining the van der Waals radii. However, with this method, only the distances at van der Waals peak between the periodic system elements and the oxygen probe have been determined and published, while the contacts for a variety of other materials (except sulphur and hydrogen probes) have not yet been studied to the knowledge of the authors of this paper. The second method is the so-called analytical method, first described in Rumpf [8], and later used as a modified version by various authors [9-12, 14]. For this method, the square root of the mean square values of the surface roughness is measured with a precise AFM (Atomic Force Microscope), or by the electron beam evaporation method. The different models based on this method assume that the asperities are hemispherical caps on a smooth substrate [8]. Matope et al. [13] have suggested that the adhesion (van der Waals) force on surfaces exhibiting asperities should be written as a combination of sphere-sphere and sphere-plane surface interactions in the form: where A is the Hamaker coefficient, R is the radius of the micro-sized spherical object, Ho is the contact distance between the surface and the object, rms is the root of mean square values of the micro-object's surface roughness, and A is the peak-to-peak distance of the asperities of the surface roughness of the micro-object. These models calculate the van der Waals force between 16 Advances in Production Engineering & Management 14(1) 2019 Determination of nano-roughness for micro-objects by measuring the van der Waals force various micro-sized objects (spheres or blunt particles), where the rms of the surface roughness is measured on only one side of the materials in contact (usually the plane surface), while the rms of the surface roughness of the probe (sphere) is not measured at all. Instead, the distance Ho = 2-3 A (lA = 1010 m) is used between the material and the probe (sphere). The drawback of this model is that it gives precise results only for Fadh, where the probe has the exact value inside H0 = 2-3 A. Moreover, the difference between Fadh for the case when Ho = 2 A or 3 A, is more than 40 %. So, this method is quite inaccurate. Of course, this model is only suitable for calculating the van der Waals force between a plane surface and a sphere particle. The third method is the so-called computational method, which is in good agreement with our experiments [14]. The drawback of the third method is its complexity (fractal surfaces, Fourier Transforms), which makes it hard to apply, especially for quick estimations of the van der Waals force for specific systems. Our presented method solves all mentioned drawbacks (distances at van der Waals peak are known only for the elements of the periodic system against an O-probe, the use of only one side of a surface in contact, the distance Ho = 2-3 A produces huge errors in order to calculate the van der Waals force, and the complexity of the Eichenlaub's method). The developed method for determining the distance at van der Waals peak in the presence of nano-roughness and the crystal structure roughness of contact surfaces, is valid for arbitrary materials (not only pure elements against an oxygen probe) of micro-sized objects. In addition, it is also suitable for situations where two objects with different geometries have their own surface roughness. The developed surface model can also determine the roughness of the materials' surfaces in contact (distances at van der Waals peak) between micro-objects with materials 1 and 2, if the previously determined roughness between micro-objects with materials 1 and 1 and materials 2 and 2 are known. Moreover, it is simple to use, because its equations rely on only one parameter (distance at van der Waals peak), which is determined easily from the van der Waals force measurements. It is not necessary to use an AFM, beam-electron or other expensive microscopes. The paper structure is as follows. The second section of the paper presents a description of the method for determining distances at van der Waals peak in the presence of nano-roughness and crystal structure roughness on contact surfaces. The next section describes the laboratory set-up and the set of used equations for calculating the van der Waals force of two micro-sized objects in contact with different geometries, different materials and different roughness of materials. The third section presents experimental results and analysis, and fourth the conclusion of the paper. Fig. 1 Scheme for determining the distance between materials in contact at van der Waals peak 2. Materials and methods for surface roughness determination (distance at van der Waals peak) The determination of the distance at van der Waals peak demands precise measurements of the van der Waals force between two objects in contact. We focused on micro-sized objects of different shapes: Plane surface, cylinder with a radius of 25 [im, and spheres with a radius of 5-50 [im, chosen because of their availability on the market, which gives us the following van der Waals Advances in Production Engineering & Management 14(1) 2019 17 Bratina, Šafarič, Uran, Šafarič force measurement pairs: Plane surface-sphere, sphere-sphere, sphere-cylinder and cylinder-cylinder. The other two possible types of measurements, plane surface-plane surface and cylinder-plane surface, are not practical, due to problems with the alignment of both objects. Therefore, our method is based on four practical geometrical pairs. The laboratory set-up hardware was designed for 3D movement of both objects against each other. 2.1 Laboratory set-up and materials used in the experiments The laboratory set-up is shown in Fig. 2a. The nano-precision 3D manipulator system consists of an optic microscope, a turbo-molecular vacuum pump and a vacuum chamber with nano-precision 3D manipulator (Fig. 2b) inside. The vacuum can be set as low as 2 [ibar. Fig. 2b shows the nano-precision 3D manipulator mechanism, with x- and y-axes consisting of magnetic linear incremental encoder sensors that operate as a planar mechanism, and a z-axis with its own linear incremental sensor. Different end-effectors (tools, grippers, etc.) can be mounted on the 3D manipulator tip at the end of the y-axis. The y-axis is placed on a movable cart that moves along the x-axis' linear guide. All three piezo electric motors with sensors are mounted on an aluminium block that serves as a vibration-absorber to limit mechanical disturbances from the environment. The position accuracy of the robotic tip, along a single axis, is ± 3.9 nm in an open loop, while the position control loop of each axis has an accuracy of ± 61 nm. We also used a long distance focus (21 mm) optical microscope for observations of micro-objects up to 3 [im. A more precise description of the lab set-up can be found in [3, 4, 15]. Different micro-sized objects were used in the experiments: Metal wires, glass (SiO2) and polystyrene beads, glass surfaces and mica surfaces. The glass beads (radius 25-50 [im and 10-30 [im) were purchased from Polysciences, Inc., USA. The polystyrene beads (radius of 30 [im) were purchased from Kisker Biotech GMBH, Germany. The nickel wire (puratronic, radius 25 [im, LOT: E22Z008), palladium wire (hard, radius 25 [im, LOT: L15T030), aluminium wire (hard, radius 25 [im, LOT: G24Z014), silver wire (Premion, radius 25 [im, LOT: 13467) and gold wire (Premion, radius 25 [im, LOT: P21A023) were purchased from Alfa Aesar GmbH, Germany. All the metal wires had 99.99 % trace metals basis. Standard microscope slides (SiO2) were used for the glass surface plane, purchased from Logitech, UK. The Muscovite mica insulating slides were purchased from EA Elektronika, Slovenia. a) b> Fig. 2 The nano-precision 3D manipulator system a], and the nano-precision 3D manipulator mechanism b] 2.2 Used methods: Pull-off measurements of the van der Waals force Small attraction forces, such as the van der Waals forces between micro-sized objects in contact, are often measured using an AFM microscope. However, the presented pull-off method consisted of measuring the attraction force using a spring traverse [16]. Fig. 3 shows a schematic diagram of the four different types of measurements of the van der Waals forces between the geometrically different objects used in our experiments. The attraction force Fatr attracts the micro-sized objects when they have been put into contact. If the lower object is pulled away by the force F with z-axis (Fig. 3), then the traverse starts to deflect with the distance f The objects are "attached" together during the deflection due to the attraction force, and the objects in contact keep this position until the opposite traverse's elastic force F becomes equal to the attraction force. At that moment, the traverse tears away from the lower object towards a position of equilibrium, 18 Advances in Production Engineering & Management 14(1) 2019 Determination of nano-roughness for micro-objects by measuring the van der Waals force hence, the deflection f is measured. Calculation of the traverse's deflection force F and inertia h [17] for a circular cross-section is presented by Eq. 2: nd4 3fEIz F = ——- I = ' 64 ^ Fatr —F — 3fEnd4 /f.64 (2) where It is the length of the traverse, E is its Young's modulus, and d is its diameter. The measurements of Fatr were conducted in a vacuum chamber with pressure lower than 1 mbar to avoid capillary force effects. The static electric charge on the SiO2 (amorphous) plane surface was discharged by putting the tip of the traverse into contact with the plane surface for a moment, thus equalising the electrical charges. Both the traverse and the plane were also grounded electrically. Consequently, the capillary and electrostatic forces were avoided. Fig. 4a shows the measurement tool on the robotic tip with a mounted golden traverse and a glass plane, where the spherical object is glued. Fig. 4b shows the golden traverse touching the spherical glass object. The traverse and the object in Fig. 4b were observed through a microscope (the diameter of the traverse is 50 [im). glued spherical object to traverse cylindrical traverse (d=S0pm} glued spherical object to traverse cylindrical traverse (d=50nm( cylindrical traverse (d=50|im) ■St IÏ 01 T3 I ] fl ' ^__ 2= glued spherical object to 2-axis h axis cylindrical traverse (d=50(iir}| glued cylindrical traverse to z-axisr(d=50tim) perpendicularto upper traverse h force f c) d) Fig. 3 Schematic diagram of the four methods used for measuring attraction forces: a] Between micro-sized spheres, b) Between micro-sized spheres and the surface plane, c) Between micro-sized spheres and a cylinder and d) Between two perpendicular cylinders a) b) Fig. 4 Measurement tool a], and zoomed view - traverse touching a spherical object b] 2.3 Proposed model for determining the distance at van der Waals peak Four models were developed for determining (calculating) the distance at van der Waals peak from the measured van der Waals force F = Fatr (Eq. 2) which are presented next. The models for determining the distance at van der Waals peak for the following examples: Sphere-sphere (Fig. 3a), sphere-surface plane (Fig. 3b), and between two perpendicular cylinders (Fig. 3d) are easy to develop from known analytical equations for the van der Waals force between different Advances in Production Engineering & Management 14(1) 2019 19 Bratina, Šafarič, Uran, Šafarič geometrical objects [18-20]. The equations used for determining the average contact distance d or the distance at van der Waals peak are as follows: a) For sphere - sphere geometrical combination: AR1RZ F = (R1 + R2)6d2 ^ d = N + R2)6F b) For sphere - surface plane there is an approximate formula: ^ (3) AR f = 6^ ~ AR — (4) 6F c) And for two infinite perpendicular cylinders of the same radius, there is again an approximate formula: AR. ARC (5) 6F where A is the Hamaker coefficient, R1, R2, R are the radii of the spheres, Rc is the radius of the cylinder, and F is the van der Waals force in contact (Fatr), measured and calculated by Eq. 2. The situation is far more complex in the case when the distance at van der Waals peak is determined between a cylinder and a sphere. We found two sources [19, 21] where the authors claimed that they had developed an analytical expression for the van der Waals force between a sphere and an infinitive cylinder. Unfortunately, the expression used by Montgomery [19] was proven experimentally to be incorrect, due to an imprecise use of the Maclaurin series. Ref. [21] showed promising results when the expression was verified experimentally for the van der Waals force in contact. We have tried, unsuccessfully, to repeat the analytical development of the final result of ref. [21]Ns complicated expression, which is written as: ^ARl^ + ^ + s^Efy-sg + s^Q)} (6) 24c5/2R3/2s2p3/2 where p = 1+ s/2, s = ((d + Rs)2 — Rs2)/(2cRc), c = Rc + Rs + d, d is the distance between the sphere and the cylinder, Rc is the radius of the cylinder, Rs is the radius of the sphere, K and E are the complete elliptic integrals defined as: r/21- E(z)=\ V1-zsin29d9, (7) Jo n/2 K(z) = í i/Vi — zsin29d9. Jo (8) Instead of Eq. 6 [21] we derived our equation (9) for van der Waals force calculation between an infinite cylinder and a sphere from the same mathematical and physical assumptions. Both Eq. 6 and Eq. 9 were compared between themselves. We can confirm that the original equation derived in [21] is correct, because both equations gave the same numerical results for F when the distance d was used between 0.2 nm to 200 nm. Unfortunately, both Eq. 6 and Eq. 9 are not completely analytical, because it is not possible to derive analytical equations from them for the distance d. Rs+Rc+d _ [ r(c2-r2+R2) p= jd3 I _^_^__(9) s J c(-r2 + (c-Rc)2)1/2(r2-(c + Rc)2)1/2(r2-R^)5/2 Rs+d Both equations demand numerical calculation of the complete elliptic integrals or finite integrals. In order to calculate the distance d from the van der Waals force F, the theory of Artificial Neural Network was used to approximate the nonlinear inverse function of Eq. 6 and Eq. 9. The 20 Advances in Production Engineering & Management 14(1) 2019 Determination of nano-roughness for micro-objects by measuring the van der Waals force classical backpropagation learning rule was used for a two-layer feedforward neural network, with one input, one output, ten neurons in a hidden layer, and one neuron in the output layer of the network. The learned Artificial Neural Network serves as a nonlinear calculator for the distance d (distance at van der Waals peak) between a sphere and an infinitive cylinder when the measured van der Waals force F is used, (see Fig. 3c) [22]. The tolerance, between the approximated and reference value of distance at van der Waals peak, after the Artificial Neural Network learning phase (150 iterations), was lower than 0.1 % for all the reference values of distance at van der Waals peak between 0.1 nm to 200 nm. The learning input samples (training vector) consisted of 100 pairs of distance at van der Waals peak and their corresponding values of the van der Waals force F. The Artificial Neural Network was learned in only 100 samples of the training vector. The approximated values of distance at van der Waals peak were also valid and accurate between the mentioned learning points, due to the generalization between data pairs. 2.4 Determining the distance at van der Waals peak when both interacting objects have roughness The experiments published in [9-12] studied the nano-roughness, distribution of nano-roughness asperities and contact distances in the case where the measurement of an SiO2 spherical probe roughness was not known, but assumed to be between 2-3 A. Our newly proposed method takes into account both contact surfaces and their roughness affected by nano-roughness asperities and the crystal structure roughness of the contact surfaces - mentioned as the distance at van der Waals peak. Fig. 5 shows the scheme for describing contact surfaces with nano-roughness asperities and asperities due to the crystal structure of the material. The scheme in Fig. 5a shows the distance at van der Waals peak due to roughness dii between two objects of material 1. Fig. 5b shows the distance at van der Waals peak due to the roughness d22 between two objects of material 2, while Fig. 5c presents the distance at van der Waals peak due to the roughness dn between two objects of both materials 1 and 2. The following equation can be stated hypothetically: d12=-^+ -2^ ^ d11 = 2d12-d22 ^ d22 = 2d12-dlt. (10) So, if we can determine distances dn and d22, then we can determine the distance d12, or vice versa. Therefore, if two distances at van der Waals peak are determined, it is possible to calculate a third one. In the following section, the experimental laboratory measurements are presented, proving Eq. 10 and the models for calculating the van der Waals force in contact, described by Eq. 3, Eq. 4, Eq. 5 and Eq. 9. Fig. 5 The scheme of a cross-section of the distance at van der Waals peak due to nano-roughness asperities and the crystal structure asperities of the material in contact Advances in Production Engineering & Management 14(1) 2019 21 Bratina, Šafarič, Uran, Šafarič 3. Results and discussion Three different geometries and several different materials of micro-objects were used in the experiments, as described in subsections 2.2 and 2.3: Au cylinder, Ag cylinder, Al cylinder, Ni cylinder, Pd cylinder, polystyrene sphere, SiO2 sphere, SiO2 plane and a mica plane. 3.1 Measurements Thirty-two sets of measurements were done between different combinations of materials and geometries. Every set of measurements was done with twenty repetitions of measurements of deflection f After that, the measurements were eliminated which departed heavily from the average (1-6 measurements out of 20). The measured van der Waals force Fm (see Eq. 2) and the corresponding Standard Deviations, were calculated from the remaining measurements of deflection. Fig. 6 shows the elimination of the first three measurements of deflection for the measurement between two aluminium cylinders with the same diameter (d = 50 [im). The first three are marked with a diamond, while the remaining 17 measurements are marked with a star. Fig. 7, left, presents Hamaker coefficients A12 [zJ] between two materials across the vacuum used in measurements and calculations in our models. We used [23] as a source for the Hamaker coefficients between the metals (Ag, Al, Au, Ni, Pd) and the sapphire in a vacuum. We used [24] as a source for the Hamaker coefficients of the polystyrene, SiO2 and sapphire in a vacuum, and we used [25] as a source for the Hamaker coefficient of mica in a vacuum. Eq. 11 was used to calculate all the Hamaker coefficients Ahmadi [24] presented in Fig. 7, left. (11) Fig. 7, right, presents the measured values of van der Waals force Fm [^N] and their Standard Deviations calculated from the measured deflections. The same Fig. 7, right, also presents the calculated van der Waals force Fc [^N] obtained from the contact model of van der Waals forces using Eq. 3, Eq. 4, Eq. 5 and Eq. 9 for control check using calculated van der Waals distance dc [A]. The distances at van der Waals peak dm [A] between different materials and geometrical appearance were determined from Eq. 3 for the sphere-sphere geometrical combination, from Eq. 4 for the sphere-surface plane geometrical combination, from Eq. 5 for two infinite perpendicular cylinders with the same radius, and from the neural network for a cylinder-sphere combination. 9.5 9 35 8 ¥ 7.5 C c e 7 a 2 6.5 6 s.s 5 4.5 0 2 1 6 8 10 12 14 16 1S 20 Measurement No. Fig. 6 Elimination of the deflection measurements that deviated significantly from the average value in contact between two aluminium cylinders, both with diameters d = 50 |im Calculated distances at van der Waals peak dc [A] were cross-calculated with Eq. 10 from determined distances at van der Waals peak d12 or d22 or dn. Both distances at van der Waals peak dm [A] and dc [A] for materials used in the experiment are presented in Fig. 8, left. The absolute value of percentage deviation |Fd| [%] between measured and calculated van der Waals forces Fm and Fc were compared to validate the models for determining the van der Waals force in con 22 Advances in Production Engineering & Management 14(1) 2019 Determination of nano-roughness for micro-objects by measuring the van der Waals force Fig. 7 Hamaker coefficients between materials across the vacuum used in calculations Measured (Fm [|^N]), and calculated Fc [|iN] van der Waals forces in contact between different materials used in the experiment tact and presented in Fig. 8, right. So, for example, when material 1 is Ag and material 2 is Ag, the measured van der Waals force Fm with a value of 5.52 ± 0.32 [iN was measured (see Fig. 7, right) using the method described by Eq. 2 and Fig. 3d. Then, the value dm = du = 6.25 A for the Ag-Ag combination of materials was calculated using Eq. 5 (see Fig. 8, left). The same was done for an Al-Al combination of materials with the value dm = d22 = 4.62 A, and an Ag-Al combination of materials with the value dm = di2 = 5.52 A. After that, using Eq. 10, the value dc = di2 = dii/2 + d22/2 = 6.25 A /2 + 4.62 A /2 = 5.43 A was calculated. The value dc was used to obtain the calculated van der Waals force Fc = 5.47 [iN for the case of the Ag-Al combination of materials, using Eq. 5 again (see Fig. 8, right). The values Fc = 5.47 [iN and Fm = 5.35 ± 0.57 [iN for the Ag-Al combination of materials were compared, and, finally, the absolute value of percentage deviation between both values Fd = 2.6 % was calculated (see Fig. 8, right). With the same method, the measured and calculated values were cross calculated, and statistical validity was verified for the proposed method and model. This method used Eq. 3, Eq. 4, Eq. 5 and Eq. 9 for calculating van der Waals forces in contact. Finally, the average values dc = d11 were calculated for material combinations where both materials are the same (Ag-Ag, Al-Al, Au-Au, Ni-Ni, Pd-Pd, Polystyrene-Polystyrene, SiO2-SiO2). By using Eq. 10, we calculated all dc = du by using all possible combinations of the dm = du determined values. For example, to calculate the average dc = du = 6.24 A (see Fig. 8, left) for the material combination of Ag-Ag, six determined values of dm = d12 material combinations can be used; Ag-Al (dm = dn = 5.52 A), Ag-Au (dm = du = 6.30 A), Ag-Ni (dm = dn = 5.36 A), Ag-Pd (dm = d12 = 6.84 A), Ag-Polystyrene (dm = d12 = 4.34 A) and Ag-SiO2 (dm = du = 4.81 A). From the value dc = d11 for the material combination of Ag-Ag, obtained from the material combination of Ag-Al, we get dc = du (of Ag-Ag) = 2 dm (of Ag-Al) - dm (of Al-Al), as seen in Eq. 10. In this way, we obtained values dc = du for the material combination of Ag-Ag from all five remaining mate- Fig. 8 Determined dm [A] and calculated dc [A] distances at van der Waals peak and for materials used in the experiment, and Absolute value of percentage deviation |Fd | [%] between Fm and Fc Advances in Production Engineering & Management 14(1) 2019 23 Bratina, Šafarič, Uran, Šafarič rial combinations (Ag-Au, Ag-Ni, Ag-Pd, Ag-Polystyrene, Ag-SiO2). These six values dc = dn were averaged to achieve a final validation of the determined and calculated value of dc = dn = 6.24 A for the material combination of Ag-Ag. 3.2 Analysis of the results and discussion The calculated van der Waals force Fc corresponded with the measured van der Waals force Fm inside the -8.4 % to 12.5 % band. The most inaccurate values are in the column called SiO2 sphere, the highest Fd [%] gives the experimental measurements between the SiO2 sphere and the SiO2 sphere (12.5 %), and between the SiO2 sphere and the Au cylinder (-8.4 %). The reason for this is that the micro-sized and nano-sized roughness of the SiO2 spheres was "huge" in comparison with other materials. The asperities of roughness for the SiO2 spheres were so big that the spherical geometry of the SiO2 sphere was compromised (see Fig. 9, left). Consequently, the correct radius of the SiO2 sphere was not determined, and this fact produced a relatively huge error in calculating the distance at van der Waals peak d from the measured van der Waals force. Fig. 9 shows the micro-sized and nano-sized irregularities on the surface of some of the used materials in the experiment. We tried to avoid these irregularity problems by repeating the measurements of the deflection fin various places. Consequently, we had to move the contact points of measurement by a few micrometres each time. These problems were the source of occasionally scattered data of deflection measurements (Fig. 6), where the first three measurements were eliminated from the set of data used for calculating the average van der Waals force and its Standard Deviation. The next reason for the mistake was, again, the radii of spheres and cylinders used in the experiment. They were determined with an accuracy of ± 1 |m, which can lead to an error in calculating the van der Waals force up to ± 4 %. Another source of errors in the model of the van der Waals force in contact could be the Hamaker coefficients used in the experiments. Different sources give different values for the Hamaker coefficients of the used materials, however, this didn't increase the relative deviation (Fd [%]), but increased the absolute error of the calculated van der Waals forces and the determined distances at van der Waals peak. Of course, distances at van der Waals peak, determined by [7], (dAl), have to be smaller than our values dn, d12 and d22, because he used the crystallographic method to determine these. Therefore, their measurements were "not spoiled" by asperities of nano-roughness and the "roughness of the crystal structure" of the materials used in the experiment. Distances at van der Waals peak determined by our method were always higher than those obtained by Alvarez (distances at van der Waals peak determined for Ag-O is dAg = 5.2 A, for Al-O is dAl = 4.0 A, for Au-O is dAu = 4.0 A, for Ni-O is dm = 4.1 A, for Pd-O dpd = 4.2 A and for O-O is do = 3.3 A; O presents the oxygen probe, such as SiO2, Al2O3, etc) from the source [7] just for comparison with our determined distances at van der Waals peak. The distances at van der Waals peak determined by our method were always higher than those obtained by Alvarez [7]. There is only one exception, where the distance at van der Waals peak was determined and calculated between the Ag cylinder and the SiO2 sphere. We double checked our force measurements, but the determined values of distances at van der Waals peak were always between 4.8-4.9 A. We believe that in [7] there is an error in obtaining the distance at van der Waals peak by using the crystallographic method for the Ag-O measurements, because the author claimed that "Ag-O has a poorly defined peak and larger uncertainty in its position". SKhephere Ncjlimto An cylinder Fig. 9 SEM images of geometrical shapes and roughness of some of the materials used in the experiments 24 Advances in Production Engineering & Management 14(1) 2019 Determination of nano-roughness for micro-objects by measuring the van der Waals force It can also be confirmed by calculating the van der Waals radius for Ag. This can be seen in [27, 28], where van der Waals radius for Ag deviates from [7]. However, other data agree on the majority of other elements of the periodic system. Young's modulus E in Eq. 2 is also an example of an error in measuring the van der Waals force in contact using the pull-off method. Young's modulus for gold varies between 79-80 GPa, which brings measurement error of up to 1 %. For the final experiment, we built a one-layer triangle structure (Fig. 10] by using many micro objects (spheres] scattered on the plane surface. By using the presented method, we were able to determine the proper size of the micro-objects from Hamaker coefficient, geometry, and distance at van der Waals peak, prior to manipulation of the objects. If the measured van der Waals force was not as expected (too small or too big], the object was not suitable to be part of the microstructure. Fig. 10 Scattered micro-objects on the plane (left], and built triangle with cca. 30 |im spheres in diameter 4. Conclusion The paper presents a method for micro/ nano 3D assembly, where visual information about the objects is not available. By knowing the material type and geometry, a micro-object's properties (e.g. size] can be determined based on van der Waals force measurement and distance at van der Waals peak determination. We present a new model for determining the distance at van der Waals peak and, consequently, measuring the van der Waals force in contact between micro-sized objects, the micro-sized objects being of different materials (metallic wires...], shapes, nano-sized roughness and crystal structure roughness. We have demonstrated experimentally that the distance at van der Waals peak determined with our pull-off method determines the sum of the van der Waals radius, the average impact of nano-sized asperities and the crystal structure roughness of the materials' contact surfaces effectively. Our model for measuring the van der Waals force in contact is more accurate than [13], and easier to use than the methods previously published in [9-12], because they used more sophisticated methods with more expensive equipment (AFM, X-ray devices]. An important outcome is the experimental confirmation of Eq. 10, where, if the distances at van der Waals peak are determined between one type of material and a second type of material, we can derive the distance at van der Waals peak for a mixture of both types of material. Consequently, an accurate value of the van der Waals force can be calculated for both materials in contact. The drawback of the presented pull-off method for measuring van der Waals forces in contact is that it is highly sensitive to micro-sized irregularities, e.g. both, or even only one of the materials in contact, have micro-sized irregularities on their surface. Acknowledgement This research was partly funded by the Slovenian Research Agency under Grant No. P2-0123(B] Clothing Engineering and Textile Materials. o, $> (Z* •• » o*. o O o ,# O O O o o Advances in Production Engineering & Management 14(1) 2019 25 Bratina, Šafarič, Uran, Šafarič References [1] Ngo, T.D., Kashani, A., Imbalzano, G., Nguyen, K.T.Q., Hui, D. (2018). Additive manufacturing (3D printing): A review of materials, methods, applications and challenges, Composites Part B: Engineering, Vol. 143, 172-196, doi: 10.1016/j.compositesb.2018.02.012. [2] Ru, C., Luo, J., Xie, S., Sun, Y. (2014). A review of non-contact micro- and nano-printing technologies, Journal of Micromechanics and Microengineering, Vol. 24, No. 5, Article 053001, doi: 10.1088/0960-1317/24/5/053001. [3] Šafarič, R., Lukman, D. (2014). 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Van der Waals radii of elements, Inorganic Materials, Vol. 37, No. 9, 871-885, doi: 10.1023/ A:1011625728803. 26 Advances in Production Engineering & Management 14(1) 2019 APEM jowatal Advances in Production Engineering & Management Volume 14 | Number 1 | March 2019 | pp 27-38 https://doi.Org/10.14743/apem2019.1.309 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper Cutting performance of solid ceramic and carbide end milling tools in machining of nickel based alloy Inconel 718 and stainless steel 316L Grguras, D.a*, Kern, M.a, Pusavec, F.a aUniversity of Ljubljana, Faculty of Mechanical Engineering, Laboratory for Machining, Ljubljana, Slovenia A B S T R A C T A R T I C L E I N F O Machining of nickel based alloys is in most of the times affected via high mechanical and thermal loads, causing high wear tendency of carbide tools, even at relatively low cutting speeds. On the other hand, ceramic as a cutting material, is more chemically stable and retains its hardness even at higher temperatures (> 800 °C) when machining difficult-to-cut materials. Therefore, to increase productivity, as an alternative to carbide tools, full body ceramic milling tools are proposed. In this paper, high speed milling process, using full body ceramic end milling tools, was analysed in parallel to carbide tools. Tool life of ceramic tools was compared with tool life of more widely used carbide tools when milling two different difficult-to-cut materials, i. e. nickel based alloy Inconel 718 and austenitic stainless steel 316L, under different cooling lubrication conditions. In addition, surface integrity and cost analysis were taken into account. Results are showing that ceramic milling tools are increasing material removal rate and productivity. However, the overall efficiency of ceramic tools can still be economically questionable. © 2019 CPE, University of Maribor. All rights reserved. Keywords: Milling; Ceramic end mill; Carbide end mill; Inconel 718; Stainless steel 316L; Productivity *Corresponding author: damir.grguras@fs.uni-lj.si (Grguras, D.) Article history: Received 22 August 2018 Revised 4 March 2019 Accepted 5 March 2019 1. Introduction Nowadays, we are increasingly focused on the sustainability of machining processes, trying to avoid conventional machining where oil based cooling lubrication fluids (oilCLFs) are used. Those are increasing manufacturing expenses and are known to be one of the contaminants in environment, as well are harmful to human's health. Therefore, significantly cleaner and more environmentally friendly machining process would be dry machining. However, lack of cooling and lubricating effect, especially when machining difficult-to-cut materials, can reflect in high temperatures in the cutting zone, which shorten tool life and decrease productivity. In such cases, one of the options to increase productivity is to use other cooling lubrication techniques, such as cryogenics [1], or different tool materials, as ceramic, which can withstand higher temperatures then widely used carbide tools. Ceramic, as a cutting material, appeared relatively early (in 1935, USA), but its use was not economically justified until the 1960s. Ceramics main advantage is that it is stable even at high temperatures and in such retains its hardness (high compressive strength), has a good wear resistance and is chemically stable at elevated temperatures. To manufacture ceramic end milling tools, sintering manufacturing process is used. The fine-grained powder is pressed under high pressure and bounded at temperatures between 1200-1800 °C. Properties of the ceramic tools depend of the composition, the density of the structure, size and distribution of the grain 27 Grguraš, Kern, Pušavec and the sintering temperature. Due to these unique ceramic properties, ceramic tools are mainly used for machining of difficult-to-cut materials, primarily thinking of titanium and nickel based alloys that are unable to be machined with carbide tools without oilCLFs [2, 3]. An additional advantage of ceramic tools is that the cutting speed is three to ten times higher as at carbide tools, which contributes to a higher material removal rate (MRR) and consequently higher productivity [4]. However, researches [5] marked poor resistance of ceramic tools to dynamic mechanical stress, as main disadvantage of these tools. Narutaki et al. [6] were observing tool wear of three different ceramic tools when turning Inconel 718. They realized, if they use lower cutting speeds (100-300 m/min), best durability offers ceramic Al2O3 with added silicon carbide. If, however, the cutting speed is raised to a 500 m/min, more durable tool turns to be Al2O3 with added TiC. They have explained this by diffusiv-ity tests and temperature measurements. When machining with high cutting speeds, flank face has reached 1250-1300 °C, while the melting point of the Inconel 718 is 1550 °C. At such high temperature, diffusion is evident; when using ceramic tool with added SiC, diffusion of nickel from the workpiece material into the tool occurs. When using Si3N4 ceramics, silicon passes into Inconel 718 and chromium backwards into the tool. They marked Al2O3-TiC tool as most stable tool in such working conditions. Kitagawa et al. [7] also came to the same conclusion. Performances of ceramic tools reinforced with SiC, when milling Inconel 718, were researched by Elbestawi et al. [8]. They noticed three types of tool wear: (i) abrasion on the flank face, (ii) notch wear and (iii) the cavity on the rake face. Notch wear was the main reason for the tool failure when milling at full depth, with cutting speeds from 200 to 400 m/min. When milling with higher cutting speeds (400-700 m/min) and a smaller depth of cut, flank wear and wear on the secondary edge were the most dominant. Li e t al. [9] have analysed performance of SiAlON ceramic tools (Si3N4-Al2O3) when turning Inconel 718. For SiAlON ceramic tools notch wear with minimal damage of the cutting edge at low cutting speed (120 m/min) is noticeable. That begins to change at 240 m/min. When the speed is increased to 300 m/min, it is already possible to see a decrease in the notch formation and increase in flank wear. From most of published scientific researches, it has been observed that removable ceramic cutting tools - inserts were used. There are only a few scientific studies in which full body ceramic cutting tools were used. The reason for this lies in the complex manufacturing processes of ceramic rods and in complex grinding processes to manufacture full body ceramic tools. Some improvements on this field are presented in a paper of Uhlmann and Hubert [10], where proved that the nature of these ceramic cutting tools heavily depends on its composition. Celile e t al. [11] investigated wear mechanisms of solid SiAlON ceramic tools when milling Inconel 718. They showed that there were present severe adhesion of workpiece and formation of diffusion layer due to chemical interaction of the tool flank face and the workpiece. Additionally, high operating temperature of the tools (>1000 °C) was observed. It was found that thermal expansion coefficient of the diffusion layer on the tool is lower than expansion coefficient of the tools material. Therefore, thermal micro cracks were formed causing tool wear. Wang and Liu [12] made another study on full body ceramic tools, where they investigated cutting performances of different solid ceramic end milling tools in comparison with carbide tool in machining hardened AISI H13 steel. They came to conclusion that cutting forces of ceramic end milling tools are lower than that of the carbide tool, mainly due to low chemical activity of ceramic with workpiece material. Overall, Ti(C, N) ceramic end milling tools present best cutting performance considering cutting forces, surface quality and tool life. Many industrial applications demand machining process to be carried out in tight and narrow pockets and this can be only done with usage of solid end milling tools. According to the above presented review on the state of the art, it can be found that most of the studies were performed on the Inconel 718, as workpiece material, and with usage of ceramic cutting inserts, as a cutting tool. Moreover, there is a lack of studies using full body ceramic tools. To fulfil that gap, authors performed preliminary experiments [13] using full body ceramic milling tools in machining of Inconel 718, where they confirmed their suitability for milling of Inconel 718. Their cutting performance, when machining other workpiece materials, and their cost efficiency, in comparison 28 Advances in Production Engineering & Management 14(1) 2019 Cutting performance of solid ceramic and carbide end milling tools in machining of nickel based alloy Inconel 718 and ... to conventional carbide tools, were still questionable. Thus in this paper, full body ceramic end milling tools were used to machine two difficult-to-cut materials, i. e. nickel based alloy Inconel 718 and austenitic stainless steel (SS) 316L, under different cooling lubrication conditions. Focus is placed on analysis of tool wear, tool life, workpiece surface and nevertheless, the productivity and costs. 2. Materials and methods 2.1 Workpiece materials Difficult-to-cut nickel based alloy Inconel 718 and austenitic stainless steel (SS) 316L in the form of rods, with a diameter of 50 mm and a length of 200 mm, were used as a workpiece materials. Physical properties of both materials are presented in Table 1. Properties as high melting point, heat and wear resistance and high hardness at room temperature, are causing difficulties in machining operations. Nickel based alloy Inconel 718 is used in the most demanding operating conditions, in the presence of high pressures and high temperatures. Inconel 718 is often used in gas turbines for turbine blades in turbo-compressors as the rotor, in the nuclear power plants, in racing cars, weapons, the high temperature heat exchangers, etc. Machining of Inconel 718 with conventional machining processes with oil CLFs is difficult, due to remarkable strain hardening [16]. Thus, when machining Inconel 718, aggressive strategy is what we are looking for in order to increase the temperature to cause material softening that improves machining performances. In this manner, ceramic tools can be used due to their high temperature resistance [17-19]. Stainless steels are chromium-nickel alloys and can be divided into three basic groups: mar-tensitic steels, ferritic steels, and austenitic steels [20]. Most stainless steels are austenitic and are non-magnetic and cannot be quenched, but they can be welded. Moreover, they are also classified as difficult-to-cut alloys. Austenitic stainless steel 316L, also used in this research, is due to its properties widely used in the food, aerospace and pharmaceutical industry [21]. Table 1 Physical properties of nickel alloy Inconel 718 and stainless steel 316L [14, 15] Physical property Inconel 718 SS 316L Density [g/cm3] 8.2 7.9 Hardness [HRc] 36 25-39 Tensile strength [MPa] 1240 485 Thermal conductivity [W/m-K] 11.4 15 Specific heat [J/kg-K] 435 500 Melting point [°C] 1260-1336 1375-1400 2.2 Cutting tools and cutting parameters Ceramic tools have unique physical and mechanical properties, such as high hardness and low chemical reactivity with steels and many other materials. Consequently, they can be used to machine difficult-to-cut materials that are hard to be carried out with traditional tool materials. Thus, in this work, the solid ceramic end mills are compared with widely used carbide cutting tools. 6 edge flat Kennametal EADE (0600A6ARF) solid ceramic end milling tools, based on Si-AlON ceramic with CVD alumina coating and grade KYS40, were chosen. They have optimised geometry for roughing nickel based high temperature alloys and are not suitable for finishing applications. Chosen carbide tools were 5 edge Kennametal HARVI II series (UCDE0600A5ASA) KC643 grade, PVD coated with fine grain grade AlTiN coat. Diameter D of the tools was 6 mm. First experiments were carried out on machining Inconel 718 with ceramic end milling tools using cutting parameters as proposed by manufacturer. However, tool breakage occurred related to the failures of cutting edges and/or tool stems, as shown in Fig 1. Advances in Production Engineering & Management 14(1) 2019 29 Grguraš, Kern, Pušavec Fig. 1 Failure of cutting edges (left) and tool stem (right) Table 2 Cutting parameters Workpiece material Teeth per tool, z [/] Rotational speed of the tool, n [min-1] Cutting speed, Vc [m/min] Depth of cut, ap [mm] Width of cut, ae [mm] Feed speed, Vf [mm/min] Feed per tooth, fz [mm/tooth] Ceramic tool Inconel 718 and SS 316L 6 31830 600 0.375 4.0 4583 0.024 Carbide Inconel 718 5 2122 40 9.00 1.8 202 0.019 tool SS 316L 5 4244 80 9.00 1.8 615 0.029 With further experiments, we came to conclusion that tools failed due to mechanical overload in radial direction because of too big depth of cut (ap = 4.5 mm) and small width of cut (ae = 0.6 mm). To change the direction of mechanical loads, from radial to axial direction, milling strategy was changed. Depth of cut was reduced and width of cut was increased without affecting the MRR, consequently milling strategy was changed from side to face milling. New cutting parameters for ceramic tools were determined in collaboration with the tool manufacturer and are shown in the Table 2. Cutting parameters for carbide tools, also shown in Table 2, were given by the manufacturer. 2.3 Execution of experiments Milling of nickel based alloy Inconel 718 and stainless steel 316L were performed under different cooling lubrication conditions: in a dry, with minimal quantity lubrication (MQL), and with a blast of air in the case of ceramic tools and, in the case of carbide tools, flooding with emulsion. The third scenario represents the reference scenario for both. As a machining strategy on a high speed machining center Sodick MC 430 L, spiral strategy towards the center of the workpiece (Fig. 2) was chosen. Thus, continuous machining without interruptions and consequentially with less temperature fluctuations, which can result in tool damage, has been assured. The machining surface of workpiece rod was top end surface, which was clamped as shown in Fig. 2. One spiral milling from the outer diameter to the center of the round represents one level. After every level of removed material, the wear of the cutting tool was measured. The measurement were executed on 3D measuring device Alicona InfiniteFocus SL, where flank wear values were determined reaching the criteria VB = 0.3 mm or VBmax = 0.6 mm. Thus, tool life was obtained. Moreover, workpiece surface was analysed over energy-dispersive X-ray spectroscopy (EDX) using the scanning electron microscope (SEM) Jeol JSM 5610. Chips were also analysed. In addition, to get justification of the process from financial point of view, cost analysis was carried out. Fig. 2 Workpiece clamping (left), shrink-fit ceramic tool clamping (middle), spiral milling strategy (right) [13] 30 Advances in Production Engineering & Management 14(1) 2019 Cutting performance of solid ceramic and carbide end milling tools in machining of nickel based alloy Inconel 718 and ... 3. Results and discussion 3.1 Tool life and tool wear mechanisms During the experiments, the flank wear of end milling tools were measured with 3D measuring device Alicona InfiniteFocusSL. Tool life shown in Fig. 3 was recorder when the flank wear of the tools reached VB = 0.3 mm or VBmax = 0.6 mm. However, this requirement was not always reached. In case fracture of the cutting tool/edge has been observed, this has also been treated as end of the tool life. In the experiments, where carbide tools were used for machining SS 316L, cooling and lubrication conditions had major influence on the tool life. Tool life in dry machining was only 25.9 min, while in MQL and flood conditions tool life was prolonged to more than 375 min (for both conditions equally). In all of the experiments, no significant flank wear could be noticed. Before the cutting edge breakage, no flank wear was noticed, minor damages of cutting edge occurred, i.e. chipping (Fig. 4). Tool life of carbide tools, when machining Inconel 718, was significantly shorter in comparison to those used for machining SS 316L. Due to strain hardening of Inconel 718, breakage of the cutting edge is the main reason for tool failure. Best result of 6.0 min was achieved when flooding was used, while in dry the tool life reached 2.3 min and with MQL3.8 min. In the experiments, where ceramic tools were used for machining SS 316L, flank wear was evident. In dry conditions, the main wear mechanism was diffusion, the threshold of tool life was achieved in 1.2 min. When air-blast and MQL were used, tool life was longer (4.8 min and 4.4 min, respectively). As the tool wear increased, the amount of BUE also increased, influencing the cutting geometry in the cutting zone. Main wear mechanism was diffusion (also confirmed in [11]), chipping of the cutting edge was also present, unlike when machining Inconel 718, where this was the main wear mechanism (Fig 5). Because of chipping, geometry of the cutting edge changed, what resulted in chips being welded on the cutting edge (BUE). As a consequence, severe deformation of the workpiece material occurred, which resulted in even more severe material strain hardening. This normally increases forces applied to the end milling tool and loads on the cutting edge. Additionally, the flow of the workpiece material also changes, what was evident by the fact that there was much more chip side flow present. In dry condition, the tool life equals 3.1 min, when using air-blast it was 3.2 min, and when using MQL, it was only 0.8 min (due to breakage of the cutting tooth). Thus, it can be concluded that carbide tools have significantly shorter tool life when machining nickel-based alloy in comparison with stainless steel. This difference is not so significant when using ceramic cutting tools. Carbide Ceramic Dryo MQL Flood Machining parameters: SS 316L: Inconel 718: vc = 80 m/min vc = 40 m/min fz = 0.029 mm/tooth fz = 0.019 mm/tooth ap = 9 mm ap = 9 mm ae = 1.8 mm ae = 1.8 mm SS 316L Inconel 718 ^1.2 3.1 Dry Machining parameters: SS 316Land Inconel 718: vc = 600 m/min fz = 0.024 mm/tooth ap = 0.375 mm ae = 4 mm Fig. 3 Tool life achieved when milling Inconel 718 and SS 316L with ceramic and carbide tools Advances in Production Engineering & Management 14(1) 2019 31 Air-blast Grguraš, Kern, Pušavec Carbide Ceramic m o» «H IV Machining parameters: SS316L Inconel 718: vt = 80 m/min vc = 40 m/min fz = 0-039 mm/tooth fx = 0.019 m m /Ixxrth iiss^V4. Fig. 10 Chip shapes formed when milling SS 316L with ceramic and carbide tools (dry conditions) 3.4 Cost analysis Selection of tools in industrial applications is not only performed based on tools' performance, but also on its costs. In this research, total manufacturing cost for using ceramic or carbide tools were calculated. Ctotal is defined by Eq. 1, where Ctool is the total tooling cost, Change is the total cost of tool changes, and Cmachining is the cost of machining time required. All three costs are nor- Advances in Production Engineering & Management 14(1) 2019 BS Grguraš, Kern, Pušavec malized in the way that present expenses required to remove 1 cm3 of workpiece material. In this way, the productivity (MRR), as well as costs, can be compared between different tool performances. With this omitted is the problem with presenting results in relation to different MRR values of processes. Ctool can be written as Eq. 2, where Ctool is the cost of the tool and Vtotai is the volume of removed material with single tool. For calculations, cost of 93 € per ceramic tool and 44.2 € per carbide tool were considered. Change can be calculated using Eq. 3, where Cmachining is the cost of machining per unit time, including machining labour cost, i.e. 40 €/h and Change that represents the time to change a single tool (that includes a collection of non-machining time, set to 5 min). Cmachining can be calculate by Eq. 4, where MRR is material removal rate given by Eq. 5, where T presents the tool life. -total Qool ^Qchange ^Qnachining Qool = ctool/^total -change ^-machining ^change 60 ^total -machining = Whimng/(MRR-60) MRR=Ftotal/T (1) (2) (3) (4) (5) Cost analyses were performed and compared for experiments where longest tool life have been achieved. Results presented in Fig. 11 are showing that regardless of workpiece material, ceramic tools are more expensive than carbide tools. In experiments, where carbide tools were used for machining SS 316L (in flood conditions), the main expenses were machining costs. Tool costs and tool changing costs were insignificant due to long tool life. On the contrary, in other three experiments, tool life results were significantly shorter, which reflected in tool costs as the main expense. Regarding productivity, ceramic milling tools are offering 115 % higher MRR than carbide tools only when machining Inconel 718. However, there are still 39 % higher overall expenses of ceramics over carbide tools, as saved time due to higher productivity has less impact on total machining costs than purchase price of the tool. Inconel 718 SS 316L Costs of tool changes [€/cmft3] Machining costs [€/cmft3] Cutting tool costs [€/cmft3] Carbide (Flood) Ceramic (airblast) Carbide (flood) Ceramic (airblast) Machining parameters: Machining parameters: Carbide: Ceramic: Carbide: Ceramic: vc = 40 m/min vc = 600 m/min vc = 80 m/min vc = 600 m/min fz = 0.019 mm/tooth fz = 0.024 mm/tooth fz = 0.029 mm/tooth fz = 0.024 mm/tooth Qp = 9 mm ap = 0.375 mm ap = 9 mm ap = 0.375 mm ae = 1.8 mm ae = 4 mm ae = 1.8 mm ae = 4 mm Fig. 11 Cost analysis when milling Inconel 718 and SS 316L with ceramic and carbide tools 36 Advances in Production Engineering & Management 14(1) 2019 6.00 5.00 4.00 3.00 2.00 1.00 0.00 Cutting performance of solid ceramic and carbide end milling tools in machining of nickel based alloy Inconel 718 and ... 4. Conclusion This research comparatively investigates the cutting performance of solid ceramic end milling tools in machining of nickel based alloy Inconel 718 and austenitic stainless steel 316L, under different cooling lubrication conditions. Main objective was to determine machining performance of solid ceramic end milling tools in comparison with solid carbide tools, as most of the studies were done using interchangeable cutting inserts. Tool wear, tool life, workpiece surface and chip shapes and machining costs were analyzed. From the results concluded can be that: • Ceramic end milling tools have the longest tool life in dry milling conditions, i.e. 3.1 min (dry) or 3.2 min (air-blast). In addition, air blasting can improve chip evacuation and therefore, can prolong tool life of the ceramic tools. Furthermore, carbide tools should be used only in wet cooling and lubrication conditions (flooding with emulsion). • Main tool wear mechanism, using ceramic tools, is chipping of the cutting edge. This wear is especially pronounced when using MQL, which indicates that ceramic tools are prone to brittle fracturing when they are exposed to fast temperature changes. • Carbide tools with appropriate cooling and lubrication outperforms ceramic tools when machining SS 316L. It can be seen, that carbide tools in comparison with ceramic tools, had longer tool life and removed more material, which resulted also in a lower overall costs. • Ceramic tools provide better cutting performance in comparison with carbide tools only when machining of nickel based alloy Inconel 718 is performed dry. Moreover, ceramic end milling tools, which are offering higher MRR, removed more material in lifetime (18.2 cm3) than carbide tools (15.6 cm3). However, it is still questionable, if these differences are sufficient to cover the 39 % higher overall expenses of ceramics over carbide tools. Acknowledgement The authors gratefully acknowledge the support of the Slovenian Research agency (ARRS) for founding the research project L2-8184 and research program P2-0266. Authors also express their gratitude to the Kennametal Tools (USA) and prof. dr. Borut Kosec from Faculty of Natural Sciences and Engineering, Ljubljana (SLO) for their support. References [1] Jawahir, I.S., Attia, H., Biermann, D., Duflou, J., Klocke, F., Meyer, D., Newman, S.T., Pusavec, F., Putz, M., Rech, J., Schulze, V., Umbrello, D. (2016). Cryogenic manufacturing processes, C1RP Annals - Manufacturing Technology, Vol. 65, No. 2, 713-736, doi: 10.1016/j.cirp.2016.06.007. [2] Kopac, J., Sokovic, M. (1993). Machining technique - Modern cutting tools, (in Slovene), University of Maribor, Faculty of Mechanical Engineering, Ljubljana, Slovenia. [3] Cus, F. (1996). 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Behaviors of end milling Inconel 718 superalloy by cemented carbide tools, Journal of Materials Processing Technology, Vol. 201, No. 1-3, 460-465, doi: 10.1016/j.jmatprotec. 2007. 11.176. 38 Advances in Production Engineering & Management 14(1) 2019 Advances in Production Engineering & Management Volume 14 | Number 1 | March 2019 | pp 39-50 https://doi.Org/10.14743/apem2019.1.310 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper Two-stage product design selection by using PROMETHEE and Taguchi method: A case study Crnjac, M.a*, Aljinovic, A.a, Gjeldum, N.a, Mladineo, M.a aUniversity of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, Croatia A B S T R A C T A R T I C L E I N F O The main goal of this paper was to introduce the methodology for product design selection. The proposed methodology combines two classical methods to find the most appropriate design for the new product, through a reduced number of alternatives (product variants) and experiments for the selection process. In the first stage, the multi-criteria decision-making method, PROMETHEE was used for selecting the most suitable design, according to the chosen preferences and criteria. In the second stage, the Taguchi method was used in order to define the most appropriate parameters for selected suitable design. The fundamental scientific contribution of this paper refers to a benefit introduced by combining these methods. This benefit is related to the reduction of product development time which has a significant effect on manufacturing process time due to the high market pressure. The proposed methodology was applied to find the appropriate table design for CNC milling machine located in the Lean Learning factory. However, this is just one case study to present the proposed methodology which can be applied for other optimization of other product designs. Before applying the proposed methodology for this case study, the methodology is validated on a simple example. © 2019 CPE, University of Maribor. All rights reserved. Keywords: Learning factory; Lean manufacturing; Design optimization; PROMETHEE method; Taguchi method; *Corresponding author: mcrnjac@fesb.hr (Crnjac, M.) Article history: Received 9 October 2018 Revised 25 February 2019 Accepted 27 February 2019 1. Introduction Decision-making support in production is very important because it increases the competitiveness of companies. The digitalization introduction into the production system brings better support for decision-making. This is especially expressed during the development process of a new product. Embedded in 3D software, which is widely used for product design, there is also a very popular function of the Finite Element Method (FEM) simulation. During the development period of a new product, the methodology is very important because of the consequences that can affect cost and quality. Simulation helps to visualize how will the new product "behave" in its environment under the influence of different environmental factors. The step where it is necessary to choose the optimal design of that product represents the step of decision-making. This step means that the decision-maker identifies and selects an alternative from the set of alternatives (new product variants) based on its own preferences. Usually, there are several criteria to deal with, thus creating the multi-criteria problem and requiring multi-objective optimization. However, product design is a very complex problem, since the criteria are very often mutually conflicting, resulting with engineering trade-off when some product properties are deliberately weakened in favour of some more important property. It means that the decision-makers preferences are known and that enables solving product design problems with some of the Multi-Criteria-Decision-Making (MCDM) methods. MCDM is a discipline that includes mathematics, 39 Crnjac, Aljinovic, Gjeldum, Mladineo management, informatics, psychology, social science and economics. To solve the problem of choice and ranking, PROMETHEE method is often used [1]. MCDM methods are very popular in different areas, especially in operation research and logistics [2-4]. Avikal et al. [5] integrated Fuzzy Analytic Hierarchy Process (AHP) and PROMETHEE method in order to select tasks for assignment to the disassembly line. Fuzzy AHP was used to calculate the weights of each selected criterion while the PROMETHEE method was used for ranking the tasks. Peko et al. [6] showed the conduction of three different methods (AHP, Fuzzy AHP and PROMETHEE) to choose an appropriate additive manufacturing process. By comparing the results of each method, it is apparent that all methods gave the same rank of observed alternatives. Vinodh et al. [7] used PROMETHEE evaluation to select the best sustainable manufacturing concepts. There are three sustainability orientations according to production methodology, material and product design. They stated that the change of material is the best way to improve sustainability for the observed case. Can and Unuvar [8] present application of Taguchi method which enables reduction of experiments, when searching for the optimal parameters in the drilling process. On the other hand, Chang and Chen [9] integrated Taguchi method and TOPSIS algorithm to enhance the attractiveness of the product form. Another example of using the Taguchi method in product design development is given by Oz-tekin et al. [10]. The method is used to determine the combination of product properties to find a design which takes consumer emotions into consideration. All of the above studies are dealing with MCDM methods to solve various problems and some of them used Taguchi method to reduce the number of experiments. This paper combines the strengths of both methods (PROME-THEE and Taguchi) to choose the optimal design. The multi-objective optimization approach to product design selection is based on complex algorithms for shape optimization or its special case - the topology optimization. These algorithms are searching for the optimal design (shape) by considering, or not considering, some constraints. Usually, they are based on FEM and if the decision-maker preferences are unknown, it takes a dozens of days or weeks till the algorithm proposes the optimal shape or Pareto set of optimal shapes. In this research, that kind of approach is avoided, instead, it uses a different approach based ona priori knowledge [11] aboutproduct variants and decision-maker preferences. The two-stage methodology is proposed for selecting the most appropriate design for the new product. In the first stage, the multi-criteria decision-making method PROMETHEE is used for selecting the most suitable design according to the chosen preferences and criteria. In the second stage, the Taguchi method is used in order to define the most appropriate parameters for selected suitable design (parameters like the diameter of the steel bar, the thickness of the steel tube, etc.). The methodology is developed so it could be applied in the Learning Factory environment, within the "Development of integrative procedure for management of production and service improvement process" (DEPROCIM) project funded by the Unity through Knowledge Fund (UKF). The Lean Learning Factory (LLF) is the realistic factory environment created in the Laboratory for industrial engineering, at the University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture (FESB). The LLF idea at FESB is to create an environment for research and development to provide knowledge transfer into the economy [12]. Learning factories should ensure appropriate and up-to-date knowledge about innovations [13]. It allows you to simulate various tasks that appear within a real-world manufacturing environment what helps students and industrial participants to gain knowledge faster [14]. The connection between digital models and methods, including simulation and 3D visualization, is done to integrate planning, implementation, control and on-going improvement [15]. This paper is organized as followed. In section 2, the observed problem is described. Section 3 shows steps of proposed methodology for product design selection. Section 4 explores the case study from the Lean Learning factory and emphasizes the advantage of using proposed methodology instead of classical methods. Section 5 sums up the contribution of this paper. 40 Advances in Production Engineering & Management 14(1) 2019 Two-stage product design selection by using PROMETHEE and Taguchi method: A case study 2. Problem description Within the DEPROCIM project, the improvement of the case study on FESB, as one project goal, required further development of existing milling machine in order to support assembly line with the production of certain parts necessary for assembly. This paper presents modelling and simulation for choosing an optimal table design for the milling machine in the LLF environment, shown in Fig. 1. The compact design will increase the rigidity of the milling machine because the table legs will overtake feed forces necessary for the milling process. Other improvements on this milling machine include steel T-slot plate and improved linear guides. Three different designs of tables had been taken into consideration. 3D models of each table design are shown in Fig. 2. For all table designs, the material is construction steel (St 44-2). The legs, frame, stiffener and table base are made of tubes with the quadratic cross-section, with thickness 3 mm. The table width, length and height are predefined. There is also the steel T-slot plate which is predefined. Fig. 1 Milling machine in LLF environment (real image and 3D) Fig. 2 3D models of Table design 1, 2 and 3 3. Proposed method for product design selection This study uses the combination of two classic methods for product design selection, PROME-THEE (Preference Ranking Organization Method for Enrichment Evaluations) method and Taguchi method. The PROMETHEE method was used for selecting the most suitable design between proposed ones. The selected design was further used in Taguchi method for evaluation of the most appropriate combination of parameters. In order to gain all the necessary data for the mentioned methods, the first step was the creation of 3D models and their simulation by using the FEM analysis. The idea of FEM is a piecewise approximation. The solution to a complicated problem is obtained by dividing the region of interest into small regions (finite elements) and approximating the solution over each sub-region by a simple function [16]. This method has become popular and it represents a powerful analytical tool for studying different engineering problems [17, 18]. The PROMETHEE method combined with Taguchi method is carried out according to the input criteria provided by decision-maker and simulation results, Fig 3. Fig. 3 Methodology for decision making for product design Advances in Production Engineering & Management 14(1) 2019 41 Crnjac, Aljinovic, Gjeldum, Mladineo 3.1 PROMETHEE method The PROMETHEE method is widely used because it has the adaptability to different problems and its implementation is simple [19-21]. This method was developed by J. P. Brans. Input information for the PROMETHEE method is a definition of several important criteria and decisionmakers' preferences. It represents the definition of the function of decision-makers' preferences [22]. The function of preferences provides quantitative determination of how decision-maker prefers an alternative a in relation to alternative b. The function of preferences is defined for each criterion and its values may be in the range between 0 and 1. If the function of preferences is low, it means that the indifference between two alternatives is bigger for the decision-maker. If the value of the function of preferences is close to 1, then the preference of one alternative is bigger than the other. Complete preference of one alternative means that the function of preferences is 1. The function f(a) represents the assessment of alternative a for specific criteria and alternative a belongs to the set A. If the two alternatives, a and b, are taken from the set A, the relation of preference of the alternative a according to the alternative b is defined by function P(a,b). In this example the function P(a,b) is P(d) where d represents: d = m-nb) (1) The function of preferences has six different types. Those types cover most cases in practice and decision-maker should define parameters according to the chosen criteria [23]. 3.2 Taguchi method The founder of the Taguchi method is Genichi Taguchi. His robust design method was applied in the quality field but it can be applied to different problems in many industries. It is also the support for decision making. There are three important design stages in the Taguchi method [24]. System design, which is characterized by definition of the problem and application of knowledge and achievements to develop a prototype that represents the initial state of the product or process features. Parameter design determines the initial states of all features, which will minimize product or process variations. In recent years, Taguchi method has become a powerful tool for improving products and processes [25]. The orthogonal field is selected depending on the number of controlled parameters. The experiments are performed based on the orthogonal field, the data are analysed and the optimal state is identified. Tolerance design determines the tolerance of features, which will minimize product or process variations. P-diagram used as the base model for the Taguchi method is shown in Fig. 4. control factors signal factor (M) 11- 1 -► product or process -► î î - Î noise factors Fig. 4 P-diagram [24] There is the signal factor and the response, but there are also control and noise factors that affect the process or the product. The main goal of the Taguchi method is to reduce losses of product or process due to deviations from its properties of the desired value. Taguchi defines quality loss as: L(y-) = k(y-m)2 (2) Where y is the quality characteristic of a product, m is the target value for y. The k is constant and represents the coefficient of quality loss. There are four variations of the quadratic loss function: nominal the best, smaller the better, larger the better and asymmetric. This paper uses the smaller the better variation of the loss function. 42 Advances in Production Engineering & Management 14(1) 2019 Two-stage product design selection by using PROMETHEE and Taguchi method: A case study 4. Case study: Results and discussion To demonstrate the advantages of the proposed methodology that will be used for concrete problem, table design for CNC milling machine, its application on less complex design was introduced in the beginning of this section. Besides the structure complexity, less complex design means a smaller number of overall possible alternatives and thereby, a smaller number of total experiments that need to carry out. In the PROMETHEE method, for the simple example, all alternatives were included in the selection of the design for Taguchi, to show the comparison of the final result obtained with the classic method and proposed methodology. 4.1 Simple example - PROMETHEE method The basic principles to implement the PROMETHEE method is a pairwise comparison of alternatives evaluated according to determined criteria which have to be maximized or minimized. According to the literature, there are many different criteria for selection. The choice depends on the concrete problem. The aim of this following example is to show the choice of criteria and selection of appropriate design, Fig. 5. For each product design, three criteria (legs, frame and stiffener) were selected. Each of these criteria has two levels: the first level of legs is 40 mm and second 50 mm, criteria frame has 40 mm and 50 mm; criteria stiffener 20 mm and 30 mm respectively. These designs were loaded with force to demonstrate displacements through X, Y and Z-axis. The legs, frame and stiffener are made of tubes with the quadratic cross-section, with 2 mm thickness. The width, height and material of construction are predefined. Through these combinations of levels, 8 alternatives were generated for each product design. That represents all possible alternatives of variants A and B. The preference functions for each of these criteria are determined according to Fig. 6. For each criterion, despite the determination min or max of function preferences, it was necessary to define the relative importance (the weights). These values of the weight coefficient are present in percentage with the total amount of 100 %. For criteria that have determined linear as preference function, the value of indifference threshold q and the value of strict preference threshold p are also defined. For each alternative, required data were entered and thus an input matrix was formed, Fig. 6. Positive outranking flow, Phi+, is an aggregated outranking sum of each alternative over the other alternatives, while negative outranking flow, Phi-, shows how alternative is dominated by the other alternatives [26]. According to the usage of mentioned outranking flows, it is possible to define two approaches for alternative ranking, PROMETHEE I and PROMETHEE II. PROMETHEE I represents the partial ranking of alternatives and PROMETHEE II represents the full ranking of alternatives. For this example, the PROMETHEE method was conducted two times. The first approach includes all possible alternatives of design A and design B. It gives their overall ranking, as is shown in Table 1. The best rank belongs to B4 alternative. The second approach presents the first step of the proposed methodology. Instead of ranking all potential combinations (16 in this case), a selection between two potential designs was made. The analysis shows that B variant should be observed for further optimization, Fig. 7. 1000 kg 1000 kg M 800 mm 4-—-► Fig. 5 Variants of product design S £ o o Advances in Production Engineering & Management 14(1) 2019 43 Crnjac, Aljinovic, Gjeldum, Mladineo Scenariol Mass Displ.X Displ.Y Pispl.Z Unit kg mm mm mm Cluster/Group ■ ♦ • Preferences Min/Max min min min min Weight 0,25 0,25 0,25 0,25 Preference F n. Linear Linear Linear Linear Tresholds absolute absolute absolute absolute -Q: Indiferente 0,00 0,0000 0,0000 0,0000 ■P: Preference 2,75 0,5000 0,5000 0,5000 -S: Gaussian n/a n/a n/a n/a Statistics Evaluations Al 8,16 0,5540 0,0470 1,8330 A2 8,76 0,5280 0,0394 1,7400 A3 8,60 0,3450 0,0780 1,3410 A4 9,19 0,3390 0,0790 1,2280 A5 □ 9,19 0,3620 0,0485 1,4520 AG ■ 9,78 0,3510 0,0356 1,4010 A7 □ 9,69 0,3000 0,0590 0,9910 A8 □ 10,28 0,2930 0,0515 0,9710 B1 ♦ 7,53 0,4340 0,0313 1,6250 B2 O 8,37 0,2800 0,2090 1,1370 B3 ♦ 7,97 0,2940 0,0600 1,2500 B4 ♦ 8,82 0,2110 0,0502 0,9900 B5 o 8,59 0,2840 0,0363 1,3340 B6 ♦ 9,41 0,2080 0,0387 1,0340 B7 o 9,08 0,2500 0,0313 0,9390 BS o 9,92 0,1970 0,0323 0,7950 THE D.«i HlKO.H PROMETHEE IZDi ■ B7 BS BS B3 A7 B2 B5 AS A4 A3 BI A5 A6 Al A2 — — ■ TJW Displ.X Oispl.Y 25% □ ¡spi.Z Fig. 6 Input matrix and results according to PROMETHEE I and PROMETHEE II (for all variants) Table 1 All alternatives of product variants Alter- Legs Frame Stiffener Displ. X Displ. Y Displ. Z Mass [kg] PROMETHEE native [mm] [mm] [mm] [mm] [mm] [mm] rank A1 40 40 20 0.5540 0.04y0 1.8330 8.16 15 A2 40 40 30 0.5280 0.0394 1.y400 8.y6 16 A3 40 50 20 0.3450 0.0y80 1.3410 8.60 11 A4 40 50 30 0.3390 0.0y90 1.2880 9.19 10 A5 50 40 20 0.3620 0.0485 1.4520 9.19 13 A6 50 40 30 0.3510 0.0356 1.4010 9.y8 14 Ay 50 50 20 0.3000 0.0590 0.9910 9.69 6 A8 50 50 30 0.2930 0.0515 0.9y10 10.28 9 B1 40 40 20 0.4340 0.0313 1.6250 y.53 12 B2 40 40 30 0.2800 0.0209 1.3y00 8.3y y B3 40 50 20 0.2940 0.0600 1.2500 y.9y 5 B4 40 50 30 0.2110 0.0502 0.9900 8.82 1 B5 50 40 20 0.2840 0.0363 1.3340 8.59 8 B6 50 40 30 0.2080 0.038y 1.0340 9.41 4 By 50 50 20 0.2500 0.0313 0.9390 9.08 2 B8 50 50 30 0.19y0 0.0323 0.y950 9.92 3 Scenariol Mass Displ.X Displ.Y Displ.Z Unit kg mm mm mm Cluster/Group ■ C • Prefe rences Min/Max min min min min Weight 0,25 0,25 0,25 0,25 Preference Fn. Linear Linear Linear Linear Tresholds absolute absolute absolute absolute -Q: Indiference 0,00 0,0000 0,0000 0,0000 -P: Preference 2,75 0,5000 0,5000 0,5000 -S: Gaussian n/a n/a n/a n/a Statistics Evaluations Variant A ■ 9,78 0,3510 0,0356 1,4010 Variant B o 9,41 0,2080 0,0387 1,0340 PROMETHE Fig. 7 Input matrix and results according to PROMETHEE I and PROMETHEE II (for two designs) 44 Advances in Production Engineering & Management 14(1) 2019 Two-stage product design selection by using PROMETHEE and Taguchi method: A case study 4.2 Simple example - Taguchi method In order to create the plan of experiments, it was necessary to define parameters and their levels as it is mentioned before. To reduce the number of experiments, the orthogonal arrays are used in the Taguchi method. It represents the partial plan of experiments. The orthogonal arrays enable the observation of the effect on an individual parameter regardless of the evaluation of the effects of other system parameters. Definition of key parameters and their levels determines an appropriate orthogonal array. For this example, the L4 is chosen as an orthogonal array because there are three key parameters on two different levels which are shown in Fig. 1. Orthogonal array L4 covers 4 experiments, according to the literature [24]. Parameters and their levels were entered in Design Expert 11.0, where Taguchi method is used to find the best combination of parameters according to chosen levels. Data about the given combination for B variant are shown in Table 2. To conduct the Taguchi method for this example, due to dispersion of response data, it was necessary to include two more experiments to gain a significant model that can be used to navigate the design space. The value of signal to noise ratio for this model is 16.43 and that indicates an adequate signal. The analysis of variance for response displacement Z is shown in Table 3, F-value is 36.17 which implies that the model is significant There is only 2.70 % chance that F-value could appear due to noise. p-values less than 0.05 indicate that the model factors (A, B, C) are significant. The main aim during the analysis of responses was the minimization of displacements and mass. For the purposes of analysis, it was necessary to define the importance for each response. According to the conducted FEM analysis, the chosen vertical loads have the greatest influence on the movements in the direction of the Z-axis, hence response displacement Z has the highest importance. The selected combination of parameters for this example is shown in Table 4. The Taguchi optimum obtained with the proposed methodology is B design with dimensions of 40x50x30 mm. By comparing this final solution with the PROMETHEE solutions in Table 1, in which rang 1 means real optimum design (B4 design), i.e. the most suitable choice, it is obvious that these two methods show the same final solution. Table 2 The plan of experiments for B variant Run Legs Frame Stiffener Displ. X Displ. Y Displ. Z Mass [mm] [mm] [mm] [mm] [mm] [mm] [kg] 1 40 40 20 0.4340 0.0313 1.6250 7,53 2 50 50 20 0.2500 0.0313 0.9390 9,08 3 40 50 30 0.2110 0.0502 0.9900 8,82 4 50 40 30 0.2080 0.0387 1.0340 9,41 5 50 40 20 0.2810 0.0364 1.3320 8,59 6 50 50 30 0.1970 0.0323 0.7950 9,92 Table 3 ANOVA for selected factorial model, response: displacement Z Source Sum of squares df Mean square F-value p-value Model 0.4551 3 0.1517 36.17 0.0270 significant A-legs 0.1060 1 0.1060 25.28 0.0374 B-frame 0.1550 1 0.1550 36.97 0.0260 C-stiffener 0.0807 1 0.0807 19.24 0.0482 Residual 0.0084 2 0.0042 Cor Total 0.4635 5 Table 4 Selected solution No Legs Frame Stiffener Displ. X Displ. Y Displ. Z Mass [mm] [mm] [mm] [mm] [mm] [mm] [kg] 1 40 50 30 0.245 0.050 1.014 8.83 0.242 selected Advances in Production Engineering & Management 14(1) 2019 45 Crnjac, Aljinovic, Gjeldum, Mladineo 4.3 Table example - Criteria formation and analysis of the results obtained by PROMETHEE method According to the presented problem in section 2, the input data necessary to select the best alternative for table design using the PROMETHEE method is defined, as is shown in Fig. 8. For this purpose, five criteria for three variants are observed. As the cost of the table is the most important factor which should fit in the limited budget, the development of three variants of the tables is done in order to get different table shapes for the approximately same cost. Considering that the cost for each table design does not deviate significantly, it is not taken as criteria for the PROMETHEE method. The preference functions for each of the criteria are determined according to [23, 27]. For criteria mass and displacements, the preference function is linear. Linear functions are the best for quantitative criteria (for example: prices, costs, power, etc.). In the case of the small number of levels, on the criterion scale (that is 5-point scale) for qualitative criteria, the usual preference function is recommended and therefore used [22]. For this scenario, criteria are defined according to subjective opinion. In the preference category, it is necessary to define max or min preferences for each criterion, which is the maximum for construction criterion and minimum for the rest. The construction criterion for this case is based on qualitative assessment of the construction strength, with regard to its shape and assembly. In this case, the assembly is not included as individual criterion because this product will be assembled in LLF. Generally, when using this method, the complexity of assembly could be included as a criterion. Through this criterion, it is possible to have an effect on the assembly process, which will reflect on whole manufacturing process efficiency. However, the contribution of this criterion on the assembly process will be affected by the definition of criteria weights, preference functions and its values. The most suitable solution is the one that acquires the overall preference as close as possible to the value +1 (greatest possible preferences). PROMETHEE I shows the ranking of alternatives at the left side of Fig. 9. The alternative with the highest priority is table design 1 and it has domination above other designs. Table design 2 and 3 are incomparable with each other because table design 2 has the better score on Phi+ and worse score on Phi- and vice versa for table design 3. At the right side of Fig. 9, there is a complete ranking with PROMETHEE II, which confirms our previous statements. The results of partial and complete ranking demonstrate that the table design 1 is the most favourable, with the preferences of +0.1801, hence this alternative is used for further optimization with Taguchi method. Scenanol Construction Mass Displ.X Displ.Y DispE.Z Unit S-point kg mm mm mm Cluster/Group ♦ ■ ■ Preferences Min/Max max min min min min Weight 0,20 0,20 0,20 0,20 0,20 Preference Fn. Usual Linear Linear Linear Linear Tresholds absolute absolute absolute absolute absolute -Q: Indiference n/a 5,00 0,0000 0,0000 0,0000 -P: Preference n/a 25,00 0,5000 0,5000 0,5000 -S; Gaussian n/a n/a n/a n/a n/a Statistics Minimum 4,00 234,00 0,0062 0,0186 0,0035 Maximum 5,00 244,00 0,0077 0,0215 0,0180 Average 4,33 239,00 0,0070 0,0201 0,0113 Standard Dev. 0,47 4,08 0,0006 0.0012 0,0060 Evaluations TableDesignl [ very good 244,00 0,0062 0,0201 0,0035 TableDesign2 Q good 239,00 0,0072 0,0186 0,0123 TableDesign3 ^ good 234,00 0,0077 0,0215 0,0180 Fig. 8 Input matrix for PROMETHEE method 46 Advances in Production Engineering & Management 14(1) 2019 Two-stage product design selection by using PROMETHEE and Taguchi method: A case study Fig. 9 Partial ranking with PROMETHEE I and complete ranking with PROMETHEE II for the best table design 4.4 Table example - Criteria formation and analysis of the results obtained by Taguchi method Table design 1 has domination above other designs and its key parameters were defined. The data about experiments are shown in Table 5. For each variant of table design 1, generated by software Design Expert, from 1 to 9, displacement and mass were calculated by using NX Siemens 10.0 software. To calculate displacement, it was necessary to define loads for table design 1. The loads are shown in Fig. 10 and the fixed constraint is set on the surface of legs that lay on the floor. Table 5 The plan of experiments from Design Expert 11.0 software Run Factor 1: Factor 2: Factor 3: Response Response Response 3: Response 4: Legs & frame Stiffener Table base 1: Displ. X 2: Displ. Y Displ. Z Mass [kg] [mm] [mm] [mm] [mm] [mm] [mm] 1 50 40 50 6.60E-03 2.10E-02 3.93E-03 239.67 2 70 40 40 6.10E-03 2.33E-02 3.56E-03 252.27 3 60 40 60 4.80E-03 1.44E-02 2.99E-03 255.96 4 50 50 60 5.40E-03 1.60E-02 2.83E-03 251.12 5 60 30 50 5.80E-03 1.87E-02 3.74E-03 244.72 6 70 50 50 5.10E-03 1.73E-02 2.55E-03 263.38 7 70 30 60 4.50E-03 1.37E-02 2.72E-03 260.95 8 60 50 40 6.60E-03 2.40E-02 4.23E-03 247.39 9 50 30 40 8.20E-03 2.85E-02 5.52E-03 228.42 200 N .SOON 200 N /lOON / 100 N on Ul// w if Fig. 10 The load distribution for table design 1 Advances in Production Engineering & Management 14(1) 2019 47 Crnjac, Aljinovic, Gjeldum, Mladineo The results of the experiments are analysed and significant parameters are detected. The analysis of variance (ANOVA) verifies the influence on system response when parameters are changing [28]. The ANOVA shows F-value 76.88 which means that the model is significant. It is 1.29 % chance that F-value could appear because of noise. p-values that are less than 0.05 indicate model terms are significant. In this case, legs & frame and table base are significant in model terms. Stiffener has p-value that is higher than 0.1, that means that it is not significant in model terms. S-N ratio measures the signal to noise ratio which is 24.98. When this ratio is greater than 4, it indicates an adequate signal as it was mentioned in a simple example. The main effect plots are shown in Fig. 11 for displacement Y. It is visible that stiffener is not significant for the model. The ANOVA for response mass shows F-value 14519.51 which means that the model is significant. It is 0.01 % chance that F-value could appear because of noise. In this case, legs & frame, stiffener and table base are significant in model terms. S-N ratio is 380.858 and it is desirable. It indicates an adequate signal. Displacement and mass were chosen as responses that should be minimum. The importance is higher for the displacement than for the mass. For displacement Y lower limit is 0.0137 mm and the upper limit is 0.0285 mm. For mass, the lower limit is 228.42 kg and the upper limit is 263.38 kg. The optimal solution is found and parameters for table design 1 are: legs & frame 60 mm, stiffener 40 mm, table base 60 mm. For this combination of parameters, displacements and mass are shown in Table 6. The Taguchi method has found 24 solutions. As the optimal solution it gives the combination of parameters under the run 3, which is part of the previous plan of experiments, shown in Table 5. A: legs+lraiiie {mm) It: s(iffener (mm) C: table base (in ill) Fig. 11 Main effects for response displacement Y, change of each factor depending on level Table 6 Solution for the best parameters of table design 1 No. Legs & Frame Stiffener Table base Displ. X Displ. Y Displ. Z Mass Desir- [mm] [mm] [mm] [mm] [mm] [mm] [kg] ability 1 60 40 60 0.005 0.014 0.003 256 0.579 selected 4.5 Two stage selection of product design using PROMETHEE and Taguchi method: Discussion The main aim of this paper was to show an advantage of the proposed methodology with an emphasis on the number of experiments that have to be done. Table 7 shows the comparison of differences between classical methods and proposed methodology in terms of the number of variants on the simple example presented in section 4 and the design of table for CNC milling machine. The simple example consists of 2 designs with 3 factors on 2 levels, which means that for the PROMETHEE method it is necessary to prepare 16 variants. If the design of table for CNC milling machine is chosen using the mentioned method, it will be necessary to prepare 81 variants. The simple example was conducted to verify the final result of the proposed methodology with the result obtained by the classical method. It can be seen that the real optimum result from PROMETHEE method coincides with Taguchi optimum gained by the proposed methodology. 48 Advances in Production Engineering & Management 14(1) 2019 Two-stage product design selection by using PROMETHEE and Taguchi method: A case study Table 7 Comparison of different approaches and number of necessary variants to include in the selection Simple example (section 4) Design for CNC milling machine Approach 2 designs, 3 factors, 2 levels 3 designs, 3 factors, 3 levels Optimum Classical selection of the best variant - 2 x 23 = 3 x 33 = real PROMETHEE method 16 variants 81 variants optimum Classical selection of the best variant - 2 x 4 = 3 x 9 = Taguchi Taguchi method 8 variants 27 variants optimum Two-stage product design selection using PROMETHEE and Taguchi method (2 - 1) + 4 = 5 variants (+2)* (3 - 1) + 9 = 11 variants Taguchi optimum * For this example it was necessary to include two more experiments to gain a significant model; detailed explanation is in subsection 4.2 5. Conclusion The research on how to combine different methods and find an optimal solution is presented in this paper. Today, time is the crucial factor in the design product stage and decision-making support is an important part in manufacturing or research and development process. The longer period of the design phase has effects on the production of a product. This situation is characteristic when it is not clear what properties product should exactly satisfy. Proposed methodology shows the reduction of variants and number of its experiments with help of criteria that should be defined in the beginning in order to reduce search space. It is visible that the number of experiments increases significantly when there is just a small increase in the number of designs, in fact, search space becomes larger. The advantages of the proposed methodology are identified through the comparison of different approaches. Time is saved for the search of appropriate variants and optimum is reached as in the case of the "whole space search". The PROMETHEE method helps to find the best solution according to the decision-makers' selection. Combining it with the Taguchi method, the number of experiments is reduced and it is easy to find out which parameter is significant and how each parameter affects the whole system (product or process). Usage of the strengths of both methods resulted in the two-stage methodology. This new combination of methods mostly contributes in the product design phase while searching for the most appropriate solution according to the "a priori" defined alternatives and criteria. Acknowledgement This work has been fully supported by the Unity Through Knowledge Fund (UKF), 1C My First Collaboration Grant, under the project 11/17 Development of integrative procedure for management of production and service improvement process. References [1] Ishizaka, A., Nemery, P. (2013). 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ANOVA for the behavioral sciences researcher, Psychology Press, New York, USA, doi: 10.4324/9780203763933. 50 Advances in Production Engineering & Management 14(1) 2019 Advances in Production Engineering & Management Volume 14 | Number 1 | March 2019 | pp 51-64 https://doi.Org/10.14743/apem2019.1.311 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper Productivity improvement with parallel adjacent U-shaped assembly lines Chutima, P.a,b*, Suchanun, T.a industrial Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, Thailand bAcademy of Science, The Royal Society of Thailand, Bangkok, Thailand A B S T R A C T A R T I C L E I N F O A novel configuration of assembly lines was proposed in this research, namely parallel adjacent U-shaped assembly lines (PAUL). Typically, in a multiple U-line facility, each U-line is designed to work independently which may cause some workstations were not fully functioned. The PAUL aimed at increasing the utilisation of the whole facility by allowing cross-trained workers to work on the opposite legs of the adjacent U-lines (multi-line workstations). This configuration is easier to implement than parallel U-lines due to no restriction in terms of the lengths of U-lines to be paralleled and hidden expenditures that could be incurred in shop floor reconstruction. Since the line balancing of the PAUL is NP-hard and many conflicting objectives need to be optimised simultaneously, the evolutionary meta-heuristic which was the hybridisation of the multi-objective evolutionary algorithm based on decomposition (MOEA/D) and particle swarm optimisation (PSO), namely MOEA/D-PSO, was developed to effectively solve the problem. In addition, the decoding algorithm to convert the solutions obtained from MOEA/D-PSO into the PAUL's configuration was proposed. The performance of MOEA/D-PSO was evaluated against MOEA/D and multi-objective particle swarm optimisation (MOPSO). The experimental results reveal that MOEA/D-PSO outperformed its rival algorithms under the convergence-related performance. © 2019 CPE, University of Maribor. All rights reserved. Keywords: Assembly line; U-shaped assembly line; Parallel adjacent assembly line; Assembly line balancing; Productivity improvement; Multi-objective optimisation; Evolutionary algorithm (MOEA/D); Particle swarm optimisation (PSO) *Corresponding author: cparames@chula.ac.th (Chutima, P.) Article history: Received 29 October 2018 Revised 20 December 2019 Accepted 21 January 2019 1. Introduction Nowadays, manufacturers are encountering shortened product life cycle because of ever-escalating technological innovation, fierce market competition and rapid change in customers' taste. To maintain their competitiveness and survive in heavily competitive businesses, the justin-time (JIT) philosophy has been adopted to reduce wastes and excessive inventories in production systems. As a result of JIT implementation, the traditional straight-shaped production lines are switched to the U-shaped ones (hereafter called U-lines) to improve their production efficiencies. Moreover, the mixed-model production, another main integral ingredient of JIT, supersedes the mass production of one model of a single product to cope with the swift growth of product varieties in a cost-effective manner. In view of the production, a U-line offers more options in task-to-workstation assignments since workers are allowed to work on both sides (Front and Back) of the line in crossover workstations apart from regular workstations which are placed only on any single side of the line. This provides a higher opportunity to consolidate more tasks into workstations resulting in higher compact workload, better workload distribution and greater line utilisation. The popular- 51 Chutima, Suchanun ity of U-lines is attributed to lots of benefits gained from production volume flexibility, operator flexibility, less number of workstations, no special material handling equipment needed, less space requirement, greater workplace visibility, increased communication and teamwork, multi-skilled workers, lower inventory, easier production planning and better quality control [1]. In most manufacturing companies which adopt JIT, after a period of production, they may notice that their current capacities are not enough to fulfil increasing demands because their businesses are flourishing and extra orders are received continuously. These orders may be the same products previously offered or even new products never been done before. The simplest way to deal with this problem is to add more duplicated or newly designed lines into the system. Since the planning and operations of these lines are conducted independently as if they cannot interact with others, the system as a whole comprising many unrelated lines is normally underutilised. Recently, Gokfen et al. [2] proposed a new line configuration, namely parallel lines, where one or more straight-lines are allowed to work simultaneously under common resources (e.g. workers or equipment) through multi-line workstations to increase the capacity of the system without the cost of additional lines. This concept was further adapted to fit in the environment of U-lines by Ku^ukkof and Zhang [3], namely parallel U-shaped lines (PUL), where two U-lines are placed in parallel to one another to take advantages of multi-line workstations which bestride between both adjacent U-lines. Although the concept of the PUL is theoretically sound, a number of practical issues could be uncovered as follows. First, the application of this configuration is limited only when the lengths of both adjacent U-lines are more or less the same. If the outer U-line is much longer than the inner U-line and multi-line workstations are located between the Bottoms of both lines, the workers who work in these workstations have to walk back and forth between two legs of the lines in a long distance. This makes multi-line workers unhappy because their jobs are more tired than those working in other places and perhaps they would refuse to work in such workstations. In contrast, if the inner U-line is much longer than the outer U-line, there will be no multi-line workstation at the Bottoms of both lines since no Bottom of the outer line is existed. Without the Bottom of the outer line, two legs (Front and Back) of the outer line are split apart and hence material transfers between these legs need a great help from material handling equipment or floating workers bringing about additional operational costs. Second, in order to reconfigure the system according to the PUL, in case of two U-lines are originally working independently, the lines must be reorganised by moving one U-line to encompass with the other. The cost of line relocation may be quite excessive, particularly when heavy machines are parts of the workstations and the foundation on the shop floor for machinery placement needs further reconstruction. In this paper, an alternative layout of multiple U-lines is proposed, namely parallel adjacent U-lines (PAUL). This layout has no limitation as of the PUL and it is much easier to implement in practice since less machinery movement is required. The PAUL's environment comprises two or more U-lines adjacently located as ubiquitously found in industry. Instead of treating each U-line as an independent entity, multi-line workers are allowed to handle tasks on both legs of the adjacent U-lines, i.e. Front of one U-line and Back of the other U-line (Fig. 1). As a result, the underutilised capacity of independent lines on some workstations, if any, could be unleashed by implementing the PAUL. To our best knowledge, this novel configuration has never been addressed in literature before. To systematically form the PAUL so that the production is flown smoothly, the disparity of workloads among workers should be minimised to minimise the unused capacity of the lines. This problem is known as the PAUL balancing problem (PAULBP). In this paper, we assume that each U-line of the PAUL produces mixed-model products to reflect real-life applications. In addition, many conflicting objectives are optimised simultaneously. Because the problem is NP-hard, evolutionary algorithms seem to be an effective solution technique. As a result, the multi-objective evolutionary algorithm based on decomposition (MOEA/D) hybridised with particle swarm optimisation (PSO) is proposed to solve the PAULBP. 52 Advances in Production Engineering & Management 14(1) 2019 Productivity improvement with parallel adjacent U-shaped assembly lines (a) (b) Fig. 1 PAUL configuration: (a) without station number, and (b) with station number The remaining sections are organised as follows. The detailed description of the PAUL is presented in Section 2. The approach to solving the PAULBP is proposed in Section 3. Experimental designs, results and discussions are explained in Section 4. Finally, the conclusion and future research are discussed in Section 5. 2. Problem definition Obviously, in a production system (e.g. electronics and electrical industry) where several U-lines are located close to each other (i.e. the walking time between adjacent U-lines of multi-line workers is negligible) could provide an opportunity for better line balancing. In this research, the layout of two U-lines laid out adjacently side-by-side is considered (Fig. 1). The entry and exit points of both lines are on the same side. By this arrangement, an additional form of workstations could be realised apart from regular and crossover workstations as typically found in traditional U-lines. This type of workstation is called a multi-line station which could occur between the Back of Line 1 and the Front of Line 2. The worker who is assigned to perform tasks in a multi-line station is cross-trained to manipulate different product families and models belonging to both U-lines of the PAUL. The assumptions used in this research are as follows: (a) both U-lines produce mixed-model products, (b) task times, cycle times and precedence diagrams of products on both U-lines are given and fixed, (c) cycle times of both U-lines could be different, (d) workers are cross-trained, and (e) walking time of the worker is negligible regardless of workstation types. 2.1 Objective functions Five objectives related to line efficiency and workload distribution are employed in this research. The reasons for using many objectives as such is to evaluate the effectiveness of the proposed algorithm in dealing with the problems with high dimensional search space and the problem itself is a multi-objective optimisation in nature. Note that these objectives are conflicted with each other; therefore, trade-offs among them are inevitable. The followings are the formulations and descriptions of the objectives. (1) Minimise the number of workstations (Nw): If the workloads assigned to all workstations in the PAUL are equal or nearly equal to the cycle time of the system, the efficiency of the system will be high resulting in less number of workstations required. f1 = Minimise Nw (1) Advances in Production Engineering & Management 14(1) 2019 53 Chutima, Suchanun (2) Minimise workload variations between workstations (Bb): This objective attempts to equalise the workload assigned to each workstation as much as possible. Highly unbalanced workload causes a bottleneck, inequality of workers and also fatigues to the worker who works in the bottleneck workstation. ^w \~'NW V3 f^kb 1 \ f2 = Minimise Bu = -— > > I —:---I (2) b N -1¿-'k=i¿-'b=i\TAD N J w \ w/ (3) Minimise unbalanced workloads within the workstation (Bw): This objective is trivial in a single-model assembly line. However, it is vital for a mixed-model assembly line in which the task times of different product models could be varied. The effect of this problem is apparent while sequencing products into the line since a worker may have to work much longer than the cycle time in some cycle, but very short in another cycle. In some cases, utility workers may be called upon to ease the problem. M / 1\2 = Minimise B = -> > (S,--) (3) 12 w Nw(M-1)^k=i^m=i\km M) LJ Dm ;0 qm = 1 (4) IM D m=l m ZM q s m=1 ^km ^m^krn , -, otherwise M „ Qm" km m=l (5) v,M KIm=1^rnSkrn (4) Minimise unrelatedness of tasks in the workstation (TUR): Two tasks assigned to a workstation are related to each other if both of them are directly interconnected in the precedence diagram. Their relationships are the predecessor or successor of the other. The related tasks normally require similar tools and skill of workers; hence, assigning related tasks to the same workstation facilitates skill development and expertise to a worker resulting in high system efficiency. Chutima and Chimklai [4] proposed the formulation to measure the unrelatedness of assigned tasks in the workstation as follows. N W f4 = Minimise TUR = Nw~—--(6) I w SNU where SNk is the network of tasks that are directly related in workstation k. (5) Minimise the number of stations (Ns): The line length of the system comprising many U-lines laid down adjacently can be measured by counting the number of stations which are compactly arranged in a longitudinal direction. Shop floor utilisation will be high if the system's line length is short. This objective can also be used to penalise the system configurations that are not an authentic PAUL which will be discussed in the next section. f5 = Minimise Ns (7) 2.2 Authentic PAUL configuration An authentic PAUL must consist of at least one crossover workstation and one multi-line workstation, possibly incorporated with or without any regular workstation. Many system configurations that claim to be the PAUL but, in reality, they are just look alike. As a result, the benefits of 54 Advances in Production Engineering & Management 14(1) 2019 Productivity improvement with parallel adjacent U-shaped assembly lines the PAUL may not be realised from such unauthentic PAULs, particularly low Nw and short line length which will be illustrated in the following examples. Fig. 1 illustrates the authentic PAUL configuration in which one crossover workstation is found in Line 1 and Line 2, one multi-line workstation is located between the adjacent legs of Line 1 and Line 2, and two regular workstations are on Line 1 and Line 2. In this case, the number of stations in the system (i.e. line length Ns) is three. Fig. 2 depicts the two-line system which consists of four regular workstations on Line 1 and Line 2, and one multi-line workstation located in between Line 1 and Line 2. This configuration is not an authentic PAUL since no crossover workstation exists. In fact, this system is parallel lines and the line length is five. Another example of unauthentic PAULs is shown in Fig. 3. The system consists of a U-line and a straight line working in parallel. There are two regular workstations and one crossover workstation on Line 1, four regular workstations on Line 2, and one multi-line laid between Line 1 and Line 2. The line length of the system is 5. Regular Workstation Line 1 st st Back Front ( WS-6 ! Line 2 Back r---- f---- ! WS-5 ! , WS-8 1 Fig. 2 Parallel lines (Ns = 5) Fig. 3 One U-line and one straight line (Ns = 5) 3. Materials and methods 3.1 Hybridisation between MOEA/D and PSO (MOEA/D-PSO) Much effort of the early research in the line balancing has been emphasised on a single objective optimisation. However, in practice, line balancing is a multi-objective optimisation problem (MOP) since many conflicting objectives need to be realised simultaneously as mentioned in Section 2. When solving this problem, we usually discover numerous optimal solutions which are non-dominated to each other, so-called Pareto optimal solutions (POSs). The best contour of these POSs plotted in the objective space is called the Pareto front (PF). Various Pareto-based evolutionary multi-objective optimisation algorithms have been developed to solve MOPs. However, with these algorithms, when the number of objectives grows Advances in Production Engineering & Management 14(1) 2019 55 Chutima, Suchanun more than three, known as many-objective optimisation problems (MaOPs), the dominance among solutions becomes weakened considerably resulting in worsening selection pressure towards the PF and sluggish the convergence rate of the algorithm. Recently, the novel algorithm to effectively tackle MaOPs namely multi-objective evolutionary algorithm based on decomposition (MOEA/D) in which an original MaOP is bisected into numerous subproblems using different weight vectors which are uniformly distributed along the objective domain was developed by Zhang and Li [5]. These single objective optimisation subproblems are collaboratively optimised simultaneously in each generation. Since the fitness assignments of MOEA/D are determined by the scalar aggregation function rather than the Pareto domination as conventional, the number of objectives has a minimal effect to its selection pressure. MOEA/D normally uses genetic operators as an offspring generating mechanism, e.g. single point crossover. However, such genetic operator has a serious drawback in computational expensive when compares with particle swarm optimisation (PSO) [6]. As a result, the genetic operator of MOEA/D is replaced with the mechanism of PSO in this research to improve the convergence rate. The hybrid algorithm is afterwards called MOEA/D-PSO. PSO was developed by Kennedy and Eberhart [7] to mimic the collaborative social movement of the large biological swarm in searching for food such as a bird flock or fish school. PSO is a population-based meta-heuristic which stochastically manipulates its offspring generation mechanism without any evolutionary operator like appearing in GA, e.g. crossover and mutation. As a result, many relative advantages offered by PSO include fast convergence, fewer parameter settings, less memory consumption, etc. In the context of PSO, a particle denotes an individual solution of the problem, a swarm represents the population of solutions, and the optimum solution is the food. Each particle has three key attributes, i.e. position (its current solution), velocity (magnitude and direction of the trajectory towards the optimum solution), and fitness (relative performance). The particle navigates its flight by regularly adjusting its velocity with the supervision from two sources, i.e. its own best flying experience (personal best known as Pbest) and entire population best flying experience (global best known as Gbest). The pseudo code of MOEA/D-PSO is described as follows. Pseudo code of MOEA/D-PSO 1. Generate weight vector X for the population size N using simplex lattice design. 2. Define the parameters of the algorithm, i.e. the neighbourhoods (T) of each weight vector, inertia weight w, and learning factors c1 and c2. 3. Determine particle position vector Xj for each particle j = 1, ...,N whose size equals the total number of tasks (d) in the PAUL using R[0,1]. 4. Determine particle velocity vector (Vj) for j = 1, ...,N whose size equals the total number of tasks (d) in the PAUL using R[0,1]. 5. Determine the configuration of the PAUL using the decoding algorithm (to be explained in the next section) and calculate all m objectives of each Xj. 6. Determine the minimum and maximum values of each objective, i.e. and /m(max). 7. Set the initial values of Pbest (P) and Gbest (G) of each particle by Pj = Xj and Gj = Xj. 8. Find the non-dominated solutions in the current population, add them into the external population (EP), find the non-dominated solution in EP, and trash all dominated solutions from EP (note that the initial EP = (/>). 9. Find the velocity vector of each particle j using Vj(t + 1) = wVj(t) + c1r1^Pj(t) — Xj(t)) + c2r2{Gj(t) — Xj(t)) and then find its new position vector using Xj{t+ 1) = Xj(t) + Vj(t + 1). 10. Find the new configuration of the PAUL using the decoding algorithm and calculate all m objectives of each Xj. U. Update z^ and fm(maXy 12. Find normalised values of each objectives using ft = —l-—L-—- for each Xj, Pj and Gj. fi(max)~zi J J J 56 Advances in Production Engineering & Management 14(1) 2019 Productivity improvement with parallel adjacent U-shaped assembly lines 13. Update Pbest of each Xj by comparing the Tchebycheff function (minimize #7-(x) = i < i™m ftij\fi\}) between Pj and Xj. If Xj is better than Pj, set Pj = Xf, otherwise, maintain current Pj. 14. Update Gbest by comparing the Tchebycheff function between Gj of the randomly selected neighbourhoods and Xj. If Xj is better than Gj, set Gj = Xj, otherwise, maintain current Gj. 15. If the termination condition is not met, go to step 8, otherwise, stop the algorithm. 3.2 Decoding algorithm The solution string in this paper is represented by a priority-based scheme where the number under the task indicates its assignment priority. For example, nine (A1,..., A9) and seven (B1,.. ,,B7) tasks are produced by Line 1 and Line 2, respectively, as shown in Fig. 4. According to the arrangement of String 1, the priorities of tasks from highest to lowest are B6, B4, B7,..., A5 and A8. Task ring - A1 A2 A3 A4 A5 A6 A7 A8 A9 B1 B2 B3 B4 B5 B6 B7 1 8 13 12 10 15 9 11 16 6 5 4 7 2 14 1 3 Fig. 4 An example of solution strings The decoding algorithm to transform the solution string into the corresponding PAUL is as follows. Decoding algorithm 1. Determine the total number of to-be-assigned tasks by adding the number of tasks in Line 1 with Line 2. 2. Determine the assignable task list which is a set of tasks that are eligible for the assignment without violating the precedence constraint. For U-line, the assignable tasks are those that locate on the left-hand side of the precedence diagram without any predecessor (assign to the Front) and on the right-hand side of the precedence diagram without any successor (assign to the Back). 3. Let S1 be the set of tasks that can be assigned to the Front of Line 1, S2 be the set of tasks that can be assigned to the Back of Line 1, S3 be the set of tasks that can be assigned to the Front of Line 2, and S4 be the set of tasks that can be assigned to the Back of Line 2. Group all assignable tasks into their appropriated sets, i.e. S1, S2, S3 and S4. 4. Open a new workstation. 5. Select the task with the highest priority from the assignable task list and assign it to the corresponding side (i.e. S1, S2, S3 and S4) of the U-line. 6. Reduce the number of to-be-assigned tasks by 1. If the number of to-be-assigned tasks is equal to 0, then the algorithm is completed, otherwise, go to (7). 7. Compute the remaining available time of the workstation. 8. Update the assignable task list by considering only those that their task times are less than the remaining available time of the current workstation without violating the precedence constraint as follows: a) If the assigned task is in S1 (the Front of Line 1), the assignable tasks are those that are in S1 (to form a regular workstation) and S2 (to form a crossover workstation). b) If the assigned task is in S2 (the Back of Line 1), the assignable tasks are those that are in 51 (to form a crossover workstation), S2 (to form a crossover workstation) and S3 (to form a multi-line workstation). c) If the assigned task is in S3 (the Front of Line 2), the assignable tasks are those that are in 52 (to form a multi-line workstation), S3 (to form a regular workstation) and S4 (to form a crossover workstation). d) If the assignable task is in S4 (the Back of Line 2), the assignable tasks are those that are in S3 (to form a multi-line workstation) and S4 (to form a regular workstation). Advances in Production Engineering & Management 14(1) 2019 57 Chutima, Suchanun 9. If the assignable task list is empty and the to-be-assigned tasks still exist, then go to (4); otherwise, select the task with the highest priority from the assignable task list and assign it to the classified side of the line. 10. Reduce the number of to-be-assigned tasks by 1. If the number of to-be-assigned tasks is empty, then the algorithm is completed; otherwise, go to (11). 11. Compute the remaining available time of the workstation. 12. Update the assignable task list by considering only those that their task times are less than the remaining available time of the current workstation without violating the precedence constraint as follows: a) If the recently assigned task still forms a regular workstation with the previously assigned tasks, the assignable tasks can be found in the same way as 8(a)-8(d). b) If the recently assigned task forms a crossover workstation with the previously assigned tasks, the assignable tasks are those that belong to S1 and S2, or S3 and S4, depending on the line (Line 1 or Line 2) where the crossover workstation is located. c) If the recently assigned task forms a multi-line workstation with the previously assigned tasks, the assignable tasks are those that belong to S2 and S3 only. 13. Repeat steps 9-12. Assume that the precedence diagrams of the products to be assembled on Line 1 and Line 2 are shown in Fig. 5. The common cycle time of the lines is 30. The numerical example of the algorithm is demonstrated in Table 1. Fig. 6 depicts the resultant PAUL which consists of three regular workstations on Line 1, one crossover workstation on Line 1, one regular workstation on Line 2, one crossover workstations on Line 2, and one multi-line workstation. (a) Line 1 (b) Line 2 Fig. 5 An example of solution strings Table 1 Task-to-workstation assignment (cycle time = 30) £ £ Assignable Task Task Time Idle Time -2 .2 ¡g « Line 1 Line 2 Select S1 S2 S3 S4 A1 A9 B1 B3, B6, B7 B6 12 18 1 A1 A9 B1 B3, B5, B7 B7 10 8 A1 A9 B1 B3, B5, B4 B4 6 2 A1 A9 B1 B3, B5 B1 1 1 A1 A9 B2 B3, B5 B2 10 20 2 A1 A9 B3, B5 B3, B5 A9 16 4 A1 A8, A6, A7 B3, B5 B3, B5 A7 3 1 A1 A8, A6 B3, B5 B3, B5 B3 7 23 A1 A6, A8 B5 B5 B5 10 13 A1 A8, A6 - - A1 15 15 A2, A3 A8, A6 - - A6 15 0 A2, A3 A8 - - A3 10 20 A2 A8 - - A2 9 11 A4 A8 - - A4 13 17 A5 A8 - - A5 10 7 7 A8 A8 - - A8 12 18 58 Advances in Production Engineering & Management 14(1) 2019 Productivity improvement with parallel adjacent U-shaped assembly lines WS-4 W5-5 Lirie-1 [Model A) Al ■ I'-: > A9 A7 A6 \ 0 ) Line-2 ¡Model B] Be B7 B4 35 E5 Fig. 6 The resultant PAUL 4. Results and discussion 4.1 Experimental design Problem set Twelve problems were used to test the performances of MOEA/D-PSO. The problems were modified from previously published research to fit in the PAUL's environment and they were classified into three sizes, i.e. small, medium and large. The number of tasks ranged from 30-50, 50100 and 100-170 for small, medium and large, respectively. In each problem, the cycle times of the lines were assumed unequal and varied in three levels; hence, the common cycle time of the system was determined according to [2]. In addition, mixed-models of the product were produced by each U-line. Table 2 shows the detail of each problem. Parameter settings of the algorithms Three algorithms were tested in this research, i.e. MOEA/D, MOPSO and MOEA/D-PSO. MOPSO is the conventional PSO algorithm but applying the Pareto-based fitness scheme to guide its search trajectory. In order to provide a fair-play contest, all algorithms were carefully coded and tuned so that they could execute at their best performances. The parameter tuning of the algorithms was based on the result obtained from statistical analyses of the experimental designs, particularly the general full factorial design. All programs were coded in MathLab on a notebook computer using Intel® Core™ i7-7700HQ CPU@2.8GHz 8.00 GB RAM 64-bit operating system operated under Microsoft Windows 10 Pro. Two parameters of MOEA/D including the number of weight vectors in the neighbourhood and the maximum number of solutions replaced by each offspring were set at 10% and 20%, respectively. The values of inertia weight, cognitive learning parameter and social learning parameter (learning) for MOPSO were set at 1, 1.5 and 1, respectively. For MOEA/D-PSO, the values of the number of weight vectors in the neighbourhood, the maximum number of solutions replaced by each offspring, inertia weight, cognitive learning parameter and social learning parameter were set at 10 %, 20 %, 1, 1.5 and 1, respectively. The number of populations in each algorithm was 133. The number of generations was 1000, 1500 and 2000 for small, medium and large problems, respectively. Pareto-based metrics To evaluate the relative performances of the algorithms in a Pareto sense, several metrics were employed in this research. The metrics which are related to the convergence performance of the algorithms including generational distance (GD), inverted generational distance (IGD), ratio of non-dominated solutions (self-comparison, Rndsi) and ratio of non-dominated solutions (Pare-to-optimum comparison, RNDS2). Spread is a metric to indicate the diversity of non-dominated solutions. The detailed formulations of all Pareto-based metrics were discussed by Coello Coello and Cortés [8] and Chutima and Olarnvanitchai [9]. Advances in Production Engineering & Management 14(1) 2019 59 Chutima, Suchanun Table 2 Problems used in the experiments Linel Line2 Total Task Common No. Problem Models MPS Cycle Time Problem Models MPS Cycle Time Cycle Time 15 10 30 1 Mitchell 3 2:1:2 18 Jackson 2 3:1 12 32 36 21 14 42 9 18 18 2 Jackson 3 1:2:1 11 Rozieg 2 3:1 22 36 22 13 26 26 17 34 34 3 Mitchell 2 2:1:2 21 Rozieg 3 1:2:1 18 46 126 21 21 21 21 42 42 4 Rozieg 3 1:2:1 25 Rozieg 3 2:1:2 50 50 50 16 32 32 138 205 28290 5 Heskiaoff 3 1:1 205 Heskiaoff 2 1:1 216 56 44280 216 324 648 41 41 41 6 Gunther 3 1:1 54 Sawyer 2 2:3 54 65 54 81 81 81 79 138 10902 7 Killbridge 3 1:1 110 Heskiaoff 2 2:3 205 73 4510 110 216 11880 57 79 4503 8 Killbridge 2 1:1 92 Kilbridge 2 1:3 110 90 5060 110 110 110 79 410 32390 9 Killbridge 3 2:1:2 110 Tonge 3 1:2:1 468 115 25740 110 527 57970 320 320 320 10 Tonge 3 1:1:1 207 Tonge 2 3:1 270 140 6210 293 220 64460 220 270 5940 11 Tonge 2 3:1 252 Wee-mag 3 1:1:1 84 145 252 303 101 303 6842 6842 6842 12 Arcusl 3 1:1:2 7571 Acrusl 3 1:2:1 7571 166 7571 6309 6309 6309 4.2 Experimental results Table 3 in Appendix A shows the relative performances of all algorithms in tackling the PAULBP. As mentioned earlier, two performance aspects can be evaluated when facing MOPs, i.e. convergence and spread. The first convergence-related metric is GD which indicates the distances between the non-dominated solutions (NDSs) on the PF obtained by the algorithm and the closest NDSs on the approximated true Pareto front (ATPF). Note that ATPF is constructed by applying non-dominated sorting to the combined PFs of all algorithms obtained after the algorithm is terminated. If GD is 0 (the best value of GD), the PF of the algorithm is perfectly overlapped with the ATPF. It is obvious that GDs of MOEa/d-PSO are always lowest, followed by MOEA/D and MOPSO, regardless of the problems' sizes. In addition, GDs obtained by MOEA/D-PSO are always very close to 0 meaning that most of its obtained NDSs are on the ATPF. IGD is similar to GD, but it measures the distances between the NDSs on the ATPF and the closest NDSs on the PF obtained by the algorithm. As a result, IGD also implies the coverage of the extreme points on ATPF by the algorithm. The algorithm with a lower IGD is the better one 60 Advances in Production Engineering & Management 14(1) 2019 Productivity improvement with parallel adjacent U-shaped assembly lines (the best value of IGD is 0). It is obvious that MOEA/D-PSO always has the lowest values of IGD comparing with MOEA/D and MOPSO, regardless of problem's sizes and cycle times. RNDSi and RNDS2 are another important convergence-related metrics. They specify how many of the NDSs on the PF of the algorithm belongs to the ATPF. Rndsi compares this number with its owned number of NDSs on the PF; whereas, Rnds2 compares this number with the NDSs on the ATPF. The higher the values of RNDSi and RNDS2 are the better algorithm. The results show clearly that MOEA/D-PSO often outperforms MOEa/d and MOPSO. When the results from RNDSi and Rnds2 are interpreted along with GD and IGD, it conveys about the PF of MOEA/D-PSO that it is located pretty close to the ATPF and all of its NDSs are almost on the ATPF. In addition, the PF of MOEA/D-PSO covers the extreme point on the ATPF. Spread is used to assess the distribution of NDSs produced by the algorithm which is related to the diversity of the solutions. This metric determines how much difference between the distance between two adjacent NDSs and the average distance. The lower Spread (i.e. more uniform distribution) is the better algorithm. Although MOPSO often provides the best Spread, particularly in large sizes' problems, its value is marginally lower than MOEA/D and MOEA/D-PSO. This result comes with unsurprising since there is no diversity preservation mechanism embedded in any algorithm tested in this research. Another aspect observed during the experiments, but does not present in this paper because of page limitation, is the number of workstations (Nw) and stations (Ns) created by each algorithm. It is found that the best value of Nw created by all algorithms is almost the same as the ideal number which calculates from dividing the total task time by the cycle time. MOEA/D-PSO always obtains the best Nw comparing with the other algorithms. In addition, the best value of Ns generated by each algorithm is the same. This reflects the effectiveness of the decoding method that is proposed in this research, as well as the PAUL's configuration. In theory, the PAUL's concept is viable and could be extended to integrate more than two or even all U-lines located in close vicinity of each other to form a multi-PAUL facility. However, in practice, a number of issues that should be carefully addressed are as follows. For some factories that do not plan to utilise the PAUL in advance, it may be necessary to re-arrange their existing U-lines to be aligned with the PAUL layout. The distance between the adjacent U-lines which will be used to form the PAUL should not be too long. In addition, multi-line workers should be more appropriate to work in a standing posture since they will have to travel back and forth between two legs of different U-lines. The need to walk while working could cause fatigue in the workplace with workers. The features of tasks assigned to two legs of a multi-line workstation of the PAUL must not be too much diverse, e.g. soldering IC's pins (expert hands) and visual inspection (expert eyes). If possible, they should be in the same category, i.e. requiring the same skill. In fact, multi-skilled workers should not be bombarded with too many skill trainings since it could prevent them from being an expert in the field. In addition, higher wages should be paid to multi-line workers since their responsibilities are much higher than workers in regular workstations. 5. Conclusion A novel assembly line configuration widely found in many multiple U-lines facilities but no one has ever utilised it, namely a PAUL, is proposed in this paper. This configuration is developed to increase the productivity of two or more U-lines placed adjacently and some of their workstations are underutilised (i.e. high idle time) while they are operated independently. To increase the utilisation rate of the whole system, paralleling these U-lines is done by allowing the formation of multi-line workstations located between their adjacent legs (Front of one U-line and Back of the other adjacent U-line). Multi-skilled labours are allocated such workstations to ensure the smoothness of mixed-model production flow on the PAUL. Several conflicting objectives of the PAULBP are optimised simultaneously and evaluated under a Pareto sense. Since the problem is NP-hard, the decomposition-based algorithm to generate good layouts of the PAUL is proposed namely MOEA/D-PSO which is the hybridisation between MOEA/D and PSO. The algorithm is tested against MOEA/D and MOPSO to assess their relative performances. Several prob- Advances in Production Engineering & Management 14(1) 2019 61 Chutima, Suchanun lems with different sizes, number of tasks, product mixes and cycle times are employed as test-bed cases. The results reveal clearly that MOEA/D-PSO outperforms MOEA/D and MOPSO in terms of converge nce-related metrics while their performances are indifferent in diversity-related metric. In addition, the decoding algorithm is quite effective in generating good PAUL layouts. The further research directions could be extended to the PAULBP Type II, considering the walking time of the worker, various skilled labour [10], asynchronous U-lines [11], or simultaneous balancing and sequencing [12]. References [1] Cheng, C.H., Miltenburg, J., Motwani, J. (2000). The effect of straight- and U-shaped lines on quality, IEEE Transactions on Engineering Management, Vol. 47, No. 3, 321-334, doi: 10.1109/17.865901. [2] Gokçen, H., Agpak, K., Benzer, R. (2006). Balancing of parallel assembly lines, International Journal of Production Economics, Vol. 103, No. 2, 600-609, doi: 10.1016/j.ijpe.2005.12.001. [3] Kuçukkoç, I., Zhang, D.Z. (2015). Balancing of parallel U-shaped assembly lines, Computers & Operations Research, Vol. 64, 233-244, doi: 10.1016/j.cor.2015.05.014. [4] Chutima, P., Chimklai, P. (2012). Multi-objective two-sided mixed-model assembly line balancing using particle swarm optimisation with negative knowledge, Computers & Industrial Engineering, Vol. 62, No. 1, 39-55, doi: 10.1016/j.cie.2011.08.015. [5] Zhang, Q., Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition, IEEE Transactions on Evolutionary Computation, Vol. 11, No. 6, 712-731, doi: 10.1109/TEVC.2007.892759. [6] Hassan, R., Cohanim, B., de Weck, O., Venter, G. (2005). A comparison of particle swarm optimisation and the genetic algorithm, In: Proceedings of 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Austin, Texas, USA, doi: 10.2514/6.2005-1897. [7] Kennedy, J., Eberhart, R. (1995). Particle swarm optimization, In: Proceedings of ICNN'95 - International Conference on Neural Networks, Perth, WA, Australia, Vol. 4, 1942-1945, doi: 10.1109/ICNN.1995.488968. [8] Coello, C.A.C., Cortés, N.C. (2005). Solving multiobjective optimisation problems using an artificial immune system, Genetic Programming and Evolvable Machines, Vol. 6, No. 2, 163-190, doi: 10.1007/s10710-005-6164-x. [9] Chutima, P., Olarnviwatchai, S. (2016). A multi-objective car sequencing problem on two-sided assembly lines, Journal of Intelligent Manufacturing, Vol. 29, No. 7, 1617-1636, doi: 10.1007/s10845-016-1201-6. [10] Corominas, A., Pastor, R., Plans, J. (2008). Balancing assembly line with skilled and unskilled workers, Omega, Vol. 36, No. 6, 1126-1132, doi: 10.1016/j.omega.2006.03.003. [11] Tiacci, L. (2017). Mixed-model U-shaped assembly lines: Balancing and comparing with straight lines with buffers and parallel workstations, Journal of Manufacturing Systems, Vol. 45, 286-305, doi: 10.1016/j.jmsy.2017.07. 005. [12] Defersha, F.M., Mohebalizadehgashti, F. (2018). Simultaneous balancing, sequencing, and workstation planning for a mixed model manual assembly line using hybrid genetic algorithm, Computers & Industrial Engineering, Vol. 119, 370-387, doi: 10.1016/j.cie.2018.04.014. 62 Advances in Production Engineering & Management 14(1) 2019 Table 3 Experimental results Problem IfSll 2 fS2) 3 (S3] 4ÎS41 5 [Ml] 6 fM2} No. of Tasks (Linel-Line2) 32 (21-11) 36 (11-25) 46 (21-25) 50 (25-25) 56 (28-28) 65 (35-30) Cycle Time 30 | 36 | 42 18 | 22 | 26 34 | 126 | 21 42 | 50 | 52 28290 | 44280 | 648 cd ■i" Generational Distance (GDI MOPSO 0.0980 0.1508 0.1379 0.1349 0.1862 0.1057 0.1110 0.1079 0.1366 0.2265 0.1294 0.1565 0.1928 0.2203 0.1171 0.3239 0.1206 0.1717 MOEA/D 0.0699 0.0749 0.0648 0.0907 0.1156 0.0842 0.0498 0.0631 0.1061 0.1471 0.0616 0.1032 0.0914 0.1538 0.0793 0.1386 0.0732 0.1066 MOEA/D-PSO 0.0412 0,0749 0.0616 0.0342 0.1027 0.0651 0.0343 0.0546 0.0180 0.1317 0.0520 0.0313 0.0877 0.0752 0.0508 0.0422 0.0510 0.073.2 Inverted Generational Distance fIGDl MOPSO 0.1031 0.1379 0.1176 0.1467 0.1482 0.1350 0.0959 0.0935 0.1680 0.2183 0.1240 0.1683 0.1968 0.1362 0.1380 0.2882 0.1730 0.1489 MOEA/D 0.0870 0.1072 0.1105 0.1468 0.1480 0.1791 0.1764 0.0972 0.1362 0.2774 0.0714 0.0930 0.1904 0.0894 0.0982 0.1531 0.1389 0.1797 MOEA/D-PSO 0.0621 0.0812 0.0727 0.1055 0.0730 0.0788 0.0415 0.0800 0.0892 0.0838 0.0618 0.0926 0.1901 0.0873 0.0956 0.1086 0.0864 0.1204 Rndsi MOPSO 0.1470 0.0527 0.0689 0.5562 0.2514 0.1472 0.0667 0.0513 0.0426 0.1176 0.1647 0.0763 0.0959 0.0291 0.1189 0.0055 0.1480 0.0603 MOEA/D 0.3883 0.4133 0.4028 0.0550 0.2906 0.3504 0.4005 0.2628 0.0736 0.2414 0.2859 0.0775 0.3473 0.1923 0.3488 0.1430 0.3194 0.3571 MOEA/D-PSO 0.4745 0.4032 0.4101 0.2341 0.3454 0.4116 0.5016 0.4773 0.7027 0.3095 0.4732 0.6759 0.4769 0.5253 0.3955 0.6063 0.3346 0.4567 rnDS2 MOPSO 0.0820 0.0283 0.0536 0.0316 0.0952 0.0727 0.0370 0.0379 0.0225 0.0476 0.0825 0.0402 0.0584 0.0227 0.0714 0.0057 0.0750 0.0443 MOEA/D 0.1914 0.2311 0.1905 0.1263 0.1619 0.1273 0.1543 0.1742 0.0449 0.1786 0.1495 0.0632 0.1948 0.1477 0.2071 0.1092 0.1375 0.2089 MOEA/D-PSO 0.2695 0.2453 0.2857 0.3421 0.2762 0.3000 0.3148 0.2879 0.432£ 0.2738 0.2732 0.4023 0.2468 0.3295 0.2214 0.3851 0.2875 0.2468 Spread MOPSO 0.7448 0.8388 0.7758 0.0550 0.8677 0.8937 0.8989 0.B550 0.9516 0.9487 0.8691 0.9537 0.7304 0.7500 0.8835 0.7142 0.7956 0.8383 MOEA/D 0.8937 0.8575 0.8745 0.2341 0.9021 0.9441 0.9871 0.9014 0.8701 0.8998 0.8486 0.6809 0.9766 0.7544 0.9103 0.7955 0.9608 0.9190 MOEA/D-PSO 0.8175 0.7379 0.8663 0.5562 0.7948 0.8827 0.9182 0.8836 0.9156 0.7955 0.8716 0.8231 0.8670 0.9083 0.8497 0.8920 0.8929 0.9720 Table 3 Experimental results (continuation] Problem 7 (M3) 8 (M4) 9 (LI) 10 [L2) 11 (L3) 12 (L4) No. of Tasks (Linel-Line2) 73 (45-28) 90 (45-45) 115 (45-70) 140 (70-70) 145 (70-75) 166 (83-83) Cycle Time 10902 4510 11880 4503 5060 110 32390 25740 57970 320 6210 64460 5940 252 303 6842 7571 6309 Generational Distance (GDI MOPSO 0.1953 0.1106 0.1576 0.1129 0.0756 0.1232 0.0872 0.1194 0.0977 0.3657 0.2195 0.1568 0.2382 0.2210 0.2321 0.2329 0.3424 0.1838 MOEA/D 0.1629 0.0516 0.0726 0.0633 0.0358 0.0817 0.0556 0.0752 0.082 3 0.0630 0.1443 0.1296 0.1029 0.1541 0.1394 0.1687 0.1962 0.1239 MOEA/D-PSO 0.0699 0.0455 0.0440 0.0484 0.0389 0.0546 0.0530 0.0751 0.0561 0.0565 0.0249 0.0245 0.0951 0.1002 0.0424 0.0758 0.0910 0.0777 Inverted Generational Distance (IGD MOPSO 0.2113 0.1304 0.2155 0.1296 0.0922 0.1203 0.1034 0.1466 0.1862 0.2495 0.2186 0.1537 0.2324 0.1902 0.2140 0.1638 0.1386 0.1349 MOEA/D 0.2096 0.0946 0.1458 0.1944 0.0996 0.1144 0.1639 0.1375 0.1541 0.1156 0.1940 0.1535 0.1648 0.1910 0.1189 0.1297 0.1369 0.1459 MOEA/D-PSO 0.1227 0.0647 0.0899 0.0888 0.0773 0.0992 0.1001 0.1070 0.1280 0.0885 0.1223 0.1056 0.1031 0.1743 0.1171 0.1220 0.1268 0.0693 KM: ji MOPSO 0.0259 0.0626 0.0526 0.2068 0.1495 0.0554 0.2564 0.0250 0.0663 0.0133 0.0450 0.0328 0.1699 0.1050 0.0473 0.0756 0.0175 0.0504 MOEA/D 0.0693 0.3656 0.4114 0.2205 0.3697 0.2094 0.4559 0.3247 0.2107 0.4583 0.0775 0.2364 0.1632 0.1327 0.2001 0.1579 0.1134 0.2835 MOEA/D-PSO 0.5857 0.4936 0.5781 0.4430 0.4330 0.3859 0.2722 0.5234 0.3968 0.6401 0.8400 0.6529 0.3818 0.5104 0.5962 0.5454 0.7155 0.3983 RNES2 MOPSO 0.0161 0.0324 0.0174 0.1115 0.0940 0.0640 0.1875 0.0192 0.0739 0.0053 0.0234 0.0152 0.0427 0.0972 0.0160 0.0577 0.0159 0.0265 MOEA/D 0.0484 0.1574 0.2:087 0.0808 0.1745 0.1628 0.1602 0.1154 0.1420 0.2090 0.0391 0.1091 0.1325 0.1157 0.1440 0.1538 0.0476 0.1549 MOEA/D-PSO 0.4355 0.3102 0.2739 0.3077 0.2315 0.2733 0.1523 0.3654 0.2841 0.2857 0.4375 0.3758 0.3248 0.2870 0.3400 0.2885 0.4365 0.3186 Spread MOPSO 0.8129 0.8611 0.7586 0.8241 0.7392 0.7719 0.7754 0.9236 0.8413 0.5435 0.7135 0.8260 0.9029 0.6685 0.7624 0.7755 1.0852 1.0123 MOEA/D 0.9164 0.8741 0.9333 0.8840 0.8809 0.9766 0.9743 1.1529 0.9164 0.8592 0.8289 0.8856 0.8968 0.9949 0.8711 0.9063 1.0978 0.9552 MOEA/D-PSO 0.8671 0.8996 0.9009 0.9164 0.8371 0.9252 0.7566 1.0200 1.0618 0.9090 0.8975 0.9622 0.9378 0.8844 1.0241 0.9837 1.1209 1.0739 Advances in Production Engineering & Management Volume 14 | Number 1 | March 2019 | pp 65-79 https://doi.Org/10.14743/apem2019.1.312 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper Achieving sustainable transport through resource scheduling: A case study for electric vehicle charging stations Gong, D.a, Tang, M.a*, Liu, S.a, Xue, G.a, Wang, L.a aSchool of Economics and Management, Beijing Jiaotong University, Beijing, P.R. China A B S T R A C T A R T I C L E I N F O Electric vehicles support low-carbon emissions to revitalize sustainable transportation, and more charging stations are being built to meet the daily charging demand. Charging piles and service workers are the most important resources for electric vehicle charging stations, and the scheduling of these resources is an important factor affecting the charging stations' profits and sustainable industrial development. In this paper, we simulate the charging piles and service workers in charging station resource scheduling and analyze the impacts of the number of service workers, the charging pile replacement policy and the charging pile maintenance times on an electric vehicle charging station's profits. An orthogonal test can achieve the following optimal resource scheduling results when their range is known: (1) In the lifetime of the charging pile, seven maintenance times are needed; (2) Even if the charging pile is still in normal condition, it needs to be replaced in order to achieve the maximum profits for the charging station; (3) a comprehensive analysis of service efficiency and service costs indicates that 8 service workers are needed to achieve the optimal profits for the charging station. Therefore, the scientific contribution of this research is to establish one resource scheduling simulation model that can assess the effects of the number of service workers, the charging pile replacement policy and the charging pile maintenance times on charging station revenues and to obtain the optimal results. In addition, if the model parameters change, we can still obtain the optimal results. © 2019 CPE, University of Maribor. All rights reserved. Keywords: Sustainable transport; Resource scheduling; Electric vehicle; Charging station; Simulation; Profit *Corresponding author: mincong@bjtu.edu.cn (Tang, M.) Article history: Received 8 September 2018 Revised 12 February 2019 Accepted 24 February 2019 1. Introduction To revitalize sustainable transportation, China is vigorously developing electric vehicles (EVs). By virtue of clean energy and total emissions reductions, electric vehicles address low-carbon emissions regulations under the new requirements and new tasks in China's auto industry [1, 2]. The next decade or even decades will be a strategic opportunity for EVs. In addition to satisfying the need for sustainable transportation, more charging stations are being built to meet the daily charging demand. Charging piles and service workers are the most important resources for electric vehicle charging stations. Charging piles are distributed in different charging stations, and each pile has a certain income if it operates normally. If failure occurs, repair or replacement is necessary, and charging piles require maintenance over the lifetime of the machine; otherwise, there is a high probability of failure. Therefore, we need to allocate charging station resources to achieve optimal charging station profits and sustainable transportation. Limited by the developmental phase of the EVs industry, resource scheduling for charging stations has not been paid adequate attention. If resource scheduling is not taken into considera- 65 Gong, Tang, Liu, Xue, Wang tion, the EV industry may not develop properly, which will hinder sustainable transportation. Simulation technology is used to model the relationships and behaviors between individuals in the whole system, and computer simulations are used to establish a model that can reproduce the real system in order to obtain an optimal solution. Therefore, based on the conception model, this paper obtains a resource scheduling mathematical model of a charging station and analyzes the model based on simulation theory using the AnyLogic tool. From the simulation point of view, this paper studies the effects of the number of service workers, the equipment replacement policy (equipment refers to the charging pile, and this is the same as follows) and the equipment maintenance times on charging station profits. Reasonable resource scheduling will result in proper electric vehicle industry development and achieve sustainable transportation. This paper is organized as follows. We first conduct a comprehensive review, which forms the theoretical foundation of this study. In section 3, an analytical model is proposed that forms the base of the research problem. In section 4, we present the mathematical materials and methods. In section 5, we verify the simulation model through a case study. Finally, conclusive remarks are presented. 2. Literature review EVs are environmentally friendly and are becoming increasingly popular in sustainable transportation. However, factors including the mileage (battery life), charging time, charging convenience, purchase price, and vehicle performance hinder the development of the EV industry [3-6]. An adequate charging infrastructure, rational national guidance and locally targeted construction planning that is, reasonable resource scheduling, can be an effective way to solve these problems of the EV industry. In the actual operations of EV charging stations, personnel time and effort are necessary, thus requiring the scheduling of a larger workload [7]. Therefore, theories and methods are needed to guide resource scheduling. Scholars have made many achievements in their research, including experience summarization, mathematical programming models, and artificial intelligence algorithms. The initial research was basically a summary. Due to the lack of scheduling experience, Miller turned to the mathematical programming model [8], and Cook viewed the scheduling problem as essentially an NP (Non-deterministic Polynomial) problem [9]. Many scholars have studied specific problems. Xi et al. used a linear integer program to simulate the number of L1 (level 1) and L2 (level 2) EV charging stations required at work and public locations and predicted the EV travel flows in central Ohio as well as the number, type, and location of EVs charging stations [10]. Zhang et al. optimized direct current, fast EV charging station allocation and temporal utilization to maximize eVMTs (electric vehicle miles traveled) through a set-cover problem. This work showed that random and late charging will increase the grid demand in the afternoon, while early, inexpensive, and reserve strategies evenly distribute charging throughout the day [11]. Chen et al. developed a mixed-integer optimization program considering budgetary constraints, which limit the total number of EV charging stations to be deployed. The forecasted parking demand was used as an input to the mixed-integer optimization program, which strategically locates 80 public charging stations across 900 traffic analysis zones in the Seattle, Washington region [12]. Yi and Bauer formulated an optimal energy-aware charging infrastructure placement framework. The multi-objective decision model located the EV charging stations to maximize the number of reachable households under an energy constraint while minimizing the overall transportation energy consumption of charging actions [13]. For complex production scheduling, a simple mathematical model cannot cover all the factors, and the solution process is very complex. Therefore, people have developed artificial intelligence technology to solve scheduling problems; for example, in Mehar [14], a modified GA (genetic algorithm) that considers an objective function based on investments and transportation costs was used to optimize charging station locations. By contrast, Bendiabdellah et al. [15] and You and Hsieh [16] employed a hybrid GA to determine the optimal number and size of public charging stations, which found the optimal location by minimizing the investments and travel 66 Advances in Production Engineering & Management 14(1) 2019 Achieving sustainable transport through resource scheduling: A case study for electric vehicle charging stations costs. Tang et al. [17] applied multi-phase particle swarm algorithm to solve resource scheduling problem. The main shortcomings of AI are its low precision and easy divergence, thus making AI solutions non-optimal. By combing the literature, we find that the existing scheduling theories have a record of solving the resource scheduling problem for EV charging stations. However, EV charging stations have their own characteristics, and many specific factors can influence resource scheduling, such as different policies, policymakers, charging station planners, battery technologies and EV manufacturers [18-21]. On the other hand, some studies have discussed the layout of EV charging stations [22-26], but they paid minimal attention to the resource scheduling of EV charging stations. Based on the mathematical model and simulation method [27], this paper builds the resource scheduling agent model of the EV charging station and analyzes the effect of the number of service workers, the equipment replacement policy and the equipment maintenance times on charging station profits. 3. Problem description The problem of resource scheduling in EV charging stations is as follows. The service workers are concentrated in a certain area. When they receive the message "equipment maintenance", "equipment repair" or "equipment replacement" sent by the message center, they go to a charging station location to complete the corresponding task. In the service process, if the equipment cannot be repaired, the worker can directly replace the equipment, and if the equipment can be repaired, the worker checks whether the equipment needs maintenance. Considering the overall profits of the charging station, the service worker can replace equipment that is in a working state. There are three main situations related to resource scheduling in charging stations. Single service worker and single equipment In the model for "single service worker and single equipment", the status of the equipment determines the worker's working time (drive time) and agenda (equipment replacement, equipment repair or equipment maintenance) (Fig. 1). The worker checks whether there is demand (equipment failure)for the equipment. If there is demand, theservice worker drives to the charging station location to complete the service and finally returns to the worker center. Equipment Fig 1 Situation 1 Single service worker and more equipment In this case, there are two pieces of equipment and only one service worker (Fig. 2). When equipment 1 detects a fault and sends a service request to the message center, the message center immediately notifies the service worker, and the service worker quickly drives to the designated charging station location to finish the service. Equipment 2 also detects a fault, which also sends a service request to the message center; however, the request of equipment 2 cannot be answered until the service for equipment 1 is finished. Advances in Production Engineering & Management 14(1) 2019 67 Gong, Tang, Liu, Xue, Wang Equipment 2 Fig 2 Situation 2 More service workers and single equipment In this case, two workers can provide service for the same equipment (Fig. 3). The message center sends an equipment failure message to all service workers. At first, two service workers are idle, so they receive the messages and check their messages at the same time. Then, only one worker arrives at the designated charging station location to complete the service, and the other worker remains idle. In reality, it is a combination of the above three conditions. Service worker 1 Service worker 2 Fig. 3 Situation 3 The remainder of this paper will analyze the impacts of the number of service workers, the charging pile replacement policy and the charging pile maintenance times on the electric vehicle charging station's profits based on the mathematical model of resource scheduling and the idea of simulation modeling. 4. Materials and methods 4.1 Model definition The assumptions in this paper are as follows: • equipment needs maintenance, repair and replacement, and service workers can complete the above tasks, • there are fixed costs in the process of equipment maintenance, repair and replacement, • there is no specific running routine for the workers, and they move at a fixed rate, • workers can provide service all day, 68 Advances in Production Engineering & Management 14(1) 2019 Achieving sustainable transport through resource scheduling: A case study for electric vehicle charging stations workers can complete the task each time, workers can always arrive at the nearest charging station regardless of the running costs. There are two types of worker-equipment constraints in the process of the worker reaching the demand point: the physical condition and the operational condition. These constraints are set as follows: ;=i j=i idle(fj) = Vidle (!) I Vidle —/ Bfype Vidie =Btype = (B0,B1,B2,B3) ^serviceÇvf) = bj where vt is the worker, bj is the equipment demand (maintenance, repair and replacement), V is the worker set, B is the demand set, idle(vj) is the condition of the worker, Vidle is the worker condition set, Btype is the demand type set, and service{vi) = bj means that worker i provides service for demand j. Only if the demand type matches the worker type can service start. Therefore, the matrix of worker -equipment constraints is set as follows: ■Vu yi2yis ■■■ yini y2i '■■ y3i ■ ■ vu A = (2) -Vml ......... Vmn- where 0 < i < n and 0 < j < m. r1 worker vt provides service for demand bj (0 worker vt cannot provide service for demand bj With the worker-equipment constraints, we aim to optimize the profits of the charging station and ensure the satisfaction of demand. The initial setting of the parameters is shown in Table 1. Table 1 Initial setting of parameters Parameter Memo Vn Number of service workers Bn Amount of equipment B0b¡,Bíbji,B2bj»,B2bji» Equipment in different states (working, repair, maintenance or replacement); j, j',j",j" = 1,2,..,Bn t-L Daily revenues generated by the equipment t2 Daily payment for the workers t3 Equipment repair costs t4 Equipment maintenance costs ts Equipment replacement costs t17(B3)Jm Battery replacement policy ^10(^2) Equipment maintenance times XlJk Equipment j is serviced by worker i in sequence k _Yi_Equipment-worker constraints_ The objective function in the model gains the maximum profits for the EV charging station. The charging station's total costs include worker costs, equipment maintenance costs, equipment repair costs and equipment replacement costs. Total worker costs: t2Vn Total equipment repair costs: lew Advances in Production Engineering & Management 14(1) 2019 69 Gong, Tang, Liu, Xue, Wang Total equipment maintenance costs: t4 Total equipment replacement costs: Bn h 7 =1 Total charging station costs: Bn Bn £ (B3bj'") t3 ^(Blty) + ^4 V) + t5 ^ (ßsV") + t2 j' = l j" = 1 ;"'=1 4.2 Model construction The total revenues of the charging station, which are generated by the normal working equipment, are as follows: Bn ti^(M) -t3 ^(Bibj')- ¡4 ^ ^ (Bibmj") ~ts ^ (ß3V') {max(t17(ß3);m + 1,0)} - t }' = ! m = 1 _/" = 1 }"' = ! if t17(ß3).-m = 0 ^10(^2) Bn 00 Bn vn I m=1 i = 1 m=t16(fl2) 7 = 1 ;" = 1 J / = 1 ^10(^2) Bn Bn -t4 ^ ^(B2bmij»)-ts^ (B3br) {max(t17(fl3);m - 1,0)} - t2 m=l j" = l j"' = l if t17(fl3)7m = 1 Considering the equipment-worker constraints, the objective function is as follows: (4) ti i=1 The following maximizes the profits for the charging station when considering t16(B2): Bn 00 Bn A Bn m=l ; = i m=t16(B2); = l J j' = 1 f 16^2) Bn Bn ~t4 ^ ^ (B2bmJ„) -ts ^ (flaty") -t27n m=l j"=l j"'=l The following maximizes the profits for the charging station when considering t17(B3)jm: Bn 00 Bn l l^mj)- 1 JJ(B2bm,j„)\ m=l j=l m=t16(B2); = l tniBsJjm Bn ti6(B2) Bn Bn [5] (6) 70 Advances in Production Engineering & Management 14(1) 2019 Achieving sustainable transport through resource scheduling: A case study for electric vehicle charging stations Max Xiik vn tniß^jm Bn ft 10(^2) Bn til Z Z^0^- Z Z^2^! m=l j=1 ^10(^2) Bn m = t16(B2) j = l - t4 £ ^(B2bmJ„) (7) Bn m=l _/" = ! -t5 ^ (ß3V'){max(t17(ß3);m + 1,0)}-t: if t17(ß3)7m = 0 Bn 00 Br Max Xiik ti 6(B2) t;k tniß^jm m=l _/=! m=t16(B2) j=l j"=l ^10(^2) Bn -t3 ^(Bibj')- t4 ^ £(fl2¿m,;") (8) Bn m=l _/" = ! Subject to t5 ^ (ß3ö;'»){max(t17(ß3);m — 1,0)} — t2 if t17(ß3)7m = 1 Fn (9) ^n Bn ^^ Xijk > 1, where i = 1,2... Vn i = 0 j = 0 Eq. 9 indicates that each instance of equipment demand can be assigned to the worker more than two times. Bn ^ Xijk = 1, where j = 1,2, ...,Bn j = 0 Only one equipment demand can be served by the worker at a time (Eq. 10). I type=0 Bfype 1 (10) (11) Equipment failure (work, repair, maintenance or replacement) can occur only once at a time, and type = 0 means that the equipment is in normal working condition (B0), (Eq. 11). t16(fl2) e[1,M] (12) Mis a positive number. Eq. 12 means that there is a certain limit for the equipment maintenance times according to the equipment operations and charging station profits. Xijk MaintenancePeriod), the worker immediately starts the maintenance service on the equipment. The operation of the equipment simulation model in AnyLogic is shown in Fig. 4. Graphic description: The equipment is working at first. Then, it breaks down (Fails) according to the failure rate and sends the required service message to the message center. When the worker receives the request information through the message center, he or she goes to the charging station location (SCArrivaldForRepair). In this case, there are two ways of handling the issue: repair or replacement. If it is in the condition of replacement, the worker replaces the equipment (StartReplacement) after the replacement time (FinishReplacement); otherwise, the worker repairs the equipment (StartRepair) after the repair time (FinishRepair). If timeSinceMaintenance > MaintenancePeriod, the equipment needs maintenance (MaintenanceDue) after the maintenance time (FinishMaintenance); otherwise, if the maintenance cycle (MaintenanceNotDue) is not reached, the equipment can begin to run after the completion of the repairs. In addition, considering the equipment replacement policy and the overall charging station profits, we can require workers to check the working equipment (SCArrivedForMtce) even if it is still in normal condition.If it meets the equipment replacement policy, the worker should replace the working equipment(PlannedReplacement); otherwise, equipment maintenance (JustMaintenance) should be performed. J f Failed V O J I FinishRepare StartReplacement SCArrivald ForRepai r Fig. 4 Equipment agent operation Advances in Production Engineering & Management 14(1) 2019 73 Gong, Tang, Liu, Xue, Wang 5.2 Worker simulation model The workers will check the equipment service request from time to time. When the demand information is found and the worker is idle, the worker quickly drives to the designated charging station to complete the corresponding service. Thus, an eight-tuple is used to represent the level of worker service capability: Cap_servive(xloc, yloc, Sn number,^idleornot,Jcost,Jworktime The first two terms of the eight-tuple represent the geographical coordinates of the worker's location, Snumberindicates the number of workers, Sidieornot indicates the current status of the worker, Sidleornot = 1 indicates an idle state, Sidleornot = 0 indicates a busy state, Scost is the payment for the worker, Sworktime is the worker service time per day, Smiiesis the maximum miles that a worker can drive every day, and Sareais the largest service area. The service process of the worker agent in AnyLogic is shown in Fig. 5. Graphic description: At first, the worker is in the idle state Sidleornot = 1 and checks the service message from the message center (Check Request Queue). After receiving the equipment failure information (RequestsWaiting), the worker drives (DrivingtoWork) to the charging station (Arrived) and finishes the corresponding service (Working), which includes replacement, repair and maintenance. When the equipment sends out the "Finished" information, the equipment reenters the working state, and the worker is in an idle state again (IAmstillEmployed).If there are new requests for equipment service, the worker can be scheduled again, or the worker leaves the system (laidoff). If there is no equipment failure information (NoRequest), the worker returns (DrivingHome) to the original location (ArrivedHome) and assumes an idle state (Sidleornot = 1). Considering the overall profit of the charging station, we need to calculate the appropriate number of workers (checkiflaidoff). e,Smiles,Sarea) Statechart checkiflaidoff idle ArrivedHome DrivingHome I „laidoff —O IAm sti 11E m pi oy ed CheckRequestQueue -O— NoRequest RequestsWaiting Finished DrivingtoWorlcj Arrived J Working Fig 5 The service process of a worker 5.3 Message Center Due to the "single service worker and more equipment" situation, the "first come, first service" mode is used to finish the corresponding service. The equipment failure information (replacement or repair) will be sent by the message center. The equipment failure information (maintenance) will also be sent by the message center. The worker checks the service message (replacement, repair, or maintenance) from the message center, and then the worker drives to the charging station and finishes the corresponding service. In the simulator, we can obtain working equipment, in-service equipment, in-maintenance equipment and failed equipment. 74 Advances in Production Engineering & Management 14(1) 2019 Achieving sustainable transport through resource scheduling: A case study for electric vehicle charging stations 6. Results and discussion According to the mathematical model and simulation model, this paper can obtain the simulation results using the AnyLogic tool. The parameter setting and their values are shown in Table 3. Note: t16(B2),t17(B3)j0 or t17{B3)j1,Vn are the decision variables, and the simulation time unit is years. We need to analyze the number of service workers, the equipment replacement policy and the equipment maintenance times. When t16(B2) = 5, t17{B3)j0 = 1 and Vn = 5, the corresponding statistics of the worker and equipment are as shown in Fig. 6. In Fig. 6, most workers will be driving or working, and few workers are idle. In addition, most equipment are working, a few pieces are in the failed state, and a few pieces of equipment are in the maintenance state, repair state or replacement state. Based on the above statistical results, we can calculate the revenues of the charging station for years. Table 3 Parametersettingand their values Parameter Memo D istribution(value) ti Daily revenues generated by equipment U[150,250] t2 Daily payment for worker y[700,800] t3 Equipment repair costs y[250,450] t4 Equipment maintenance costs ^[100,200] ts Equipment replacement costs u[3000,4000] t6 Equipment repair time Tr¡[tsl ■0.5,tsl,tsl -2.5],tsin U[0.5,1.5] tB Equipment maintenance time Tr;[t7 -0.5, t7,t7 -1.5],t7~U[0.3,07] ^10 Equipment replacement time Tri[tg ■0.5,t9,t9 ■ 1.5],t9~U[1.5,2.5] t11 Equipment replacement rate EXP[À],À = 10 Equipment maintenance cycle U[80,100] Last maintenance time for equipment y[-ti2,0] t14 Last replacement time for equipment y[-3ti2,0] tis Basic equipment failure rate EXP[À1\,À = 100/3 t16(B2) Equipment maintenance times 5 tn(B3) j0 t17(B3)j1 Equipment replacement policy t17(ß3);o = 1 or t17(fl3)yi = 0 Worker driving miles per day U[400,600] vn Worker number 3 Bn Equipment number 100 t?A Service area 300000 Equipment availability [annual averages! 100% ÍMTfl ÎMTÇ H Working í>i1, 000 - 2,000 0 ¡wo - Revenue vr&s ?nsn 5nrfi — Expenses ^Profit Fig. 7 Statistics of results 1 Table 4 Parameter setting in the orthogonal test Parameter Type The minimum The maximum Step size t16(B2) Integer 2 8 1 ^17(^3)70 Boolean - - - v„ Integer 1 9 1 Table 5 The optimal results Decision variables Results t16{B2) ^17(^3) jo t17(B3)jo = 0or t17(fl3)yi = 1 JL 76 Advances in Production Engineering & Management 14(1) 2019 Achieving sustainable transport through resource scheduling: A case study for electric vehicle charging stations Equipment availability [annual averages] íiyití ?nan ?rws ?f»ri «vk jinn ?irw ?nn ?iif; H Idle M Driving Working Revenue S Expenses |aunual, yuan] o -1-'-Í-I-I-;-.-!-!-!-.— 7070 ?n7R ?nan ?ran ?inn ?ins ?tin ?iif; — Revenue —Expenses ^Profit Fig 8 Statistics of results 2 Based on the results in Table 5, we can achieve additional profits of 5,928,336 yuan in one year. Therefore, we need to incorporate the following. • Seven equipment maintenance instances. In Table 5, we known that the maximum number of maintenance instances is 8 and the minimum is 2, while it needs 7 maintenance instances for equipment during its life cycle. Therefore, it is not "the bigger, the better" for equipment maintenance. In this model, t16(B2) = 7. • Replace equipment that is still in working condition. After a comprehensive analysis of labor costs, equipment maintenance costs, equipment replacement costs and equipment repair costs, equipment needs to be replaced even if it is working normally. In this model, tiyMjo = 0 or t17(fl3)yi = 1. • Eight workers are necessary for a charging station to achieve the optimal profits. Fewer workers will lead to a low service efficiency, and too many workers can create very large service costs. In the model, Vn = 8. 7. Conclusion The development of EVs is an important way to improve sustainable transportation, energy security and the low-carbon economy. According to the statistics of the ISO in 2009, 25% of newly purchased vehicles (approximately 50 million) will be EVs by 2030. China has achieved a great deal in terms of the infrastructure, marketing and standardization of the EV industry. In particular, more charging stations will be built around central areas of cities. Investors or governments should optimize the resource scheduling in order to reduce investment costs due to the limited charging facilities. However, poor management, that is, unreasonable resource scheduling (including service workers and charging piles), will affect the revenues and the future development of the EV industry, thus hindering sustainable transportation; accordingly, resource scheduling for EV charging stations should be a top priority. Therefore, this paper models and simulates the resource scheduling of an EV charging station. A mathematical resource scheduling model of a charging station is established. Due to the solution problem of the mathematical model, AnyLogic implements the communication mechanism of the multi-agent, including the worker agent, equipment agent and the message model, in order to acquire the model's results. For the simulation results, it is possible to know the effect of the number of service workers, the charging pile replacement policy and the charging pile Advances in Production Engineering & Management 14(1) 2019 77 Gong, Tang, Liu, Xue, Wang maintenance times on charging station revenue. Our findings are mainly the following: (1) In the lifetime of the charging pile, seven maintenance times are needed; (2) Even if the charging pile is still in normal condition, it needs to be replaced in order to achieve the maximum profits for the charging station; (3) A comprehensive analysis of service efficiency and service costs indicates that 8 service workers are needed to achieve the optimal profit for the charging station; (4) We can still obtain the optimal results if the model parameters change. Acknowledgement This paper is supported by the Fundamental Funds for Humanities and Social Sciences of Beijing Jiaotong University (2018RCW005,2018YJS051). We appreciate their support very much. References [1] Liu, S., Gong, D. (2014). Modelling and simulation on recycling of electric vehicle batteries - Using agent approach, International Journal of Simulation Modelling, Vol. 13, No. 1, 79-92, doi: 10.2507/IISIMM13(1)CQ1. [2] Johanyák, Z.C. (2017). 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Advances in Production Engineering & Management 14(1) 2019 79 Advances in Production Engineering & Management Volume 14 | Number 1 | March 2019 | pp 80-92 https://doi.Org/10.14743/apem2019.1.313 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper Product quality improvement and air pollutant emission reduction in a mining metal three-stage supply chain under cap-and-trade regulation Homaei, H.a,b*, Mahdavi, I.c, Tajdin, A.c, Khorram, E.d aMazandaran University of Science and Technology, Babol, Iran bGolgohar Mining and Industrial Co., Sirjan, Iran cMazandaran University of Science and Technology, Faculty of Industrial Engineering, Babol, Iran dAmirkabir University of Technology, Faculty of Mathematics and Computer Science, Tehran, Iran A B S T R A C T In today's competitive market, all industries such as mine industries try to increase their profit and keep their customers. Product quality improvement is the miner's most important key to success in competitive market because the mining metals price depends on their quality level. On the other hand, nowadays the management of air pollutant emissions with harmful environmental and health effects is one of the most pressing problems. This paper studies the decision behaviour and coordination issue of a mining metal three-level supply chain with one supplier (extractor), one mineral processor and one manufacturer in which product quality improvement cost at the processor level is higher than the supplier level and at the level of the manufacturer is more than the processor level. We compare the decentralized and centralized systems and identify the optimal product quality level for each supply chain member by designing a revenue sharing contract for decentralized supply chain under cap-and-trade regulation. Finally, numerical example shows that the designed contract not only provides a win-win condition for all supply chain members and increases whole supply chain profit but also increases the final product quality level and reduces harmful air pollutant emissions. © 2019 CPE, University of Maribor. All rights reserved. A R T I C L E I N F O Keywords: Mining metals; Supply chain; Quality improvement; Channel coordination; Emissions reduction; Cap-and-trade regulation *Corresponding author: h.homaei@in.iut.ac.ir (Homaei, H.) Article history: Received 16 May 2018 Revised 31 January 2019 Accepted 24 February 2019 1. Introduction In today's globalized economy, supply chain management is one of the most useful management practices for industries to increase their profit and competitiveness. Nowadays product quality is one of the key competitive dimensions of industries. Industries are always trying to increase their profits, and mines are one of these industries whose profit depends on their product's quality level; but product quality level improvement in mine industries usually emits air pollutants that are serious threats to human health and environment On the other hand, since rapid economic development brings huge amounts of pollutant emissions, governmental pressures such as cap-and-trade regulation are made to force companies to find new methods to reduce these emissions across all the stages of their supply chains. Under a cap-and-trade regulation, companies get predetermined free emission credits from the government [1]. They could sell/buy credits in the air pollutants trading market when they have surplus/lack credits; this emission credit price is determined by the market. There are two common practices for improv- 80 Product quality improvement and air pollutant emission reduction in a mining metal three-stage supply chain ... ing product quality in mine industries: (1) Technology changing and (2) Practical policies. Since the first method is very costly, the second method is a competitive advantage for miners; therefore, one of the most important concerns miners have is how to increase their profit through product quality level enhancement by operational approaches without increasing harmful pollutant emissions. There are two decision making systems in a supply chain: centralized and decentralized. In the centralized system, supply chain members operate jointly as a single firm and make their decisions to maximize the total profit of the system; but in the decentralized system, supply chain members make their decisions separately to maximize their own profits. The decision making system in most supply chain models such as this study is assumed to be decentralized. To improve the overall performance of the supply chain, a coordination mechanism is needed. Different definitions and perspectives on the supply chain coordination exist in the literature (refer to [2, 3]) for the comprehensive review of supply chain coordination. A supply chain is coordinated when the members make the decisions that are optimal for the whole supply chain. For coordinating a supply chain, contracts are designed to reduce the difference between the outcome of a centralized system and a decentralized system. Different kinds of contracts such as commitment to purchase quantity, credit option, two-part tariff, revenue sharing [4, 5], buy back, sales rebate, and mail-in-rebate, have been used in supply chains as the ways improving supply chain performance. Revenue sharing is one of the widely used contracts in the supply chain that is between an upper and lower level of supply chain, where the upper level provides better selling condition to the lower level and then the lower level shares a fraction of its revenue with upper level. There are three streams of literature related to the research in this paper. The first stream focuses on improving the quality level of products in the supply chain. Many efforts have been made to improve product quality in the supply chain. Radej et al. provided an overview of the quality tools and methods such as quality techniques and linked it to manufacturing process quality and manufacturing cost-effectiveness; [6]. Singer et al. studied a single product distribution channel and suggested a contract that simultaneously increases profit and improves quality [7]. Xiao et al. presented a game-theory model to show how the manufacturer coordinates the supply chain by revenue-sharing contract [8]. El Ouardighi discussed the potential coordinating power of revenue-sharing contracts in supply quality management [9]. Yan explored a joint pricing and product quality decision problem in a two level decentralized supply chain [10]. Zhu et al. investigated a supply chain, where the buyer has the option to invest in the supplier's quality improvement [11]. Gao et al. considered quality improvement effort coordination in a decentralized supply chain with a partial cost allocation contract [12]. The second part of literature explores operational decisions in the supply chain under the cap-and-trade regulation in order to reduce harmful gas emissions. The cap-and-trade regulation is a mechanism to control air pollutant emissions [13]. Many researches have studied the problems in supply chains considering the cap-and-trade regulation and it has been recommended by many senior researchers such as [14] and [15] and implemented in many parts of the world. Xu et al. studied the joint production and pricing problem of a manufacturer under cap-and-trade and carbon tax policies. [16]. Gong and Zhou proposed an optimal manufacturing strategy under carbon trading policy through a dynamic model [17]. Hua et al. explored how companies manage carbon footprints in inventory management under the carbon-trading regulation [14]. Xu et al. investigated the production and pricing problems in make-to-order supply chain under cap-and-trade regulation. [18]. He et al. considered the impact of cap-and-trade regulation on company's carbon emission decisions [19]. Zhang and Xu investigated a company's optimal manufacturing quantities under cap-and-trade regulation. [13]. Benjaafar et al. studied the multi-period operational decision-making of a company under cap-and-trade regulation [20]. The last subset of literature related to this research is the supply chain coordination under revenue sharing contract. Cachon provided a good survey on this contract [21]. Cachon and Lariviere proved that revenue sharing contracts for decentralized supply chains are beneficial in achieving coordination for various types of supply chains [22]. Qin and Yang used the Stackelberg game to model the revenue sharing contract problem. They showed that the party that Advances in Production Engineering & Management 14(1) 2019 81 Homaei, Mahdavi, Tajdin, Khorram keeps more than half the revenue should serve as the leader of the Stackelberg game [23]. Hsueh presented a new revenue sharing contract embedding corporate social responsibility to coordinate a two level supply chain [24]. Yao et al. proposed a revenue sharing contract to coordinate a two stage supply chain. They illustrated that the provision of revenue sharing in the contract can increase supply chain performance more than a price-only contract [25]. Palsule-Desai proposed a game theory model for revenue-dependent revenue sharing contracts in which the supply chain revenue is shared among the members depending on the quantum of revenue generated [26]. Zhang et al. discussed the revenue sharing contracts for coordinating a supply chain in which demands are disrupted [27]. Hu et al. studied supply chain coordination via revenue sharing contracts in a three-stage supply and a two-stage supply chain [28]. However, a few researches have been done on the three level supply chain coordination with revenue sharing contract considering environmental aspects under cap-and-trade regulation; also the three-level supply chain coordination research literature mentioned above neither take the product quality improvement into account nor focuses on mining metal supply chain coordination. Therefore the main purpose of this study is to design a revenue sharing contract for a mining metal three level supply chain in order to: 1) coordinate supply chain and provide a win-win condition for all its members and decrease the difference between the outcome of a centralized system and a decentralized system, 2) reduce air pollutant emissions in the supply chain under cap-and-trade regulation, 3) improve the final product quality level of the supply chain. The rest of this paper proceeds as follows. Section 2 presents the notations definition and the supply chain descriptions and assumptions used in this paper. We have analysed the decision behaviour the decentralized and centralized supply chain in Section 3. Section 4 develops a new revenue sharing contract for coordinating the decentralized supply chain. Section 5 provides a numerical example to illustrate the proposed contract performance. Conclusions are provided in Section 6. 2. Model description and assumptions A decentralized mining metal three-stage supply chain in which minerals will convert to concentrate after extraction is assumed in this paper. The considered supply chain is consists of a supplier (extractor), a processor, and a manufacturer. The first level extracts processed minerals and sells them to second level who processes minerals and sells the mineral concentrate to the manufacturer, who in turn produces mineral products such as pellets and ingots and sells them to the customers. The product price of each supply chain level depends on the quality of that product Therefore all of these supply chain members try to increase their product quality. Extracted materials Processed materials Supplier Processor Manufacturer Level 1 Level 2 Level 3 Fig. 1 Mining metal three level supply chain The following notations are used to describe the proposed model: Index for supply chain levels; S for supplier, P for processor and M for manufacturer Minimum acceptable product quality level in considered supply chain selling price of unit product produced at the supply chain level i with quality level j The amount of product quality level improvement in supply chain level i Constant production cost for a unit product in supply chain level i Cost coefficient for increasing product quality level with quality level j in supply chain level i Price increasing coefficient for product produced in supply chain level i per unit product quality improvement in supply chain level i Advances in Production Engineering & Management 14(1) 2019 Jo PU di cdi a,- 82 Product quality improvement and air pollutant emission reduction in a mining metal three-stage supply chain ... Pi Price increasing coefficient for product produced in supply chain level i per unit product quality improvement in supply chain levels before level i Yi Quality improvement cost increasing coefficient in supply chain level i per unit product quality improvement in supply chain levels before level i ni Supply chain level i profit Processor's revenue share, 0 < <1 02 Manufacturer's revenue share, 0 < 02 <1 cpi Unit air pollutant emissions trading price for supply chain level i Ki Air pollutant emissions cap for supply chain level i gi Amount of air pollutant emission for a unit product quality level improvement in supply chain level i In this paper and 02 are decision variables. Product quality level improvement at the supplier level doesn't emit air pollutants because improving product quality at that level is done by some activities such as more samplings for accurate identification of underground mineral veins (Fig. 3) and performing explosive operation optimally (cps = 0 ). But product quality improvement in supply chain levels 2 and 3 emit air pollutants; the emitted air pollutant type at the processor level is usually dust because of the physical processes at this level and the emitted air pollutant at the manufacturer level is of the chemical type, such as SO2, due to chemical processes. That is why the parameter cp for the manufacturer is higher than the processor (cpM >cpP). The government monitors pollutant emissions of the supply chain members by online measuring equipment (Fig. 2). Product quality level improvement is not mandatory for supply chain members but supplier must supplies raw material with minimum quality level j0. Product quality improvement for each supply chain member requires more operating costs but these cost enhancements are different for each member because of different production processes in each supply chain level and it is assumed to be a nonlinear ascending. The product quality improvement cost increases from supplier to manufacturer due to the increasing complexity of production processes from supplier to manufacturer (cdSj 1p„P„j0+2cdSj0PMPMj0 It is necessary to note that we have to obtain the optimal values of and 02 by solving the systems of two equations. 86 Advances in Production Engineering & Management 14(1) 2019 Product quality improvement and air pollutant emission reduction in a mining metal three-stage supply chain ... Therefore, the optimal value of total supply chain profit under revenue sharing contract can be written as n'-f = n's +n'p + (21) Also, optimal product quality improvement for final product can be calculated as follows = d's* + d+ (22) The amount of air pollutant emissions depends on product quality improvement at the processor and manufacturer levels. In other words, the more product quality improvement at the processor and manufacturer levels, the greater air pollutant emissions. The Propositions 11 and 12 obtain the upper bound and the lower bound for the decision variable 02 respectively and guarantee that processor and manufacturer's air pollutant emissions after considering proposed revenue sharing contract is less than that without the coordination case. Proposition 11: The optimal product quality level improvement by the processor in considered decentralized supply chain without coordination is more than the coordinated with designed revenue sharing contract case (dp iPpPpjo + 4>iPmPmj0 + «*%,)) ^^rt^+yrasps,9^ -cdpj^pPpj^-^djjXapPpj, -cpPgP) 02 >-7------TT- PmPmJo (2cds;0 + 0i cdPlo \2cdsj0 + Yp{4>iPpPpj0 + 0i PmPmJo + asPsjJ)) 5. Results and discussion In this section, we provide a numerical example in order to illustrate the designed revenue sharing contract performance by using the parameters below: Cs = 150; CP = 250; CM = 350; Psjo = 20; PPjo = 30; PMJo = 40; as = 3; aP = 5; aM = 7; fiP = 6; = 20; yP = yM = 10; cdsjo = 4; cdPjo = 5; cdMjo = 6; cpP = 2; cpM = 5; gP = 3; gM = 4; KP = 50, and KM = 40. The MATLAB software is used to solve the numerical example considering mentioned parameters and its results are presented in tables 1-3 and Figs. 4-6. Table 1 Optimum value of key variables for centralized supply chain Key variables_d*_d*_d^_df_rc*_n*__a:** Optimum value 99.92 0.0793 0.214 100.21 -34093 11834 61908 39649 (24) Table 1 shows the optimum value of key variables for the centralized supply chain. As it can be observed from Table 1, the highest increase in product quality level in the centralized supply chain is done by the supplier (d;* »d*>, d;* »d*^) and that is why that his profit is negative. It is necessary to note that the negative profit of the supplier in the centralized supply chain is not important because all members in the centralized supply chain operate jointly as a single company and achieving the win-win condition for supply chain members is not important in this case. Table 2 Optimum value of key variables for decentralized supply chain without coordination Key variables ds d*P d* UM dp * * np * nM * Optimum value 7.5 0.1894 0.2781 7.9675 95 773 4669 5537 Advances in Production Engineering & Management 14(1) 2019 87 Homaei, Mahdavi, Tajdin, Khorram 200,00% 100,00% 0,00% -100,00% d*S d*P d*M d*T TI*S TI*P ti*M ti*T -92,49 138,84 29,95% -92,05 -100,2 -93,47 -92,46 -86,03 Fig. 4 Key variables change percentage of the decentralized supply chain without coordination compared to centralized supply chain From Table 2 and Fig. 4, we observe that the profit of all supply chain members, whole supply chain profit, product quality improvement by supplier and the final product quality in decentralized supply chain without coordination are much lower than that in the centralized case; But product quality improvement by the processor and manufacturer in decentralized supply chain is higher than that in the centralized system. As mentioned before, since the air pollutant emissions depend on the product quality improvement at the processor and manufacturer level of supply chain, so increasing product quality improvement by the processor and manufacturer leads to the enhancement of air pollution emissions; therefore we can say that air pollutant emissions in the decentralized supply chain are higher than that in the centralized system. As mentioned before, we obtain the optimal values of 01 and 02 by solving the systems of two equations using Eqs. 19 and 20. In this example, the lower bound and upper bound for the decision variable 02 are obtained -0.102 and 2.879, respectively and the conditions mentioned in Propositions 11 and 12 are satisfied because the optimal values of and 02 are obtained 0.438 and 0.190 respectively. Table 3 Optimum value of key variables for coordinated decentralized supply chain with designed revenue sharing contract Key variables d*P d*M d*T n^ Up n1^ n? Optimum value 25.67 0.1148 0.0836 25.8684 2507 3127 11944 17579 3000,00% 2538,95% 2500,00% 2000,00% 1500,00% 1000,00% 304,53% 155j81O/o217, 48% 500,00% 242,27% 224,67% [VALUE] -69M% ^ 0,00% -500,00% d*S d*P d*M d*T tt*S TT*P TT* M TT*T Fig. 5 Key variables change percentage of the coordinated decentralized supply chain compared to without coordination case As it is shown in Table 3 and Fig. 5, the designed revenue sharing contract increases the whole supply chain profit and total product quality improvement by 217.48 % and 224.67 % respectively; Also the proposed revenue sharing contract increases the supplier, processor and manufacturer's profit by 2538.95 %, 304.53 % and 155.81 % respectively so we can say that this contract provides a win-win condition for all supply members. It should be mentioned that we can never increase the whole supply chain profit and the final product quality of the decentralized supply chain to its centralized case due to the necessity of the win-win condition for all members in the decentralized supply chain. Also we can say that the designed revenue sharing contract decreases air pollutant emissions 39.39 % and 69.94 % at the processor and manufacturer supply chain level respectively. 88 Advances in Production Engineering & Management 14(1) 2019 Product quality improvement and air pollutant emission reduction in a mining metal three-stage supply chain ... Fig. 6 shows supply chain members and the total supply chain profit for different values of 02 by fixing the decision variable to its optimum value 0.438 after coordinating supply chain with the proposed revenue sharing contract. The purple line in Fig. 6 indicates the value of 02 which maximizes the manufacturer's profit. Also the numbers on intersection points of this line with the other curves can be seen in Table 3. Fig. 6 Supply chain members and total supply chain profit for different values of 02by fixing 01 to its optimum value 6. Conclusions One of the main concerns of miners is to increase the quality level of their products because the mining metals price depends on their quality level; but increasing the quality level of these products has different costs at different levels of the supply chain. These costs usually increase after extractor level. The two main practices for increasing product quality in industries are technology changing and practical policies; the first method is rarely used by miners because it's very expensive, so miners try to increase their profit through product quality level improvement by operational approaches without increasing air pollutants emissions. This paper studied the coordination issue of a decentralized three-level mining metal supply chain with one supplier (extractor), one processor and one manufacturer under cap-and-trade regulation and compared it with the centralized system. Due to different product quality improvement costs of supply chain members, a revenue sharing contract designed and optimal product quality level for each of them was obtained. It is necessary to say that the proposed model is designed for some kinds of metals that have impurities and will be processed after extraction (such as Iron and Copper) Finally, the numerical example illustrated that the proposed revenue sharing contract can (a) increase the final product quality level, (b) provide a win-win condition for all supply chain members, (c) increase the whole supply chain profit, and (d) reduce harmful air pollutant emissions in the supply chain. 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Appendix A Proof of Proposition 1: Since the ns is concave in ds, there exists a unique optimal product quality level improvement dS that maximizes supplier's profit because the second derivative of equation nP is negative dn^ = —2cdc; < 0 d2ds SJ° Therefore the optimal value of dS can be obtained as follows dns * aspsj0 — = 0 - asPsjo — 2cdsjods = 0 -ds = — This completes the proof. Proof of Proposition 2: Since the nP is concave in dP, there exists a unique optimal product quality level improvement dP that maximizes the processor's profit because second derivative of the function nP is negative % dnp = -2cdPjo(1 + yPds) < 0 Therefore the optimal value of dP can be obtained as follows dnP , . * apPpjn — cPp9p = 0 ^ aPPPj0 — 2cdpj0dp{l + Ypds) — cPp9p = 0 ^ dp — ddp - -'-"0 ■ ™ - -, 2cdpjo (1 + Ypd}) This completes the proof. Proof of Proposition 3: Since the nM is concave in dM, there exists a unique optimal product quality level improvement dM that maximizes the manufacturer's profit because second derivative of the function nM is negative dnj] ■rp^- = -2cdMj0 (1 + Ym(ds + dP)) < 0 Therefore the optimal value of dM can be obtained as follows „ n 0 j j f„ , , , , , ^ „ aMPMj0—cVMdM ddM = 0 - auPuio 2cdMJodM(1 + YM(ds + dP)) cpMgM = 0 -d*M = 2cdpo(i + YM(d; + d;)) This completes the proof. Proof of Propositions 4 and 7 is similar to proof of Proposition 1. Proof of Propositions 5 and 8 is similar to proof of Proposition 2. Proof of Propositions 6 and 9 is similar to proof of Proposition 3. Proof of Proposition 10: Since the n'p is concave in i(MmPm¡0 + ßpPpin) = 0 ^ 0))tßMPMj° cd-JodMyM) 2cd Ppj0apßMPMj0 I ^lßMPMj0 , ßMPMj0 \ 0 I 4>lßpPpj0 , apPpj0-CPpdp Sjo 2cdPjo(1+ Ypd's) M}0\ 2cdsjo 2cdPjo(1 + Ypd's)) ™ M]0\ 2cdsjo 2cdPjo(1 + Ypd's) _1 cdMj0d'MYM cdPjo(1 + Ypd's)(2 2cdPJo(l + Yp(d*s + d*P)) ^ (d's* + d'P*) > (d*s + d*P) ^ (d's* - d*) > (d*P - d'P*) a $iPpPpj0 + gpPpj0 - cpPgP ^2PMpM]0 + apPpJo - cPP9P a 2cdsja 2cdsja 2cdPjo (1 + Ypd0 2cdPJo(1 + YPd'st) (2cdsjo + yP(icdpj0 (2cdsja + Yp($iPpPpj0 + 2; A = {%, a2, — ,am} is a non-empty finite set of attributes, including the set of efficiency indexes C and the set of cost indexes D; the larger the index attribute value of set C, the better, while the smaller the index attribute value of set D, the better. Let Ac an d Ad be the subscript sets of efficiency indexes and cost indexes, respectively, where = AcVAd , Ac nAd = 0 and m>2. The indexes are divided into conditional attribute CA and decision attribute DA, and CAUDA = A , CA nDA = 0, VteU, V^.e A, V represents the set of the value of indexes, and vtj represents the observed value of the object i about the indicator aj. In the system, each index in the indicator set has different dimensions and attributes, and the type of attribute value has two forms, namely clear number and linguistic items, and the attribute value of the same attribute has the same information form. For convenience, let Ad and At respectively denote the attribute subset whose attribute values are clear number and the formal information of the linguistic items. Ad = (A1,A2, — ,Ahj, Al = {Ah+1, Ah+2, — ,Am}, and Ad VAl =A; Let S-L and S2 be the subscript sets of attribute subsets Ad and Al, respectively. S-l = {1,2, ••• ,h}, S2 = {h+ 1, h + 2, ••• ,m}. For attribute values, the specific description is as follows: • If aj e^d, then vtj =v'tj, j e S1,i e U, where v\j is a real numeric value, without losing generality, here suppose v\j >0. • If aj eAt , then vtj =v"ij,j e S2, i e U, where v"tj is a linguistic item, v"tj eP. Here P is a set of linguistic items, P = |pt|i = 0,1,• -1,-^,^ + 1,— ,l|, where Pt represents the (t + 1)-th linguistic item in P, and (L + 1) represents the number of items in P. When L = 6, P = {Po,Pi,P2,P3,P4,P5,Pe} = {PP(particularlypoor),Wo(worse),P(poor), M(medium), We(well), B{better),EW{especially well)} when z>b, Pz is better than or equal to Pb; if Pz is better than or equal to Pb, then max{pz,pb} = PZ, min{pz,pb] = Pb; when b = L — z, inv(pz) = pb, where inv is an inverse operator. The specific normalized calculation formulas are respectively expressed, as shown below: (a) If aj eAd, then the normalized calculation formula is as follows: Advances in Production Engineering & Management 14(1) 2019 97 Zhang, Wang, Li rd _ where ij vj vP-vf ,i 6 U,j 6 nAc vj~v'íj ,¿ 6 U,j 6StnAd P N vf-vf v? =mai[max1fk lxic _x/ | + ômçix max—xJi | sA _ ym gj On this basis, grey incidence matrix between objects can be established as follows: (7) (8) .A '11 '12 . PA • • 'lfc .A '1 n '21 '22 t •• '2fc tA '2 n 4= > '¿1 '¿2 . * • • 'ifc ? 'in .A 'nl ? •• 'n2 • t " 'nfc ■ t According to the grey incidence matrix, gyfcis the correlation degree of the decision objects f, k on attribute set A, which represents the possibility that the object belongs to the same classification, and the best critical value can be determined by the Bayesian criterion. The specific method is as follows: (i) Ca, Cm, and Cu respectively denote that objects f, k have a high correlation degree AF^'^in), a medium correlation degree MB^x,^-'(n), a low correlation degree DN^^^^n); E(Cak), E(Cmk) and E(Cuk) respectively denote the expected loss function, and that object f belongs to ¿^(n), MB^in) and DN^in). The calculation formula of expected loss function is shown as Eq. 9, Eq. 10, and Eq. 11: 98 Advances in Production Engineering & Management 14(1) 2019 Inventory control model based on multi-attribute material classificaiton: An integrated grey-rough set and probabilistic ... E(Cak ) = SaAtfk + SaD(l-tfk) (9) E{Cmk ) = ^^mD (1 - (10) E{Cuk ) = SuAffk + SuD (l- (11) where SaA, SmA and SuA respectively indicate the loss function, and that the decision makers take under a high correlation degree AFAa'^(n). SaD,SmD and SuD respectively indicate the loss function, and that the decision makers take under low correlation degree (ii) According to the Bayesian decision criterion, the optimal action plan needs to be selected as the action set with the minimum expected loss. The specific decision rules are as follows: Decision rules of AFAa'^: if both E(Cak) E(Cmk) and E(Cuk) >E(Cmk) are true, then k e MB^in); Decision rules of N^: if both E(Cuk) a and > a, then the correlation degree of decision object /, k is high; If p < < a and ft < ¿;Ak < a, then the correlation degree of decision object /, k is medium; If

a} (12) MB[a,IS\n) = [ke U\f3< ,*Afk = 72V2; lead time p = 8, and the demand distribution within the lead time p is: 108 Advances in Production Engineering & Management 14(1) 2019 Inventory control model based on multi-attribute material classificaiton: An integrated grey-rough set and probabilistic ... D¿p~N(1480,82 x8), that is ^ = 1480, aD¡r¡ = 1óV2; the service level is 95 %, and the 'ip ' ^ip shortage rate r =0.05, and set H(fí¿) = JR (Dip — •h d(D¿p).Eq.32 is rewritten thus: jRÍ H(RÙ = VXCivXßDlt-Si^Qi vxcivXßD.t (46) 2 _ 2ßDit{Ci + rjXCiv[ aD.p2Xh(Ri)-[Ri-ßDlp)x(l-H(Ri))]] ^ ~ S~t 0.05x420x6660 — 2.5x36xq¿ 90qi 0.05x420x6660 139860 2 2x6660{24885+0.05x420[512Xh(Ri)-(Ri-1480)Xi;|°^(j0]] (47) ~ 2.5x36 Take Qt = J^f1 = J2*6^*^885 = 1919.11 and substitute Qi = Q1 in Eq. 1 for Eq.47 to obtain R1; then R¿ = RÍ in Eq. 2 is substituted with Eq. 47 to obtain Q2; substitute Qt = Q2 in Eq. 1 for Eq. 47 to obtain R2; then = R2 in Eq. 2 is substituted with Eq. 47 to obtain Q3; iterate over and over again until the convergence state of Qk+1 = Qk is reached. At this point, Qk and Rk are solved. The final solution is: (Qk = 2064 \Rk = 1848 • Application of (s, S) strategy model From the matching model of inventory control strategy, it can be seen that (s, S) strategy is suitable for inventory control of general materials. This paper takes material 59 (packaging materials) as an example to apply (s, S) strategy model. According to the personnel experience of inventory managers, the lead time of material 59 is two weeks, the service level is 90 %, and the safety factor is 1.28, which is obtained by Table 6. The mean demand in lead time is ^ = 7198 and the standard deviation is c=3288. Therefore, Order point s = ¡¿xp + k • Jp • a = 7198 x 2 + 1.28 x V2x 3288 = 20348 pieces; Maximum inventory level S = s + ^p = 20348 + 7198 x2 = 34744 pieces; Material 59 is inspected once a week. If the inventory level is 18,000 on Monday, which is less than 20,348 at the ordering point, the order should be issued. If the minimum number of packaging units for the material is 1,000, then: Order quantity Q = roundup [(34744 - 18000)/1000] x 1000 = 17000 pieces. • Application of (T, s, S) strategy model According to the matching model of inventory control strategy, it can be seen that (T, s, S) strategy is suitable for inventory control of leveraged materials. This paper takes Material 2 (petroleum special pipe) as an example to apply (T, s, S) strategy model. According to the personnel experience of inventory management of Material 2, the inspection cycle is generally set for eight weeks; thus, T = 8, the lead time is two weeks, that is p = 2; the service level is 95 %, and the minimum packing number is 2 tons. From the common customer service level and safety factor table (Table 6), the safety factor k = 1.65. According to the normal distribution results of enterprise demand prediction, ^=18, g = 7. Therefore, Order point s = pi(T + p) + ko(T + p) = 18 x 10 + 1.65 x 7x 10 = 295.5 tons; Maximum inventory level S = s + ^(T + p) = 295.5 + 18 x 10 = 475.5 tons. If the inventory level after inspection is 280 tons, less than the order point 295.5 tons, and the minimum package quantity is 2 tons, then: Order quantity Q = roundup[(475.5 — 280)/2] x2 = 196 tons. Advances in Production Engineering & Management 14(1) 2019 109 Zhang, Wang, Li 5. Conclusion Inventory control is an important issue in supply chain management. There are many attributes of inventory materials in enterprises, and the degree of influence of different materials on enterprises is also different. Faced with the new production and delivery, the manner of scientifically classifying the materials of the enterprises and making scientific inventory control strategy are of great practical significance for effectively reducing the operating costs of enterprises, improving the ability of material support, and further promoting the development, transformation and upgrading of the enterprises. In this paper, the classification and inventory control strategies of multi-attribute materials were systematically studied. Firstly, the evaluation index system of material attributes was constructed from three aspects: procurement risk, proportion of the value and strategic importance. Then, the grey rough set algorithm was used to reduce the attribute of the material attribute index to achieve the aim of removing repetitive and redundant attributes. On this basis, the discriminate model of material classification was constructed based on the PNN approach. It is simple and practical; it has a fast training speed and a good output effect on network simulation, which can solve the material classification problem well. Then, based on the classification results, different inventory control strategy models for strategic materials, bottleneck materials, general materials and leveraged materials were proposed. That is to say, an inventory control strategy matching model based on material classification was built to provide a powerful basis for enterprises to formulate targeted inventory control strategies. Finally, taking a chemical enterprise (i.e., Enterprise A) as an example, using the classification approach, inventory control strategy and the corresponding model proposed in this paper, the material classification scheme of Enterprise A was obtained, and the order schemes under different inventory control strategies were obtained by calculation. 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Advances in Production Engineering & Management 14(1) 2019 111 Advances in Production Engineering & Management Volume 14 | Number 1 | March 2019 | pp 112-124 https://doi.Org/10.14743/apem2019.1.315 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper A multi-product pricing and inventory model with production rate proportional to power demand rate Keshavarzfard, R.a, Makui, A.b, Tavakkoli-Moghaddam, R.c,d'* aSchool of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran bSchool of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran cSchool of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran dArts et Métiers ParisTech, LCFC, Metz, France A B S T R A C T A R T I C L E I N F O This paper deals with an economic lot size model when demand follows a power law and changes with time, owing to the fact that this kind of pattern is suitable for so many real situations. Production rate is presumed to be proportional to demand rate. Also since that demand is price sensitive in reality, we suppose that demand decreases linearly with price. With regard to these points, in this article a joint pricing and inventory model is presented where demand depends on time with a power pattern and price linearly, production rate changes pro rata with demand rate and multiple items are considered. The principal consideration of the study is to satisfy the demand and optimize the profit for all items in the system, simultaneously. Setup, holding, backlog-ging and production costs are involved in the inventory system. The aim is to maximize total profit function and achieve optimum values of scheduling period, reorder point and price. Employing mathematical modelling and optimization methods, the existence of the optimal solutions is proved, and then a simple heuristic algorithm is presented to maximize total inventory profit and determine the best values of variables. A numerical analysis is carried out to illustrate the applications of the proposed models. © 2019 CPE, University of Maribor. All rights reserved. Keywords: Pricing model; Inventory model; Economic production quantity (EPQ); Backordered shortages; Power demand pattern *Corresponding author: tavakoli@ut.ac.ir (Tavakkoli-Moghaddam, R.) Article history: Received 14 August 2017 Revised 15 February 2019 Accepted 24 February 2019 1. Introduction The constant demand rate is one of the presumptions of the conventional Economic Production Quantity (EPQ) model proposed by Taft [1] that is not common in practice. In the most real situations demand of consumers varies with time. Therefore, many researchers have worked on time-varying inventory models. Barbosa and Friedman [2] worked on a special type of time-varying demand to find a complete solution. Mitra et al. [3] used a demand pattern that increases or decreases with time in an inventory system. A multi-period inventory model is presented by Sakaguchi [4] assuming that demand varies with time. Also Khanra et al. [5] proposed a quadratic-time demand for an EOQ with shortages and allowable delay in payments. Sarkar et al. [6] studied a production system with demand depending on time and price together with considering the influence of inflation and reliability. Escuin et al. [7] discussed inventory models using stochastic and time varying demand for a paper manufacturer. In this paper, we use a kind of demand pattern called power demand. It can be applied for the situations that a high percentage of requests for products happen at the beginning of the cycle, like breads, yogurt, fruits, prepared food, vegetables, fresh meat, etc., or at the end of the cycle, 112 A multi-product pricing and inventory model with production rate proportional to power demand rate like tea, coffee, sugar, oil, etc. Naddor [8] introduced an inventory system with a power demand pattern. Lee and Wu [9] presented an optimal order quantity model allowing for shortages, power demand and deteriorating items. Singh et al. [10] studied an EOQ model where demand has a power pattern and partial backlogging and perishable products are allowed. Sicilia et al. [11] analyzed systems with deterministic power demand pattern and different situations: with and without shortages, with full backordering or completely lost sales. Rajeswari and Vanjikkodi [12] worked on an inventory system considering Weibull deterioration and demand following a power law. Mishra and Singh [13] proposed an economic ordering model with demand having a power pattern, perishable units and partially backordered shortages. Sicilia et al. [14] offered an optimal order size model taking into account power demand along with constant deterioration rate. Sicilia et al. [15] presented an optimum lot size model in which demand has a power pattern, production rate changes pro rata with demand rate and backordered items are allowed. Sicilia et al. [16] studied lot size models where demand follows a power law and the replenishment rate is uniform. San-José et al. [17] analyzed an inventory system with demand following a power law and partial backordering. Demand of consumers is price sensitive, so that pricing is one of the most important decisions in a company. Tripathi et al. [18] investigated inventory dependent demand with a power rate and holding cost functions for two situations. Lau et al. [19] worked on a joint ordering and pricing problem with deteriorating products and a two period life. Yang et al. [20] studied a model considering price dependent demand, deterioration and partial backordering. Banerjee and Sharma [21] investigated an inventory model in which seasonal demand varies with time and price. Soon [22] developed a review of multi-products pricing models. Maihami and Kamalabadi [23] proposed a joint inventory and pricing system with deteriorating products, price dependent demand and partial backordering. Shavandi et al. [24] presented a constrained inventory and pricing model with multiple items. Pal et al. [25] studied an economic ordering model with multiple products and price break sensitive demand. Zhu [26] worked on joint production, replenishment and pricing policies where demand is random and price sensitive and there is a supply disruption. Qin et al. [27] employed joint lot-sizing and pricing policies for fresh products with deterioration. Liu et al. [28] studied a joint investment and pricing problem for perishable products considering price and quality dependent demand. Panda et al. [29] presented a replenishment and pricing problem for a high tech item in a dual-channel supply chain. Alfares and Ghaithan [30] worked on a pricing and inventory system considering price dependent demand and time-varying holding cost along with quantity discounts. Chiu et al. [31] investigated the impact of delayed differentiation on a vendor-buyer system with rework and multiple items. Gholamian and Heydari [32] developed a mixed integer stochastic programming model by using METRIC stochastic relations in a location-routing-inventory problem. The remainder of this paper is organized as follows. In Section 2 problem definition and mathematical model are presented. Concavity and optimal decision are proposed in section 3. A procedure for determining the optimum values can be found in section 4. Numerical analysis is presented in section 5. Finally, in section 6 some conclusions and future researches are given. 2. Problem definition and mathematical model Consider a factory which produces N different items (where i = 1,2,.. ,N). Each item has an average demand v¿ that must be satisfied. The demand varies with time with a power pattern and decreases linearly with price. Also the production rate changes pro rata with demand rate. The manager desires to satisfy the customer demand and optimize the total profit of the system, simultaneously. The inventory cycle starts with s units of net stock at time 0. At the same time t = 0, production begins with the production rate P¿(í), at time t1¿ reaches zero and continues until t = t¿ for each product i, consequently the replenishment quantity Qi will be produced. Also during the interval [0,x¡], the inventory level of product i increases at a rate P¿(t) — Di(t). After that the stock level decreases up to t = t2i according to demand. Finally, during the interval [í2¿, T], demand is backlogged. Assume that /1¿(t) and /2¿(í) are the on-hand inventory levels of item í at time t in the intervals [0, t¿] and [t¿, T], respectively. The scheduling period, the Advances in Production Engineering & Management 14(1) 2019 113 Keshavarzfard, Makui, Tavakkoli-Moghaddam backorder size and the selling price are three decision variables of the system. In the following, an approach is presented to find the optimal values. The following notation will be applied in the rest of the paper. T Scheduling period (time) N Number of items Qi Production quantity for item i (units) Si Reorder point for item i (units) Di Demand quantity during the inventory cycle for item i (units) Ti Production period length for item i (time) v¡ Average demand vt =Dt/T for item i (units) A¿ Production setup cost for item i ($/replenishment) Pi Selling price for item i, where pt >ct ($/unit) Ci Unit producing cost for item i ($/unit) A Unit carrying cost for item i ($/unit/unit time) Wi Unit backlogging cost for item i ($/unit/unit time) hi (t) Net stock level at time t for item ¿(0 < t < t) hi (t) Net stock level at time t for item i (0 < t 0 , bi >0. • Multiple items are assumed for the inventory system. • The demand rate is less than the production rate for each item. • The production rate P£(t) is proportional to demand rate D^t) for each item i at any time t(0 < t < Ti) and is defined by PÉ(t) = aiDi (t) with at >1. The demand over the scheduling period [0, T] is defined by the following: fT fT viit\1/Ki~1 (1) I Di(t)dt=l (ai-biPi)-!-) dt = (Oi -bipi)viT J0 Jo Ki ' The differential equations governing the system are as following: = Pi(t) -Di(t) = (a, -1)Di(t) = (a, -1)^ , (2) /li(0) = si, 0o J o V¿ m1^-1 biPí)~\r) dt = (ai-bipi)viT (7) (8) As it was expected, the lot quantity is equal to the demand of scheduling period. We assume that I(ji) >0 and Si <0, So that —(a^ — bipi)<"a'' ^rT < S; < 0. Suppose that the stock level reaches ai zero in the production period at time t1£. Since In^tn) = 0, from Eq. 4 we obtain tu for item i according to decision variables st and T: hi = -Si (9) — — bipi)viT The net stock level of interval [t^T] reaches zero at time t2i. Solving equation I2i(.t2i) = 0, t2i can be obtained for item i according to decision variables st and T: (10) tu = 11 + (ai ~bipi)viT) We consider four various cost in the inventory system for each product i as follows. Note that the average number of production runs is p The carrying cost: At rTi CH>=i(l tu. Si + (a¿ — 1)(a¿ -bipi)viT[- dt + Jt: ^VK Si + (Oi -bipi)viT- (a¡ -bipi)viT ( - Kí + l dt) = (-s¿)Kí+1 Q¿ + (a¿ -bjPi)ViT)K (Ki + lXai-biPi)KiViKiTKi ' (Ki + lXai-1)Hai-biPi)KiViKiTKi Ca¿-b¿p¿)v¿T' (k¿ + 1)«¿k (11) The shortage cost: CB t^/K s¿ + (a¡ -1)(a¡ -bipi)viT[-j +Ï Jt2í (s¡ + (a¿ ~bipi)viT)Ki+1 Si + (a¡ — biPi)ViT— (a¡ -bipi)viT (- ^Vk di dt I = (12) ■ + (-s¿)Kí Kí + l (a¿ — biPi)ViT (k¿ + 1)(a¡ -biPi)KiViKiTKi (k¿ + 1)(a¿ -1)k'(a¿ -bipi)KiviKiTKi (k¿ + 1) Advances in Production Engineering & Management 14(1) 2019 115 Keshavarzfard, Makui, Tavakkoli-Moghaddam The production cost: The setup cost: The sales revenue is: Qi CPi = Cí-^= {ai-bipi)civi (13) CSt = ^ (14) SRÍ =Pi y = (a¿ -bipi)pivi (15) The total profit of product i can be calculated then as: TPiQpi,si,T) =SRi -CHt -CBi -CPi -CSi = {Si + (aj ~bipi)viT)Ki+1{Ai + wO = (a¿ ~bipi)pivi (Ki + 1){ai-bipi)KiviKiTKi (-s¿)Kí+1(A¿ +w¿) (at -biPi)ViT ( h, \ (16) + ,„ ■ ^ Kzrr + Wi (kj + -1)^ -bipi)KiviKiTKi (KJ + 1) Aj + WiSi Now we define = (Pi,P2,---,Pn) and s = (s1,s2,...,sN). So that the total profit of the system can be obtained as follows: N noun = ^TPi(pi,si,T) (17) i=l 3. Concavity and the optimal decision With regard to the purpose of this paper that is finding the best production policies to maximize the total profit per unit time for the multi-product inventory system, we first prove that for any given p, the optimum solution of (s,T) not only exists but also is unique. Because nQp, s,T)is a function of ¡p, s and T, so for any given the essential conditions to maximize the total profit per unit time is equaling partial derivatives of the nQp,is,r) to zero, with respect to decision variables st and T, simultaneously. Thus, dnQp,s,T) = (-Sj)1^ (5t + (at -biPi)viT)Ki(Ai + Wj) ^ f18_ dst (at — 1)Ki(aj -bipi)KiviKiTKi (a£ -biPi)KiviKiTKi ^ 1 N dn@,s,T) v 2(k¡ -S dT L^ (k¿ + 1)(a¡ — 1)Kí(a¿ -bipi)KiviKiTKi+1 N (.Si + (a¿ -biPi)ViT)Ki((ai -biP^T- k¡S¡)(A¡ + w¿) í=i N (Ki + 1)(ai-biPi)KiViKiTKi+í (19) v- (a¡ -biPi)Vi ( A, \ If=1A¿ \ "liTlJ'll "l . \ . ¿-11 = 1 "I „ + Z (K^-H) + + = 0 ¿=i Theorem 1: For any given ¡p, The total profit function n(p,s,T) is concave. Proof: Please see Appendix A. 116 Advances in Production Engineering & Management 14(1) 2019 A multi-product pricing and inventory model with production rate proportional to power demand rate —S' (a—V) Defining a new variable xt by xt = —————, the region — biPi)—-—rT < st <0 is \p,i—bipi)viT ai a—1 equivalent to 0 < xt < —— and Eq. 18 and Eq. 19 are respectively equivalent to ai Wi (1-x¿)Kí-7--;—=0 (20) N KixiKi+1(ai -bipi)vi(Ai + Wi) v (1-x¿)Kí(1 + K¿x¿)(a¿ -bipi)vi(Ai + w¿) ZKiXff^ai-biPQViWi+Wi) y O,- + DO,- -1)Ki Li (— + 1)(ai -1)— ^ (— + 1) i-i i-i (21) ( y (at ~bipi)vi( At \ If=1Ai + Z (—,+1) {^ + W'i)+—=0 ¿ = 1 Proposition: There is a unique solution xt* for the function (1 — xt)Ki — _ . = 0, on the interval (0 ai Proof: The proof is similar to proposition 1 in [15]. The optimal solution of Eq. 20 can be obtained using any numerical method like the Newton-Raphson method (see, i.e. [33]). Also from Eq. 20 we have XjKi Wj (22) -l--= f1-xïKi---—=0 ( ) Substituting Eq. 22 in Eq. 23 we obtain following equation N N Zfai -bipi)vi(Ai + Wj)(1 - Xj)K' y KjCa, -bipi)viwixi . 1 (Kt + 1) Zl (— + 1) 1=1 1=1 (23) , y (gj -bjpQvif At \ £f=1A 0 + Z (Kt-H) W~i+W'i)+~Tr~ = 0 ¿=i Then substituting the optimal solution xt* obtained by Eq. 20 in Eq. 23, the best cycle length T* for a given ~p is T* = M A, yW vÂai~biPÙvi\ (r Li=l[{ (Ki + 1) ^ Ai + W¿)(1- Xj*)K' + KjWjXj* - (24) Also, the best reorder point and the optimal lot quantity are st* = —xi*{ai — bipi)viT* and Qi* = (at -bipi)viT* respectively. Now for any s1*,s2*,...,sN*,T*, the first order condition to maximize the total profit function n0,r,r) is dn(^,s*,r) biViT* (Ai = aiVi -2bipivi + bicivi ---—— \—— + wi dPi 11 1 1 1 1 (Ki + 1)W^ (Zb) . f n bj \(si* + (ai-bipi)viT*)Ki((ai-bipi)viT*-Kisi*) Ki(-si*)Ki+1 1 0 ^ * (Ki+1 )ViKiT*Kl I (.at-bmri^ {ai-irKai-blpi)Ki+ij-0 Theorem 2: The total profit function nQp, s*,T*) is a concave function of •p for a given Proof: Please see Appendix B. Advances in Production Engineering & Management 14(1) 2019 117 Keshavarzfard, Makui, Tavakkoli-Moghaddam 4. Procedure for determining the optimal values of the model In this section, with regard to that solving Eq. 25, using numerical methods takes a noticeable time and the optimized answers are hard to achieve, a simple procedure is presented to obtain good values for ~p,s,T and n. Step 1: For each product i; p{ = q, where < —. If bi yN a- 1 >0, + ^i)(1-Xi*)K* + KjWjXj* -(-iL + calculate period length T* and find out s*and nQp,is*,r*); otherwise, there is no feasible solution and then go to Step 5. Step 2: For each product i (i = 1, ..., N), do: suppose that pt = Pi + £ and pj =Pj, Vj ^ i. Then, calculate the best reorder vector, the economic scheduling period and total profit function, and name them (s*i,T*i) and nid^,'i^*i,T*i), respectively. Step 3: Choose the product m that has the conditions below: • T*m can be calculated. • Pm,s*,T*) Advances in Production Engineering & Management 14(1) 2019 A multi-product pricing and inventory model with production rate proportional to power demand rate Table 1 Optimal policies for the proposed EPQ model, considering several values for a and c A = 100, A = 4, w = 5 v = 1200, a = 100, b = 2 and k = 3 Production Production X* T* s* Q* P* n* rate cost a= 1.1 c = 10 0.064156 0.1580 -486.6977 7394.1 30 958730 c = 15 0.1714 -448.7131 6785.3 33 733230 c = 20 0.1825 -421.4925 6347.0 35 538900 c = 25 0.2040 -376.9944 5626.0 38 373420 c = 30 0.2235 -344.1472 5089.3 40 239110 a= 1.3 c = 10 0.135125 0.0900 -583.7937 4211.0 30 957780 c = 15 0.0976 -538.2312 3864.3 33 732350 c = 20 0.1039 -505.5802 3614.7 35 538080 c = 25 0.1162 -452.2047 3204.1 38 372680 c = 30 0.1273 -412.8045 2898.2 40 238430 a= 1.5 c = 10 0.161603 0.0735 -570.1081 3438.5 30 957280 c = 15 0.0797 -525.6137 3155.4 33 731890 c = 20 0.0849 -493.7281 2951.6 35 537640 c = 25 0.0949 -441.6038 2616.3 38 372290 c = 30 0.1039 -403.1273 2366.5 40 238080 a= 1.7 c = 10 0.170823 0.0666 -546.0560 3115.7 30 957000 c = 15 0.0722 -503.4388 2859.1 33 731630 c = 20 0.0769 -472.8984 2674.5 35 537400 c = 25 0.0860 -422.9732 2370.7 38 372070 c = 30 0.0942 -3861199 2144.4 40 237880 a= 1.9 c = 10 0.174358 0.0630 -527.5052 2948.8 30 956830 c = 15 0.0684 -486.3358 2706.0 33 731470 c = 20 0.0728 -456.8329 2531.2 35 537250 c = 25 0.0814 -408.6038 2243.7 38 371940 c = 30 0.0891 -373.0025 2029.5 40 237760 Table 2 shows the optimal policies of the system considering combinations of parameters k and c using following parameters: a = 100, A = 4,w = 5,v = 1200, a = 100, b = 2 and a = 1.5. Table 3 shows the optimal policies of the system considering different values of a using following parameters: a = 100, h = 4, w = 5 v = 1200, b = 2, c = 10,k = 4 and a = 1.7. Table 2 Optimal policies for the proposed EPQ model, considering several values for K and c a = 100, A = 4,w = 5v = 1200, a = 100, b = 2and a = 1.5 Production Production rate cost x* T* s* Q* P* n* k = 0.5 c = 10 0.081199 0.0744 -290.1504 3482.8 30 957310 c = 20 0.0860 -251.2777 2989.7 35 537670 K= 1 c = 10 0.148148 0.0750 -533.3328 3508.8 30 957330 c = 20 0.0866 -461.8791 3012.0 35 537690 K = 2 c = 10 0.175842 0.0756 -638.0297 3536.6 30 957350 c = 20 0.0873 -522.5499 3035.8 35 537710 K = 3 c = 10 0.161603 0.0735 -570.1081 3438.5 30 957280 c = 20 0.0849 -493.7281 2951.6 35 537640 Table 3 Optimal policies for the proposed EPQ model, considering different values of a a = 100, A = 4,w = 5v= 1200, b = 2, c = 10, K = 4and a = 1.7 a x* T* s* Q* P* n* a = 100 0.170823 0.0666 -546.0560 3115.7 30 957000 a = 200 0.0444 -819.0840 4741.4 30 4855500 a = 300 0.0356 -1021.6 5937.5 30 11754000 Advances in Production Engineering & Management 14(1) 2019 119 Keshavarzfard, Makui, Tavakkoli-Moghaddam Table 4 Optimal policies for the proposed EPQ model, considering different values of b _a = 100, A = 4, w = 5, v = 1200, a = 100, c = 10, K = 4and a = 1.7_ b_x*_T*_s*_Q*_ft*_n* b = 1 0.170823 0.0628 -579.1799 3352.6 55 2426800 b = 2 0.0666 -546.0560 3115.7 30 957000 b = 3 0.0722 -503.4388 2814.1 22 486130 Table 4 shows the optimal policies of the system considering different values of b using following parameters: a = 100, A = 4, w = 5, v = 1200, a = 100, c = 10, k = 4 and a = 1.7. Figs. 2 and 3 show the cycle length and the total profit as functions of unit production cost, when input parameters are used from Table 1. In each figure different values of a are considered (a = 1.1,1.3,1.5,1.9). Figs. 4 and 5 show changes of the lot size and total profit respect to the changes of the index of demand pattern using Table 2. In each figure two values of production cost c are considered (c = 10,20). Figs. 6 and 7 show changes of the price respect to the changes of the parameters a and b using Table 3 and 4, respectively. Some managerial insights can be expressed as follows. In Table 1, by fixing the replenishment rate parameter a, if the unit production cost c increases then the total profit function n*, the best lot size Q* and the value of s* decrease. However, the optimal cycle length T* and the optimum price p* increase in the same situation. In the same Table 1, fixed the unit production cost c, the total profit function n*, slightly, the best scheduling period T* and the economic lot quantity Q* decrease as the production rate a increases. However, In the same conditions the optimal price p* does not change. Fig. 2 Changes of cycle length respect to the changes of unit Fig. 3 Changes of total profit respect to the changes of production cost using Table 1 unit production cost using Table 1 1.5 2 2.5 Index of power demand pattern Fig. 4 Changes of lot size respect to the changes of k using Table 2 1.5 2 2.5 Index of power demand pattern Fig. 5 Changes of reorder point respect to the changes of k using Table 2 120 Advances in Production Engineering & Management 14(1) 2019 A multi-product pricing and inventory model with production rate proportional to power demand rate Fig. 6 Changes of price respect to the changes of parame- Fig. 7 Changes of price respect to the changes of parameter a using Table 3 ter b using Table 4 Using Table 2, by fixing the index of power demand k unit production cost c, if the unit production cost c increases then the total profit function n*, the economic lot quantity Q* and the value of s*decrease. In the same conditions the best price p* and the optimum cycle length T* increase. In Table 3, fixing c, a, k and b, if parameter a increases then the total profit function n*, the price p* and the economic lot quantity Q* increase. However the optimal scheduling period T* decreases in the same conditions. In Table 4, fixing c, a, k and a, if parameter b increases then the total profit function n*, the best price p* and the economic lot quantity Q* decrease. However the optimum scheduling period T* increases in the same conditions. 6. Conclusions and future research In this paper, an economic production model has been presented using kind of demand rate named power demand. Also it is supposed that demand of customers dependes on price linearly and production rate changes pro rata with demand rate. Multiple products are assumed to be in the inventory system and shortages are allowed and fully backlogged. Mathematical modeling and optimization methods are used to find optimal solutions for both single-product and multiple-products situations. Also since that achieving optimum inventory policies for second situation is hard a simple heuristic procedure is proposed to obtain the near-optimal solutions for multi-items form. Several examples are presented to illustrate the applications of the model using various values of parameters. The outcomes reveal that fixing the production rate parameter, if the unit production cost increases then the total profit function and the economic lot size decrease, while the best cycle length and the optimum price increase. The total profit function slightly, the best scheduling period and the optimal lot quantity decrease as the production rate increases. By fixing the index of power demand, if the unit production cost increases, the total profit function and the economic lot quantity decrease while the best price and the optimal cycle length increase. In the end, the following suggestions for further research are made: • The proposed model can be extended using deterioration in the inventory system. • Allowing for shortages that are lost sales or partially backorderd could be considered. • Imperfect items are produced in many production systems as well as perfect items. So it could be considered in the inventory system. • Since that different price functions may be possible in the real world situations, they could be considered in the inventory system. • The proposed model can be considered with manufacturing disruption costs. • Taking sustainability concerns into account could be another interesting recommendation. Advances in Production Engineering & Management 14(1) 2019 121 Keshavarzfard, Makui, Tavakkoli-Moghaddam References [1] Taft, E.W. (1918). The most economical production lot, The Iron Age, Vol. 101, 1410-1412. [2] Barbosa, L.C., Friedman, M. (1978). 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Introduction to numerical analysis, Springer Science & Business Media, New York, USA. Appendix A For any given ~¡p, The total profit function n(p, s, T) is concave. Proof: The Hessian matrix can be used to prove the concavity of n(p, s, T). N N (Si + (ai-biPi )viT)Ki+1(Ai + Wi) nÇjp, s, T) = ^ TPi (Pi, Si, T) = ^ [(ai — biPi )PiVi — - (Ki + 1)(üí — biPi)KiViKiTKi i=i i=i (—Si yt+1(Ai + Wi ) (ai — biPi )viT(Ai \ (A1) ---\--I--r /tO/■ I + /LW-S--- (Ki + 1)(ai — 1)K (ai — biPi )kíV¿kÍTkÍ (Ki + 1) Wi 7 11 T — (ßi — biPi)ciVi] düQp, s, T) (—Si )K (Ai + Wi ) (Si + (ai — biPi)ViT)Ki (Ai + ) ds¡ (a¡ — 1)K (a¡ — b¡pi )KiViKiTKi (at — biPi )KiViKiTKi N dUqp, s, T) v Kí(—Sí)kí+1(Aí + wd + Wi, Vi (A2) = I; dT Z-, (Ki + 1)(ai — 1)Ki(ai — biPi)KiviKiTKi+1 i=i N Z(Sj + (aj — bjPi )vjT)Kl ((aj — bjPj )viT — KjSj )(Aj + wi) (A3) (K, + 1)(a, — b:P: )KlV:KlTKl+1 ( ) (Ki + 1)(ai — biPi)KiViKiTKi í=i V (at — biPi)vi(A¡ \ Yd=i*i +1 K +1) fe + + T2 =i d2U(p, s,T) Kj (—Sj )K i-i(A j + Wj ) K j (Sj + (a ¿ — b iP ¿ )vt T)K-i(A ¿ + wj) -=----< 0 V i (A4) d Si2 (ai — 1)K (a i — bip i )Kív¿KiTKi (a¿ — b¿p ¿ )kív¿kí Tkí , ( ) d2n(p, s,T) V K (—si)K+i(ñ,i + wt ) dT2 ¿-¡ (a, — 1)K¡(a, — btpt)KtviKtTKt+ i=i 1 ( a í ^^ T / / n'KíSí2(sí + (ai — biPi)viT)K-i(Ai + htí) 2 ^ti^ o (a i — ^p i )KiViKiTKí+2 T3 (A5) d2n(p, s,T) = k j (—s j )K j (A j + -UTj) + k ¿Sj (Sj + (a ¡ — b iP ¿ )Vj T)Ki-i(A ¿ + Wi) (A6) d Sí d T (a¿ — 1)K (ai — bip í)kívíkítkí+i (a¿ — biP ¡ )KiViKiTKi+i , 1 ( ) Advances in Production Engineering & Management 14(1) 2019 123 Keshavarzfard, Makui, Tavakkoli-Moghaddam d2nÇp, s, T) dsidsj We suppose that Si + (at — biPi~)vtT > 0. = 0, Vi, j [T, Su, S2,..., sN] d2n d2n d2n ] dT2 dTds1 dTdsN rT d2n d2n d2n S1 ds1dT ds12 . " ds1dsN S2 d2n d2n d2 n -SN .dsNdT dsNds1 " dsN2J _ 2d2U 2 = T dT2 +Sl dSl2 + " +Sn dS;-2 d2n ( d2n d2n + + " + sn- ds-tdT dsNdT 2 T3 < 0 (A7) (A8) Appendix B The total profit function n(p, s*, T*) is a concave function of ~p for a given (s*, T*). Proof: We have dn(p,s*,T*) biViT* / At \ --- = a;V; - IbiPjV; + bjCjV: ---— I--+ W; I dpt 11 iri 1 111 (kl +aiKi 7 ,.Ki'T*Kl [ + bi&i+Wi) r(si*+(ai-bipi)viT*)Ki ((ai-bipi)viT*-Kisi*) Ki(-si*)Ki+1 (Ki + l)ViKiT* (ai-bipi)Ki+ ■HI J _"I (ai-l)Ki (ai-bipi)Ki+li d2n(p, r, t*) Kib2(—s*)Ki+1(Ai + ^ ) --= —2bivi (ai — l)KiviKiT*Ki(ai — bipi)Ki+2 Kibi2si*2(si* + fa — bjpj )viT*)Ki-1(Ai + w¡ ) ViKiT*K (ai — biPi )Ki+2 d2n(ß, s*, T*) <0 dpídpj =0 And so that P2,..■, Pn] d2n d2n d2n d2n d2n d2n dpNdpi dpNdp2 d2n 1UPN 2 d2n dp2dpN d2n P1 P2 N Y Pn. = í=1 ,d2n(ß, r, t*) dpi2 <0 (B1) (B2) (B3) (B4) 12 124 Advances in Production Engineering & Management 14(1) 2019 Advances in Production Engineering & Management Volume 14 | Number 1 | March 2019 | pp 125-135 https://doi.Org/10.14743/apem2019.1.316 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper Maximum-minimum distance clustering method for split-delivery vehicle-routing problem: Case studies and performance comparisons Min, J.N.a, Jin, C.a*, Lu, L.J.ab aTaihu University of Wuxi, School of Economics and Management, Jiangsu, P.R. China bNanjing University, School of Management, Nanjing, Jiangsu, P.R. China A B S T R A C T A R T I C L E I N F O The split-delivery vehicle-routing problem in which delivery to a demand point can be served by any number of vehicles is an important branch of classic VRP. Objective function is used to minimise travel distance while using the lowest number of vehicles. According to the maximum-minimum distance clustering method, a three-stage algorithm is proposed. First, the maximumminimum distance method is employed to cluster customer points into the lowest number of groups. Second, according to the maximum vehicle capacity, the load demand in each group is adjusted to create suitable customer points in each clustering group by adopting 'push-out' and 'pull-in' operations. Third, a tabu search is used and an optimised route for each group is generated to minimise the total travel distance. Numerical experiments, some on the benchmark data set, are presented to verify the feasibility and effectiveness of the proposed algorithm. The computational results show that the performance of the proposed algorithm is better in terms of both optimised travel distance and less computation time when the problem size is less than 75. The results also show that when the customer points are in a cluster distribution around the depot, the algorithm achieves better performance. © 2019 CPE, University of Maribor. All rights reserved. Keywords: Split-delivery vehicle-routing problem; Maximum-minimum distance method; Load-demand adjustment; Route optimisation; Tabu search; Clustering first and routing later *Corresponding author: mjn3862@126.com (Jin, C.) Article history: Received 5 December 2018 Revised 12 February 2019 Accepted 25 February 2019 1. Introduction The split-delivery vehicle-routing problem (SDVRP) was formally introduced by Dror and Trudeau [1] in 1989. In SDVRP, the constraint in which each customer is visited only once, which is imposed in the classic VRP, is relaxed [2]. In other words, in SDVRP, delivery to a demand point can be split among any number of vehicles [1-3]. This relaxation can further optimise the VRP in terms of the number of vehicles used, travel distance, and carbon emissions, which have recently become a significant environmental protection problem. The fractional capacity of a vehicle can be better utilised. When the remaining capacity of the vehicle is insufficient to provide complete service to a customer, that vehicle can still provide service to the customer that is equal to the residual capacity, and the remaining customer demand can be served by other vehicles. The transportation cost can be reduced because of the following reasons. (1) The optimal solution of the number of vehicles used in SDVRP might be lower than that used in the VRP. (2) Largest savings are obtained when the average customer demand is only more than half of the vehicle capacity, and the variance in the customer demands is low [4, 5]. Therefore, the SDVRP has quickly 125 Min, Jin, Lu become an important branch of VRP since it has been introduced and has received increasing attention over time [2]. Studies have mainly focused on attempting to solve the problem in designing heuristic and meta-heuristic solution approaches [2]. Dror and Trudeau [1] proposed a first heuristic algorithm for the SDVRP. Two types of methods were introduced: the first method is the k-split interchange, i.e. a customer demand is split into different routes in which the remaining capacity is sufficient for the split customer. The second method is route addition, i.e. a split customer is removed from all the routes where the customer lies and a new route is created, which is composed of that customer only. The computational results showed that main savings are achieved for large values of customer demands. Archetti et al. [4] proposed the first tabu search algorithm (TSA) called SPLITABU. At each iteration, a neighbour solution is obtained by removing a customer from a set of routes in which the customer is currently visited and inserting the customer into either a new route or an existing route with sufficient residual capacity. A numerical experiment proved that this is much more effective than the algorithm of Dror and Trudeau [1] even though it is obviously much slower. Chen et al. [5] proposed the first hybrid heuristic algorithm. In this algorithm, the initial solution is obtained using the Clarke-Wright saving algorithm for the VRP. Then, an endpoint mixed-integer program (EMIP) is applied to this initial solution to optimally reallocate the endpoints of each route. The solution obtained from EMIP is then improved using a variable-length record-to-record travel algorithm. The computational results showed that the performance of this approach is better than that of the TSA in [4] under the same set of instances even if the CPU time tends to be quite high in large instances. Archetti et al. [6] proposed an improved three-stage algorithm based on the TSA proposed in [4]. First, the SDVRP is solved by applying the TSA in [4]. Then, the solutions are analysed to ascertain particular information, namely, (1) if an edge is often traversed in these solutions, then this edge is included in high-quality solutions with a high probability, and (2) if a customer is never or rarely split in the TSA solution, then that customer is probably not split in high-quality solutions. Once the TS ends, the information from (1) is used to reduce the original graph by discarding those edges that are never or rarely traversed by the TSA. All possible routes are constructed based on this reduced graph. The information from (2) is used to construct a route-based formulation to identify the best routes among the set of generated routes. Finally, the mixed-integer linear programming (MILP) model is repeatedly applied on small subsets of routes in the ascending order, which is sorted according to the 'desirable' parameter. The computational results of this algorithm improved those produced under the same set of instances presented by the TSA in [4] in many cases. Gulczynski et al. [7] allowed split deliveries only if a minimum fraction of a customer demand was serviced by a vehicle and developed an EMIP with an enhanced record-to-record travel algorithm to solve this problem. Wilck IV and Cavalier [8] developed a construction heuristic algorithm to solve the SDVRP, and their computational results showed that its performance is better than the two-phase method under the same data set in terms of travel distance and computation speed. Liu et al. [9] proposed the k-means clustering algorithm and designed two different algorithmic approaches: one was the grouping first and routing later; the other was the routing first and grouping later. A comparison of these two approaches indicated that the approach of grouping first and routing later exhibited better performance. Lu et al. [10] proposed a routing optimisation algorithm for different electric-vehicle-movement situations. A multi-agent simulation model was run using city real data. Wang et al. [11] proposed a bee-colony optimisation model for the SDVRP based on the reaction threshold and stimulatory value. The experimental results indicated the feasibility of the algorithm. Zhu et al. [12] addressed a multi-depot capacitated VRP where the client demand is composed of two-dimensional weighted items. A quantum-behaved particle swarm optimisation and an exploration heuristic local search algorithm were proposed, and computational experiments on the benchmark instances were effectively carried out Wen [13] proposed a multi-re-start iteration local search (MRSILS) algorithm. First, a large travelling salesman problem (TSP), which includes all customer points, is solved by adopting GENIUS. The solution is partitioned into groups according to the vehicle capacity in order for each group to meet the load-demand limitations. Then, for each point, a greedy point re-insertion algorithm is used to delete a point from its current group and 126 Advances in Production Engineering & Management 14(1) 2019 Maximum-minimum distance clustering method for split-delivery vehicle-routing problem: Case studies and performance re-insert it into an optimal position in the current solution by considering the delivery-split tactics. This re-insertion is iterated until no further improvement occurs. Finally, the 'perturbation' and solution pool are adopted to repeat the re-insertion in order to obtain the optimisation result The experimental results on the benchmark data set showed that the MRSILS is competitive. Wu et al. [14] introduced a multi-objective algorithm to solve VRPs using time windows. The algorithm combines a discrete particle swarm optimisation based on a set-decoding scheme and variable neighbourhood searches to find the Pareto optimal routing solutions. Tang et al. [15] developed a model and the corresponding multi-phase particle swarm optimisation algorithm for bulk-cargo port scheduling. Xiang et al. [16] proposed a clustering algorithm of 'routing after grouping'. The grouping is based on the 'nearest' principle. A split threshold is set to limit the vehicle load to within a certain range, and the ant-colony optimisation algorithm is used to arrange the routes. Cao et al. [17] proposed an improved wolf-pack algorithm to solve the VRP using multiple fuzzy-time windows. Johanyak et al. [18] proposed a modified particle swarm optimisation algorithm, which was combined with a local-search technique, to solve large-scale nonlinear optimisation problems. Wang et al. [19] adopted a hybrid fruit-fly optimisation algorithm integrated with three local search methods (two-opt, swap, and insert) to solve the multicompartment VRP. Research in the SDVRP solution also extends to exact algorithms [2]. Belenguer et al. [20] proposed a cutting-plane approach wherein a polyhedron model was built. Some facet-inducing and other valid inequalities were embedded in the cutting-plane algorithm. They solved a relatively smaller problem and achieved satisfactory results. Lee et al. [21] proposed the shortest-path approach in which the SDVRP is formulated as a dynamic programming model, where the routes are sequentially constructed using a labelling algorithm. The solution space and corresponding states were reduced according to the ^-split-cycle property. They tested their approach on instances with up to seven customers. Jin et al. [22] proposed a two-stage algorithm with valid inequalities (TSVI). The first stage divided the customers into clusters and established a lower bound. The objective function minimised the clustering cost in which the cost of each cluster was initially set to zero. The second stage calculated the minimum travel distance in each cluster by solving the corresponding TSP. The sum of the minimum distance travelled over all clusters yielded an upper bound. The minimum distance of each TSP was used to update the objective function in the first stage, and the procedure was iterated. Valid inequalities were developed and added to strengthen the MILP model. The approach was able to solve instances with up to 22 vertices but with a large computational effort. Archetti et al. [23] implemented a branch-price-cut algorithm based on the principle of problem decomposition. Each column generated by the sub-problem represented a route with delivery quantities. The generated columns were used to find an optimal heuristic solution to the problem. Both cases where the fleet of vehicles was unlimited and limited to the minimum possible number of vehicles were considered. The computational results showed that the algorithm reduced the optimality gap in most of the benchmark instances. Archetti et al. [24] proposed a branch-price-cut algorithm for a commodity-constrained SDVRP. They solved up to 40 customers with three commodities per customer. Luo et al. [25] proposed branch, price, and cut for the SDVRP with time windows and linear weight-related cost. Ozbaygin et al. [26] proposed an exact flow-based formulation using vehicle indexes. The size of this vehicle-indexed formulation was reduced via a relaxation procedure by aggregating the decision variables over all vehicles. The optimal solutions could be obtained either by locally extending the formulation using the vehicle-indexed variables or by node splitting. Most techniques used in this research field are heuristic and meta-heuristic methods. These are time-consuming methods because multiple iterations or comparisons of many results are necessary to find the optimal solution. Meanwhile, most of the exact algorithms provided in the literature can only solve small-size SDVRPs. To solve these time-consuming and large-scale problems, we propose an algorithm of 'clustering first and routing later' [27]. It consists of firstly clustering the domain of the customer points according to the 'nearest' principle, adjusting the load demands for each sub-domain according to the maximum vehicle-load capacity, and finally routing each sub-domain to minimise the travel distance. In this manner, a near-optimal solution can be obtained in less time. To obtain more optimised results, the modified version of the first Advances in Production Engineering & Management 14(1) 2019 127 Min, Jin, Lu two stages are provided, and TS is used in the third stage in this study. More case studies on the benchmark data set are used, and the computational results are compared to verify the feasibility and effectiveness of the algorithm proposed in this study. The proposed algorithm can be of practical value for both reducing the time consumption and shortening the travel distance. The remainder of this paper is organised as follows. In Section 2, the SDVRP is described. In Section 3, a three-stage algorithm based on the 'clustering first and routing later' strategy plus TS (CRTS) for the SDVRP is presented. In Section 4, the computational results are shown and discussed. Finally, the conclusion is presented in Section 5. 2. Problem description SDVRP is undigraph G = (V,E), where V is the vertex set, i.e. V = {0,1, ...,m}. 0 stands for the depot, and the other vertices stand for the customer points. E is the edge set. c^ is the length of edge (i,y) (cij e E); it is non-negative and satisfies the triangle inequality. dt stands for the demand of customer point i, where ieF - {0}. The vehicles in the fleet are homogenous, and the maximum load capacity of a vehicle is Q. The lowest vehicle number is [£f=1 dt/Q] [2]. Each vehicle starts from and ends at the depot. The customer demands should be completely satisfied. The carrying weight of a vehicle in each route cannot be larger than Q. The following notations are used. is equal to one when vehicle v directly moves from i to j; otherwise, x^ = 0. yiv is the quantity of the demand of i delivered by vehicle v. The objective function is to minimise the total travel distances of the vehicles and is formulated as follows: n n m minZZZCijXl7 (1) ¿=0 j=0 v=l s. t. n m i=0 v=l xvij>1,j = 0,1.....n (2) ZX¿P ~^xtpJ = 0,p = 0,l,2, ...,n;v = 1,2, ...,m (3) i=0 j=0 ^^ xvtj < |S| - 1, v = 1,2.....m; Sç ^-{0} (4) íes jes n = 1,2, ...,n;v = 1,2, „,,m (5) lit. IL I 7=0 m yiv = di,i = 1,2,.,n (6) V=1 n yiv0,i = 1,2, ...,n;v = 1,2, ...m. (9) Eq. 2 states that each customer point can be visited atleast once. Eq. 3 is the flow-conservation constraint. Eq. 4 is the sub-route elimination constraint. Eq. 5 states that customer point i is served by vehicle v only if vehicle v visits customer point i. Eq. 6 ensures that all customer demands are met. Eq. 7 ensures that each vehicle does not exceed its maximum load capacity. 128 Advances in Production Engineering & Management 14(1) 2019 Maximum-minimum distance clustering method for split-delivery vehicle-routing problem: Case studies and performance 3. Used methods: Proposed algorithm The proposed algorithm is a three-stage algorithm based on the CRTS. The first stage clusters the customers. The maximum-minimum distance method (Max-Min dis) is adopted to cluster the customer points according to their geographic locations. The second stage adjusts the load weight for each cluster. The 'push out' and 'pull in' operations are used to adjust the load weight to collect all possible points in each cluster according to the load demand. The 'push out' operation directs the extra weight away from a cluster, and the 'pull in' operation directs some demands from the nearest customer points of neighbour clusters into clusters whose weights are less than Q. The third stage optimises the route, which uses the TSA. The details of the proposed algorithm are described in the next sections. 3.1 Pre-processing Load demand of each customer point dt> Q should be handled before the CRTS. Weight Q can be transported by one vehicle, and remaining weight dt = dt — Q at this point is handled using the following procedures. 3.2 Clustering the customers Basic idea of the maximum-minimum distance Max-Min dis is a type of pattern recognition method, which can improve the efficiency of dividing the initial data set [28]. Procedure of the Max-Min dis Step 1: Take x1 (normally x1 is the depot) as first clustering centre zv Step 2: Calculate distances Dtl at each point i to zx, i = 1,2,..., n. Step 3: Take xk as second clustering centre z2 if Dkl = max{Dil}. Step 4: Calculate distances Dn and Di2 at each point i to zr and z2. Step 5: Take xl as third clustering centre z3; if Dt = max{min(D(1,D(2)} and Dl> 0 • D12, D12 is the distance of zx and z2, where 0is in [0,1], a selectable parameter to meet the requirement of \T^=1di/Q], Step 6: Calculate Dj = max{min(D(1,D(2,D(3)} and Dj > 0 • D12; if z3 exists, Xj is taken as fourth clustering centre z4 and so on until Dj < 0 • D12; finally, end the procedure. Step 7: Classify all points into the nearest clusters according to the principle of minimum distance. 3.3 Adjusting the load weight for each cluster After clustering the customer points, the calculation and adjustment of the load weight for each cluster is performed as follows. 'Push out' procedure Step 1: If load weight wg of a cluster is in [a ■ Q, Q] and the number of points in this cluster is two, then these two points form a route. If ju1 clusters similar to this exist, then ju1 routes are created. Step 2: If load weight wg of a cluster is in [Q, 2 • Q] and the number of points in this cluster is two, then these two points form an inner route, and load wg — Q is pushed out. If u2 clusters similar to this exist, then u2 routes are created. Step 3: If load weight wg of a cluster is larger than rj • >2), then —1) inner routes are formed in this cluster, and the remaining demand wg — (j—1) • Q is pushed out. If u3 clusters similar to this exist, then — 1) routes are created. After the abovemen- tioned three steps are completed, clustering of the remaining customer points in these clusters proceeds to Step 4. Step 4: The remaining customer points are re-clustered to form [£f=i dt/Q 1 — u> U = Ui + U2 + U3 * J —1) clustering groups, where a is in [Ef=i^i/([Ef=i dt/Q\*Q), 1]. Advances in Production Engineering & Management 14(1) 2019 129 Min, Jin, Lu 'Pull in'procedure Step 1: The clusters with less than Q are visited according to the cluster number sequence, e.g. the first one is group A(wgA {Q — wgA") and the load weight of cluster B wgB is larger than Q, then point t is split into t and t', dti = Q—wgA is moved to cluster A, and dt = dt — (Q— wgA) is maintained. Step 4: If point t has demand dt = {Q —wgA) and the load weight of cluster B wgB is larger than Q, then point t is moved (merged) into cluster A. Step 5: If point t does not have sufficient load demand dt <(Q — wgA), then point t is first moved (merged) into cluster A. Second, point t', which is nearest to t in cluster B, is searched if wgB is sufficient; otherwise, point t' is searched in cluster C of the next nearest neighbour from cluster A. Third, Step 3 is performed. Step 6: If the load weight of group A is in [a ■ Q, Q\, then handling for cluster A is terminated. If the load weight of group A wgA < a • Q, then Step 2 is performed. Step 7: If all groups are visited, the procedure is terminated; otherwise, Step 1 is performed. 3.4 Optimising the routes The problem domain has been divided into several smaller-sized clusters after the abovemen-tioned three operations. Thus, many algorithms can be used to optimise the solution. We adopt the TSA to optimise the route in each cluster. The detailed procedure for the TS is described as follows. Step 1: Initialising the variables Set: tL (tabu length) = T, MIs (terminal condition maximum iterations) = NG, cN (customerNum) = N Create tabu [tL]; Generate randomly serialNum [cN] (initial route solution) Step 2: Calculate the objective function value serialNum [cN] and deposit it into the variable bestValue Step 3: If iteration = NG, terminate the program and output the optimal results; otherwise, continuously iterate and execute the following steps in each loop. Step 4: Generate rr neighbourhood of the current solution by adopting suitable selection functions (e.g. two-opts). Step 5: Sort it according to a non-descending order and store it into variable tempDist [rr]. Step 6: If tempDist [0] < bestValue, let (assumed at the mth iteration): bestValue = tempDist [0]; currentBestValue = tempDist [0] bestQueue = the corresponding objects of tempDist[0] currentBestQueue of NGm = the corresponding objects of tempDist[0] tabu = corresponding objects of tempDist[0]. Go to Step3 Otherwise, execute the following steps: Step 7: Analyse the tabu attributes of the corresponding objects of tempDist [rr] currentBestValue = the best value of tempDist [i] (assume the ith one) currentBestQueue of NGm = the corresponding objects of tempDist[i] Step 8: Go to Step3. 4. Case studies To verify the feasibility and effectiveness of the proposed algorithm, three case studies were adopted. Case study 1 was from [22] and was compared with its TSVI algorithm. Case study 2 was from [16] and was compared with its clustering algorithm with a splitting threshold and the k-means clustering algorithm in [9], which are all based on the 'routing after grouping' strate- 130 Advances in Production Engineering & Management 14(1) 2019 Maximum-minimum distance clustering method for split-delivery vehicle-routing problem: Case studies and performance gy. Case study 3 involved the benchmark data set from the Capacitated Vehicle Routing Problem library (CVRPLIB) and was compared with the SPLITABU algorithm in [4] and MRSILS in [13]. The numerical experiments were implemented on C in a Windows 7 64-bit machine with an Intel (R) Core processor and 8 GB of memory. 4.1 Case study 1 Case study 1 contains three instances (N7L1-N7L3). The number of clients in each instance is N = 7, the maximum load of the vehicle is one, and the coordinates of the depot are (0, 0). In Table 1, the columns indicate the total travel distance (Dis.), consumed computational (CPU) time (T) of the TSVI (the data come from [22]) and CRTS, and the relative deviation percentage (RDP) of the distance between the CRTS and TSVI. RDP (Dis.) is equal to ((Distance crts - Distance algorithm) /Distancealgorithm)-100%, and RDP (T) is equal to ((Timecrts - Timealgorithm)/Timealgorithm>100 %. The executions in which RDP was equal to or less than 1.0 % comprised 48.49 % of the total 66 executions. The executions in which RDP was larger than 5.0 % were 12.12 % of the total 66 executions. The CPU time (T) of CRTS listed in Table 1 is equal to 100 times the actual value (to save display space), which indicates that the consumed CPU time of the CRTS is much lower than that of the TVSI. The results of the total travel distance obtained by the CRTS and TSVI in the three instances in case study 1 are shown in Fig. 1. The good consistency of the curves of the two different algorithms indicates that the CRTS algorithm is feasible and effective. Table 1 Comparisons of the results between the CRTS and TSVI N7L1 execution results N7L2 execution results N7L3 execution results No. TSVI CRTS RDP TSVI CRTS RDP TSVI CRTS RDP Dis. T Dis. T % Dis. T Dis. T % Dis. T Dis. T % Q1 52.33 <1 55.34 0.2 5.75 65.48 <1 66.04 0.2 0.86 38.35 <1 41.22 0.2 7.48 Q2 54.47 <1 55.34 0.2 1.6 66.70 <1 66.70 1.2 0 39.21 <1 41.22 0.2 5.13 Q3 64.67 <1 64.16 1.2 -0.79 73.02 <1 73.02 1.2 0 42.60 <1 42.6 1.4 0 Q4 77.27 2 79.75 1.1 3.21 81.14 <1 81.70 1.2 0.69 48.89 <1 51.18 1.1 4.68 Q5 71.86 <1 71.87 1.3 0.01 77.34 <1 76.44 1.2 -1.16 45.95 <1 47.66 1.1 3.72 Q6 88.67 1 90.34 0.2 1.88 90.11 <1 91.01 0.2 1.0 53.14 <1 55.62 1.1 4.67 Q7 85.80 <1 87.33 1.1 1.78 99.76 1 110.61 1.1 10.88 55.62 <1 55.62 1.1 0 Q8 96.76 1 98.79 1.4 2.1 111.74 1 122.37 1.4 9.51 62.45 <1 63.31 1.7 1.38 Q9 93.46 <1 96.35 1.1 3.09 112.52 <1 120.34 1.3 6.95 69.24 <1 71.97 1.2 3.94 Q10 107.60 2 112.76 1.3 4.8 116.85 <1 116.91 1.6 0.05 71.39 2 72.63 1.4 1.74 Q11 101.79 <1 101.79 0.2 0 136.10 <1 136.10 0.2 0 83.52 <1 85.18 1.2 1.99 Q12 120.26 2 124.86 1.2 3.83 120.04 <1 120.04 1.1 0 78.59 <1 78.59 1.2 0 Q13 128.50 23 129.54 1.3 0.81 114.39 1 119.56 1.3 4.52 61.92 <1 63.14 1.3 1.97 Q14 128.15 <1 129.38 1.4 0.96 158.24 <1 158.55 1.4 0.2 91.37 <1 94.78 1.2 3.73 Q15 133.13 2 133.18 1.3 0.04 161.42 1 162.69 1.2 0.79 86.84 1 86.84 1.2 0 Q16 149.70 3 150.53 0.2 0.55 161.46 1 166.79 1.1 3.3 90.37 3 91.82 1.2 1.6 Q17 144.97 <1 145.80 0.2 0.57 161.91 1 163.85 1.2 1.2 93.89 1 95.24 1.0 1.44 Q18 164.07 2 166.12 1.4 1.25 154.89 1 156.32 1.2 0.92 95.13 <1 97.97 13 2.99 Q19 153.07 1 165.20 1.2 7.92 193.60 3 192.71 1.5 -0.46 99.02 5 99.90 1.2 0.89 Q20 159.19 7 169.07 1.2 6.21 164.49 10 164.81 1.1 0.19 105.11 5 105.11 1.2 0 Q21 180.87 1 185.27 1.2 2.43 188.13 8 189.16 1.8 0.55 125.13 1 125.12 1.1 0 Q22 175.68 8 176.48 1.3 0.46 196.13 2 195.83 1.1 -0.15 116.02 2 118.20 1.1 1.88 Execution result«! TSVI and CRTS on N711 Joatj(ioaöodc:&3 -IjVJ -T Du !» - taut™ result:, et TSUI and CUTS on N7L! "»»"-»össsssssssjsä Dis Em »traiMilt! of TSVI and CRTS on NIlî 1« 0®aaa9 " ®« 53 o 33 3 5 5 3 3 3 S 3 N7L1 N7L2 Fig. 1 Computational results of the three instances in case study 1 N7L3 Advances in Production Engineering & Management 14(1) 2019 131 Min, Jin, Lu 4.2 Case study 2 Case study 2 contains three instances. The basic information of the customer number, total customer demand, capacity of vehicles, and vehicle number required in each instance are listed in Table 2. In Table 3, the columns indicate the total travel distance (Dis.), consumed CPU time (T) of the fr-means clustering algorithm, the clustering algorithm with splitting threshold and the CRTS (the former two data come respectively from [9] and [16]), and RDP of the distance and time between the CRTS and each of the above-described algorithms. A positive RDP value indicates that the CRTS value is large, whereas a negative RDP value indicates that the CRTS value is small. Table 3 lists the following. (1) From the perspective of the total travel distance, the clustering algorithm with a split threshold is the lowest in the two instances of N = 15 and N = 20, and the RDP (Dis.) values are 0.815 % and 4.067 % lower than those of the CRTS, respectively. Meanwhile, the CRTS at N = 36 is the lowest, and the RDP (Dis.) values are 0.805 % and 1.25 % lower than the resolutions of the other two algorithms, respectively. (2) From the perspective of the consumed CPU time, the CRTS consumes the lowest CPU time. Fig. 2 clearly shows that the CRTS is feasible and effective. The curves in Fig. 2(a) show that the gap in the total travel distances of the three algorithms in each of the three instances, namely, N = 15, N = 20, and N = 36, is relatively small. The CRTS obtains better results. Fig. 2(b) shows that the CRTS performance is between that of the fr-means and split-threshold approaches in terms of the total travel distance. Table 2 Basic information of each instance in case study 2 Instance Customer number Total demand Capacity of vehicles Vehicle number 2-1 2-2 2-3 15 20 36 4,881 40 15.29 500 5 1 10 8 16 Table 3 Computational results of the three algorithms fc-means Split threshold CRTS N Dis. T RDP(Dis.)% RDP(T)% Dis. T RDP(Dis.)% RDP(T)% Dis. T 15 1,800.27 5.276 -3.18 -81.8 1,728.9 1.33 0.815 -27.82 1,742.99 0.96 20 182.712 5.15 -0.90 -81.8 173.99 1.35 4.067 -30.37 181.07 0.94 36 354.7 4.26 -1.25 -44.1 353.1 2.99 -0.805 -20.40 350.26 2.38 Results of the three algorithms in three instances 2000 1SOO 1SOO 1100 1200 1000 800 600 400 -N=1S -N=30 - rj-36 I IS1.066 Splirthreihold (a) (b) Fig. 2 Computational results of the three instances in case study 2 4.3 Case study 3 To evaluate the CRTS performance on larger sized instances, we adopted six instances in case study 3 from CVRPLIB and compared the results obtained by SPLITABU in [4] and MRSILS in [13]. The basic information of customer number, total customer demand, capacity of vehicles, and vehicle number required in each instance is listed in Table 4. In Table 5, the columns indicate the total travel distance (Dis.), consumed CPU time (T) by each of the three algorithms (the former two data come respectively from [4] and [13]), and RDP of the CRTS distance compared with those of the other two algorithms. 132 Advances in Production Engineering & Management 14(1) 2019 Maximum-minimum distance clustering method for split-delivery vehicle-routing problem: Case studies and performance Table 4 Basic information in each instance in case study 3 Instance_Name_Customer number_Total demand Capacity of vehicles Vehicle number 3-1 vrpnc1 50 777 160 5 3-2 vrpnc2 75 1,364 140 10 3-3 vrpnc3 100 1,458 200 8 3-4 vrpnc4 150 2,235 200 12 3-5 vrpnc5 199 3,186 200 16 3-6 vrpnc11 120 1,375 200 7 Table 5 Computational results of the three algorithms SPLITABU MRSILS CRTS Dis. T RDP(Dis.)% Dis. T RDP(Dis.)% Dis. T 50 527.66 17 5.69 531.03 24 5.02 557.71 2.18 75 853.61 64 7.91 831.85 24 10.74 921.16 5.94 100 840.12 60 12.61 834.52 24 13.37 946.06 6.26 150 1,055.08 440 14.45 1,066.04 24 13.28 1207.57 10.42 199 1,338.36 1,900 16.06 1,343.67 24 15.60 1553.32 13.38 120 1,056.96 39 2.04 1,048.00 24 2.91 1,078.47 8.34 Dis, The execution results for the three algorithms in six intances 1S00 1600 1S53.32 MOO 1200 1000 800 Jj'Tms.os JdSSSSi-spuTAiu ¿m 0Di:Dwmi2 -«-MftsiLs 600 400 200 0 50 75 100 150 199 120 N Fig. 3 Computational results for six instances in case study 3 Table 5 indicates the following. (1) The total travel distance of the CRTS is the highest among the three algorithms, and RDPs (Dis.) of SPLITABU and MRSILS are all positive. (2) When N = 50 and N = 75, the RDP (Dis.) values of SPLITABU and MRSILS are lower than or very close to 10 %. (3) When N = 120 in which all customer points are in a cluster distribution around the depot, the RDP (Dis.) values of SPLITABU and MRSILS are lower than 3 %. (4) The consumed CPU time by the CRTS is much lower than those by the other two algorithms. Fig. 3 clearly shows that the CRTS is feasible and effective. Fig. 3 shows the curves of the total travel distances of the three algorithms in each of the three instances, namely, N = 50, N = 75, and N = 120. It also shows that the gap in the total travel distances between SPLITABU and the CRTS in each of the three instances, namely, N = 50, N = 75, and N = 120, is relatively small. The CRTS achieves near-optimal results even though no iteration is performed in the first two stages. 5. Conclusion In this study, a mathematical model for SDVRP was described. On the basis of the CRTS, a three-stage algorithm was proposed. In the first stage, clustering was employed to partition the domain of customer points into sub-domains. In the second stage, 'push-out' and 'pull-in' operations were adopted to adjust the load demand in each sub-domain according to vehicle capacity Q. In the third stage, a proven TSA for TSP was used to optimise the total travel distance. Numerical experiments for the three cases were performed, and the computational results showed that the proposed CRTS algorithm provides feasible and effective solutions to the SDVRP in most parts of the test data set. The CRTS obtained approximate optimal solutions in 75 % of the instances. Three competing algorithms, namely, TSVI, fr-means clustering method, and clustering method with a split threshold, were evaluated alongside the proposed method. These algorithms Advances in Production Engineering & Management 14(1) 2019 133 Min, Jin, Lu were based on a 'routing after grouping' strategy. The CRTS performance in cases 1 and 2 was very close to that of the other three evaluated algorithms in finding the total travel distance. Comparison was also conducted for the computational results in case 3, which is a benchmark data set. When N = 50 and N = 75 in which the customer points were uniformly distributed around the depot, the RDP (Dis..) values were 5.69 % and 7.91 %, respectively. When N = 120, i.e. where the customer points were in a cluster distribution around the depot, RDP (Dis) was less than 3 %. Interestingly, the consumed CPU time by the proposed algorithm was much lower than that of any of the other algorithms evaluated in this study. Acknowledgement This work was financed by the National Natural Science Foundation of China (Grant No. 61872077), the Natural Science Fund of Jiangsu Province Education Commission (Grant No. 17KJB520040), the Humanities and Social Sciences Research Base Fund of Jiangsu Province Education Commission (Grant No. 2017ZSJD020), and the Jiangsu Key Construction Laboratory of IoT Application Technology, Taihu University of Wuxi. References [1] Dror, M., Trudeau, P. (1989). 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Advances in Production Engineering & Management 14(1) 2019 135 Calendar of events • International Conference on Industrial Engineering and Engineering Management, December 16-19, 2018, Bangkok, Thailand. • 11th International Conference on Computer Modeling and Simulation, January 16-19, 2019, Melbourne, Australia. • International Conference on Green Manufacturing and Production Engineering, January 1718, 2019, Rome, Italy. • 16th Annual Congress on Materials Research and Technology, February 18-20, 2019, Amsterdam, Netherlands. • 3rd International Conference on 3D Printing Technology and Innovations, March 25-26, 2019, Rome, Italy. • International Conference on Intelligent Manufacturing and Intelligent Materials, May 9-11, 2019, Sanya, China. • International Conference on Agile and Flexible Manufacturing Systems, May 21-22, 2019, Berlin, Germany. • International Conference on Advanced Manufacturing Technologies and Intelligent Machining, May 29-30, 2019, Osaka, Japan. • 17th Annual Industrial Simulation Conference, June 5-7, 2019, Lisbon, Portugal. • International Conference on Design and Implementation of Intelligent Manufacturing Systems, June 10-11, 2019, Tokyo, Japan. • 6th International Conference and Exhibition on Automobile & Mechanical Engineering, July 89, 2019, Zurich, Switzerland. • 23rd International Conference on Advanced Materials & Nanotechnology, August 19-20, 2019, Tokyo, Japan. • AI Manufacturing 2019: Machine Learning and Artificial Intelligence, The Fourth Industrial Revolution, August 28-29, 2019, Westin O'Hare, Rosemont, Illinois, USA. • 9th IFAC Conference on Manufacturing Modeling, Management, and Control, August 28-30, 2019, Berlin, Germany. • 30th DAAAM International Symposium, October 23-26, 2019, Zadar, Croatia. 136 Advances in Production Engineering & Management 14(1) 2019 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. Manuscript should be written in English. Responsibility for the contents of the paper rests upon the authors and not upon the editors or the publisher. Authors of submitted papers automatically accept a copyright transfer to Chair of Production Engineering, University of Maribor. For most up-to-date information on publishing procedure please see the APEM journal homepage apem-journal.org. Submission of papers A submission must include the corresponding author's complete name, affiliation, address, phone and fax numbers, and e-mail address. All papers for consideration by Advances in Production Engineering & Management should be submitted by e-mail to the journal Editor-in-Chief: Miran Brezocnik, Editor-in-Chief UNIVERSITY OF MARIBOR Faculty of Mechanical Engineering Chair of Production Engineering Smetanova ulica 17, SI - 2000 Maribor Slovenia, European Union E-mail: editor@apem-journal.org Manuscript preparation Manuscript should be prepared in Microsoft Word 2010 (or higher version) word processor. Word .docx format is required. Papers on A4 format, single-spaced, typed in one column, using body text font size of 11 pt, should not exceed 12 pages, including abstract, keywords, body text, figures, tables, acknowledgements (if any), references, and appendices (if any). The title of the paper, authors' names, affiliations and headings of the body text should be in Calibri font. Body text, figures and tables captions have to be written in Cambria font. Mathematical equations and expressions must be set in Microsoft Word Equation Editor and written in Cambria Math font. For detail instructions on manuscript preparation please see instruction for authors in the APEM journal homepage apem-journal.org. The review process Every manuscript submitted for possible publication in the APEM journal is first briefly reviewed by the editor for general suitability for the journal. Notification of successful submission is sent. After initial screening, and checking by a special plagiarism detection tool, the manuscript is passed on to at least two referees. A double-blind peer review process ensures the content's validity and relevance. Optionally, authors are invited to suggest up to three well-respected experts in the field discussed in the article who might act as reviewers. The review process can take up to eight weeks on average. Based on the comments of the referees, the editor will take a decision about the paper. The following decisions can be made: accepting the paper, reconsidering the paper after changes, or rejecting the paper. Accepted papers may not be offered elsewhere for publication. The editor may, in some circumstances, vary this process at his discretion. Proofs Proofs will be sent to the corresponding author and should be returned within 3 days of receipt. Corrections should be restricted to typesetting errors and minor changes. Offprints An e-offprint, i.e., a PDF version of the published article, will be sent by e-mail to the corresponding author. Additionally, one complete copy of the journal will be sent free of charge to the corresponding author of the published article. APEM journal Chair of Production Engineering (CPE) University of Maribor APEM homepage: apem-journal.org Advances in Production Engineering & Management Volume 14 | Number 1 | March 2019 | pp 1-138 Contents Scope and topics 4 An integrated optimization of quality control chart parameters and preventive maintenance using 5 Markov chain Farahani, A.; Tohidi, H.; Shoja, A. Determination of nano-roughness for micro-objects by measuring the van der Waals force 15 Bratina, B.; Safaric, J.; Uran, S.; Safaric, R. Cutting performance of solid ceramic and carbide end milling tools in machining of nickel based alloy 27 Inconel 718 and stainless steel 316L Grguras, D.; Kern, M.; Pusavec, F. Two-stage product design selection by using PROMETHEE and Taguchi method: A case study 39 Crnjac, M.; Aljinovic, A.; Gjeldum, N.; Mladineo, M. Productivity improvement with parallel adjacent U-shaped assembly lines 51 Chutima, P.; Suchanun, T. Achieving sustainable transport through resource scheduling: A case study for electric 65 vehicle charging stations Gong, D.; Tang, M.; Liu, S.; Xue, G.; Wang, L. Product quality improvement and air pollutant emission reduction in a mining metal three-stage 80 supply chain under cap-and-trade regulation Homaei, H.; Mahdavi, I.; Tajdin, A.; Khorram, E. Inventory control model based on multi-attribute material classification: An integrated grey-rough set 93 and probabilistic neural network approach Zhang, Z.L.; Wang, Y.F.; Li, Y. A multi-product pricing and inventory model with production rate proportional to power demand rate 112 Keshavarzfard, R.; Makui, A.; Tavakkoli-Moghaddam, R. Maximum-minimum distance clustering method for split-delivery vehicle-routing problem: Case studies 125 and performance comparisons Min, J.N.; Jin, C.; Lu, L.J. Calendar of events 136 Notes for contributors 137 Copyright © 2019 CPE. All rights reserved. apem-journal.org 9771854625008