ISSN 1854-6250 APEM journal Advances in Production Engineering & Management Volume 17 | Number 4 | December 2022 Published by CPE apem-journal.org Advances in Production Engineering & Management Identification Statement APEM journal ISSN 1854‐6250 | Abbreviated key title: Adv produc engineer manag | Start year: 2006 ISSN 1855‐6531 (on‐line) Published quarterly by Chair of Production Engineering (CPE), University of Maribor Smetanova ulica 17, SI – 2000 Maribor, Slovenia, European Union (EU) Phone: 00386 2 2207522, Fax: 00386 2 2207990 Language of text: English APEM homepage: apem‐journal.org University homepage: www.um.si APEM Editorial Editor‐in‐Chief Miran Brezocnik editor@apem‐journal.org, info@apem‐journal.org University of Maribor, Faculty of Mechanical Engineering Sme‐ tanova ulica 17, SI – 2000 Maribor, Slovenia, EU Desk Editor Website Technical Editor Martina Meh Lucija Brezocnik desk1@apem‐journal.org desk3@apem‐journal.org Janez Gotlih desk2@apem‐journal.org Editorial Board Members Eberhard Abele, Technical University of Darmstadt, Germany Bojan Acko, University of Maribor, Slovenia Joze Balic, University of Maribor, Slovenia Agostino Bruzzone, University of Genoa, Italy Borut Buchmeister, University of Maribor, Slovenia Ludwig Cardon, Ghent University, Belgium Nirupam Chakraborti, Indian Institute of Technology, Kharagpur, India Edward Chlebus, Wroclaw University of Technology, Poland Igor Drstvensek, University of Maribor, Slovenia Illes Dudas, University of Miskolc, Hungary Mirko Ficko, University of Maribor, Slovenia Vlatka Hlupic, University of Westminster, UK David Hui, University of New Orleans, USA Pramod K. Jain, Indian Institute of Technology Roorkee, India Isak Karabegović, University of Bihać, Bosnia and Herzegovina Janez Kopac, University of Ljubljana, Slovenia Qingliang Meng, Jiangsu University of Science and Technology, China Lanndon A. Ocampo, Cebu Technological University, Philippines Iztok Palcic, University of Maribor, Slovenia Krsto Pandza, University of Leeds, UK Andrej Polajnar, University of Maribor, Slovenia Antonio Pouzada, University of Minho, Portugal R. Venkata Rao, Sardar Vallabhbhai National Inst. of Technology, India Rajiv Kumar Sharma, National Institute of Technology, India Katica Simunovic, J. J. Strossmayer University of Osijek, Croatia Daizhong Su, Nottingham Trent University, UK Soemon Takakuwa, Nagoya University, Japan Nikos Tsourveloudis, Technical University of Crete, Greece Tomo Udiljak, University of Zagreb, Croatia Ivica Veza, University of Split, Croatia Subsidizer: The journal is subsidized by Slovenian Research Agency Creative Commons Licence (CC): Content from published paper in the APEM journal may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any fur‐ ther distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Statements and opinions expressed in the articles and communications are those of the individual contributors and not necessarily those of the editors or the publisher. No responsibility is accepted for the accuracy of information contained in the text, illustrations or advertise‐ ments. 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Advances in Production Engineering & Management is indexed and abstracted in the WEB OF SCIENCE (maintained by Clarivate Analytics): Science Citation Index Expanded, Journal Citation Reports – Science Edition, Current Contents – Engineering, Computing and Technology • Scopus (maintained by Elsevier) • Inspec • EBSCO: Academic Search Alumni Edition, Academic Search Complete, Academic Search Elite, Academic Search Premier, Engineering Source, Sales & Marketing Source, TOC Premier • ProQuest: CSA Engineering Research Database – Cambridge Scientific Abstracts, Materials Business File, Materials Research Database, Mechanical & Transportation Engineering Abstracts, ProQuest SciTech Collection • TEMA (DOMA) • The journal is listed in Ulrich’s Periodicals Directory and Cabell's Directory Chair of Production Engineering (CPE) Advances in Production Engineering & Management Volume 17 | Number 4 | December 2022 | pp 397–516 Contents Scope and topics Verification of intelligent scheduling based on deep reinforcement learning for distributed workshops via discrete event simulation 400 401 Demand prediction and optimization of workshop manufacturing resources allocation: A new method and a case study 413 Monte Carlo Tree Search improved Genetic Algorithm for unmanned vehicle routing problem with path flexibility 425 End-of-line delivery vehicle routing optimization based on large-scale neighbourhood search algorithms considering customer-consumer delivery location preferences 439 An approach to maintenance sustainability level assessment integrated with Industry 4.0 technologies using Fuzzy-TOPSIS: A real case study 455 Optimization of the rhomboidity of continuously cast billets using linear regression and genetic programming: A real industrial study 469 Cause-related marketing strategy in a supply chain: A theoretical analysis and a case study 479 Impact of Cobot parameters on the worker productivity: Optimization challenge 494 Study on scheduling and path planning problems of multi-AGVs based on a heuristic algorithm in intelligent manufacturing workshop 505 Calendar of events Notes for contributors 514 515 Yang, S.L.; Wang, J.Y.; Xin, L.M.; Xu, Z.G. Wan, J. Wang, Y.D.; Lu, X.C.; Song, Y.M.; Feng, Y.; Shen, J.R. Niu, X.Y.; Liu, S.F.; Huang, Q.L. Patalas-Maliszewska, J.; Łosyk, H. Kovacic, M.; Zuperl, U.; Brezocnik, M. Xu, G.Y.; Liu, H.; Duan, H.W. Javernik, A.; Buchmeister, B.; Ojstersek, R. Wang, Y.J.; Liu, X.Q.; Leng, J.Y.; Wang, J.J.; Meng, Q.N.; Zhou, M.J. Journal homepage: apem-journal.org ISSN 1854-6250 (print) ISSN 1855-6531 (on-line) Published by CPE, University of Maribor. Scope and topics Advances in Production Engineering & Management (APEM journal) is an interdisciplinary refereed international academic journal published quarterly by the Chair of Production Engineering at the University of Maribor. The main goal of the APEM journal is to present original, high quality, theoretical and application-oriented research developments in all areas of production engineering and production management to a broad audience of academics and practitioners. In order to bridge the gap between theory and practice, applications based on advanced theory and case studies are particularly welcome. For theoretical papers, their originality and research contributions are the main factors in the evaluation process. General approaches, formalisms, algorithms or techniques should be illustrated with significant applications that demonstrate their applicability to real-world problems. Although the APEM journal main goal is to publish original research papers, review articles and professional papers are occasionally published. Fields of interest include, but are not limited to: Additive Manufacturing Processes Advanced Production Technologies Artificial Intelligence in Production Assembly Systems Automation Big Data in Production Block Chain in Manufacturing Computer-Integrated Manufacturing Cutting and Forming Processes Decision Support Systems Deep Learning in Manufacturing Discrete Systems and Methodology e-Manufacturing Evolutionary Computation in Production Fuzzy Systems Human Factor Engineering, Ergonomics Industrial Engineering Industrial Processes Industrial Robotics Intelligent Manufacturing Systems Joining Processes Knowledge Management Logistics in Production 400 Machine Learning in Production Machine-to-Machine Economy Machine Tools Machining Systems Manufacturing Systems Materials Science, Multidisciplinary Mechanical Engineering Mechatronics Metrology in Production Modelling and Simulation Numerical Techniques Operations Research Operations Planning, Scheduling and Control Optimisation Techniques Project Management Quality Management Risk and Uncertainty Self-Organizing Systems Smart Manufacturing Statistical Methods Supply Chain Management Virtual Reality in Production Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 4 | December 2022 | pp 401–412 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.4.444 Original scientific paper Verification of intelligent scheduling based on deep reinforcement learning for distributed workshops via discrete event simulation Yang, S.L.a, Wang, J.Y.b,c,*, Xin, L.M.d, Xu, Z.G.b,c,* aSchool of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai, P.R. China Institute of Automation, Chinese Academy of Sciences, Shenyang, P.R. China cInstitutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang, P.R. China dSchool of Computer Engineering and Science, Shanghai University, Shanghai, P.R. China bShenyang ABSTRACT ARTICLE INFO Production scheduling, which directly influences the completion time and throughput of workshops, has received extensive research. However, due to the high cost of real-world production verification, most literature did not verify the optimized scheduling scheme in real-world workshops. This paper studied the verification of scheduling schemes and environments, using a discrete event simulation (DES) platform. The aim of this study is to provide an efficient way to verify the correctness of scheduling environments established by programming languages and scheduling results obtained by intelligent algorithms. The system architecture of scheduling verification based on DES is established. The modelling approach via DES is proposed by designing parametric workshop generation, flexible production control, and real-time data processing. The popular distributed permutation flowshop scheduling problem is selected as a case study, where the optimal scheduling scheme obtained by a deep reinforcement learning algorithm is fed into the production simulation model in Plant Simulation software. The experiment results show that the proposed scheduling verification approach can validate the scheduling scheme and environment effectively. The utilization and Gantt charts clearly show the performance of scheduling schemes. This work can help to verify the scheduling schemes and programmed scheduling environment efficiently without costly real-world validation. Keywords: Production scheduling; Distributed flowshop scheduling; Discrete event simulation (DES); Deep reinforcement learning; Production simulation; Modelling; Scheduling verification; Plant Simulation software *Corresponding author: jywang@sia.cn (Wang, J.Y.) zgxu@sia.cn (Xu, Z.G.) Article history: Received 14 November 2022 Revised 12 December 2022 Accepted 15 December 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Production scheduling is an important problem for real-world manufacturers. Effective scheduling schemes can help to reduce production costs, decrease completion time, and increase throughput. For several decades, production scheduling has received extensive research interest. For example, only for the permutation flowshop scheduling problem, more than 100 kinds of heuristic and meta-heuristic algorithms have been proposed according to the reviews of Fernandez-Viagas et al. [1]. 401 Yang, Wang, Xin, Xu Under the globalized economy, companies tend to establish production bases in different regions to fulfill the production requirement of customers distributed in different areas. Under distributed manufacturing, the distributed permutation flowshop scheduling problem (DPFSP) was proposed by Naderi, Ruiz [2]. In the DPFSP, a set of factories are distributed in different regions. A set of jobs can be processed in one of the factories. The optimization problem is to minimize the total completion time of all jobs by properly assigning jobs to factories and scheduling jobs in each factory. The DPFSP has been solved by several kinds of intelligent algorithms, such as iterated greedy algorithm [3], artificial bee colony algorithm [4], cooperative memetic algorithm [5], etc. Some realistic characteristics have been considered in the DPFSP, such as sequence-dependent setup times[6, 7], blocking constraint [8, 9], no-wait constraint [10], no-idle constraint [11], hybrid flowshop [12], batch delivery [13], etc. Most product scheduling is optimized by intelligent algorithms. Usually, intelligent algorithms are written in programming languages, such as C++, Java, MATLAB, Python, etc. At the same time, the production environment for simulating and optimizing the scheduling scheme is also programmed using programming languages. Although the scheduling scheme can be optimized through the programmed scheduling simulation environment, the correctness of the scheduling simulation environment and scheduling scheme remains a problem. Since the verification for an optimized scheduling scheme is crucial for implementation in real-world factories, the verification for the simulation environment and scheduling schemes should be performed. In current literature, only very few studies applied proposed scheduling models and algorithms to real production workshops, such as applied to the manufacturing execution system (MES) of a real factory. A few studies only used real-world data as production instances. However, most literature did not apply the scheduling algorithms and methods to real-world production cases. For the scheduling application in real-world production, Zhou et al. [14] studied the multi-objective flexible job shop scheduling problem using multi-agent-based hyper-heuristics and applied the proposed methods and algorithms to an aero-engine blade manufacturing plant. For the usage of real-world data, Jiang et al. [15] studied a real case scheduling problem for aerospace industry components in a flexible job shop. Li et al. [16] solved the welding shop scheduling problem using a discrete artificial bee colony algorithm and applied the algorithm in a realworld girder welding shop. Yankai et al. [17] studied the hybrid flowshop scheduling problem, in which numerical experiments are carried out based on real-world cases in a hot-rolling workshop. Wang et al. [18] studied the energy-aware welding shop scheduling problem using a decomposition-based multi-objective evolutionary algorithm and applied the proposed algorithm to a real-world case. Schumacher, Buchholz [19] studied the hybrid flow shop scheduling problem under uncertainty and applied the proposed methods to a real-world production case. Ojstersek et al. [20] studied the multi-objective scheduling problem of flexible job shops using a real-world manufacturing dataset. Although some literature used real-world data for problem-solving, most scheduling literature did not verify the correctness of scheduling simulation and scheduling results. The reasons may be as follows. Firstly, the implementation of production scheduling in a real-world workshop costs too much with a lot of production resources required. In addition, some researchers do not have suitable industrial cooperation for validation or lack a production line in the laboratory for proper production validation. With the development of simulation software, discrete event simulation (DES) servers as an efficient tool for production optimization and validation. The Plant Simulation software is one of the widely used production simulation platforms. Some researchers used the Plant Simulation to optimize production processes and validate the production scenarios. Yang et al. [21] proposed a modelling method for workshop modelling in Plant Simulation and optimized the production configurations of an assembly shop. Xu et al. [22] studied the optimization problem of multi-stage production scheduling. Wang et al. [23] studied the reliability allocation method for a production system using Plant Simulation. Pekarcikova et al. [24] studied the simulation testing of the E-Kanban to improve the efficiency of logistics processes. Yang et al. [25] optimized the assembly transport optimization problem in a reconfigurable flow shop. Pekarcikova et al. [26] studied the bottleneck problem in the logistics flow of a manufacturing company using Plant Simulation software. Li et al. [27] dealt with the bottleneck 402 Advances in Production Engineering & Management 17(4) 2022 Verification of intelligent scheduling based on deep reinforcement learning for distributed workshops via discrete event … identification and alleviation in a blocked serial production line via Plant Simulation. JurczykBunkowska [28] studied the tactical manufacturing capacity planning of a medium-sized production enterprise by Plant Simulation. Gregor et al. [29] verified the routes of an automated guided vehicle using Plant Simulation. Li et al. [30] studied resource allocation in a production logistics system using Plant Simulation software. Gola et al. [31] used the Plant Simulation software to identify the bottlenecks in a reconfigurable manufacturing system. In addition to optimizing and verifying the production process, Plant Simulation software has also been used to optimize some scheduling problems by using the built-in intelligent algorithm packages. Xu et al. [22] optimized a multi-stage production scheduling problem of an automated production system by using Plant Simulation software. Istokovic et al. [32] determined the order and size of production batches in a flow shop using the genetic algorithm optimization tool of Plant Simulation. Ferro et al. [33] used Plant Simulation to optimize the production planning of the textile industry. From the above literature review, we can know that the verification of the scheduling scheme has not received adequate research, and Plant Simulation software has been used to optimize and verify some production processes. Verifying the scheduling scheme and programmed environment via the Plant Simulation platform is an efficient way. However, few studies investigated the verification of scheduling schemes and programmed production environment with the help of Plant Simulation. This paper studied the verification of scheduling schemes and environments based on a discrete event simulation platform—Plant Simulation software. The distributed permutation flowshop scheduling problem is verified in Plant Simulation. The aim of this study is to provide efficient and costless verifications for the programmed scheduling environment and obtained scheduling schemes, before applying those scheduling schemes in real-world workshops. The overall system architecture of verifying scheduling schemes via Plant Simulation platform is established. The distributed permutation flowshops are established in Plant Simulation platform. The simulation results in Plant Simulation validate the correctness of the programmed scheduling environment programmed in Python and the scheduling results obtained by algorithms. Particularly, the main contributions of this paper are as follows: • The system architecture of scheduling verification based on scheduling optimization and Plant Simulation is established. The scheduling scheme is optimized by intelligent algorithms programmed in Python language. Then, the optimized scheduling scheme is simulated and verified in the established production model in Plant Simulation platform. • The modelling approach for production workshops via Plant Simulation platform is proposed. The production simulation model is established by designing parametric modelling of workshops, flexible production control, and real-time data processing. • The whole verification process is validated by a case study on the distributed permutation flowshop scheduling problem. The videos of scheduling optimization and production simulation are provided. The rest of the paper is listed as follows. Section 2 illustrates the system architecture of the scheduling verification approach. Section 3 establishes the production workshops using Plant Simulation platform. Section 4 verifies the scheduling environment and scheme using a case study. Section 5 concludes the paper and provides suggestions for future research. 2. System architecture of the scheduling verification approach The scheduling validation approach contains intelligent scheduling optimization via intelligent algorithms and production simulation via Plant Simulation. The intelligent scheduling optimization generates the scheduling scheme and results. Based on the scheduling scheme, the production model built in Plant Simulation platform executes the production process. The results obtained from Plant Simulation and those obtained from the intelligent scheduling algorithms are compared to verify whether the programmed scheduling environment and scheduling algorithms are correct. The system architecture of the scheduling verification approach is shown in Fig. 1. Advances in Production Engineering & Management 17(4) 2022 403 Yang, Wang, Xin, Xu Scheduling scheme inst Verify: the same? Scheduling results Production results inst 14 8 43 … Cmax 8444 8593 12703 14 8 obj 111.43 190.29 253 f f1 f2 f3 f1 f2 f3 1st 3 2 4 3 2 1 2nd 18 16 22 16 18 22 3rd … 33 25 10 25 33 36 Scheduling optimization based on intelligent algorithms Production simulation using Plant Simulation Production modelling Distributed manufacturing Factory 1 PM1 Jobs J1 J2 ... PM2 ... PM m Finished jobs Factory 2 PM1 Jn Factory f PM1 PM2 ... PM m ... Jn ... PM2 J1 J2 ... PM m Fig. 1 The system architecture of the proposed scheduling validation approach based on intelligent scheduling optimization and Plant Simulation 2.1 Scheduling optimization based on intelligent algorithms Most production scheduling in the literature is optimized using intelligent algorithms. Before optimizing the scheduling scheme, the scheduling simulation environment should be programmed. The scheduling simulation environment can process jobs and calculate the objective of candidate schedule schemes. Some popular languages for programming the environment are C++, C#, MATLAB, Java, Python, etc. However, the real-time production interface reflecting the real-time production process is seldom programmed due to the coding complexity. Thus, it is difficult to check the correctness of the production simulation process for the programmed production environment. The optimal scheduling scheme is obtained by performing the optimization process using intelligent algorithms. Due to extensive research, many kinds of algorithms have been proposed to solve the scheduling problems, such as heuristics, meta-heuristics [3], deep reinforcement learning algorithms [34], etc. After the optimization process, the optimal scheduling schemes, including the job sequence for each factory, and the beginning and end processing time, are obtained. Besides, the scheduling results, including the completion time of all factories and the objective value for the scheduling scheme, are returned. 2.2 Production modelling and simulation execution The production simulation model is established in Plant Simulation platform according to the production resources and processes of the studied scheduling problem. Plant Simulation software can build the production model efficiently by constructing machines, flow lines, jobs, buffers, and source jobs. The production control is programmed by SimTalk language in Plant Simulation platform. The scheduling scheme obtained by intelligent algorithms is fed to the production model in Plant Simulation to get the correct scheduling results. 2.3 Verification by comparing production and scheduling results After the exact execution of the job sequences in each factory, the production results for the selected scheduling scheme are obtained from Plant Simulation platform. Then, the production results are compared with the scheduling results obtained from the intelligent algorithms. For each production scheme, the maximum completion time Cmax and objective value obj are compared between the production and scheduling results. 404 Advances in Production Engineering & Management 17(4) 2022 Verification of intelligent scheduling based on deep reinforcement learning for distributed workshops via discrete event … 3. Modelling of production workshops via Plant Simulation The production model can be established efficiently via Plant Simulation platform, which contains powerful production modelling tools. The main components of a production simulation model are the production resources, production control methods, production data, and visualization tools, as shown in Fig. 2. The production resources contain machines, buffers, production lines, etc. The production control is realized by control methods. The production data contains some necessary production and real-time data, such as processing times, arrival time, due date, etc. The visualization tools provide various charts for the real-time production status and workshop performance. Production resources Production control Production data Visualization Fig. 2 The main compensates of a production model in Plant Simulation platform 3.1 Parametric modelling of workshops Workshops are established through parametric modelling. Each workshop contains job storage, buffer, machines, and transfer line between machines. To increase the efficiency of modelling, all of the above production resources are generated by the control method Start as shown in Fig. 3. The code for generating machines and buffers is shown in algorithm 1. The production process is modelled exactly as those used in the scheduling algorithms. Thus, the unlimited buffer size is adopted between machines, the transfer time is not considered. Algorithm 1. Procedure of parametric modelling for generating a workshop using the SimTalk language 1: for j:=1 to n 2: for i:=1 to m loop 3: if i>1 then 4: Name:=Sprint("BF",j,i) 5: Obj2:=.Materialflow.Buffer.createObject(current, 40+i*100, 100+(26+60*n)/n*(j+1), Name) 6: Obj2.ZoomX:=0.5, Obj2.ZoomY:=0.5, Obj2.Proctime:=0, Obj2.Capacity:=-1 7: .Materialflow.Connector.connect(Obj, Obj2), Obj:=Obj2 8: end 9: Name:=Sprint("M",j,i) 10: Obj2:=.Materialflow.Singleproc.createObject(current, 80+i*100,100+(26+60*n)/np*(j+1), Name) 11: Obj2.Label := sprint("M",j,i), OBj2.EntranceCtrl:="Set_time" 12: obj2.entrancectrlbeforeactions:=true 13: if i>1 then 14: .Materialflow.Connector.connect(Obj, Obj2) 15: end 16: Obj:=Obj2 17: next 18: next Advances in Production Engineering & Management 17(4) 2022 405 Yang, Wang, Xin, Xu 3.2 Modelling of production control The production control ensures that workshops produce jobs according to the correct production processes and job sequences. Jobs are released from the source to the workshop when the arrival time is reached. The processing time is set for each machine when a new job arrived at this machine. When a job is finished in a machine, the job is transferred to the buffer of the next machine, and the next job is transferred from the previous buffer. When a job is finished in all machines of a workshop, the job is transferred to the Drain. 3.3 Modelling of production data In addition to the production process, the production data is also fundamental to correctly simulate the production schedule. As shown in Fig. 3, the arrival time and due date of jobs are stored in the table file Attri. Jobs are created by the jobs_create method based on the arrival time of jobs. The table file PT stores the processing times of jobs on machines. The processing time is extracted by the method Set_time and set for the corresponding machines. 3.4 Statistical analysis and visualization One of the advantages of the Plant Simulation platform is its powerful statistical and visualization function. As shown in Fig. 3, in the production model, the variables Cmax and obj denote the maximum completion time of workshops and the objective value of the current scheduling scheme, respectively. The Gantt chart shows the job sequence and processing durations on machines. The utilization chart reflects the production performance under the current scheduling scheme and production processes. In addition, the occupation of a buffer is provided to show how many jobs exist in buffers before a machine. Since buffer capability is supposed to be infinite, the exact number of existing buffer jobs can help to set buffer sizes in a real production environment. Fig. 3 The production simulation model for the distributed permutation flowshop scheduling problem 4. Verification experiments: A case study This section verifies the scheduling results obtained by the trained deep reinforcement learning (DRL) algorithm in Plant Simulation software using the modelling and validation approach proposed above. The scheduling results, including the scheduling scheme, total completion time, and objective value, are generated by a DRL algorithm—advanced actor-critic (A2C). Then, the scheduling scheme is executed exactly in the production model in Plant Simulation platform. The production simulation results verified that the scheduling results obtained by the programming environment are correct. In addition, the statistical analysis and visualization were provided via Plant Simulation platform. 406 Advances in Production Engineering & Management 17(4) 2022 Verification of intelligent scheduling based on deep reinforcement learning for distributed workshops via discrete event … 4.1 Scheduling scheme obtained by deep reinforcement learning The distributed permutation flowshop scheduling problem, which has attracted increasing research interest in recent several years, is selected for verification. A production case with 130 jobs, 8 machines, and 3 factories is selected as the case instance by referring to the production characteristics shown in the literature [3]. The scheduling scheme for this production instance is generated by a deep reinforcement learning algorithm A2C. After the dynamic scheduling, the scheduling results of the DRL version are obtained. Table 1 provides the production data of the selected production instance. Since the production instance has as many as 130 jobs, Table 1 only provides the data of the first 10 jobs. As shown in Table 1, for each job j, the arrival time ATj, due date dj, unit tardiness cost αj, and processing times on all of the 8 machines pM1,j-pM8,j are provided. Table 1 Production data of the studied production instance (only the data of the first 10 jobs are provided) j ATj dj αj pM1,j pM2,j pM3,j pM4,j pM5,j pM6,j pM7,j pM8,j 1 2 3 4 5 6 7 8 9 10 0.00 0.00 0.00 0.00 5.40 18.14 18.14 21.74 23.33 24.29 2676.00 1850.00 2711.00 2520.00 4383.40 4528.14 2593.14 1780.74 1767.33 4436.29 0.6 1.2 1.3 0.9 1.0 1.2 0.6 1.6 0.1 1.7 137 116 118 187 163 108 170 176 168 109 112 101 184 187 161 188 121 126 125 167 172 176 111 194 122 113 149 152 198 123 109 171 128 196 157 147 157 180 187 127 175 106 129 186 101 172 103 141 107 137 105 125 114 113 100 130 168 182 126 157 179 150 150 109 160 171 124 115 125 183 164 120 168 107 181 103 143 164 122 138 The scheduling scheme and results are obtained using a deep reinforcement learning algorithm by inputting the production data. The scheduling optimization interface in the Python programming environment for the studied case is shown in Fig. 4. The video of using deep reinforcement learning to solve the studied scheduling problem is provided online. The specific solving procedures are as follows. • Build the production environment and variable matrix in the Python environment; • Load the production data of the studied scheduling problem; • Load the trained model of the A2C algorithm; • Use the loaded A2C model to make scheduling decisions at each rescheduling point; • Record the processed jobs sequences of each factory, and calculate the objective value; • If all jobs are finished in the system, export the total completion time of the system, the objective value of the scheduling plan, and the job sequence of each factory. The job sequence of the three factories for the instance 14 The maximum completion time and objective of for the instance 14 under current scheduling scheme Fig. 4 The scheduling optimization interface in the Python programming environment. (The video of obtaining the optimal scheduling scheme by loading the DRL model is available at https://osf.io/qxze5?view_only=e10ee0e3cec44b85ba2f569cd26071f2) Advances in Production Engineering & Management 17(4) 2022 407 Yang, Wang, Xin, Xu Table 2 The scheduling results obtained from the DRL algorithm (only the job sequence of the first 10 jobs are presented) Factory Completion time Objective value Job sequence 1 3 18 33 43 66 80 37 106 114 2 8444 111.43 2 16 25 36 53 75 8 102 113 3 4 22 10 51 46 49 54 101 57 123 128 72 After the optimization, the scheduling results are provided in Table 2. As shown in Table 2, the total completion time of the system is 8444, the objective value is 111.43. Besides, the job sequence of the three factories is provided. For factory 1, job j3, j18, j33,…, is processed successively. Only the first ten processed jobs of each factory are presented in Table 2. 4.2 Verification using Plant Simulation The scheduling scheme resulting from the deep reinforcement learning is executed exactly in the production simulation model built in Plant Simulation platform. After production simulation, the scheduling results obtained from Plant Simulation are compared with the results obtained from the Python environment. Fig. 5 shows the production simulation results in Plant Simulation platform. As shown in Fig. 5, the number of jobs that enter and exit the system is 130, indicating all jobs are processed in the system successfully. The completion time of the system is 8444, and the objective of the scheduling plan is 111.43. The scheduling results obtained in the Plant Simulation platform are the same as those in the Python environment. This verifies the correctness of the simulation environment programmed in Python and the correctness of the scheduling scheme calculation. In addition, Fig. 6-8 show the Gantt chart of the three factories. From Figs. 6-8, we can see that the jobs are processed closely in each factory. Since production validations in a real production environment cost too much, most scheduling literature did not validate the scheduling results. However, the correctness of the programmed scheduling environment should be checked before performing further scheduling optimizations, and the correctness of the scheduling scheme should be verified before applying the scheduling scheme in real workshops. Our proposed scheduling verification approach provides the necessary support for verifying the scheduling environment and plans. Besides, more statistical analysis and clear visualization can be performed via Plant Simulation platform. Fig. 5 Production simulation results in Plant Simulation platform (The video of production simulation via Plant Simulation platform is available at https://osf.io/dzc3u?view_only=e10ee0e3cec44b85ba2f569cd26071f2) 408 Advances in Production Engineering & Management 17(4) 2022 Verification of intelligent scheduling based on deep reinforcement learning for distributed workshops via discrete event … Fig. 6 The Gantt chart of factory 1 for the studied scheduling problem Fig. 7 The Gantt chart of factory 2 for the studied scheduling problem Fig. 8 The Gantt chart of factory 3 for the studied scheduling problem 4.3 Statistical analysis and visualization The Plant Simulation platform can provide powerful statistical analysis and visualization. In addition to the completion time and objective value, some production indicators are also important for assessing the efficiency and production status of the system. The utilization of machines and the occupation of buffers are analyzed. Fig. 9 shows the real-time utilization of all machines for the three factories. As shown in Fig. 9, under the optimized scheduling plan, the utilization of machines is approximately 75 %, which is relatively high. Besides, the utilization between machines differs little, indicating that the workloads between those workshops and machines are balanced. Fig. 10 provides the occupation of buffers in the three factories. Since infinite buffer capability is adapted as used in the scheduling literature, the number of jobs in a buffer can be 0-inf. As shown in Fig. 10, the most portion occurs when the number of jobs is 0. This indicates that for most cases, approximately 70-90 %, no jobs exist in the buffers. The number of jobs in all buffers can be 0,1,2,3, and 4. The second most frequent portion occurs when the number of jobs is 1. For factories 1 and 2, only a 5-10 % portion occurs when the number of jobs in buffers is 2. Factory 3 requires more buffers in BF32 and BF36. From the above analysis, we can know that for each buffer the buffer size set to 2 can fulfil most production requirements. Fig. 9 The utilization of machines in the three factories Advances in Production Engineering & Management 17(4) 2022 409 Yang, Wang, Xin, Xu The analysis for buffer occupation is very necessary for efficient production, since if no buffers are set the blocking will occur during production and therefore increase the completion time of the system. Most traditional scheduling literature simply assumes that infinite buffers exist between machines. However, in reality, it is impossible to set an infinite buffer size because the area between machines is limited. The buffer occupation analysis can help to determine the best buffer size to support efficient production. 5. Conclusion Fig. 10 The occupation of buffers in the three factories This paper studied the verification of production scheduling via discrete event simulation. Since most scheduling literature did not consider the verification of programmed scheduling environment and optimized scheduling schemes, this paper proposed a verification approach to validate the correctness of programmed scheduling environment and intelligent algorithms, by establishing the production simulation model in a Plant Simulation platform. The system architecture for validating the programmed production environment and optimized scheduling schemes are proposed. The parametric modelling method for production workshops with correct production processes is proposed. The verification experiment is carried out by taking the distributed permutation flowshop scheduling problem as a case study. Experimental results show that the scheduling results obtained by a deep reinforcement learning algorithm programmed in Python language are the same as results obtained in Plant Simulation platform. This verifies the correctness of the programmed production environment and scheduling algorithms. Besides, the utilization and Gantt charts clearly show the production efficiency under the selected scheduling scheme. The occupancy of buffers helps to determine the best buffer size before each machine. The proposed scheduling verification approach can help to verify the production environments programmed by researchers and the scheduling results obtained by intelligent algorithms. In the future, more realistic production resources, such as automated guided vehicles, production lines, and workers, can be considered with the help of Plant Simulation platform after the verification stage to further optimize the scheduling scheme obtained by programmed scheduling algorithms. In addition, the real-time interaction between Python and Plant Simulation can be studied to check the problems of the programmed scheduling environment when the programmed environment is not correct. Acknowledgement This work was supported by the National Defense Basic Scientific Research Program of China (Grant No. JCKY2021208B003), the National Key Research and Development Program of China (Grant No. 2022YFB3306000), and the National Natural Science Foundation of China (Grant No. 62073211). 410 Advances in Production Engineering & Management 17(4) 2022 Verification of intelligent scheduling based on deep reinforcement learning for distributed workshops via discrete event … References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] Fernandez-Viagas, V., Ruiz, R., Framinan, J.M. (2017). A new vision of approximate methods for the permutation flowshop to minimise makespan: State-of-the-art and computational evaluation, European Journal of Operational Research, Vol. 257, No. 3, 707-721, doi: 10.1016/j.ejor.2016.09.055. Naderi, B., Ruiz, R. (2010). 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An optimization tool for production planning: A case study in a textile industry, Applied Sciences, Vol. 11, No. 18, Article No. 8312, doi: 10.3390/ app11188312. [34] Yang, S., Xu, Z. (2022). Intelligent scheduling and reconfiguration via deep reinforcement learning in smart manufacturing, International Journal of Production Research, Vol. 60, No. 16, 4936-4953, doi: 10.1080/00207543. 2021.1943037. 412 Advances in Production Engineering & Management 17(4) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 4 | December 2022 | pp 413–424 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.4.445 Original scientific paper Demand prediction and optimization of workshop manufacturing resources allocation: A new method and a case study Wan, J.a,* a School of Economics, Wuhan Donghu University, Wuhan, P.R. China ABSTRACT ARTICLE INFO At present, great changes are taken place in the internal production management and resource allocation model of manufacturers. Under the premise of rational resource allocation, the completion period of products largely depends on the timeliness of resource allocation. The related studies mostly tackle the allocation of a single type of production resources in a single workshop, without considering much about the mutual influence between workshops. Through in-depth research on workshop manufacturing practices, this paper chooses to explore the planning, allocation, and demand prediction of manufacturing resources, which has long been a difficulty in workshop production. The research has great scientific research significance and practical value. The authors designed an algorithm based on the difference of the mean stagnation time of different production processes in the execution process, and used the algorithm to predict the number of production resources required in each period, before formulating the optimal configuration plan. This method is highly reasonable and applicable. After presenting a prediction method for the allocation demand of workshop manufacturing resources, the authors discussed whether the manufacturing resource allocation between different workshops is balanced in a fixed period. Then, a new idea was proposed for collaborative production between machines of different workshops in a specific environment, and an optimization algorithm was put forward to optimize the manufacturing resource allocation to machines facing the operation execution process. Through experiments, the authors compared the utilization rate of material, technological or human production resources in each period, and thereby verified the effectiveness of the proposed algorithm. Keywords: Workshop; Manufacturing resources; Resource demand; Allocation; Optimization; Simulation; Modelling; Prediction *Corresponding author: wanj@wdu.edu.cn (Wan, J.) Article history: Received 6 July 2022 Revised 8 October 2022 Accepted 15 October 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction As consumers demand more and more personalized products, manufacturers are engaged in an increasingly fierce competition. As a result, great changes are taken place in the internal production management and resource allocation model of manufacturers [1-7]. Currently, the main challenges to manufacturers include the diversity of customized products, the small batch size, and the strict delivery period. This requires manufacturers to manage production and allocate resources scientifically and efficiently [8-11]. From the perspective of resource supply, the management department of workshop manufacturing resources must allocate resources rationally, in order to enhance machine utilization, and shorten the completion period [12-19]. Under the premise of rational resource allocation, the completion period of products largely depends on the timeliness of resource allocation. 413 Wan The demand prediction for workshop manufacturing resources is to build a proper prediction model according to the workshop layout, order quantity, machine production attributes, and internal/external production conditions, and make overall forecast of the allocation demand of workshop manufacturing resources. Clark [20] developed three models and the corresponding fast heuristics methods to identify production plans and instant setting plans for production lines with switching time. The three methods were tested statically, and then tested based on rolling period. The test results show that the methods differ in demand prediction accuracy, capacity tightness, and period length. Schneider et al. [21] described the Markov decision process of production scheduling, and constructed a value function specific to the current demand prediction, which can generate the optimal scheduling decision online. In addition, an industrial application and reinforcement learning approach was developed for generating the similar value function in the field. Experimental results show that value function approximation is effective in both deterministic and noisy environments. Fiasché et al. [22] combined evolutionary algorithm with its quantum version into a hybrid approach. The simulation environment is ideally located inside two factories, partners and use cases of the white'R FP7 FOF MNP Project, with high manual activity to produce optoelectronics products, switching with the use of the new robotic (re)configurable island, the white’R, to highly automated production. Results show that the hybrid approach provided better answers and faster convergence than other methods. In recent years, many enterprises have shifted from single-point production to a more complex manufacturing environment, involving several multiproduct facilities. Ackermann et al. [23] proposed a mixed integer linear programming (MILP) model, and applied to the simultaneous material supply and scheduling of multi-site and multi-product intermittent plants with heterogenous parallel units. The applicability and performance of the model was demonstrated with numerical examples. Chernigovskiy [24] introduced ant colony optimization (ACO) to production scheduling, and compared the efficiency of the algorithm with other production scheduling algorithms on real cases. Through the comparison, they summarized the strengths of ACO, and its benefits to the manufacturing process. The related studies mostly tackle the allocation of a single type of production resources in a single workshop, without considering much about the mutual influence between workshops. To fill the gap, this paper carries out the demand prediction and optimization simulation for workshop manufacturing resource allocation [25-31]. Based on the mean stagnation time of different production processes in the execution process, this paper designs an algorithm to predict the number of production resources required in each period, and formulate the optimal configuration plan. This method is highly reasonable and applicable. Compared with the existing algorithms, our algorithm optimizes the simulation of the allocation of workshop production and manufacturing resources under multiple working conditions, and achieves high application value for improving the workshop scheduling system. Section 2 presents a prediction method for the allocation demand of workshop manufacturing resources. After determining the prediction method, Section 3 discussed whether the manufacturing resource allocation between different workshops is balanced in a fixed period. Section 4 proposed a new idea for collaborative production between machines of different workshops in a specific environment, aiming to obtain the optimal resource allocation plan for minimizing the mean stagnation time during the execution of production operations. In addition, an optimization algorithm was put forward to optimize the manufacturing resource allocation to machines facing the operation execution process, and its flow was illustrated. Through experiments, the simulation tools based on discrete event simulation were compared with the proposed simulation optimization model. The experimental results verify the effectiveness of the proposed algorithm. 2. Demand prediction In the actual situation of manufacturers, the management department of workshop manufacturing resources does not allocate resources to each workshop, but choose one workshop for resource allocation. Moreover, the resources are only allocated to a workshop when the manufac414 Advances in Production Engineering & Management 17(4) 2022 Demand prediction and optimization of workshop manufacturing resources allocation: A new method and a case study turing resources is out of balance. Therefore, this paper presents a new prediction method for workshop manufacturing resource allocation, and an index reflecting whether the resource allocation is balanced between workshops. To predict the demand for workshop manufacturing resource allocation, the key is to forecast the variation in the resource demand of each machine in the workshop. Thus, it is necessary to project the cumulative resource demand of each machine, as well as the overall resource demand of the workshop. The XGBoost-based stacking model was adopted to predict the variation in the resource demand of each machine. On this basis, the resource demand of all machines in a workshop was predicted. Then, the demands of different workshops were added up to obtain the final prediction of resource allocation demand. In a workshop 𝑋𝑋, the set of machines is denoted by 𝑅𝑅 = {𝑟𝑟1 , 𝑟𝑟2 , . . . , 𝑟𝑟𝑚𝑚 }. Then, the resource demand variation of each machine 𝑟𝑟𝑖𝑖 can be calculated by: 𝐺𝐺�𝑆𝑆 (𝑜𝑜) = 𝑔𝑔𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 (𝑟𝑟𝑖𝑖 , 𝑜𝑜) (1) 𝑅𝑅𝑖𝑖 where, 𝑔𝑔 is the prediction model trained by the corresponding sample set 𝐸𝐸; 𝑜𝑜 is the time interval. Then, the resource demand variation of workshop 𝑋𝑋 can be calculated by: 𝐺𝐺�𝑆𝑆𝑋𝑋 (𝑜𝑜) = � 𝐺𝐺�𝑆𝑆𝑅𝑅 (𝑜𝑜) 𝑖𝑖 𝑟𝑟𝑖𝑖 ∈𝑅𝑅 (2) Suppose the predicted resource demand variation of each machine 𝑟𝑟𝑖𝑖 has an error of 𝜀𝜀𝑖𝑖 . Then, 𝐺𝐺�𝑆𝑆 (𝑜𝑜) = 𝐺𝐺𝑆𝑆 (𝑜𝑜) + 𝜀𝜀𝑖𝑖 (3) 𝑅𝑅𝑖𝑖 𝑅𝑅𝑖𝑖 The resource demand variation of each machine in a workshop can be expressed as: 𝐺𝐺�𝑆𝑆𝑋𝑋 (𝑜𝑜) = ∑𝑟𝑟𝑖𝑖∈𝑅𝑅 𝐺𝐺𝑆𝑆𝑅𝑅 (𝑜𝑜) + ∑𝑖𝑖∈𝑚𝑚 𝜀𝜀𝑖𝑖 𝑖𝑖 𝐺𝐺�𝑆𝑆𝑋𝑋 (𝑜𝑜) = 𝐺𝐺𝑆𝑆𝑋𝑋 (𝑜𝑜) + ∑𝑖𝑖∈𝑚𝑚 𝜀𝜀𝑖𝑖 The resource allocation demand of a workshop can be obtained as: (4) (5) 𝐸𝐸𝑋𝑋 (𝑜𝑜) = −𝐺𝐺�𝑆𝑆𝑋𝑋 (𝑜𝑜) (6) 𝐺𝐺�𝑆𝑆𝑋𝑋 (𝑜𝑜) = 𝑔𝑔𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 (𝑋𝑋, 𝑜𝑜) (7) 𝐺𝐺�𝑆𝑆𝑋𝑋 (𝑜𝑜) = 𝐺𝐺𝑆𝑆𝑋𝑋 (𝑜𝑜)+∈ (8) The resource allocation demand of a workshop is the sum of the resource demand of each single-point machine. During the summation, the prediction error of each machine is also added up. It is very difficult to eliminate that error. Then, the resource demand variation of workshop 𝑋𝑋 can be calculated by: The XGBoost-based stacking model was directly applied to forecast the resource demand variation of each machine in a workshop. where, 𝑔𝑔 is the prediction model trained by the corresponding sample set 𝐸𝐸; 𝑜𝑜 is the time interval. Suppose the predicted resource demand variation of each machine in workshop 𝑋𝑋 has an error of 𝜀𝜀. Then, The resource allocation demand of workshop 𝑋𝑋 can be expressed as: 𝐸𝐸𝑋𝑋 (𝑜𝑜) = −𝐺𝐺�𝑆𝑆𝑋𝑋 (𝑜𝑜) (9) The error of overall prediction is smaller than the cumulative error. Hence, the overall demand prediction of workshop resource allocation achieves an ideal effect. Advances in Production Engineering & Management 17(4) 2022 415 Wan 3. Balance analysis After determining the prediction method, it is necessary to discuss whether the manufacturing resource allocation between different workshops is balanced in a fixed period. Before the discussion, overall consideration should be given to the future demand variation of manufacturing resources, the maximum quantity of manufacturing resources, and the minimum quantity of manufacturing resources in each workshop. Let 𝐸𝐸 = {𝑒𝑒1 , 𝑒𝑒2 , . . . , 𝑒𝑒𝑚𝑚 } be the quantity of manufacturing resources corresponding to each machine 𝑅𝑅 = {𝑟𝑟1 , 𝑟𝑟2 , . . . , 𝑟𝑟𝑚𝑚 } in workshop 𝑋𝑋. Then, the total quantity of manufacturing resources that can be accommodated by workshop 𝑋𝑋 can be calculated by: 𝑌𝑌𝑀𝑀𝑀𝑀𝑥𝑥𝑋𝑋 = ∑𝑒𝑒𝑖𝑖∈𝐸𝐸 𝑒𝑒𝑖𝑖 (10) 𝜑𝜑𝑑𝑑𝑑𝑑𝑑𝑑𝑛𝑛𝑋𝑋 = 𝑌𝑌𝑀𝑀𝑀𝑀𝑥𝑥𝑋𝑋 ∗ 𝜉𝜉𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 (12) 𝜙𝜙𝑢𝑢𝑝𝑝𝑋𝑋 = 𝑌𝑌𝑀𝑀𝑀𝑀𝑥𝑥𝑋𝑋 ∗ 𝜉𝜉𝑢𝑢𝑢𝑢 (13) The maximum 𝜑𝜑𝑢𝑢𝑢𝑢 and minimum 𝜑𝜑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 of the quantity of manufacturing resources can be respectively defined as: 𝜑𝜑𝑢𝑢𝑝𝑝𝑋𝑋 = 𝑌𝑌𝑀𝑀𝑀𝑀𝑥𝑥𝑋𝑋 ∗ 𝜉𝜉𝑢𝑢𝑢𝑢 (11) where, 𝜉𝜉𝑢𝑢𝑢𝑢 and 𝜉𝜉𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 are two parameters that control 𝜑𝜑𝑢𝑢𝑢𝑢 and 𝜑𝜑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 , respectively. Let 𝑌𝑌𝑀𝑀𝑀𝑀𝑥𝑥𝑋𝑋 denote the highest resource demand of each machine in workshop 𝑋𝑋. Then, the maximum and minimum quantities of manufacturing resources can be respectively described by 𝜑𝜑𝑢𝑢𝑝𝑝𝑋𝑋 and 𝜑𝜑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑋𝑋 , respectively: 𝜙𝜙𝑑𝑑𝑑𝑑𝑑𝑑𝑛𝑛𝑋𝑋 = 𝑌𝑌𝑀𝑀𝑀𝑀𝑥𝑥𝑋𝑋 ∗ 𝜉𝜉𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 The balance of resource allocation between workshops can be detailed as follows: (14) (1) If 𝐸𝐸𝑋𝑋 (𝑜𝑜) is greater than zero, then workshop manufacturing resources diminish. In this case, when 𝐸𝐸𝑋𝑋 (𝑜𝑜) ≤ 𝜑𝜑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑋𝑋 , the manufacturing resource allocation of a workshop is balanced, eliminating the need for replenishing manufacturing resources. When 𝜑𝜑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑋𝑋 < 𝐸𝐸𝑋𝑋 (𝑜𝑜) ≤ 𝜑𝜑𝑢𝑢𝑝𝑝𝑋𝑋 , the allocation is out of balance, i.e., the machines are not fully utilized, and manufacturing resources should be replenished immediately to meet the demand 𝐸𝐸𝑋𝑋 (𝑜𝑜). When 𝐸𝐸𝑋𝑋 (𝑜𝑜), the allocation is still out of balance, but simple addition of manufacturing resources will bring another problem, i.e., the manufacturing resource quantity may far exceed the capacity of machines. Thus, it is necessary to set 𝐸𝐸𝑋𝑋 (𝑜𝑜) = 𝜑𝜑𝑢𝑢𝑝𝑝𝑋𝑋 . (2) If 𝐸𝐸𝑋𝑋 (𝑜𝑜) is smaller than zero, then workshop manufacturing resources increase. In this case, when |𝐸𝐸𝑋𝑋 (𝑜𝑜)| ≤ 𝜑𝜑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑋𝑋 , the manufacturing resource allocation of a workshop is balanced, eliminating the need for transferring manufacturing resources. When 𝜑𝜑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑋𝑋 < |𝐸𝐸𝑋𝑋 (𝑜𝑜)| ≤ 𝜑𝜑𝑢𝑢𝑝𝑝𝑋𝑋 , the allocation is out of balance, i.e., the machines are unable to handle so many manufacturing resources, and the excessive quantity |𝐸𝐸𝑋𝑋 (𝑜𝑜)| of manufacturing resources should be transferred away immediately. When |𝐸𝐸𝑋𝑋 (𝑜𝑜)| > φup, the allocation is still out of balance, but simple reduction of manufacturing resources will bring another problem, i.e., the manufacturing resource quantity may fall far short of the capacity of machines. Thus, it is necessary to set |𝐸𝐸𝑋𝑋 (𝑜𝑜) |= −𝜑𝜑𝑢𝑢𝑝𝑝𝑋𝑋 . 4. Proposed allocation optimization approach The production tasks of machines are planned by the workshop, and each machine has a fixed production efficiency. When the order quantity increases, the shortage of manufacturing resources may occur easily. This will definitely affect the mean stagnation time during the execution of some operations. To solve the problem, we proposed a new idea for collaborative production between machines of different workshops in a specific environment, aiming to obtain the optimal resource allocation plan for minimizing the mean stagnation time during the execution of production op416 Advances in Production Engineering & Management 17(4) 2022 Demand prediction and optimization of workshop manufacturing resources allocation: A new method and a case study erations, and avoid the unfavorable state that some machines are busy while some machines are idle. This section details the optimization algorithm was put forward to optimize the manufacturing resource allocation to machines facing the operation execution process. Fig. 1 lists six functions of the optimization algorithm, including reading and storage of production state data, calculation of machine delay function, visual simulation of machines, calculation of mean stagnation time of each operation, resource allocation optimization for collaborative production, and update of manufacturing resource allocation schedule. The six functions are intercorrelated, and work together to ensure the realization of the optimization objective of manufacturing resource allocation. Fig. 2 shows the three-layer architecture of the optimization algorithm. The functional display layer mainly realizes the man-machine interaction during the simulation. The main functions on this layer include generation of new allocation plan, display of mean stagnation time of each operation, selection of machines for collaboration request, display of production task planning, and real-time visual simulation of production state. The logical processing layer is responsible for all computations and data processing. It mainly has five functions: processing of production state data, update of unoptimized number of machines, calculation of delay function, calculation of mean stagnation time of each operation, and sorting of delay functions. The data access layer stores the important information collected and calculated by the algorithm, mainly including production state data file, production task database, and resource allocation database. The above architecture connects all functional modules of the algorithm, realizes the target functions, and meets the actual production needs of workshops. Fig. 1 Some functions of the optimization algorithm Fig. 2 Architecture of optimization algorithm The logical processing layer is the core of the algorithm. The structure of this layer is detailed in Fig. 3. If the initial schedule of manufacturing resources allocation is known, then the manufacturing resources pending allocation optimization will be selected based on the delay function. Next, an optimization model would be constructed for manufacturing resources for simulation and optimization. Then, the allocation of all resources would be optimized iteratively, thereby minimizing the mean stagnation time of each operation in execution. Advances in Production Engineering & Management 17(4) 2022 417 Wan Fig. 3 Structure of logical processing layer This paper introduces the idea of collaborative production to the optimization algorithm for the manufacturing resource allocation to machines facing the operation execution process: Under certain production conditions, machines with similar production efficiencies can borrow manufacturing resources from each other to execute the same operation, such as to improve the allocation effect of resources throughout the execution process. After incorporating the above idea, our optimization algorithm breaks the limit of the original schedule of resource allocation: For each operation, only one machine receives manufacturing resources, making it impossible to optimize the resource allocation. Our algorithm can also reasonably reallocate resources to solve the problem that the machines, which are assigned insufficient production tasks, cannot easily respond to the real-time changes of order quantity. In other words, the traditional algorithms are unable to effectively reduce the mean stagnation time of operations, while our algorithm overcomes this limitation. The collaborative production involves a requestor and a responder. Before optimization simulation, it is important to determine which machines need to request collaboration from others. Two types of machines may become requestors. The first type refers to the machines that cannot timely execute operations, because they are assigned insufficient production tasks. Even if the allocation of a certain type of resources is optimized, these machines have the maximum delay. Then, such machine would request collaboration from others. The second type of machines are selected based on the limitation of the optimization algorithm. If only one machine receives manufacturing resources, and if it has a large delay, then it needs to request collaboration from others. The responding machine should have the same operations with the requestor, and the minimum delay. The manufacturing resources of the responder needs to be transferred to the requestor. Then, the manufacturing resource allocation is optimized for both parties engaging in collaboration. The above process is implemented iteratively until the algorithm meets the termination condition. Let 𝑚𝑚 be the current operation; 𝐸𝐸𝑚𝑚 be the set of delay functions of all machines in operation ∗ 𝑚𝑚; 𝐸𝐸𝑚𝑚 be the set of delay functions of all machines facing the same operations in operation 𝑚𝑚; ∗ 𝑤𝑤𝑚𝑚 be the machine selected from operation m for optimizing the allocation of manufacturing ∗ be the machine facing the same operations selected from operation 𝑚𝑚 for reresources; 𝑧𝑧𝑚𝑚 sponding to collaboration requests; ST be the set of all machines; DE(𝑚𝑚) be the mean stagnation time of operation m after the optimization of manufacturing resource allocation; 𝑣𝑣 be the unoptimized number of machines during operation m. 418 Advances in Production Engineering & Management 17(4) 2022 Demand prediction and optimization of workshop manufacturing resources allocation: A new method and a case study Fig. 4 Steps of our optimization algorithm As shown in Fig. 4, the specific steps of our optimization algorithm are as follows: In the initial allocation schedule of manufacturing resources, all ∀w satisfy w ∈ ST, i.e., all machines belong to the optimization range of manufacturing resource allocation. Step 2. The manufacturing resources of all machines are initially allocated as per the original schedule, with 𝑚𝑚 = 0, and 𝑤𝑤0∗ = ∅. Step 3. The initial schedule is simulated to solve the current DE(𝑚𝑚). Step 4. For all w ∈ ST, the delay function of each machine is obtained for the current moment. Step 5. All 𝐸𝐸𝑚𝑚 values are sorted in descending order, with 𝑣𝑣 = 1 and 𝑚𝑚 = 𝑚𝑚 + 1. Step 6. If |𝑣𝑣 ≤ |ST|, go to Step 7; otherwise, terminate the iteration. ∗ . Step 7. The 𝑢𝑢-th 𝑤𝑤 of 𝐸𝐸𝑚𝑚−1 [𝑣𝑣] is selected as 𝑤𝑤𝑚𝑚 ∗ ∗ Step 8. If 𝑤𝑤𝑚𝑚 = 𝑤𝑤𝑚𝑚−1 , all 𝐸𝐸𝑚𝑚 values are sorted in descending order. Then, the machine with the ∗ ∗ is selected, and its resources are transferred to 𝑤𝑤𝑚𝑚 . minimum delay 𝑧𝑧𝑚𝑚 ∗ ∗ Step 9. The resource allocation is optimized for the requestor 𝑤𝑤𝑚𝑚 and the responder 𝑧𝑧𝑚𝑚 separately, according to the allocation optimization model. ∗ does not receive resources after optimization, 𝑣𝑣 = 𝑣𝑣 + 1, and go to Step 6; Step 10. If 𝑤𝑤𝑚𝑚 otherwise, go to Step 11. Step 11. The new allocation schedule is simulated to obtain the corresponding DE(𝑚𝑚). Step 12. If DE(𝑚𝑚) < DE(𝑚𝑚 − 1), go to Step 4; otherwise, 𝑣𝑣 = 𝑣𝑣 + 𝑘𝑘, and go to Step 6. Step 1. 5. Simulation results analysis and discussion Our optimization algorithm for the manufacturing resource allocation to machines facing the operation execution process was verified through multiple simulations. The performance of our algorithm was compared with the traditional manufacturing resource allocation algorithm under the same case, using our independently developed software solution. Table 1 displays the delay functions of all machines in each operation, and the machines needing collaboration in each operation. It can be inferred that the case involves eight operations from the initial allocation schedule of manufacturing resources to the optimal schedule. Some machines requested collaboration in two consecutive operations. These machines lack manufacturing resources seAdvances in Production Engineering & Management 17(4) 2022 419 Wan verely, failing to meet the real-time demand. Then, out of the machines with the same operations, the machine with the minimum delay should be selected to respond to the collaboration request: their resources should be transferred to the requestor. The calculation results show that the delays of the requestors dropped significantly in a few operations, but the delays of other machines remained largely the same. This verifies the feasibility of collaborative production. Table 2 shows the stagnation and waiting of each machine in each operation, after the optimization of manufacturing resource allocation. The data in the table further verifies the feasibility of our optimization algorithm. Our simulation optimization model is more effective than the simulation tools of discrete event simulation. It can be seen that the resource allocation to each machine in each operation was improved, and the optimal solution of the allocation schedule was about 50 % lower than the initial solution in terms of stagnation, and 3/4 lower in terms of waiting time. Both stagnation and waiting times were declined from the levels of the traditional resource allocation algorithm. Figs. 5 and 6 present the quantities of material type and technology/manpower type manufacturing resources pending allocation in each period, respectively. The red and purple lines indicate the resource quantities in the initial situation, and those under the optimal allocation schedule. It can be observed that both types of resources declined significantly, indicating that the new allocation schedule can effectively weaken the obstacles to the flow of manufacturing resources between machines. In addition, different types of manufacturing resources varied in the quantity being processed by machines, owing to the interplay between production efficiencies of different machines in the same workshop. Figs. 7 and 8 present the machine utilizations of material type and technology/manpower type manufacturing resources in each period, respectively. The red and purple lines indicate the machine utilizations in the initial situation, and those under the optimal allocation schedule. It can be inferred that the machine utilizations improved obviously for both types of resources. In the initial allocation of resources, some machines may be busy, while others may be idle, and some machines were continuously engaged in high-intensity production, owing to the imbalance between resources. These problems were basically eliminated after the allocation optimization. Machine number Operation 0 Operation 1 Operation 2 Operation 3 Operation 4 Operation 5 Operation 6 Operation 7 Operation 8 Table 1 Delay function of each machine in each operation 1 2 3 4 5 6 0.251 0.562 93.154 61.592 0.374 132.651 0.284 0.469 152.43 52.618 0.218 41.629 0.359 0.526 21.417 62.352 0.348 13.607 0.152 0.564 25.168 53.627 0.241 13.521 0.137 0.462 24.847 52.195 0.418 11.415 0.168 0.641 28.415 14.219 0.482 16.294 0.159 0.451 27.462 13.258 0.374 18.492 0.156 0.537 18.526 11.416 0.351 15.415 0.193 0.412 7.652 8.439 0.318 5.627 7 114.518 132.542 152.041 56.128 28.419 25.318 15.625 18.207 18.439 Table 2 Stagnation and waiting of resources in each operation Operation 0 Operation 1 Operation 2 Operation 3 Mean stagnation time 1.251 1.748 1.625 1.205 Mean waiting time 1.326 1.485 0.718 0.625 Operation 5 Operation 6 Operation 7 Percentage of reduction Mean stagnation time 0.961 0.815 0.853 52.64 Mean waiting time 0.357 0.495 0.285 74.51 420 8 0.025 0.021 0.029 0.027 0.024 0.023 0.025 0.028 0.051 Operation 4 0..947 0.495 Advances in Production Engineering & Management 17(4) 2022 Demand prediction and optimization of workshop manufacturing resources allocation: A new method and a case study Fig. 5 Quantities of material type manufacturing resources pending allocation Fig. 6 Quantities of technology/manpower type manufacturing resources pending allocation Fig. 7 Machine utilizations of material type manufacturing resources Advances in Production Engineering & Management 17(4) 2022 421 Wan Fig. 8 Machine utilizations of technology/manpower type manufacturing resources 6. Conclusions This paper carries out the demand prediction and optimization simulation for workshop manufacturing resource allocation. After presenting a prediction method for the allocation demand of workshop manufacturing resources, the authors discussed whether the manufacturing resource allocation between different workshops is balanced in a fixed period. Then, a new idea was proposed for collaborative production between machines of different workshops in a specific environment, and an optimization algorithm was put forward to optimize the manufacturing resource allocation to machines facing the operation execution process. The algorithm flow was detailed. Through experiments, we displayed the delay functions of each machine in each operation, identified the machines needing collaborative production in each operation, and verified the feasibility of the idea of collaborative production. The effectiveness of our algorithm was further confirmed by obtaining the stagnation and waiting situation of each machine in each operation, after the resource allocation is optimized. Finally, we compared the quantities of material type and technology/manpower type manufacturing resources pending allocation in each period, and contrasted the machine utilizations of material type and technology/manpower type manufacturing resources in each period. This paper mines the historical dataset of workshop production and manufacturing, researched and established a model and an analysis method, and achieved certain research results. However, the allocation of workshop production and manufacturing resources is affected by various factors, which have intricated correlations. For reasons of dataset and data quality, it is impossible to fully consider and thoroughly explore all the influencing factors and their correlations. In the future, these issues will be considered for further improvement. 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Advances in Production Engineering & Management 17(4) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 4 | December 2022 | pp 425–438 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.4.446 Original scientific paper Monte Carlo Tree Search improved Genetic Algorithm for unmanned vehicle routing problem with path flexibility Wang, Y.D.a, Lu, X.C.b,*, Song, Y.M.c, Feng, Y.d, Shen, J.R.e aBeijing Jiaotong University, Shangyuan Village, Haidian District, Beijing, P.R. China Jiaotong University, Shangyuan Village, Haidian District, Beijing, P.R. China cBeijing Jiaotong University, Shangyuan Village, Haidian District, Beijing, P.R. China dBeijing Jiaotong University, Shangyuan Village, Haidian District, Beijing, P.R. China eBeijing Capital Agribusiness & Food Group Co. Ltd., Xicheng District, Beijing, P.R. China bBeijing ABSTRACT ARTICLE INFO With the gradual normalization of the COVID-19, unmanned delivery has gradually become an important contactless distribution method around China. In this paper, we study the routing problem of unmanned vehicles considering path flexibility and the number of traffic lights in the road network to reduce the complexity of road conditions faced by unmanned vehicles as much as possible. We use Monte Carlo Tree Search algorithm to improve the Genetic Algorithm to solve this problem, first use Monte Carlo Tree Search Algorithm to compute the time-saving path between two nodes among multiple feasible paths and then transfer the paths results to Genetic Algorithm to obtain the final sequence of the unmanned vehicles fleet. And the hybrid algorithm was tested on the actual road network data around four hospitals in Beijing. The results showed that compared with normal vehicle routing problem, considering path flexibility can save the delivery time, the more complex the road network composition, the better results could be obtained by the algorithm. Keywords: Unmanned vehicle; Path flexibility; Vehicle routing problem; Genetic Algorithm (GA); Monte Carlo Tree Search algorithm (MCTS); COVID-19; Pandemics *Corresponding author: xclu@bjtu.edu.cn (Lu, X.C.) Article history: Received 15 August 2022 Revised 9 October 2022 Accepted 15 October 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction The Novel Coronavirus Disease (COVID-19) broke out globally in 2020, and in November 2021, the mutant virus Omicron was discovered and spread rapidly around the world. According to WHO, the strain spreads faster and is more transmissible. By February 2022, the Omicron strain has become a major epidemic strain worldwide. Due to the wide range and high contagiousness of the epidemic, especially the significant characteristics of human-to-human transmission, the Chinese government has always taken strict precautions and implemented closed-off management in high-risk areas to minimize the spread of the epidemic. Thus, unmanned and contactless techniques have become important force in the fight against the epidemic. With the spread of the epidemic, more and more cities, such as Changsha and Shanghai have begun to use unmanned vehicles to distribute medical suppliers to the epidemic areas. 425 Wang, Lu, Song, Feng, Shen Compared to conventional manned vehicles, unmanned delivery vehicles are far more reliant on road conditions. For technical reasons, unmanned vehicles are less able to adapt to complex road conditions than normal vehicles. Hence the major research on unmanned vehicles usually focus on the design of algorithms based on uncertain traffic situations or obstacle avoidance for unmanned vehicles. However, under circumstance of the epidemic, considering of all technological aspects to plan thorough routes for unmanned vehicles can better meet the requirements of contactless delivery. The traditional vehicle routing problems consider the distribution sequences between demand points solely and ignore the fact that there are frequently multiple alternate paths between demand points in the actual distribution processes. The traffic situations and journey times of various routes are different and have substantial impact on the safety and efficiency of unmanned vehicles. In reality, usually the more traffic lights need to go through, the more complex information needs to be processed, so this paper incorporates the number of traffic lights in the road network into the vehicle routing problem, considers to select a safer and faster path for unmanned vehicles. Establishing a vehicle routing problem model with paths flexibility (VRP-PF) with the goal of minimizing distribution time for unmanned vehicles. 2. Literature review Since the unmanned vehicles relies heavily on road conditions and traffic situations, for unmanned delivery vehicles, most researchers take into account the unmanned vehicles’ ability of avoiding obstacles and adapting to the traffic conditions. Hu [1] et al. designed a genetic simulated annealing algorithm to solve the unmanned vehicles routing problem with road conditions updates, and adjusted the delivery plan in real time based on the local update strategy for the pre-optimize paths based on the road condition information, and the results showed that the algorithm has more advantages than traditional genetic algorithms under complex road conditions. Guan [2] proposed an unmanned vehicles routing problem model based on traffic situations. To improve the adaptability of unmanned vehicles to road conditions, a DQN local optimization model with heuristic reward and adaptive exploration strategy was proposed. This model could reduce delivery time and increase delivery efficiency, but it did not involve the obstacle avoidance problem of unmanned vehicles and was not tested on real traffic data. Zhu [3] and Han [4] both studied the unmanned vehicle routing problem using deep reinforcement learning, with the difference that Zhu’s research targeted the obstacle avoidance problem of unmanned vehicles in dynamic environments, while Han's research considered the objective of minimizing distance and the number of vehicles from the perspective of unmanned fleets. Tavoosi [5] et al. designed an improved particle swarm algorithm to process certain and uncertain obstacles to obtain the optimal paths. Based on total driving distance and waiting time, Shi W. et al. proposed a multi‐objective scheduling model to solve the path conflict problem of automated guided vehicles (AGVs) and used the A* path planning algorithm to search the shortest path of AGV [6]. Erenoglu used the Unmanned Aerial Vehicles (UAV) based 3D city modelling approach to be manage and plan urban areas [7]. In view of many scholars consider the real-time traffic conditions in unmanned vehicles routing problem, Wang [8] et al. proposed a routing model for unmanned vehicles in the case of GPS system failure. Additionally, Levy [9] et al. considered the unmanned vehicles routing problem under fuel-limited conditions and designed multiple neighbourhood shakes to improve the variable neighbourhood search algorithm, which was able to obtain better results compared with the traditional variable neighbourhood search algorithm but the result was not an optimal solution. Zhao [10] designed a genetic algorithm to solve the unmanned vehicles routing problem considering the charging and switching requirements of unmanned vehicles. It can be seen that the research on unmanned vehicles routing problem mainly focus on obstacle avoidance considering traffic conditions and energy supply of unmanned vehicles. Besides, heuristic algorithms are the main solution approaches used. There are many different variants of the VRP, like Split-Delivery VRP [11], Heterogeneous VRP with Time Windows [12], stochastic VRP [13], VRP with Pickup and Delivery [14], ConVRP (Consistent Vehicle Routing Problem) [15] and EVRP (electric vehicle routing problem) [16] etc. But 426 Advances in Production Engineering & Management 17(4) 2022 Monte Carlo Tree Search improved Genetic Algorithm for unmanned vehicle routing problem with path flexibility few research focus on the vehicle routing problem with path flexibility (VRP-PF). This problem was first defined by Huang [17] et al. in 2017, and they developed model considering time windows under deterministic and uncertain traffic conditions. The model was solved by CPLEX and obtained the approximate optimal solutions. Liu [18] et al. proposed a green vehicles routing model considering the fuel consumption of vehicle acceleration and waiting at traffic lights and established the model with path flexibility to minimizing fuel and other costs. Due to the high complexity of the model, it could only solve instances with 10 demand points. But their research proves that routes planning considering path flexibility can save costs. Wang [19] et al. proposed a vehicle routing problem model with path flexibility for electric vehicles, considering the selection of charging stations. Then they designed a variable neighbourhood search algorithm to solve this problem, but they only considered multiple choices of charging stations, multiple paths between the stations are not involved. Guo [20] et al. developed a time-dependent bus routing problem model considering traffic congestions with path flexibility, and designed a tabu search algorithm to solve it. Given that the safety of unmanned vehicles is highly dependent on road conditions and the distribution of epidemic supplies are time-efficient, we incorporate the waiting time during traffic lights to measure road conditions and establish a vehicle routing problem model with path flexibility. Then we design a hybrid heuristic algorithm, using Monte Carlo tree search algorithm to improve the Genetic Algorithm to solve the routing problem with path flexibility. 3. Model and algorithm of vehicle routing problem with path flexibility 3.1 Problem description and mathematic model The vehicle routing problem with path flexibility is defined on a directed graph 𝐺𝐺 = (𝑉𝑉, 𝑃𝑃), where 𝑉𝑉 = {0,1,2, . . . , 𝑛𝑛} is the set of vertices, 𝑃𝑃 = {(𝑖𝑖, 𝑗𝑗, 𝑝𝑝): 𝑖𝑖, 𝑗𝑗 ∈ 𝑉𝑉, 𝑖𝑖 ≠ 𝑗𝑗, 𝑝𝑝 ∈ 𝑃𝑃𝑖𝑖𝑖𝑖 } is the set of paths, and 𝑃𝑃𝑖𝑖𝑖𝑖 is the optional path from vertex 𝑖𝑖 to vertex 𝑗𝑗. In the set 𝑉𝑉, vertex 0 denotes the starting point and the rest vertices denote the demand points. In the set 𝑃𝑃, the length of the path 𝑝𝑝𝑖𝑖𝑖𝑖 is 𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖 , the number of traffic lights is 𝑙𝑙𝑖𝑖𝑖𝑖𝑖𝑖 . N denotes the set of unmanned vehicles, where all vehicles are homogeneous, and the capacity of the vehicle is 𝐶𝐶. The vehicle meets a red light with a certain probability 𝑆𝑆 and the waiting time is w. The speed of unmanned vehicle is 𝑣𝑣𝑖𝑖𝑖𝑖𝑖𝑖 , which is related to time and the road area where the unmanned vehicle is located. The objective is to minimise the time cost and find a solution that satisfies the following constraints: (1) the demand at each demand point is satisfied and the demand cannot be split; (2) all vehicles depart from and return to the starting point; (3) minimise the number of traffic lights in the optimal paths. An example diagram of this problem is shown in Fig. 1. Fig. 1 Schematic diagram of VRP-PF Assuming the fleet of unmanned vehicles are homogeneous, the yellow dot 0 in Fig. 1 indicates the departure point of all vehicles in the fleet, the green square dots 1,2,3,4 are demand points, the traffic light marker indicates that there is a traffic light at this junction and vehicles may need to wait for a while when the light is red. The blue triangular dots are non-demand nodes in the Advances in Production Engineering & Management 17(4) 2022 427 Wang, Lu, Song, Feng, Shen road network. Suppose that all nodes in the diagram are disconnected, and the unmanned vehicle needs to travel from point 0 to demand point 1, there are multiple paths to choose, such as 0-5-67-1, 0-19-7-1 or 0-19-20-1. For the road network with only 22 nodes shown in Fig. 1, there are more than dozens of feasible paths between each two demand points, which greatly increases the complexity of the problem than traditional routing problem. Unmanned delivery vehicles are low-speed vehicles, and the Implementation Rules for the Management of Unmanned Delivery Vehicles promulgated by the Beijing Economic and Technological Development Area in May 2021 requires that the speed of unmanned delivery vehicles should not exceed 15 km/h. Besides, the speed of unmanned vehicles varies with the traffic conditions in real life. Therefore, we map the traffic indexes crawled from Baidu map to the speeds of unmanned vehicles, and the corresponding table of traffic indexes and speeds is shown in Table 1. The expression of speed is a piecewise function which is shown in Fig. 2. Table 1 Correspondence between traffic index and travel speed Real-time vehicle speed Traffic index Unmanned vehicle's speed >30 1 15 10-30 2 10 <10 3 5 Fig. 2 Speeds of unmanned vehicles on different roads 1. The optimization objective in this paper is delivery time of unmanned vehicles, as shown in Eq. 𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖 min 𝑇𝑇 = ∑(𝑖𝑖,𝑗𝑗)∈𝑉𝑉 ∑𝑝𝑝∈𝑃𝑃 𝑣𝑣 𝑖𝑖𝑖𝑖𝑖𝑖 𝑘𝑘 𝑘𝑘 𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 + 𝑆𝑆𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖 𝑙𝑙𝑖𝑖𝑖𝑖𝑖𝑖 𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 , ∀𝑘𝑘 ∈ 𝑁𝑁 Define the decision variables and associated parameters as follows. 1, if arc (𝑖𝑖, 𝑗𝑗) 𝑖𝑖s on the optimal route 𝑘𝑘 𝑥𝑥𝑖𝑖𝑖𝑖 =� 0, otherwise 𝑘𝑘 =� 𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 1, (1) if the vehicle travels path 𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖 on the arc (𝑖𝑖, 𝑗𝑗) 0, otherwise 𝑘𝑘 is actual capacity when vehicle 𝑘𝑘 is on arc (𝑖𝑖, 𝑗𝑗, 𝑝𝑝), and 𝑞𝑞𝑖𝑖 is demand of customer 𝑖𝑖. There𝐶𝐶𝑖𝑖𝑖𝑖𝑖𝑖 fore, the question can be formulated as follows. s.t. � 𝑥𝑥𝑖𝑖𝑖𝑖 − � 𝑥𝑥𝑗𝑗𝑗𝑗 = 0, 𝑖𝑖∈𝑉𝑉,𝑖𝑖≠𝑗𝑗 𝑖𝑖∈𝑉𝑉,𝑖𝑖≠𝑗𝑗 ∀𝑗𝑗 ∈ 𝑉𝑉 𝑞𝑞𝑗𝑗 𝑥𝑥𝑖𝑖𝑖𝑖 ≤ 𝐶𝐶𝑖𝑖𝑖𝑖𝑘𝑘 ≤ (𝐶𝐶 − 𝑞𝑞𝑖𝑖 )𝑥𝑥𝑖𝑖𝑖𝑖 , ∀(𝑖𝑖, 𝑗𝑗) ∈ 𝑉𝑉 𝑘𝑘 � 𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑥𝑥𝑖𝑖𝑖𝑖 , 𝑝𝑝∈𝑃𝑃 428 ∀(𝑖𝑖, 𝑗𝑗) ∈ 𝑉𝑉 (2) (3) (4) Advances in Production Engineering & Management 17(4) 2022 Monte Carlo Tree Search improved Genetic Algorithm for unmanned vehicle routing problem with path flexibility � 𝐶𝐶𝑖𝑖𝑖𝑖𝑖𝑖 = 𝐶𝐶𝑖𝑖𝑖𝑖 , 𝑝𝑝∈𝑃𝑃 ∀(𝑖𝑖, 𝑗𝑗) ∈ 𝑉𝑉 𝑘𝑘 𝑞𝑞𝑗𝑗 𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝐶𝐶𝑖𝑖𝑖𝑖𝑖𝑖 ≤ (𝐶𝐶 − 𝑞𝑞𝑖𝑖 )𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 , ∀(𝑖𝑖, 𝑗𝑗) ∈ 𝑉𝑉, 𝑝𝑝 ∈ 𝑃𝑃 𝑥𝑥𝑖𝑖𝑖𝑖 ∈ {0,1}, ∀(𝑖𝑖, 𝑗𝑗) ∈ 𝑉𝑉 𝐶𝐶𝑖𝑖𝑖𝑖 ≥ 0, ∀(𝑖𝑖, 𝑗𝑗) ∈ 𝑉𝑉 𝑥𝑥𝑖𝑖𝑖𝑖𝑖𝑖 ∈ {0,1}, ∀(𝑖𝑖, 𝑗𝑗) ∈ 𝑉𝑉, 𝑝𝑝 ∈ 𝑃𝑃 𝐶𝐶𝑖𝑖𝑖𝑖𝑖𝑖 ≥ 0, ∀(𝑖𝑖, 𝑗𝑗) ∈ 𝑉𝑉, 𝑝𝑝 ∈ 𝑃𝑃 𝑞𝑞𝑖𝑖 > 0, ∀𝑖𝑖 ∈ 𝑉𝑉\{0} 𝑞𝑞0 = 0 (5) (6) (7) (8) (9) (10) (11) (12) Eq. 2 is the vehicle flow conservation constraint. Constraint Eq. 3 ensures that the volume of unmanned vehicles at each node does not exceed the maximum vehicle capacity. Eq. 4 ensures that each unmanned vehicle selects only one feasible path from node 𝑖𝑖 to node 𝑗𝑗. Constraints Eqs. 5-6 ensure that supplies are transported on only one feasible path and do not exceed the maximum vehicle capacity. The rest are specific constraints of the variables. 3.2 Monte Carlo Tree Search algorithm (MCTS) The vehicle routing problem belongs to NP-hard problem, and the vehicle routing problem with path flexibility is more difficult because the decisions to make are not only the routing decision but also the path selection decision depending on the departure time and the congestions in the relevant road network. The problem can be regarded as a two-stage problem with finding the optimal sequence of demand points and the optimal path selection between demand points. Moreover, the sequence of demand points affects path selection between points, and different paths affect the sequence of demand points in reverse. Since in the real road network, roads are crisscrossed and there are often numerous feasible paths between two points, Huang [17] et al. used Dijkstra's algorithm to find the shortest path between two points when considering path flexibility. However, the contrasting traffic conditions of different roads and the variational speed on different roads increase the difficulties of using exact algorithms. Hence, we apply the Monte Carlo tree search algorithm (MCTS) to solve the path flexibility of the problem and adopt MCTS to improve the genetic algorithm to solve the whole problem. MCTS is a method for determining the optimal policy in a given domain. It is a simulation-based search algorithm with a tree structure that combines depth-first search and breadth-first search. Furthermore, it maintains superior results when the search space is huge and is widely used in fields such as games [21-24]. Therefore, MCTS is able to find the acceptable path rapidly for the large datasets. The process of MCTS can be divided into four steps: selection, expansion, simulation, and backpropagation, repeated these four steps until convergence [25]. The selection process is commonly implemented using the Upper Confidence Bound for Tree (UCT) algorithm, which searches and selects the next node to be visited among all the nodes, the formula of UCT is shown as Eq. 13. 2 ln 𝑛𝑛 𝑈𝑈𝑈𝑈𝑈𝑈 = 𝑋𝑋�𝚥𝚥 + 2𝐶𝐶𝑝𝑝 � 𝑛𝑛𝑗𝑗 (13) where 𝑛𝑛 is the number of times the current parent node has been visited, 𝑛𝑛𝑗𝑗 is the number of times �𝚥𝚥 usually bethe child node has been visited, 𝐶𝐶𝑝𝑝 is a constant greater than zero, and the value of 𝑋𝑋 tween [0,1], [24]. Even though the UCT strategy can provide acceptable outcomes, the rate of convergence is modest. To improve the efficiency, the weight of the node depends on the travel time, and the shorter the travel time is, the higher the weight is and the node is more likely to be selected. Therefore, the pseudo for the algorithm can be written as Algorithm1. Advances in Production Engineering & Management 17(4) 2022 429 Wang, Lu, Song, Feng, Shen Algorithm1：path search for MCTS Input：origin node no, destination node nd Output: optimal path p between no and nd 1: function PathSearch(Array, no, nd) 2: Disconnect no from other nodes and initialize trial nodes list L 3: if Array[doj] != 0 then 4: L ← add nj to L 5: end if 6: while ni != nd do 7: ni ← Select a node ni from L according to the weight 8: p ← add ni to p 9: end while 10: return p 11: end function Unlike complex games such as Go (Weiqi), game theory is not involved during the routing search process and therefore there is no need to switch decisions, so we omit the backpropagation process. The routing search is able to find a solution inevitably (if the path is not feasible can be named as a non-feasible solution), so by setting a certain number of iterations we can implement the simulation process in MCTS. By simulating kmax times, the final output of the path with the highest weight can be fed back to the genetic algorithm, the flow chart of MCTS algorithm is shown in Fig. 3. Fig. 3 Flow Chart of MCTS Algorithm 3.3 Monte Carlo Tree Search Improved Genetic Algorithm (MCTS-GA) The Monte Carlo tree search algorithm can find the optimal path between two nodes effectively, but it cannot solve the vehicle routing problem. In contrast, the genetic algorithm has better search capability and scalability, so we use the framework of the genetic algorithm and combined with the Monte Carlo tree search algorithm to solve the entire problem. Coding design Chromosomes are encoded using decimal coding that is frequently used in genetic algorithms in this paper, but each node includes an attribute label. The nodes in the road network are divided into four categories, starting nodes (point 0 in Fig. 1), customer demand nodes (green square nodes in Fig. 1), road nodes without demand (blue triangular nodes in Fig. 1) and traffic lights 430 Advances in Production Engineering & Management 17(4) 2022 Monte Carlo Tree Search improved Genetic Algorithm for unmanned vehicle routing problem with path flexibility nodes (nodes with traffic light signs in Fig. 1), which together form a complete road network. In the actual distribution work, the customer demand nodes are the nodes that required to make decisions about the order of distribution for the vehicle routing problem, while the road nodes and traffic lights nodes are the nodes that required to make decisions about whether or not to pass for path flexibility. Therefore, the attribute labels of the different nodes need to be assigned to the nodes in order for the algorithm to identify the nodes to be processed at different stages when coding. A schematic of the coding scheme is shown in Fig. 4 (using a feasible path in the road network of Fig. 1 as an example). Fig. 4 shows a complete feasible route for an unmanned vehicle, which includes both the demand nodes to be delivered and all road nodes in the road network to be passed through during delivery. But when computing the vehicle routing problem with genetic algorithm, the code of chromosome can be streamlined to retain only the starting nodes and customer demand nodes, which means the code shown in Fig. 4 only needs to be processed as (0,2,1,0). This route is the delivery route for an unmanned vehicle without path flexibility (assuming that the sum of the demand does not exceed the vehicle capacity). In contrast, in the process of MCTS, the entire road network needs to be processed, that means the path with minimized travel time and traffic lights between each two nodes in the route needs to be found in turn. For example, a feasible path from the starting point to customer demand node 2 can be expressed as (0,19,20,2). Fig. 4 Schematic of complete route coding scheme Crossover, mutation and heredity Both the crossover and mutation operations are directed at the vehicle routing problem, without considering path flexibility. The crossover process uses a two-opt crossover. To avoid duplicate fragments or missing fragments in the offspring generated after the crossover, we first randomly select sample fragments from parent 2 and inserts them into the corresponding positions of the offspring, and then traverses parent 1 and inserts the genes that are not duplicated with the sample fragments therein in turn to form new offspring. The crossover process is shown in Fig. 5 (the crossover process does not consider road nodes and traffic lights nodes, assuming that all nodes except node 0 in Fig. 5 are customer demand nodes). The mutation process is a two-point mutation, which means that two genes on a chromosome that do not contain the first and last gene are randomly selected to swap positions. To improve the efficiency of the search, an elitist selection strategy is used, whereby the top 2 % of the offspring in each generation are retained and placed directly into the next generation. Besides, the idea of an invasive weed algorithm is involved so that the more adapted individuals produce relatively more offspring. Adaptability function Fig. 5 Schematic diagram of the crossover process After the allocation sequence of customer demand nodes has been generated by the genetic algorithm, the MCTS can be used to obtain the optimal path between the customer demand nodes then the travel time and total length of the path as well as the times of traffic lights passed can be Advances in Production Engineering & Management 17(4) 2022 431 Wang, Lu, Song, Feng, Shen calculated. The individual with the greater the fitness is more retainable, so according to Eq. 1 the fitness function can be expressed as Eq. 14. MCTS-GA algorithm flow 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 = 1�𝑇𝑇 (14) The above describes the process of selecting feasible paths between nodes using the MCTS algorithm and the solution of the vehicle routing problem using genetic algorithm respectively, but the two processes need to be carried out in unison to obtain a complete solution for the problem. The flowchart of the Monte Carlo Tree Search Improved Genetic Algorithm (MCTS-GA) is shown in Fig. 6. After generating the sequence of customer demand nodes by the genetic algorithm, we use the MCTS to find the optimal path between each two nodes and the search result is transferred to the genetic algorithm for population fitness calculation. Then cross and mutation operations are carried out to generate the new population, and the complete path is finally output after repeated iterations until reach the maximum number of iterations. Fig. 6 Flow chart of MCTS-GA algorithm 4. Numerical experiments: Results and discussion In this section, the algorithm performance is tested by numerical experiments using real road network in Beijing. As adopting unmanned vehicles to delivery epidemic medicine is considered, we choose some of the hospitals in Beijing as the starting points for medicine distribution. The unmanned vehicles start from the hospital to the community, and the road networks around the target hospitals are established as examples for testing. The algorithm is implemented using Python code in an Intel(R) Core (TM) i5-8250U CPU @ 1.60 GHz and 8GB of RAM. The parameters of algorithm and unmanned vehicles are shown in Table 2, the example information is shown in Table 3. 432 Advances in Production Engineering & Management 17(4) 2022 Monte Carlo Tree Search improved Genetic Algorithm for unmanned vehicle routing problem with path flexibility Table 2 Algorithm parameters and unmanned vehicle performance parameter settings Parameters Crossover probability mutation probability Iterations of GA Iterations of MCTS Probability of encountering a red light Red light waiting time capacity of unmanned vehicle Instance name Hospital23 Hospital29 Hospital39 Hospital58 Number of customer nodes 6 8 11 15 Table 3 Instance information table Number of road Number of traffic nodes lights 11 5 17 3 21 7 28 14 Value 0.8 0.2 100 500 0.5 90 seconds 20 pieces Total amount of nodes 23 29 39 58 In this paper, three Beijing hospitals are selected as target hospitals, and two small-scale road networks and one medium-scale road network were established as examples. Example Hospital23 is the Sixth Hospital of Peking University, with a road network consisting of 23 nodes; Example Hospital29 is Hospital 466, with a total of 29 nodes in the road network. Example Hospital39 is the Chinese Armed Police General Hospital, with a total of 39 nodes in the road network. Example Hospital58 is the Bayi Children’s Hospital, with a total of 58 nodes in the road network. The results of examples are shown in Figs. 7-10 respectively, where the road network is shown in Figs. (a) and the distribution results are shown in Figs. (b), and the green square nodes in Figs. (b) are customer demand nodes. Tables 4-7 show the specific distribution paths of each example. Fig. 7 Results of Hospital23 Unmanned vehicle 1 2 3 Customer nodes 21,13,1 8,5 19 Table 4 Detailed distribution paths of Hospital23 Load Load Distribution Times of passing pieces Factor (%) path through traffic lights 16 80 0,2,21,13,12,1,0 0 20 100 0,2,3,8,9,10,11,6,5,4,3,2,0 3 15 75 0,2,21,13,14,15,19,15,14,13,21,2,0 2 Advances in Production Engineering & Management 17(4) 2022 433 Wang, Lu, Song, Feng, Shen Fig. 8 Results of Hospital29 Table 5 Detailed distribution paths of Hospital29 Unmanned vehicle Customer nodes Load pieces Load factor 2 3 4 5 6 3 6 9,12 20 28 20 18 19 20 18 100 90 95 100 90 1 18,22,27 20 100 Distribution path 0,4,7,9,11,14,15,22,15,14,26 ,17,18,17,10,27,9,7,4,0 0, 4, 5, 3, 5, 4,0 0, 4, 5, 6, 5, 4,0 0, 4, 7, 9, 11, 12, 11, 9, 7, 4,0 0, 1, 21, 20, 25, 8, 7, 4,0 0,4,5,3,2,28,2,3,5,4,0 Times of passing through traffic lights 0 0 0 0 0 0 Fig. 9 Results of Hospital39 Unmanned vehicle Customer nodes 2 7,30 1 3 4 434 5 8,15 22 4,18,27 24,32,36 Table 6 Detailed distribution paths of Hospital39 Load Load Distribution pieces factor (%) path 0,4,3,9,10,12,15,35,14,8,1 20 100 4,35,15,12,10,9,3,4,0 0,16,7,16,19,31,30,31,19,1 17 85 6,0 18 90 0,16,7,1,23,22,23,1,7,16,0 0,4,3,9,10,11,5,18,17,27,5, 19 95 9,3,4,0 0,4,3,9,5,27,25,24,26,36,3 16 80 7,32,29,18,13,5,9,3,4,0 Times of passing through traffic lights 0 0 4 2 3 Advances in Production Engineering & Management 17(4) 2022 Monte Carlo Tree Search improved Genetic Algorithm for unmanned vehicle routing problem with path flexibility Fig. 10 Results of Hospital58 Unmanned vehicle Customer nodes 2 30,31,43,56,5 4 4 5 14 5 1 3 22,23 17,18,8 6 7 Indicator Total time (min) Total distance (m) Times of passing through traffic lights 4,51 37 Table 7 Detailed distribution paths of Hospital58 Load Load Distribution pieces factor (%) path 0, 7, 8, 28, 27, 25, 24, 19, 19 95 20, 23, 22, 26, 25, 27, 28, 8,7,0 0, 7,6,30,29, 31, 32, 34, 20 100 42, 43, 45, 56, 54, 55, 46, 48, 47, 40, 36, 6,7,0 0,1,11,14,17,18,15,10,9, 17 85 8,7,0 15 75 0, 1, 11,14, 11, 1,0 12 60 0, 7, 6, 5, 4, 1,0 0, 1, 4, 37, 38, 39, 49, 48, 17 85 51, 48, 47, 40, 36, 6, 7,0 20 100 0, 1, 4, 37, 4, 1,0 Table 8 Comparison of VRP-PF and VRP-SP Instance VRP-PF VRP-SP Hospital23 20 23 Hospital29 44 50 Hospital39 59 69 Hospital58 64 79 Hospital23 5742 5532 Hospital29 11380 9680 Hospital39 15188 12352 Hospital58 16322 15243 Hospital23 5 7 Hospital29 0 2 Hospital39 9 21 Hospital58 11 16 Times of passing through traffic lights 4 2 1 0 0 4 0 D -3 -6 -10 -15 210 1700 2836 1079 -2 -2 -12 -5 The results illustrate that 3 unmanned vehicles are required for delivery in Example Hospital23, with an average load factor of 85 %. 6 unmanned vehicles are required for delivery in Example Hospital29, with an average load factor of 96 %. 5 unmanned vehicles are required for delivery in Example Hospital39, with an average load factor of 90 % and 7 unmanned vehicles are required for delivery in Example Hospital58, with an average load factor of 86 %. As Hospital23, Hospital39 and Hospital58 contains many traffic lights in the road networks, it is difficult to avoid going through the traffic lights during path selection. In the result of Example Hospital39, the Advances in Production Engineering & Management 17(4) 2022 435 Wang, Lu, Song, Feng, Shen times of passing through traffic lights is obviously reduced. Table 8 shows the results of considering path flexibility compared with considering the shortest path between two points, where VRPPF is the results considering path flexibility using the algorithm proposed in this paper, VRP-SP is the results without considering path flexibility using Dijkstra algorithm to find the shortest path between two points. Meanwhile, D is the optimization difference, where the negative value means our algorithm got better results than Dijkstra algorithm. From the results, it can be seen that considering path flexibility can reduce the times of passing through traffic lights and improve the delivery efficiency at the expense of increasing the total path length. For the sake of presentation, the reduction in total distance is divided by a thousand to uniform the order of magnitude with other indicators in Fig. 11. It can be seen that in Example Hospital58, total time decreases 15 minutes compared with Dijkstra algorithm while total time only decreases 3 minutes in Example Hospital23. The times of passing through traffic lights reduces 5 and 12 times in Example Hospital58 and Hospital39 respectively while this indicator only reduce 2 times in Hospital29 and Hospital23. The optimization is more obvious in the case of complex road network with more traffic lights. 5. Conclusion Fig. 11 Comparison of numerical examples The normalization of epidemics has prompted the development of contactless distribution. In this paper, the path flexibility between demand points is considered when dealing with vehicle routing problem for unmanned vehicles. In the case where there are multiple feasible paths between two demand points, the number of traffic lights in the road network is considered from the perspective of driving safety of unmanned vehicles. We build the mathematic model of path flexibility vehicle routing problem with the objective to minimize the distribution time. The MCTS algorithm is used to select the feasible paths between two nodes, and the results are fed back to the genetic algorithm for further optimization to finally determine the complete driving scheme. Finally, we adopt actual road networks in Beijing as examples, obtain solutions under different sizes of road networks, and the results show that the algorithm can select better paths with less driving time for different sizes of instances, and can maintain a high vehicle full load rate. Compared with routing problem that does not consider path flexibility, the results show that considering path flexibility can not only reduce the delivery time but also reduce the times of passing through traffic lights for unmanned vehicles. For more complex road conditions, the better results the algorithm can get. The algorithm considering path flexibility can not only be used for the routing planning of unmanned vehicles in the distribution of emergency supplies, but also for the path planning of AGV picking and distribution in the warehouse. In the process of vehicle navigation, the algorithm based on Monte Carlo tree search can also flexibly take into account the driver's experience and other factors, and get better results in the congested road sections. Hence the algorithm proposed in this paper can also enrich the navigation algorithms. However, the method requires complete road network information in the process of preliminary data preparation, including node 436 Advances in Production Engineering & Management 17(4) 2022 Monte Carlo Tree Search improved Genetic Algorithm for unmanned vehicle routing problem with path flexibility coordinates, connectivity between nodes as well as distances and driving speed of segmented roads, which is the weakness of the algorithm. In addition, for unmanned vehicles, real-time road condition can also be considered to be passed into the algorithm to improve distribution efficiency while improving the ability of unmanned vehicles to cope with complex road conditions and driving safety. Acknowledgement We thank the Editor and anonymous referees for their many helpful comments on an earlier version of our paper. This work was supported in part by the National Natural Science Foundation of China under grant numbers 72171016; and the Beijing Logistics Informatics Research Base. 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Vol. 40, No. 8, 2389-2395, doi: 10.16208/j.issn1000-7024.2019.08.048. 438 Advances in Production Engineering & Management 17(4) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 4 | December 2022 | pp 439–454 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.4.447 Original scientific paper End-of-line delivery vehicle routing optimization based on large-scale neighbourhood search algorithms considering customer-consumer delivery location preferences Niu, X.Y.a, Liu, S.F.a,*, Huang, Q.L.a aSchool of Economics and Management, Beijing Jiaotong University, Beijing, P.R. China ABSTRACT ARTICLE INFO Logistics is an important guarantee for economic and social development. Among the various aspects of logistics, the urban logistics end distribution link, which involves the direct connection between distribution personnel and customers, has a direct impact on customers' sense of experience and satisfaction with logistics services. At present, there are unscientific and unreasonable selection methods for logistics end distribution paths, often based on the subjective experience of distribution personnel, which often results in a mismatch between distribution paths and distribution needs, affecting market demand while further increasing the distribution costs of enterprises. Therefore, based on the characteristics of customer-consumers, this paper considers that consumers can select multiple receiving addresses, and each address has a corresponding time window limit. This paper finds that it needs to spend a lot of costs for the enterprise to improve the service level of distribution, and the enterprise can save the cost from time window, as well as obtain the better distribution time by using alternative addresses through the verification and analysis of an example. Based on the above analysis, this paper proposes the urban logistics terminal distribution path optimization path based on large-scale neighbourhood search algorithm, which can promote the further matching between logistics distribution enterprises and customer needs, so as to improve the probability of consumers receiving goods in time as well as reduce the cost of enterprises. Keywords: Distribution; Vehicle routing; Optimization; Path optimization; End-of-line; Large-scale neighbourhood search algorithm *Corresponding author: (Liu, S.F.) shfliu@bjtu.edu.cn Article history: Received 29 January 2022 Revised 23 August 2022 Accepted 3 September 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction With the development of e-commerce and the residents' travel behaviour always change, consumers often encounter the problem of receiving express delivery effectively at the end of the delivery. For customers, each day's life trajectory is distributed in different areas, there are living areas, work areas, entertainment areas, etc. Each area is often distributed in different places, and the life trajectory and time have a close relationship. For office workers, during the working day, the 9 to 5 hours are at the company, while the time spent at home is usually in the evening. The mismatch between courier services and customers' usage needs and living habits can result in lower service satisfaction. If the delivery address is filled in as the place of residence, there may be a situation where the customer is at work and signs for the delivery in person, which may end up being collected by the doorman or placed at an inconvenient pick-up point, easily resulting in lost items. If the delivery address is the workplace, there may be a meeting or business trip where the courier cannot be signed for in person. This puts the flexibility of the "last 439 Niu, Liu, Huang mile" delivery location to the test. The current courier delivery model can only choose one address for a customer's delivery, which can easily cause a mismatch between the delivery location and the customer's location of activity, which can also cause the consumer to not receive the goods in a timely manner, and the courier company's delivery failure will also increase the cost of delivery. The changing nature of consumers' activity locations over time has led to new consumer expectations for services with diverse delivery locations. If consumers can provide multiple delivery locations in a single delivery service, the delivery company can flexibly deliver according to the consumer's delivery location, which not only increases the probability of timely receipt of goods by the consumer, but also avoids the cost of secondary delivery. This paper considers the vehicle path problem with alternative addresses, which is an extension of the vehicle path problem with time windows. In this case, each customer may provide more than one delivery address in a delivery, each delivery address has priority, and each delivery address has its own time window. A large-scale neighbourhood search algorithm is also designed to solve the problem. The analysis of consumers who do not follow the first address for delivery reveals the following characteristics of these consumers: the time window does not match other consumers in that neighbourhood of the path; the preferred address is far from the delivery area of the path, while the alternative address is closer to the delivery area; and consumers who choose the alternative address tend to be at the beginning or the end of the path. The relationship between a company's distribution costs and service level was also analysed and it was found that the service level required the highest costs when the service level was in the medium to high range. 2. Literature review The vehicle path problem was originally proposed by Dantzig and Ramser [1] equal to 1959 and applied to logistics and distribution activities. The vehicle path problem refers to the method of seeking the goods from the distribution centre to the customer under the constraints of multiple factors, such as the number of goods, the number of distribution vehicles, the address of the distribution centre and the address of the passenger and cargo receipt, etc. Through analysis and planning of reasonable distribution routes, the whole distribution process can achieve the least distribution time, the shortest distance and the lowest distribution cost. With the continuous expansion and deepening of theories in the field of logistics, the optimization of vehicle paths for end-of-line distribution has gradually become a key and hot issue of concern in the logistics industry in recent years, causing scholars to explore and research continuously. The article summarizes and analyses the vehicle path problem of end-delivery from three perspectives: path optimization considering self-pickup service, path optimization considering consumer preference, and path optimization considering differentiated service. 2.1 Vehicle route optimisation considering self-pick-up services Self-pick-up service is an important part of terminal distribution, and with the diversification of consumer demand for self-pick-up, it has become increasingly important to improve the level of service, so it is imperative to continuously optimise the vehicle path of self-pick-up service. In the process of optimising the delivery route, the main considerations are the radiation range of the pick-up site, the service capacity of the site, the layout of the site, consumer satisfaction, the operating cost of the site and the price of the pick-up service. In recent years, scholars at home and abroad have carried out diverse and extensive in-depth studies on the optimization of self-pickup services. Current and Schilling [2] pointed out that the pickup site must be within the service area of the delivery vehicle, and used the travel merchant problem to analyse and interpret the self-pickup behaviour of consumers. Li and Mao [3, 4] pointed out that no matter what form of self-pickup points such as Jingdong self-pickup cabinets, Feng Chao express cabinets, CaiBird post stations, etc., they all face the problem of optimizing the path for reasonable self-pickup services, and then the authors used indicators such as construction cost, customer satisfaction, and service capability to evaluate the service capability of 440 Advances in Production Engineering & Management 17(4) 2022 End-of-line delivery vehicle routing optimization based on large-scale neighbourhood search algorithms considering … self-pickup points, and also established a combined integer planning model with the lowest logistics service cost as the goal. Zhou et al. [5, 6] proposed the current path optimization problem faced by self-pickup services, i.e., consumers are widely and densely distributed, and it is impossible to accurately calculate the distribution path of goods, and took the customer points within the streets of Yudong in Banan District of Chongqing as the research object, argued the relationship between the location of self-pickup points and path optimization, and built a path optimization model for self-pickup distribution. Koç et al. [7] and Hua et al. [8] pointed out that the location of logistics distribution centres is an important task in the overall network optimisation of logistics systems, and a scientific centre location can assist in improving the relevant effects of path optimisation. To solve the location problem of distribution centres, Hua et al. [8] proposed an adaptive particle swarm optimisation algorithm with non-linear inertia weights and timevarying acceleration coefficients. Sankaran et al. [9] sorted out the problem of siting two groups of high-capacity facility locations and proposed a method for optimizing the siting of self-pickup sites by aggregating consumer pickup point information. Wang et al. [10] pointed out that there is a certain correlation between the price of self-service and brand image, and constructed a correlation function between the reachable distance of self-pickup path, the price of self-pickup service and the brand of self-pickup service. Guo et al. [11] conducted a study on vehicle route optimization and service strategies based on consumers' pickup radius, and pointed out that self-pickup considering consumers' pickup radius can effectively reduce the number of delivery vehicles and personnel, which can achieve the purpose of reducing the operation cost of enddistribution. 2.2 Vehicle path optimisation considering consumer preferences and behavior In end-of-line delivery, consumers will consider various factors such as delivery method, delivery time and delivery price, and their preferences and behaviour towards different choices will also have an impact on vehicle route optimisation. In terms of delivery methods, 2.1 summarises the vehicle path optimisation considering self-pick-up services; meanwhile, domestic and international scholars have conducted in-depth and extensive research on vehicle path optimisation for home delivery, which is summarised in this summary. In terms of path optimisation for enddelivery home delivery services, Khouadjia [12] et al., and Okulewicz and Mańdziuk [13] argue that in the end-delivery process, once a delivery person has accepted the instruction to deliver to a consumer, he or she cannot change the new delivery target until the current delivery task is completed before the next task can be carried out; based on this premise, Okulewicz and Mańdziuk [13] used a meta-heuristic to optimise the paths associated with the receipt of delivery instructions to vehicle assignment. Abdallah et al. [14] considered the end-of-pipe delivery problem as dynamic vehicle path optimisation and suggested that, for more efficient delivery of continuous goods, delivery personnel should go to a nearby planning delivery node at the completion of the delivery task and wait at the node for new delivery instructions and vehicle scheduling solutions. Keçeci et al. [15] pointed out the path optimisation for home delivery as variational path optimisation with pickup and delivery functions, and proposed a hybrid metaheuristic based on simulated annealing algorithm and local search algorithm of SA-LS with minimum delivery cost as the objective. Silvestrin and Ritt [16] analysed the scenario of multicarriage vehicles, where several different qualities or types of products that must be kept or handled separately and use a forbidden search algorithm to solve the problem. Soto et al. [17] solve the multi-warehouse open vehicle routing problem, which is a generalised case of capacity vehicle path optimisation; in this scenario, vehicles perform delivery services from different warehouses, visit consumers and complete the delivery of goods, without the goods deliverer then having to return to the end of the route at the warehouse. Consumers' preferences for delivery time and delivery price also affect the path optimisation of delivery vehicles. Most of the current research on delivery time focuses on time window theory, while most of the research on delivery price focuses on delivery pricing theory. In terms of end distribution time, Taş et al. [18] studied the vehicle path problem with time window and random travel time, combined the relationship between transportation cost and service cost, i.e., the total vehicle travel distance and cargo arrival time, and proposed a path optimisation model Advances in Production Engineering & Management 17(4) 2022 441 Niu, Liu, Huang based on this. Zhu et al. [19] considered the constrained situation of time window and built a path optimisation model for multi-vehicle logistics distribution under different environments with the objective of lowest total delivery cost and shortest delivery time. Gutierrez et al. [20] set the vehicle travel time and service time as random variables and solved the vehicle path optimisation problem under the premise that each consumer is served. Guedes and Borenstein [21] borrowed the processing method of space-time grid for distribution path optimisation and analysed the multi-warehouse vehicle type scheduling problem. Veenstra et al. [22] studied the problem of goods distribution and delivery based on the time window. Kim et al. [23] combined the uncertainties of delivery time, delivery demand, and real-time traffic conditions to build a logistics and delivery model for path optimisation. In terms of end-delivery prices, Tounsi et al. [24] develop a new heuristic algorithm for the delivery service pricing problem, where the delivery service and path optimization are carried out by the delivery side according to the price of the service chosen by the consumer. Hayel et al. [25] point out that consumer behaviour, especially the choice of a reasonable price, affects the path optimisation of end-delivery, and the authors later use a game theoretical. The topic was studied from a game theoretical perspective; Yang et al. [26] considered the different delivery costs of consumers for different delivery time slots, thus building a route optimization model with real-time pricing. End-delivery is the last link in the transportation of goods, and the consumer as the participant in the final link can have a profound impact on route optimisation, regardless of the behaviour, in addition to the factors summarised above. For example, Ren et al. [27] argue that consumer preference behaviour can have an impact on end delivery and that customers may hold different attitudes towards different types of goods, while the authors later build a 4PL path optimisation model to conduct relevant research, proving the scientific validity of their view. Therefore, paying attention to consumer preferences and their behaviours has a positive significance and important role in the route optimisation of end-delivery, and can effectively improve the service efficiency of end-delivery. 2.3 Vehicle route optimization considering differentiated service provision In the process of end-delivery, in addition to the service demand for ordinary delivery, increasingly diverse and differentiated services have emerged [28, 29], with the existence of cold chain logistics end-delivery, takeaway delivery, same-city delivery and end-delivery services in emergency scenarios (such as the delivery of emergency materials after a disaster). In addition, some end-delivery services are subject to certain additional top-up fees to ensure efficient delivery of goods. The delivery target of cold chain logistics is usually frozen food, so the delivery service has to be completed within the period of food refrigeration to avoid food spoilage. As cold chain logistics plays an indispensable role in people's lives, research on cold chain logistics has been a hot topic for experts and scholars at home and abroad. Among them, in the end distribution of cold chain logistics, Deng et al. [30] and others believe that the end distribution process of cold chain logistics needs to increase the consideration of factors such as the degree of goods loss and goods refrigeration market, and through the introduction of the concepts of penalty cost, goods loss cost, refrigeration cost, out-of-stock cost, transportation cost and fixed cost, the path optimization of the end distribution of cold chain logistics is carried out. Zhang et al. [31] and others constructed a path optimisation model for cold chain logistics vehicles using a soft time window model and solved the optimal solution using an improved genetic algorithm. Ren et al. [32] studied a distribution scenario with multiple distribution centres sharing resources under the premise of ensuring on-time food delivery and established a vehicle path optimisation model for delivery at the lowest delivery cost of fresh food. Food delivery service is a special kind of end delivery driving, the start and end point of food delivery are in the same city, and the delivery distance is significantly shortened compared to other methods. In addition, as consumers have the actual demand for fast meals, there are higher requirements for their takeaway delivery speed. Wang et al. [33] argued that merchants would have certain time requirements for delivery services to improve consumers' satisfaction with takeaway delivery, while the authors later used the relevant random travel time based on 442 Advances in Production Engineering & Management 17(4) 2022 End-of-line delivery vehicle routing optimization based on large-scale neighbourhood search algorithms considering … the purpose of improving consumer satisfaction Chen and Shi [34] considered factors such as consumer time satisfaction and optimised the traditional pick-up and delivery vehicle path model. Liu [35] introduced the k-means concept to build a dynamic demand-based path optimisation model for the complexity of the takeaway model. Similar to takeaway delivery, same-city delivery also belongs to same-city proximity delivery, and now also belongs to the category of end-of-line delivery, and the route optimization approach is also very similar to that of takeaway delivery. Tounsi et al. [24] developed a new heuristic algorithm for the delivery service pricing problem, in which the delivery service is developed by the delivery provider according to the price level of the service chosen by the consumer Hayel et al. [25] show that consumers' behaviour, especially their choice of reasonable price, affects the route optimisation of end-delivery, and then use a game-theoretic perspective to study this topic. Yang et al. [26] build a route optimisation model with real-time pricing by considering the different delivery costs of consumers at different delivery timeslots. Scholars have widely applied large-scale neighbourhood search algorithm in the research of terminal distribution vehicle routing to solve the vehicle routing problem, such as the routing problem with delivery options, the terminal distribution routing problem using UAVs, the routing optimization of multiple warehouses and vehicles, and the vehicle routing optimization problem with time windows [7, 36-38]. The studies summarised above are all about the distribution of goods in safe and stable scenarios, but there are also demands for the distribution of goods in various unexpected scenarios caused by accidents, and emergency scenarios, such as the emergency distribution of materials after a disaster, play an even more vital and irreplaceable role. The scenarios analysed above do not cover all the differentiated logistics distribution [39]. Different distribution modes of different nature are applicable to different consumer needs or distribution occasions, all of which play a unique role in people's production life and are indispensable in the logistics service industry. 3. Model building and algorithm design 3.1 Model building A distribution station in the city is responsible for supply, and goods are transported from the distribution station to each consumer point by multiple vehicles within the time required by the consumer, and then the delivery vehicles return to the distribution station. Each customerconsumer may provide more than one delivery address in a single delivery, and each delivery address has priority, and each delivery address has its own time window. The vehicle can select any one of these locations for delivery. As shown in Fig. 1, the blue triangle in the diagram represents the distribution center from which the vehicle departs from the delivery station and delivers to each consumer point. The same-coloured dots represent the delivery locations set by the consumer. The vehicle simply serves one of these and eventually returns to the distribution station. The precise algorithm is still more suitable for small-scale distribution scenarios. Although the algorithm can calculate the optimal route of vehicles, it considers fewer constraints and has a slow speed in large-scale and complex scenarios Genetic algorithm (GA) is an algorithm for searching the optimal solution, which is proposed by simulating the genetic principle and evolutionary process of biology. It has certain advantages in solving complex combinatorial problems and has been widely studied and applied by many industries. Therefore, the application scope of the precise algorithm in the end distribution route optimization is less than that of the meta heuristic algorithm and the adaptive large-scale neighbourhood search algorithm. The neighbourhood search algorithm searches for the "neighbourhood" solution of the current solution through countless iterations and obtains a better solution through comparative analysis. The larger the neighbourhood, the better the solution. At present, the application of neighbourhood search algorithm has been extended to the field of vehicle routing optimization in terminal distribution. Each customer i has a demand 𝑞𝑞𝑖𝑖 and each customer has a preferred delivery location. As a result, customers have different satisfaction levels for each address and the overall delivery of the vehicle needs to meet the overall satisfaction level constraint. Advances in Production Engineering & Management 17(4) 2022 443 Niu, Liu, Huang The earliest and latest time windows [𝑒𝑒𝑖𝑖 𝑎𝑎 , 𝑙𝑙𝑖𝑖 𝑏𝑏 ] are different for different delivery locations 𝑖𝑖 𝑎𝑎 for each customer i. The vehicle may arrive earlier than the earliest time window of the customer, but needs to wait until the earliest time window to be served, being subject to a waiting cost, and is subject to a delayed service penalty if it arrives later than the latest time window. The vehicle arrives at customer point 𝑖𝑖 𝑎𝑎 with a service time of 𝑠𝑠𝑖𝑖 𝑎𝑎 and leaves immediately after servicing that point. There is no limit to the number of vehicles 𝑘𝑘 available for use at the depot, but each vehicle incurs an operating cost 𝜃𝜃𝑘𝑘 . The vehicles are homogeneous. The model notation is illustrated as follows: 0 𝐶𝐶 𝑁𝑁 𝐾𝐾 𝐿𝐿𝑖𝑖 𝑑𝑑𝑖𝑖𝑎𝑎 𝑗𝑗𝑏𝑏 𝑐𝑐𝑖𝑖𝑎𝑎 𝑗𝑗𝑏𝑏 𝑞𝑞𝑗𝑗 𝑒𝑒𝑖𝑖𝑎𝑎 , 𝑙𝑙𝑖𝑖𝑎𝑎 𝜀𝜀𝑗𝑗𝑏𝑏 𝑟𝑟𝑖𝑖𝑎𝑎 𝑠𝑠𝑖𝑖𝑎𝑎 𝑡𝑡𝑗𝑗𝑏𝑏 P 𝜃𝜃𝑘𝑘 𝑄𝑄𝑘𝑘 𝐷𝐷𝑘𝑘 𝑣𝑣𝑘𝑘 S M 𝑢𝑢𝑖𝑖𝑙𝑙 𝑥𝑥𝑖𝑖𝑘𝑘𝑎𝑎 𝑗𝑗𝑏𝑏 𝑦𝑦𝑗𝑗𝑘𝑘𝑏𝑏 𝑧𝑧𝑘𝑘 444 Fig. 1 Distribution vehicle route planning diagram Warehouse Collection of customers, 𝐶𝐶 = {1,2, … , 𝑚𝑚} Collection of customers and warehouses, 𝑁𝑁 = {0,1,2, … , 𝑚𝑚} Vehicle collection, 𝐾𝐾 = {1,2, … , 𝑘𝑘} Collection of optional distribution locations for 𝐿𝐿𝑖𝑖 customer 𝑖𝑖 Arc the distance between (𝑖𝑖 𝑎𝑎 , 𝑗𝑗𝑏𝑏 ), i.e. the distance from ath optional distribution location of customer 𝑖𝑖 to b-th optional distribution location of customer 𝑗𝑗 Arc running cost between (𝑖𝑖 𝑎𝑎 , 𝑗𝑗𝑏𝑏 ) Customer 𝑗𝑗 demand Time window for customer 𝑖𝑖's a-th optional delivery location Customer satisfaction when vehicle delivers customer j's b-th delivery location The time to start serving customer 𝑖𝑖's a-th optional delivery location Service time of customer 𝑖𝑖's a-th optional delivery location Minimum waiting time or minimum delayed service time for customer 𝑖𝑖's a-th optional delivery location Unit waiting costs or delayed service penalty costs for P vehicles Operating costs of 𝜃𝜃𝑘𝑘 vehicles Capacity limits for 𝜃𝜃𝑘𝑘 vehicles Distance limit for vehicles Average speed of the vehicle Overall customer satisfaction required by warehouse S A sufficiently large positive number Auxiliary decision variables Is 1 if vehicle k passes through arc(𝑖𝑖 𝑎𝑎 , 𝑗𝑗𝑏𝑏 ); otherwise it is 0 Is 1 if customer 𝑗𝑗's bth optional delivery location is served by vehicle k; 0 otherwise 𝑧𝑧𝑘𝑘 Vehicle 𝑘𝑘 is used or not Advances in Production Engineering & Management 17(4) 2022 End-of-line delivery vehicle routing optimization based on large-scale neighbourhood search algorithms considering … Based on the above scenario description and assumptions, the model for this path planning problem is shown below. Objective function: 𝑚𝑚𝑚𝑚𝑚𝑚 𝑐𝑐 � � � � � 𝑥𝑥𝑖𝑖𝑘𝑘𝑎𝑎 𝑗𝑗𝑏𝑏 𝑑𝑑𝑖𝑖𝑎𝑎 𝑗𝑗𝑏𝑏 + � 𝑧𝑧𝑘𝑘 𝜃𝜃𝑘𝑘 + � � 𝑃𝑃𝑡𝑡𝑗𝑗𝑏𝑏 (1) � � 𝑥𝑥𝑖𝑖𝑘𝑘𝑎𝑎 𝑗𝑗𝑏𝑏 = 𝑦𝑦𝑗𝑗𝑘𝑘𝑏𝑏 , ∀𝑘𝑘 ∈ 𝐾𝐾, 𝑗𝑗 ∈ 𝑁𝑁𝑐𝑐 , 𝑏𝑏 ∈ 𝐿𝐿𝑗𝑗 (2) 𝑘𝑘∈𝐾𝐾 𝑖𝑖∈𝑁𝑁 𝑎𝑎∈𝐿𝐿𝑖𝑖 𝑗𝑗∈𝑁𝑁 𝑏𝑏∈𝐿𝐿𝑗𝑗 Binding conditions： 𝑖𝑖∈𝑁𝑁 𝑎𝑎∈𝐿𝐿𝑖𝑖 𝑘𝑘∈𝐾𝐾 � � 𝑦𝑦𝑗𝑗𝑘𝑘𝑏𝑏 = 1, ∀𝑗𝑗 ∈ 𝐶𝐶 𝑘𝑘∈𝐾𝐾 𝑏𝑏∈𝐿𝐿𝑗𝑗 � � � � 𝑥𝑥𝑖𝑖𝑘𝑘𝑎𝑎 𝑗𝑗𝑏𝑏 = 1, 𝑘𝑘∈𝐾𝐾 𝑗𝑗∈𝑁𝑁 𝑎𝑎∈𝐿𝐿𝑖𝑖 𝑏𝑏∈𝐿𝐿𝑗𝑗 𝑢𝑢𝑖𝑖𝑎𝑎 − 𝑢𝑢𝑗𝑗𝑏𝑏 + 𝑗𝑗∈𝑁𝑁 𝑏𝑏∈𝐿𝐿𝑗𝑗 ∀𝑖𝑖 ∈ 𝐶𝐶 𝑘𝑘 𝑘𝑘 � � 𝑥𝑥0𝑖𝑖 ∀𝑘𝑘 ∈ 𝐾𝐾 𝑎𝑎 = � � 𝑥𝑥𝑖𝑖 𝑎𝑎 0 , 𝑖𝑖∈𝐶𝐶 𝑎𝑎∈𝐿𝐿𝑖𝑖 |𝑁𝑁|𝑥𝑥𝑖𝑖𝑘𝑘𝑎𝑎 𝑗𝑗𝑏𝑏 ≤ |𝑁𝑁| − 𝑑𝑑𝑖𝑖𝑎𝑎 𝑗𝑗𝑏𝑏 𝑖𝑖∈𝐶𝐶 𝑎𝑎∈𝐿𝐿𝑖𝑖 1, ∀𝑖𝑖, 𝑗𝑗 ∈ 𝐶𝐶, 𝑖𝑖 ≠ 𝑗𝑗, 𝑎𝑎 ∈ 𝐿𝐿𝑖𝑖 , 𝑏𝑏 ∈ 𝐿𝐿𝑗𝑗 , 𝑘𝑘 ∈ 𝐾𝐾 ≤ 𝑀𝑀 �1 − 𝑥𝑥𝑖𝑖𝑘𝑘𝑎𝑎 𝑗𝑗𝑏𝑏 � + 𝑟𝑟𝑗𝑗𝑏𝑏 ∀ 𝑖𝑖, 𝑗𝑗 ∈ 𝑁𝑁, 𝑘𝑘 ∈ 𝐾𝐾 𝑣𝑣 𝑦𝑦𝑖𝑖𝑘𝑘𝑎𝑎 𝑒𝑒𝑖𝑖𝑎𝑎 ≤ 𝑟𝑟𝑖𝑖𝑎𝑎 ∀𝑖𝑖 ∈ 𝐶𝐶, 𝑘𝑘 ∈ 𝐾𝐾, 𝑎𝑎 ∈ 𝐿𝐿𝑖𝑖 𝑟𝑟𝑖𝑖𝑎𝑎 + 𝑠𝑠𝑖𝑖𝑎𝑎 + 𝑡𝑡𝑗𝑗𝑏𝑏 ≥ 𝑚𝑚𝑚𝑚𝑚𝑚 �𝑦𝑦𝑗𝑗𝑘𝑘𝑏𝑏 𝑒𝑒𝑗𝑗𝑏𝑏 − �𝑟𝑟𝑖𝑖𝑎𝑎 + 𝑠𝑠𝑖𝑖𝑎𝑎 + 𝑑𝑑𝑖𝑖𝑎𝑎 𝑗𝑗𝑏𝑏 𝑣𝑣 � , 0, 𝑦𝑦𝑗𝑗𝑘𝑘𝑏𝑏 �𝑟𝑟𝑗𝑗𝑏𝑏 + 𝑠𝑠𝑗𝑗𝑏𝑏 � − 𝑙𝑙𝑗𝑗𝑏𝑏 � , ∀𝑖𝑖, 𝑗𝑗 ∈ 𝐶𝐶, 𝑖𝑖 ≠ 𝑗𝑗, 𝑎𝑎 ∈ 𝐿𝐿𝑖𝑖 , 𝑏𝑏 ∈ 𝐿𝐿𝑗𝑗 , 𝑘𝑘 ∈ 𝐾𝐾 � � 𝑦𝑦𝑗𝑗𝑘𝑘𝑏𝑏 𝑞𝑞𝑗𝑗 ≤ 𝑄𝑄𝑘𝑘 , 𝑘𝑘∈𝐾𝐾 𝑏𝑏∈𝐿𝐿𝑗𝑗 ∀ 𝑘𝑘 ∈ 𝐾𝐾 � � � � 𝑥𝑥𝑖𝑖𝑘𝑘𝑎𝑎 𝑗𝑗𝑏𝑏 𝑑𝑑𝑖𝑖𝑎𝑎 𝑗𝑗𝑏𝑏 ≤ 𝐷𝐷𝑘𝑘 , ∀ 𝑘𝑘 ∈ 𝐾𝐾 𝑖𝑖∈𝑁𝑁 𝑎𝑎∈𝐿𝐿𝑖𝑖 𝑗𝑗∈𝑁𝑁 𝑏𝑏∈𝐿𝐿𝑗𝑗 � � � 𝑦𝑦𝑗𝑗𝑘𝑘𝑏𝑏 𝜀𝜀𝑗𝑗𝑏𝑏 ≥ 𝑆𝑆(|𝑁𝑁| − 1) 𝑘𝑘∈𝐾𝐾 𝑗𝑗∈𝐶𝐶 𝑏𝑏∈𝐿𝐿𝑗𝑗 𝑥𝑥𝑖𝑖𝑘𝑘𝑎𝑎 𝑗𝑗𝑏𝑏 𝑧𝑧𝑘𝑘 ≥ 𝑦𝑦𝑗𝑗𝑘𝑘𝑏𝑏 , ∀𝑖𝑖 ∈ 𝐶𝐶, 𝑏𝑏 ∈ 𝐿𝐿𝑗𝑗 , 𝑘𝑘 ∈ 𝐾𝐾 ∈ {0,1}, 𝑦𝑦𝑗𝑗𝑘𝑘𝑏𝑏 ∀𝑖𝑖, 𝑗𝑗 ∈ 𝑁𝑁, 𝑎𝑎 ∈ 𝐿𝐿𝑖𝑖 , 𝑏𝑏 ∈ 𝐿𝐿𝑗𝑗 , 𝑘𝑘 ∈ 𝐾𝐾 ∈ {0,1}, ∀𝑗𝑗 ∈ 𝐶𝐶, 𝑏𝑏 ∈ 𝐿𝐿𝑗𝑗 , 𝑘𝑘 ∈ 𝐾𝐾 𝑢𝑢𝑖𝑖𝑎𝑎 , 𝑢𝑢𝑗𝑗𝑏𝑏 > 0, ∀𝑖𝑖, 𝑗𝑗 ∈ 𝑁𝑁, 𝑎𝑎 ∈ 𝐿𝐿𝑖𝑖 , 𝑏𝑏 ∈ 𝐿𝐿𝑗𝑗 (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) Eq. (1) is the objective function with two components: distribution cost and vehicle operating cost. Constraints Eqs. 2 to 4 indicate that all of each customer can only be delivered by one vehicle. Constraint Eq. 5 indicates that the vehicle departs from and returns to the warehouse. Constraint Eq. 6 is a Miller-Tucker-Zemlin constraint that prevents the creation of subloops so that each vehicle's delivery route forms a loop, where 𝑢𝑢𝑖𝑖𝑙𝑙 , 𝑢𝑢𝑗𝑗𝑒𝑒 are auxiliary variables. Constraint Eq. 7 represents the relationship between the starting service moments of two adjacent customer points visited by the vehicle. Constraint Eq. 8 represents the service time of the delivery vehicle cannot be earlier than the time requested by the customer. Constraint Eq. 9 represents the minimum waiting time or delayed service time for each customer point. Constraint Eq. 10 represents the vehicle capacity constraint, each vehicle cannot exceed its maximum load capacity. Advances in Production Engineering & Management 17(4) 2022 445 Niu, Liu, Huang Constraint Eq. 11 represents the vehicle travel distance constraint, the constraint Eq. 11 represents the vehicle distance constraint that each vehicle cannot travel more than its maximum distance. Constraint Eq. 12 represents the overall satisfaction rate of the delivery to be higher than the required satisfaction rate. Constraint Eq. 13 determines whether the vehicle is used or not. Constraints Eqs. 14 to 16 are the decision variables definition fields. 3.2 Algorithm design Initial setting Since the objective function is profit maximisation, we need to start with the objective function. Eq.17 is the corresponding function expression. 𝑇𝑇 = 𝑂𝑂(𝑆𝑆 0 ) × 𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 Neighbourhood structure (17) Since the delivery method of customers who have ticked the value-added service will no longer change, we add new removal and insertion policies to the original removal and insertion policies to improve the feasibility of the path. For ease of description, we will refer to consumers who have ticked the value-added service as value consumers. The basic idea behind these two strategies is that the higher the proportion of value consumers included in a path, the lower the number of solutions generated by adjusting the customer delivery method for that path, and the less favourable it is to generate feasible solutions in the early stages of the algorithm. Therefore, our two strategies operate mainly on such paths to ensure the convergence speed of the algorithm. Path removal strategy Step1: Count the proportion of each path in a solution S that contains consumers of value, and then arrange them in descending order. Step2: Remove the paths until the number of removed is 𝑛𝑛𝑟𝑟 . Distribution location factor insertion strategy The distribution location factor insertion strategy is based on the distribution location to determine whether consumer points are allowed to be inserted. Step1: Calculate the distribution location association of the arc with the consumer point to be inserted. Since the arc (𝑖𝑖, 𝑗𝑗) is assumed to be an arc on the P path, K is the target insertion point and 𝐸𝐸𝑖𝑖 ≤ 𝐸𝐸𝑘𝑘 ≤ 𝐸𝐸𝑗𝑗 . The association between the arc (𝑖𝑖, 𝑗𝑗) and the consumer point K distribution location is calculated as 𝑚𝑚𝑚𝑚𝑚𝑚{ 𝐿𝐿𝑖𝑖 − 𝐸𝐸𝑘𝑘 , 0} 𝐸𝐸𝑖𝑖 ≤ 𝐸𝐸𝑘𝑘 𝜎𝜎𝑖𝑖𝑖𝑖 = �𝑚𝑚𝑚𝑚𝑚𝑚{ 𝐿𝐿𝑖𝑖 , 𝐿𝐿𝑘𝑘 } − 𝐸𝐸𝑖𝑖 𝐸𝐸𝑘𝑘 < 𝐸𝐸𝑖𝑖 ≤ 𝐿𝐿𝑘𝑘 (18) 𝑚𝑚𝑚𝑚𝑚𝑚{ 𝐿𝐿𝑘𝑘 − 𝐸𝐸𝑖𝑖 , 0} 𝐸𝐸𝑖𝑖 > 𝐿𝐿𝑘𝑘 𝜎𝜎𝑘𝑘𝑘𝑘 𝑚𝑚𝑚𝑚𝑚𝑚{ 𝐿𝐿𝑘𝑘 − 𝐸𝐸𝑗𝑗 , 0} 𝐸𝐸𝑘𝑘 ≤ 𝐸𝐸𝑗𝑗 𝑚𝑚𝑚𝑚𝑚𝑚{ 𝐿𝐿𝑘𝑘 , 𝐿𝐿𝑗𝑗 } − 𝐸𝐸𝑘𝑘 𝐸𝐸𝑗𝑗 < 𝐸𝐸𝑘𝑘 ≤ 𝐿𝐿𝑗𝑗 =� 𝑚𝑚𝑚𝑚𝑚𝑚{ 𝐿𝐿𝑗𝑗 − 𝐸𝐸𝑘𝑘 , 0} 𝐸𝐸𝑘𝑘 > 𝐿𝐿𝑗𝑗 𝜎𝜎𝑖𝑖𝑖𝑖 = 𝜎𝜎𝑖𝑖𝑘𝑘 + 𝜎𝜎𝑘𝑘𝑘𝑘 (19) (20) Step2: Insert the consumer point K into the arc (𝑖𝑖, 𝑗𝑗) with the highest correlation to the distribution location. The delivery location correlation here is different from the previous chapter, mainly because later in the algorithm, due to the presence of value consumers, basic constraints such as vehicle capacity are easy to satisfy, but satisfying the delivery location constraint is more difficult and incurs a larger penalty cost that needs to be specifically addressed for the delivery location. In contrast, the increased cost of considering arcs (𝑖𝑖, 𝑗𝑗) to insert consumer points K does not require much consideration. Therefore, we need to recalculate the correlation. 446 Advances in Production Engineering & Management 17(4) 2022 End-of-line delivery vehicle routing optimization based on large-scale neighbourhood search algorithms considering … 4. Example analysis: Results and discussion 4.1 Calculation example using In this paper, five neighbourhoods near Beixiaoguan Street in Haidian District, Beijing are used as the basis for the calculation of the example analysis. Steel Research Community, Jiaoda Jiayuan, Mingguang Village neighbourhood, Tianzhao Home and Changhewan neighbourhood are selected as the community delivery area, and the number of delivery customers in each neighbourhood is 89, 87, 99, 85 and 75 respectively. To simplify the analysis and to better present the results, the delivery points of consumers in each neighbourhood are simplified to 5 (see Fig. 2). Based on the research of the actual courier company, the distribution centre was selected in this paper at the ground floor of the Yihai Business Hotel, No. 33 College South Road, Haidian District. Fig. 2 Community distribution district selection 4.2 Optimal route and delivery method First path analysis The primary delivery area for Path 1 is in the Mingguang Village neighbourhood. The numbering of those consumers who are not at their preferred delivery address is as follows in Table 1. The time windows for these consumers' preferred addresses are in the afternoon, and if delivery is made to the preferred address, there is a long wait time. To save time window waiting time costs, the delivery person should deliver to these consumers' second or third addresses (Table 2). In addition, this consumer's alternative address is also closer to the Mingguang Village neighbourhood, and delivering these consumers together with the Mingguang Village neighbourhood could reduce costs (see Fig. 3). Serial No. 1 2 3 4 5 6 7 8 Table 1 Table of path results Path [0,200,367,399,293,403,424,427,309,142,246,304,225,349,82,402,385,8,129,44,141,283,429,325,338,71,87,114,120,149,289,131, 324,308,110,166,102,162,206,207,209,247,279,316,331,397,400,421,428,431,328,9,255,124,136,178,321,226,21,83,224,152,30,0] [0,258,274,359,391,194,327,416,299,377,99,395,145,157,244,61,89,37,176,184,195,48,20,201,222,251,317,330,271,323,128,96,4 30,273,352,197,307,411,92,150,305,27,42,74,57,298,75,93,112,155,223,172,272,280,379,387,393,396,10,77,239,84,58,122,0] [0,132,35,50,115,436,337,390,264,350,346,168,270,230,2,426,62,368,404,40,189,343,205,334,383,250,101,358,23,39,290,372,43 2,281,417,98,180,183,243,186,314,144,1,277,109,116,103,164,284,419,153,364,67,49,407,127,4,143,192,126,287,0] [0,265,326,237,345,348,433,41,175,312,319,306,167,181,216,435,214,282,382,68,80,117,208,66,295,365,212,3,170,320,14,229,1 65,146,19,63,130,335,344,418,204,18,218,11,28,160,177,187,231,275,398,107,233,422,356,106,234,81,51,0] [0,73,333,156,260,388,232,256,384,140,125,238,423,235,353,425,378,413,303,286,374,373,242,7,249,31,252,104,147,16,105,78, 43,64,297,69,95,301,190,60,196,203,245,254,217,360,278,336,339,340,351,406,357,434,76,354,161,253,262,0] [0,313,137,219,148,113,261,292,266,25,276,329,53,72,210,386,401,26,90,311,392,310,332,36,47,52,355,97,65,86,94,179,408,322, 376,100,185,34,410,227,381,108,22,6,236,118,220,409,79,135,241,291,13,55,29,294,375,173,0] [0,17,268,347,199,341,369,202,415,88,134,5,56,121,380,389,45,139,318,366,257,123,420,414,302,159,191,394,12,54,151,171,17 4,32,405,363,24,211,163,91,138,296,111,361,248,371,267,38,300,33,133,198,85,269,59,70,188,193,221,240,263,412,362,119,342, 315,0] [0,15,35,132,213,169,50,115,436,259,288,370,154,182,215,285,46,158,228,0] Advances in Production Engineering & Management 17(4) 2022 447 Niu, Liu, Huang Fig. 3 Distribution of consumers for path 1 and the optimal path Table 2 Consumers in path 1 who were not delivered to their preferred address No. 200 367 399 225 Address serial number 2 3 2 2 Fig. 4 Distribution of consumers for path 2 and the optimal path The main delivery areas for Path 2 are in the Mingguang Village neighbourhood and the Tianzhao Home (see Fig. 4). The consumers who are not preferred delivery addresses are numbered 416 and 239, both of which are second addresses. By analysing the characteristics of the consumers, it can be found that the preferred address of consumer 416 is in Mingguang Village Subdistrict, but the time window of the preferred address is after 3pm, while the consumers in Mingguang Village Sub-district all made their deliveries before 1pm, so to deliver consumer 416, they need to drive from Tianzhao Home to Mingguang Village Sub-district and back to Tianzhao Home after 3pm. However, the time window for the second address of consumer 416 is in the morning and is between Mingguangcun Subdistrict and Tianzhao Home, so it is a better choice to deliver according to the second address.239 The time window for the preferred address of con448 Advances in Production Engineering & Management 17(4) 2022 End-of-line delivery vehicle routing optimization based on large-scale neighbourhood search algorithms considering … sumer 239 is in the afternoon, but the preferred address is in Steel Research Community, which is farther away from Tianzhao Home and Mingguangcun Subdistrict, and the second address is closer to Tianzhao Home, and the time window of the second address also better match, so delivery at the second address is more appropriate. The main delivery area for Path 3 is also in the Mingguang Village neighbourhood and Tianzhao Home, but there are also a small number of consumers in the Jiaoda Jiayuan and Steel Research neighbourhoods (see Fig. 5). The consumers who are not the preferred delivery address are numbered 132 and 35, both of which are second addresses. By analysing the characteristics of the consumers, we can find that the preferred address of consumer 132 is in Jiaoda Jiayuan, but the time window of the preferred address is 8:00-12:00, while the consumers in Jiaoda Jiayuan in route 3 all deliver after 8:00 pm, so it is not suitable for delivery with other consumers in Jiaoda Jiayuan. In this case, it is more appropriate to choose the second address of consumer 132 and deliver in the morning.35 The preferred address of consumer 35 is in Changhewan district, but there are no other consumers in Changhewan district in route 3, and the second address of this consumer is closer to Tianzhao Home and Mingguang Village district, so delivery can be made through the second address. Fig. 5 Distribution of consumers for path 3 and the optimal path The main delivery areas for Path 4 are in Jiaoda Jia Yuan and the Steel Research community. The consumers who are not preferred delivery addresses are numbered 265 and 41, both of which are second addresses (see Fig. 6). By analysing the characteristics of the consumers, it can be found that the preferred addresses of both 265 and 41 consumers are in Jiaoda Garden. However, the time window for consumer 265's preferred address was after 1pm, which did not lend itself to delivery in the morning with other consumers in Jiaoda Jiaoyuan, so delivery to the second address was chosen. In fact, Consumer 265's second address was closer to the Tianzhao Home and Mingguang Village neighbourhoods, so why was it not delivered in a path where the main delivery area was these two neighbourhoods? The reason is that although the distance is close, the time window for 265's second address is after 10am, whereas the initial delivery time in the other paths is often before 10am, so the time windows do not match. Consumer 41, although both the time window and address match those in the Long River Bay subdivision in path 4, is preferable to its second address for delivery due to the high number of consumers in the Long River Bay subdivision and the fact that they are mainly concentrated in the afternoon and do not have the spare time to make additional deliveries to 41. Advances in Production Engineering & Management 17(4) 2022 449 Niu, Liu, Huang Fig. 6 Distribution of consumers for path 4 and the optimal path Fig. 7 Distribution of consumers for path 5 and the optimal path The primary delivery area for Path 5 is in Jiaoda Jia Yuan and the Steel Research community. The consumers who are not preferred delivery addresses are numbered 333 and 353, both of which are second addresses (see Fig. 7). 333 and 353 consumers' preferred addresses are both in the main delivery area of Path 5, but why are they not delivered at their preferred addresses? Analysis of the consumers' characteristics reveals that the time window for consumer 333's preferred address is after 12pm, while other consumers in the Steel Research community where consumer 333 is located concentrate their deliveries in the morning, so they can be delivered at the second address in the morning through the time window. The main reason for Consumer 353 to deliver with a second address is also due to the more suitable time window for 353 and the proximity of the second addresses of 333 and 353 to the Steel Research Community and Jiaoda Jiayuan. The main delivery areas for path 6 are in Jiaoda Jiayuan, the Steel Research community and the Changhewan neighbourhood (see Fig. 8). The number of the consumer who is not the preferred delivery address is 137, the second address. 137 The preferred address is Jiaoda Jiayuan and the time window is after 4pm, but the time window for all other consumers in Path 6 is before 4pm, so in order not to have to make additional deliveries separately, the closer second address can be chosen for delivery. 450 Advances in Production Engineering & Management 17(4) 2022 End-of-line delivery vehicle routing optimization based on large-scale neighbourhood search algorithms considering … Fig. 8 Distribution of consumers for path 6 and the optimal path Fig. 9 Distribution of consumers for path 7 and path 8 and optimal path Path 7 and Path 8 have a wider delivery area coverage, both with more than 4 heel cells (see Fig. 9). There were more of these consumers who were not preferred delivery addresses, with consumer numbers 17, 268, 88, 151, 296, 111, 248, 362, 342, 15, 35, and 132. An analysis of consumers who are not preferred addresses for delivery reveals the following characteristics of these consumers: • Time windows that do not match other consumers in that neighbourhood on that path. • The preferred address is further away from the delivery area of the path, while the alternative address is closer to the delivery area. • Consumers who choose the alternative address tend to be at the beginning or the end of the path to reduce detours. 4.3 Cost analysis This paper compares the total cost of the model without alternative addresses with the total cost of the model with alternative addresses. The comparison shows that the total cost of the model with alternative addresses is 283.43 compared to the total cost of the model without alternative addresses of 307.89, a total cost saving of 24.46. By consumers providing alternative addresses, the distribution company saves 24.46. For consumers, total satisfaction decreased as there were Advances in Production Engineering & Management 17(4) 2022 451 Niu, Liu, Huang some consumers who did not receive goods from the preferred address. In terms of time window penalty cost, the model saved mainly in terms of time window, which was reduced through alternative addresses and thus better delivery times. Although consumer satisfaction is reduced, consumers are also willing to provide alternative addresses as alternative addresses may allow consumers to get their goods earlier. 4.4 Sensitivity analysis During the calculations, it was observed that the presence of a service level constraint tends to make the VRPBA algorithm more difficult to solve, so a sensitivity analysis is performed in this section to explore more precisely the effect of different service levels on the total cost, computation time and number of optimal solution instances. Due to the service level constraint, we make the service level required for the first priority vary between 60 % and 100 % in 4 % steps, i.e. note that a 4 % increase means that 10 additional consumers out of 250 are required whose delivery method must be the first delivery method chosen by the consumer. The relationship between average path cost and service level is depicted in Fig. 10. As expected, increasing the level of service leads to an increase in total costs. 𝛽𝛽1 = 1.0 is approximately 22 % higher than 𝛽𝛽1 = 0.6. The impact on total cost and calculation time is analysed according to the VRPBA example. Fig. 9 also shows the average running time and confirms that the problem difficulty decreases when the service level is increased. Furthermore, the service level requires the highest costs, i.e. the absolute slope of the curve, when the service level is at the upper end of the medium range, i.e. when the value of 𝛽𝛽1 is between 0.7 and 0.85. Fig. 10 Relationship between service levels and costs 5. Research conclusions In this paper, a vehicle path optimisation model based on consumer delivery locations was established to optimise the driving paths and delivery methods of end-of-line delivery vehicles, and the same solution algorithm was designed. Based on the improved algorithm and the construction method of consumer portraits, this paper establishes a solution algorithm based on the data of five real communities and plans the delivery routes and delivery methods. This paper considers the vehicle path problem with alternative addresses, which is an extension of the vehicle path problem with time windows. In this case, each consumer may provide more than one delivery address in a delivery, each delivery address has a priority, and each delivery address has its own time window. The analysis of the arithmetic solution shows that the model saves mainly in terms of time window penalty costs, which are reduced by alternative addresses and thus better delivery times, and therefore time window violation costs. Although consumer satisfaction is reduced, consumers are also willing to provide alternative addresses, as alternative addresses may allow consumers to get their goods earlier. In addition, this paper considers the vehicle routing problem with multiple delivery addresses, and use large-scale neighbourhood search algorithm to analyse the characteristics of 452 Advances in Production Engineering & Management 17(4) 2022 End-of-line delivery vehicle routing optimization based on large-scale neighbourhood search algorithms considering … users who do not deliver according to the first address, and analyse the relationship between the distribution cost and service level of enterprises. 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Time-dependent and bi-objective vehicle routing problem with time windows, Advances in Production Engineering & Management, Vol. 14, No. 2, 201-212, doi: 10.14743/apem2019. 2.322. 454 Advances in Production Engineering & Management 17(4) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 4 | December 2022 | pp 455–468 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.4.448 Original scientific paper An approach to maintenance sustainability level assessment integrated with Industry 4.0 technologies using Fuzzy-TOPSIS: A real case study Patalas-Maliszewska, J.a,*, Łosyk, H.a aInstitute of Mechanical Engineering, University of Zielona Góra, Poland ABSTRACT ARTICLE INFO Sustainable development (SD) activities within a manufacturing should be integrated with the Industry 4.0 (I4.0) technologies implementation due to ensure the continuous evaluation and even prediction the SD level. Such integration should be provided cross all company areas but must be strictly defined for each core process realised within a company. Therefore, the main purpose of the study is to build the new approach to assess the maintenance sustainability (MS) level in a manufacturing company, as a good example of integrating I4.0 technologies and SD activities within a company, using Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (F-TOPSIS). The major contributions of the work are as follows: 1) to the existing literature by identification the key objectives of MS, in the context of Industry 4.0 2) using the F-TOPSIS method and based on the empirical data received from 125 Polish manufacturing enterprises, 3) the establishment of the integrated approach, which allow continuous monitor the level of the MS within a manufacturing, 4) demonstrating the usefulness of the fresh framework in managerial practice through its verification in the five Polish manufacturing companies. Managers of manufacturing enterprises, thanks to the use of the proposed approach, may assess and constant monitor the MS level, while application of the I4.0 technologies. Keywords: Maintenance sustainability (MS); Assessment; Manufacturing; Industry 4.0; Multi-criteria decision making (MCDM); Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (Fuzzy TOPSIS); Empirical research; Real case studies *Corresponding author: j.patalas-maliszewska@iim.uz.zgora.pl (Patalas-Maliszewska, J.) Article history: Received 8 February 2022 Revised 19 December 2022 Accepted 21 December 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Production and industrial systems consume a huge amount of resources and energy, constituting a sector with a large percentage of emissions to the environment. That is why the modern industry is directed in its activities to support the three pillars of Sustainable Development (SD): social, economic and environmental. In that way, industrial enterprises and more precisely manufacturing ones seek to integrate the environment into their strategy by conducting an innovative rationalization of production as promoted by industrial ecology and circular economy paradigms [1]. Maintenance plays a key role in this regard, as a possibility for the prolong the life of manufacturing [2]. Standard maintenance is an integration of technical, administrative and managerial aspects of production [3]. Usually, the view of maintenance activities is narrowed down to the economic dimension. However, the increasing complexity of production systems indicates the need to broaden the horizons related to the effects of maintenance activities with an environmental and 455 Patalas-Maliszewska, Łosyk social dimension. It seems necessary to the implementation of the process approach to the design and operations of a company, an integrated management system based on the application of certain standards (quality, environment, safety at work, etc.) and elements of business excellence of a company [4]. The growing interest in the field of maintenance management is indicated by numerous publications in this area [5-8] indicating the possibility of including SD objectives in the maintenance management strategy. The literature on the subject indicates attempts to imply the assumptions of Sustainable Development (SD) in the assessment of maintenance results [9-12]. The Global Reporting Initiative - GRI [13] provides guidance on SD reporting for organizations where "the G4 Guidelines provide global guidance for a standardized approach to reporting, promoting clarity and consistency of information that is necessary to acquire useful and reliable content for the market and the public" [13]. SD reporting in accordance with the standards set by GRI is used by, among others, such companies as Orlen, Allegro, and PGNiG. SD, within manufacturing, should also be seen in the three areas: (1) production processes, (2) production durability and (3) product development. In the article, based on the literature (e.g., 14-16) the objectives of maintenance sustainability (MS) were defined. The contemporary challenge of society is, therefore, the implementation of SD goals in the era of Industry 4.0. Zhou et al. [17] indicate that it is a futuristic and multifaceted process with many opportunities and challenges. Industry 4.0 can be started as the industrial transformation that provides new technological solutions by integrating information technologies and automation that communicate among themselves to achieve better results [18]. However, the growing importance of industry requires extensive measures to protect the well-being of m.in stocks, the environment, and dignified life. There is growing interest in sustainability practices for organisations [19]. Industry 4.0 can be used to increase SD's ability to achieve its goals by enabling organizations to diagnose in real-time and to optimize and improve the system's ability to adapt to a dynamically changing environment [20]. Thus, the organization is able to capture data from the actual implementation of production and quickly analyse the state of individual process parameters. Active data collection helps managers track, monitor, and then make sustainable decisions about their processes. Another important aspect is the use of the latest technologies in production systems to increase efficiency. This solution, in turn, provides a competitive advantage to the organization by producing high-quality products at a lower cost [21]. Therefore, the main idea of this paper is to evaluate the maintenance sustainability level in manufacturing companies integrated with Industry 4.0 technologies using one of the Decision Making (MCDM) methods. In the research process, two methods of multi-criteria analysis were considered to evaluate the maintenance sustainability level in manufacturing companies integrated with Industry 4.0 technologies: Analytic Hierarchy Process (AHP) and Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (F-TOPSIS). The choice of the AHP method was considered due to the ability to capture quantitative and qualitative attributes in a simple way, as well as the ability to handle rare or low-quality data. The use of the AHP method also allows for simple verification of the quality of expert judgments by performing a consistency test. The next step in the research process was the use of the F-TOPSIS method due to the complete autonomy of individual experts in making assessments. The IFWA operator was used to aggregate expert assessments. In the process of verification of selected MCDM methods, the F-TOPSIS method was used in the further part of the work due to the uncertainty and imprecision of the assessment of decision options in relation to the adopted criteria in the context of multifacetedness: evaluate the maintenance sustainability level in manufacturing companies. MCDM methods are designed to solve such manufacturing problems [22]. It is indicated that the MCDM constitutes an excellent decision-making tool for evaluating and ranking/prioritizing the alternatives even when the criteria involved are complex [23]. The literature indicates the effective application of MCDM in the field of manufacturing enterprises, including flow control in a manufacturing system with three production lines is described [24], selection of the lean six sigma project [25], identifying key performance factors for sustainability development [26], materials selection [27]. To build the new approach to assess the maintenance sustainability level in manufacturing companies, using F-TOPSIS and IFWA operator the Decision Makers (DMs) 456 Advances in Production Engineering & Management 17(4) 2022 An approach to maintenance sustainability level assessment integrated with Industry 4.0 technologies using Fuzzy-TOPSIS … opinions are needed. Therefore 125 Polish manufacturing companies from western Poland in the automotive industries were researched to assess the activities of the organization for the benefit of MS. Next, the research results obtained using the F-TOPSIS method represent the key objectives of MS in production enterprises. The values of the key MS objectives set should be determined based on the data included in applied I4.0 technologies within manufacturing. Finally, the universality of the proposed approach and its adaptability to the specificity of a given company was demonstrated and employed in five different types of Polish manufacturing enterprises. 2. Materials and methods In the industrial scope, one of the key areas that directly influence the manufacturing sustainability of each company is maintenance [15]. The Decision Making (MCDM) methods refer to the methods of utilizing different data sources comprehensively to select optimization alternatives [28]. The MCDM methods focus on decision problems in which the set of all permissible decisions is a discrete set containing a finite, predetermined number of possible solution variants. MCDM tool can handle concurrently the various criteria which may be dimensional or non-dimensional in nature [23]. It is indicated that the MCDM constitutes an excellent decision-making tool for evaluating and ranking/prioritizing the alternatives even when the criteria involved are complex [23]. The literature indicates the effective application of MCDM methods in the field of a manufacturing company, including flow control in a manufacturing system with three production lines is described [24], selection of the lean six sigma project [25], identifying key performance factors for sustainability development [26], materials selection [27]. For the purpose of the assessment of the MS level, the F-TOPSIS and IFWA methods seem to be appropriate for this research. The F-TOPSIS method was presented by [29]. Fuzzy TOPSIS method and IFWA operator to rank the adopted alternatives and criteria. Along with the TOPSIS method, Intuitionistic Fuzzy Sets (IFS) were used. IFS A in the finite set X can be defined as follows [30]: (1) 𝐴𝐴 = {< 𝑥𝑥, 𝜇𝜇𝐴𝐴 (𝑥𝑥), 𝑣𝑣𝐴𝐴 (𝑥𝑥) > |𝑥𝑥 ∈ 𝑋𝑋}, where: (2) 𝜇𝜇𝐴𝐴 : 𝑥𝑥 → [0,1], 𝑣𝑣𝐴𝐴 : 𝑥𝑥 → [0,1] and 0 ≤ 𝜇𝜇𝐴𝐴 (𝑥𝑥) + 𝑣𝑣𝐴𝐴 (𝑥𝑥) ≤ 1 ∀ 𝑥𝑥 ∈ 𝑋𝑋 𝜇𝜇𝐴𝐴 (𝑥𝑥) and 𝑣𝑣𝐴𝐴 (𝑥𝑥) determine the degree of membership and non-membership of 𝑥𝑥 to 𝐴𝐴. For each IFS A of X there is also a third parameter called the degree of fluctuation, defined as: 𝜋𝜋𝐴𝐴 (𝑥𝑥) = 1 − 𝜇𝜇𝐴𝐴 (𝑥𝑥) − 𝑣𝑣𝐴𝐴 (𝑥𝑥) (3) 𝐴𝐴 ⨂ 𝐵𝐵 = {𝜇𝜇𝐴𝐴 (𝑥𝑥). 𝜇𝜇𝐵𝐵 (𝑥𝑥), 𝑣𝑣𝐴𝐴 (𝑥𝑥) + 𝑣𝑣𝐵𝐵 (𝑥𝑥) − 𝑣𝑣𝐴𝐴 (𝑥𝑥). 𝑣𝑣𝐵𝐵 (𝑥𝑥)| 𝑥𝑥 ∈ 𝑋𝑋 (5) therefore, it is obvious that: 0 ≤ 𝜋𝜋𝐴𝐴 (𝑥𝑥) ≤ 1 (4) When the value of 𝜋𝜋𝐴𝐴 (𝑥𝑥) is small, then the information about 𝑥𝑥 is more certain, whereas when the value of 𝜋𝜋𝐴𝐴 (𝑥𝑥) has a larger range, the information becomes uncertain. The multiplication operator for intuitionistic fuzzy numbers (IFNs), where A and B belong to the set F is as follows: Multiplication of matrix components is calculated by the formula: 𝐴𝐴 ∘ 𝐵𝐵 = [< 𝑚𝑚𝑚𝑚𝑚𝑚{𝜇𝜇𝐴𝐴 (𝑥𝑥), 𝜇𝜇𝐵𝐵 (𝑥𝑥)}, 𝑚𝑚𝑚𝑚𝑚𝑚{𝜇𝜇𝐴𝐴 (𝑥𝑥), 𝜇𝜇𝐵𝐵 (𝑥𝑥)} >] (6) In order to establish the integrated approach, which allows continuous monitor the level of the MS within manufacturing the F-TOPSIS and IFWA methods were employed according to the following steps: Step I. Calculation of weights for selected DMs The group was assumed to include l decision-makers. The importance of individual decision-makers is represented by intuitionistic fuzzy numbers. Assuming that 𝐷𝐷𝑘𝑘 = [𝜇𝜇𝐴𝐴 , 𝑣𝑣𝐴𝐴 , 𝜋𝜋𝐴𝐴 ], then IFN is showing the overall importance of Decision Maker 𝑘𝑘-th in the ranking. The 𝑘𝑘-th DM weight is calculated using the following formula: Advances in Production Engineering & Management 17(4) 2022 457 Patalas-Maliszewska, Łosyk 𝜇𝜇𝜇𝜇 (𝜇𝜇𝜇𝜇 + 𝜋𝜋𝑘𝑘 ( ) (𝜇𝜇𝜇𝜇 + 𝑣𝑣𝑣𝑣 ) 𝜆𝜆𝑘𝑘 = , 𝜇𝜇𝜇𝜇 𝑙𝑙 𝛴𝛴𝑘𝑘=1 (𝜇𝜇𝜇𝜇 + 𝜋𝜋𝑘𝑘 ( ) 𝜇𝜇𝜇𝜇 + 𝑣𝑣𝑘𝑘 where assuming that: (7) 𝑙𝑙 � λ𝑘𝑘 = 1 𝑘𝑘=1 Step II. Create the aggregated intuitionistic fuzzy decision matrix according to the DMs opinions It was assumed that intuitionistic fuzzy decision matrix for each DM takes the form of (𝑘𝑘) 𝑅𝑅 𝑘𝑘 = �𝑟𝑟𝑖𝑖𝑖𝑖 � = {1,2, … , 𝑙𝑙}, then weights of individual DM ∑𝑙𝑙𝑘𝑘=1 𝑘𝑘 = 1 ∈ [0,1]. Opinions of all 𝑚𝑚𝑚𝑚𝑚𝑚 members should be combined into a group decision. For this purpose, the operator Intuitionistic Fuzzy Weighted Averaging (IFWA) proposed by [19] was used, assuming that: (1) (2) (𝑙𝑙) (1) (2) (𝑙𝑙) 𝑟𝑟𝑖𝑖𝑖𝑖 = 𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴λ �𝑟𝑟𝑖𝑖𝑖𝑖 , 𝑟𝑟𝑖𝑖𝑖𝑖 , … , 𝑟𝑟𝑖𝑖𝑖𝑖 � = 𝜆𝜆1 𝑟𝑟𝑖𝑖𝑖𝑖 ⨁ 𝜆𝜆2 𝑟𝑟𝑖𝑖𝑖𝑖 ⨁ … ⨁ 𝜆𝜆𝑙𝑙 𝑟𝑟𝑖𝑖𝑖𝑖 = and (𝑘𝑘) (𝑘𝑘) (𝑘𝑘) (𝑘𝑘) = �1 − ∏𝑙𝑙𝑘𝑘=1 �1 − 𝜇𝜇𝑖𝑖𝑖𝑖 � λ𝑘𝑘 , ∏𝑙𝑙𝑘𝑘=1 �𝜈𝜈𝑖𝑖𝑖𝑖 � λ𝑘𝑘 , ∏𝑙𝑙𝑘𝑘=1 �1 − 𝜇𝜇𝑖𝑖𝑖𝑖 � λk − ∏𝑙𝑙𝑘𝑘=1 �𝜈𝜈𝑖𝑖𝑖𝑖 � λ𝑘𝑘 � (8) 𝑟𝑟𝑖𝑖𝑖𝑖 = (𝜇𝜇𝐴𝐴𝐴𝐴 (𝑥𝑥𝑥𝑥), 𝜈𝜈𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 ), 𝜋𝜋𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 )) ( 𝑖𝑖 = (1,2, … , 𝑚𝑚; 𝑗𝑗 = 1,2, … , 𝑛𝑛) Then, the aggregated IF decision matrix can be presented as: μA1 (x1), νA1 (x1), πA1 (x1) μ (x1), νA2 (x1), πA2 (x1) R = � A2 ⋮ μAm (x1), νAm (x1), πAm (x1) μ (x1), ν (x1), π (x1) A1 A1 ⎡ A1 μ (x1), ν (x1), π ⎢ A2 A2 (x1) R = ⎢ A2 ⋮ ⎢ ⎣μAm (x1), νAm (x1), πAm (x1) μA1 (x2), νA1 (x2), πA1 (x2) μA2 (x2), νA2 (x2), πA2 (x2) ⋮ μAm (x2), νAm (x2), πAm (x2) ⋯ μA1 (x3), νA1 (x3), πA1 (x3) ⋯ μA2 (x3), νA2 (x3), πA2 (x3) � ⋱ ⋮ ⋯ μAm (xn), νAm (xn), πAm (xn) μA1 (x2), νA1 (x2), πA1 (x2) ⋯ μA1 (x3), νA1 (x3), πA1 (x3) ⎤ μA2 (x2), νA2 (x2), πA2 (x2) ⋯ μA2 (x3), νA2 (x3), πA2 (x3) ⎥ ⎥ ⋮ ⋱ ⋮ ⎥ μAm (x2), νAm (x2), πAm (x2) ⋯ μAm (xn), νAm (xn), πAm (xn)⎦ 𝑟𝑟11 𝑟𝑟12 ⋯ 𝑟𝑟1𝑚𝑚 𝑟𝑟21 𝑟𝑟22 ⋯ 𝑟𝑟2𝑚𝑚 R= � ⋮ ⋮ ⋮ � 𝑟𝑟𝑛𝑛1 𝑟𝑟𝑛𝑛2 𝑟𝑟𝑛𝑛𝑛𝑛 (9) (10) (11) To create the aggregated intuitionistic fuzzy decision matrix, a set of alternatives and also the Decision Makers (DMs) opinions are needed. Therefore, at the end of 2020, we researched 125 Polish manufacturing companies from western Poland (from the Lubuskie Voivodeship, Lower Silesia, Opole, Greater Poland and West Pomeranian Voivodeship) in the automotive industries to assess the activities of the organization for the benefit of SM. The tests were carried out using the survey method. The survey questionnaire included multi-choice, closed questions. The research group represents 1 % of manufacturing companies from the automotive industry, in western Poland [31] based on data from the Central Statistical Office of Poland, Warsaw. 61 % of the companies surveyed carry out an analysis in the area of energy consumption, although it is an essential tool for energy efficiency measures in the plant. Improving energy efficiency can have measurable effects in the form of energy savings, thereby reducing costs and reducing negative environmental impacts. It should be emphasised that energy efficiency protects land resources and is an important element of sustainable development. The survey data shows that 67 % of the companies surveyed carry out an analysis. So, based on the research results the set of decision-makers were defined: DMs = {DM1, DM2}. DM1 (an Owner) and DM2 (a Maintenance Manager) were selected based on the survey results, where the responses received in the positions of an owner and a maintenance manager accounted 458 Advances in Production Engineering & Management 17(4) 2022 An approach to maintenance sustainability level assessment integrated with Industry 4.0 technologies using Fuzzy-TOPSIS … for the largest number of responses. The percentage for each position that was responsible for completing the survey is as follows: an owner 34 %, a co-owner 6.7 %, a board chairman 3.5 %, a board member 1.6 %, an administrative director 2.4 %, a sales director 0.8 %, a managing director 0.8 %, a director 0.8 %, a manager 3.2 %, a production manager 7.1 %, a maintenance manager 20 %, an assistance maintenance manager 0.8 %, a workshop manager 1.6 %, a service manager 0.8 %, a process engineer 4%, an engineer 0.8 %, a superintendent/caretaker 2.4 %, a chief accountant 0.8 %, an accountant 0.8 %, a technical specialist 0.8%, a maintenance specialist 1.7 %, a financial controller 0.8 %, a specialist 3.2 %. Step III. Determine the weights of criteria and sub-criteria Since it cannot be assumed that all criteria and sub-criteria are equally important, a W degree of importance should be set for them. To obtain the W parameter, opinions of individual DMs on the validity of criteria and sub-criteria must be combined into one assessment. (𝑘𝑘) (𝑘𝑘) (𝑘𝑘) (𝑘𝑘) Suppose that 𝑤𝑤𝑗𝑗 = �𝜇𝜇𝑗𝑗 , ν𝑗𝑗 , 𝜋𝜋𝑗𝑗 �, then IFN is assigned to criterion Xj by 𝑘𝑘-th decision maker. Next, the weight for a particular criterion and sub-criterion is determined using the IFWA operator: (1) (2) (𝑙𝑙) (1) (2) (𝑙𝑙) 𝑤𝑤𝑖𝑖𝑖𝑖 = 𝐼𝐼𝐼𝐼𝐼𝐼𝐴𝐴λ �𝑤𝑤𝑗𝑗 , 𝑤𝑤𝑗𝑗 , … , 𝑤𝑤𝑗𝑗 � = λ1 𝑤𝑤𝑗𝑗 ⨁ λ2 𝑤𝑤𝑗𝑗 ⨁ … ⨁ λ𝑙𝑙 𝑤𝑤𝑗𝑗 (𝑘𝑘) (𝑘𝑘) (𝑘𝑘) (𝑘𝑘) = = �1 − ∏𝑙𝑙𝑘𝑘=1 �1 − 𝜇𝜇𝑖𝑖𝑖𝑖 � λ𝑘𝑘 , ∏𝑙𝑙𝑘𝑘=1 �𝜈𝜈𝑖𝑖𝑖𝑖 � λ𝑘𝑘 , ∏𝑙𝑙𝑘𝑘=1 �1 − 𝜇𝜇𝑖𝑖𝑖𝑖 � λ𝑘𝑘 − ∏𝑙𝑙𝑘𝑘=1 �𝜈𝜈𝑖𝑖𝑖𝑖 � λ𝑘𝑘 � where 𝑊𝑊 = �𝑤𝑤1 , 𝑤𝑤2 , . . . , 𝑤𝑤𝑗𝑗 �, 𝑤𝑤𝑗𝑗 = (𝜇𝜇𝑗𝑗 , 𝑣𝑣𝑗𝑗 , 𝜋𝜋𝑗𝑗 ) (𝑗𝑗 = 1,2, … , 𝑛𝑛) (12) (13) Then a multiplication of the matrix components is used to combine the weights of each criterion with the corresponding sub-criteria (Eq. 6). Step IV. Create the aggregated weighted intuitionistic fuzzy decision matrix Calculation of criteria and sub-criteria weights (𝑊𝑊) allows to create the aggregated weighted IF decision matrix. The aggregated weighted IF decision matrix based on [32]: and 𝑅𝑅 ⨂ 𝑊𝑊 = {𝑥𝑥, 𝜇𝜇𝐴𝐴𝐴𝐴 (𝑥𝑥) • 𝜇𝜇𝑊𝑊 (𝑥𝑥), 𝜈𝜈𝐴𝐴𝐴𝐴 (𝑥𝑥) + 𝜈𝜈𝑊𝑊 (𝑥𝑥) − 𝜈𝜈𝐴𝐴𝐴𝐴 (𝑥𝑥) + 𝜈𝜈𝑊𝑊 (𝑥𝑥)| 𝑥𝑥 ∈ 𝑋𝑋 𝜋𝜋𝐴𝐴𝐴𝐴•𝑊𝑊 = 1 − 𝜈𝜈𝐴𝐴𝐴𝐴 (𝑥𝑥) − 𝜈𝜈𝑊𝑊 (𝑥𝑥) − 𝜇𝜇𝐴𝐴𝐴𝐴 (x) • 𝜇𝜇𝑊𝑊 (𝑥𝑥) + 𝜈𝜈𝐴𝐴𝐴𝐴 (𝑥𝑥) + 𝜈𝜈𝑊𝑊 (𝑥𝑥) (14) (15) Step V. Appoint the intuitionistic fuzzy positive-ideal solution and intuitionistic fuzzy negative-ideal solution Suppose that J1 is a benefit criterion, while J2 is a cost criterion. 𝐴𝐴+ is intuitionistic fuzzy positive ideal solution and 𝐴𝐴− is intuitionistic fuzzy negative ideal solution. Eqs. 16 and 17 determine 𝐴𝐴+ and 𝐴𝐴− : where: 𝐴𝐴+ = (𝜇𝜇𝐴𝐴+𝑊𝑊 (𝑥𝑥𝑗𝑗 ), 𝜈𝜈𝐴𝐴+𝑊𝑊 (𝑥𝑥𝑗𝑗 ) and 𝐴𝐴− = (𝜇𝜇𝐴𝐴−𝑊𝑊 (𝑥𝑥𝑗𝑗 ), 𝜈𝜈𝐴𝐴−𝑊𝑊 (𝑥𝑥𝑗𝑗 ) (16) ν𝐴𝐴+𝑊𝑊 (𝑥𝑥𝑗𝑗 ) = ((𝑚𝑚𝑚𝑚𝑚𝑚𝑖𝑖 ν𝐴𝐴𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 )| 𝑗𝑗 ∈ 𝐽𝐽1), (𝑚𝑚𝑚𝑚𝑚𝑚𝑖𝑖 ν𝐴𝐴𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 )| 𝑗𝑗 ∈ 𝐽𝐽2) (18) 𝜇𝜇𝐴𝐴+𝑊𝑊 (𝑥𝑥𝑗𝑗 ) = ((𝑚𝑚𝑚𝑚𝑚𝑚𝑖𝑖 𝜇𝜇𝐴𝐴𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 )| 𝑗𝑗 ∈ 𝐽𝐽1), (𝑚𝑚𝑚𝑚𝑚𝑚𝑖𝑖 𝜇𝜇𝐴𝐴𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 )| 𝑗𝑗 ∈ 𝐽𝐽2) μ𝐴𝐴+𝑊𝑊 (𝑥𝑥𝑗𝑗 ) = ((𝑚𝑚𝑚𝑚𝑚𝑚𝑖𝑖 μ𝐴𝐴𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 )| 𝑗𝑗 ∈ 𝐽𝐽1), (𝑚𝑚𝑚𝑚𝑚𝑚𝑖𝑖 μ𝐴𝐴𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 )| 𝑗𝑗 ∈ 𝐽𝐽2) ν𝐴𝐴−𝑊𝑊 (𝑥𝑥𝑗𝑗 ) = ((𝑚𝑚𝑚𝑚𝑚𝑚𝑖𝑖 ν𝐴𝐴𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 )| 𝑗𝑗 ∈ 𝐽𝐽1), (𝑚𝑚𝑚𝑚𝑚𝑚𝑖𝑖 ν𝐴𝐴𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 )| 𝑗𝑗 ∈ 𝐽𝐽2) Step VI. Calculate the separation measures and closeness coefficient (17) (19) (20) Measuring the separations between alternatives in Intuitionistic fuzzy set can be done by using a number of distance measures proposed by [33] or [32] including Hamming distance, Euclidean distance and their normalized distance measures [1]. After selecting the distance measure, the Advances in Production Engineering & Management 17(4) 2022 459 Patalas-Maliszewska, Łosyk separation measures (𝑆𝑆𝑖𝑖+ and 𝑆𝑆𝑖𝑖− ) for each alternative from intuitionistic fuzzy positive ideal and negative ideal solutions the selection is made. The article uses normalized Euclidean distance: 1 𝑆𝑆 + = �2𝑛𝑛 ∑𝑛𝑛𝑗𝑗=1[(𝜇𝜇𝐴𝐴𝐴𝐴𝐴𝐴 �𝑥𝑥𝑗𝑗 � − 𝜇𝜇𝐴𝐴+𝑊𝑊 (𝑥𝑥𝑗𝑗 ))2 + (𝜈𝜈𝐴𝐴𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 )2 − 𝜈𝜈𝐴𝐴+𝑊𝑊 (𝑥𝑥𝑗𝑗 ))2 + (𝜋𝜋𝐴𝐴𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 )2 − 𝜋𝜋𝐴𝐴+𝑊𝑊 (𝑥𝑥𝑗𝑗 ))2 ] 1 𝑆𝑆 − = �2𝑛𝑛 ∑𝑛𝑛𝑗𝑗=1[(𝜇𝜇𝐴𝐴𝐴𝐴𝐴𝐴 �𝑥𝑥𝑗𝑗 � − 𝜇𝜇𝐴𝐴−𝑊𝑊 (𝑥𝑥𝑗𝑗 ))2 + (𝜈𝜈𝐴𝐴𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 )2 − 𝜈𝜈𝐴𝐴−𝑊𝑊 (𝑥𝑥𝑗𝑗 ))2 + (𝜋𝜋𝐴𝐴𝐴𝐴𝐴𝐴 (𝑥𝑥𝑗𝑗 )2 − 𝜋𝜋𝐴𝐴−𝑊𝑊 (𝑥𝑥𝑗𝑗 ))2 ] Then the relative closeness coefficient to the ideal solution is: 𝐶𝐶𝑖𝑖 = Step VII. Rank the alternatives 𝑆𝑆𝑖𝑖− , where 0 ≤ 𝐶𝐶𝑖𝑖 ≤ 1 𝑆𝑆𝑖𝑖− + 𝑆𝑆𝑖𝑖+ (21) (22) (23) After calculating the relative closeness coefficients of each alternatives, a ranking of the alternative has been made, based on 𝐶𝐶𝑖𝑖 ’s decreasing value. 3. Research results In order to create a framework for assessing the maintenance sustainability level in manufacturing companies, integrated with I4.0 technologies, the following elements should be defined: Element 1: a set of criteria: C = {C1, C2,…., C12}, Element 2: a set of sub-criteria: I = {I1, I2,…, I14}, Element 3: a set of alternatives: Av = {Av1, Av2, Av3}. Based on the analysis of our previous works and based on the literature, e.g. [14-16, 34], the set of criteria: C = {C1, C2,…, C7} and a set of sub-criteria: I = {I1, I2,…, I14} were determined. It should be noted that the selected criteria and sub-criteria for maintenance sustainability are related to the industry concerned (manufacturing) to meet the unique needs of the manufacturing sector. A set of alternatives: Av = {Av1, Av2, Av3} was determined as the management levels within an enterprise: the operational (Av1), as well as tactical (Av2) and strategic level (Av3). The adopted criteria (Table 1) were also divided into a benefit (criteria for which the higher value then better) and cost (criteria for which the lower value then better). Benefit and cost criteria are presented in Table 2. Criteria Table 1 Selected criteria and sub-criteria Staff education C1 Timeliness Reduction of downtime costs C2 C3 Reduction of production costs C5 Environmental protection Safety Investment profitability Resources saving Good practices Innovation and modernization Use of renewable energy Reduction of non-renewable energy consumption 460 C4 C6 C7 C8 C9 C10 C11 C12 Sub-criteria Cost of training for maintenance Preventive maintenance time causing downtime Timeliness of order Total number of downtime related to maintenance Number of failures causing potential damage to the environment Reduction costs of losses related to production stoppages resulting from breakdowns Reduction costs connected with potentially accidental events and accidents of maintenance workers, operators and third parties during maintenance works Return on eco-friendly maintenance investment and innovation Total of spare parts used/ Original spare parts used Recycled spare parts used/ Re-purposed spare parts used Skill improvement related to sustainable maintenance practices Modernization carried out in the last six months related to sustainable maintenance Renewable energy consumption Non-renewable energy consumption I1 I2 I2 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13 I14 Advances in Production Engineering & Management 17(4) 2022 An approach to maintenance sustainability level assessment integrated with Industry 4.0 technologies using Fuzzy-TOPSIS … Action MS (maintenance sustainability) Table 2 Benefit and cost criteria Criteria C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 Benefit x x Cost x x x x x x x x x x Selected DMs (section 2) was assigned the importance of weights based on their involvement in the adopted action (maintenance sustainability). To determine the importance of weights for DM, the following formula was used Eq. 7. The results of the studies allowed to assess the involvement of the selected DMs in the activities of the organization for the benefit of SD. The assessment of involvement in the implementation of particular DMs criteria was carried out on the basis of the adopted linguistic terms and Intuitionistic Fuzzy Numbers. Linguistic terms for ranking the importance of the DMs, criteria and subcriteria: little consequence (LC) – IFN ∈ (0.10, 0.90); medium consequence (MC) – IFN ∈ (0.25, 0.70); important (I) – IFN ∈ (0.45, 0.50; very important (VI) – IFN ∈ (0.75, 0.20); crucial (C) –IFN ∈ (0.90, 0.10). The importance of DMs and their weights: DM1 – Crucial; Weight 0.539, and DM2 – Very Important; Weight 0.461. Action SD objective C1 C2 C3 C4 C5 MS C6 C7 C8 C9 C10 C11 C12 Table 3 The ratings of the alternatives Level of management in company ST TA OP ST TA OP ST TA OP ST TA OP ST TA OP ST TA OP ST TA OP ST TA OP ST TA OP ST TA OP ST TA OP ST TA OP Advances in Production Engineering & Management 17(4) 2022 DM1 VHL SL IL SL HL ML HL VHL IL VHL HL IL VHL HL IL HL VHL IL SL HL ML VHL HL IL HL SL NL VHL VHL IL VHL HL ML VHL VHL IL DM2 VHL HL ML HL VHL ML HL VHL ML VHL SL NL HL ML IL HL VHL IL HL VHL SL VHL HL NL HL SL NL VHL VHL ML VHL HL SL VHL HL NL DMs DM1 (1.00, 0.00) (0.55, 0.35) (0.20, 0.65) (0.55, 0.35) (0.75, 0.25) (0.40, 0.50) (0.75, 0.25) (1.00, 0.00) (0.20, 0.65) (1.00, 0.00) (0.75, 0.25) (0.20, 0.65) (1.00, 0.00) (0.75, 0.25) (0.20, 0.65) (0.75, 0.25) (1.00, 0.00) (0.20, 0.65) (0.55, 0.35) (0.75, 0.25) (0.40, 0.50) (1.00, 0.00) (0.75, 0.25) (0.20, 0.65) (0.75, 0.25) (0.55, 0.35) (0.00, 1.00) (1.00, 0.00) (1.00, 0.00) (0.20, 0.65) (1.00, 0.00) (0.75, 0.25) (0.40, 0.50) (1.00, 0.00) (1.00, 0.00) (0.20, 0.65) DM2 (1.00, 0.00) (0.75, 0.25) (0.40, 0.50) (0.75, 0.25) (1.00, 0.00) (0.40, 0.50) (0.75, 0.25) (1.00 , 0.00) (0.40, 0.50) (1.00, 0.00) (0.55, 0.35) (0.00, 1.00) (0.75, 0.25) (0.40, 0.50) (0.20, 0.65) (0.75, 0.25) (1.00 , 0.00) (0.20, 0.65) (0.75, 0.25) (1.00, 0.00) (0.55, 0.35) (1.00, 0.00) (0.75, 0.25) (0.00, 1.00) (0.75, 0.25) (0.55, 0.35) (0.00, 1.00) (1.00, 0.00) (1.00, 0.00) (0.40, 0.50) (1.00, 0.00) (0.75, 0.25) (0.55, 0.35) (1.00, 0.00) (0.75, 0.25) (0.00, 1.00) 461 Patalas-Maliszewska, Łosyk The linguistic terms (LT) and IFNs for the adopted alternatives were then determined: • • • • • • LT: Very high level (VHL) – IFN ∈ [1.00;0.00] LT: High level (HL) – IFN ∈ [0.75;0.25] LT: Significant level (SL) – IFN ∈ [0.55;0.35] LT: Medium level (ML) – IFN ∈ [0.40;0.50] LT: Insignificant level(IL) – IFN ∈ [0.20;0.65] LT: Nonsignificant level (NL) – IFN ∈ [0.00;1.00] Based on Table 1, the experts assessed the criteria in terms of the alternatives adopted (Table 3). The aggregated Intuitionistic Fuzzy Decision Matrix according to the DMs opinions presented on Table 4 (Eq. 8). C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 R= Table 4 Aggregated Intuitionistic Fuzzy Decision Matrix ST (1.000, 0.000, 0.000) (0.657, 0.299, 0.043) (0,750. 0.250, 0.000) (1.000, 0.000, 0.000) (1.000, 0.000, 0.000) (0,750. 0.250, 0.000) (0.656, 0.210, 0.043) (1.000, 0.000, 0.000) (0,750. 0.250, 0.000) (1.000, 0.000, 0.000) (1.000, 0.000, 0.000) (1.000, 0.000, 0.000) TA (0.656, 0.210, 0.043) (1.000, 0.000, 0.000) (1.000, 0.000, 0.000) (0.672, 0.291, 0.036) (0.625, 0.344, 0.030) (1.000, 0.000, 0.000) (1.000, 0.000, 0.000) (0,750, 0.250, 0.000) (0.550, 0.350, 0.150) (1.000, 0.000, 0.000) (0,750. 0.250, 0.000) (1.000, 0.000, 0.000) OP (0.299, 0.576, 0.124) (0.400, 0.500, 0.100) (0.299, 0.576, 0.125) (0.113, 0.792, 0.093) (0.200, 0.650, 0.150) (0.200, 0.650, 0.150) (0.475, 0.424, 0.101) (0.113, 0.792, 0.093) (0.000, 1.000, 0.000) (0.299, 0.576, 0.125) (0.475, 0.424, 0.101) (0.133, 0.793, 0.094) DMs evaluated selected criteria and sub-criteria using linguistic terms (Table 5, Table 6). The opinions received in form of linguistic terms were then translated into intuitionistic fuzzy numbers (Table 7, Table 8). Action MS Action MS 462 Table 5 The criteria importance weight Criteria C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C13 DM1 C VI VI I C I MC VI I VI C C Table 6 The sub-criteria importance weight Sub-criteria I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13 I14 DM1 C VI I VI C MC I I VI MC C VI VI C DMs DMs DM2 VI C VI VI VI MC I VI I VI C C DM2 VI C VI I VI LC I VI VI I VI VI I C Advances in Production Engineering & Management 17(4) 2022 An approach to maintenance sustainability level assessment integrated with Industry 4.0 technologies using Fuzzy-TOPSIS … Action MS Action MS Table 7 The rating of criteria based on intuitionistic fuzzy numbers Criteria DM1 (0.90, 0.10) (0.75, 0.25) (0.75, 0.25) (0.45, 0.55) (0.90, 0.10) (0.45, 0.55) (0.25, 0.75) (0.75, 0.25) (0.45, 0.55) (0.75, 0.25) (0.90, 0.10) (0.90, 0.10) I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 DMs Table 8 The rating of sub-criteria based on intuitionistic fuzzy numbers Sub-criteria DM1 (0.90, 0.10) (0.75, 0.25) (0.45, 0.55) (0.75, 0.25) (0.90, 0.10) (0.25, 0.75) (0.45, 0.55) (0.45, 0.55) (0.75, 0.25) (0.25, 0.75) (0.90, 0.10) (0.75, 0.25) (0.75, 0.25) (0.90, 0.10) I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13 I14 DMs DM2 (0.75, 0.25) (0.90, 0.10) (0.75, 0.25) (0.75, 0.25) (0.75, 0.25) (0.25, 0.75) (0.45, 0.55) (0.75, 0.25) (0.45, 0.55) (0.75, 0.25) (0.90, 0.10) (0.90, 0.10) DM2 (0.75, 0.25) (0.90, 0.10) (0.75, 0.25) (0.45, 0.55) (0.75, 0.25) (0.10, 0.90) (0.45, 0.55) (0.75, 0.25) (0.75, 0.25) (0.45, 0.55) (0.75, 0.25) (0.75, 0.25) (0.45, 0.55) (0.90, 0.10) Aggregation of criteria and sub-criteria importance according to DMs opinions is presented in Table 9 (Eq. 6). The final weights for aggregated criteria and sub-criteria (ACI) are presented in Table 10 (Eq. 11). Action MS Table 9 The aggregated importance of criteria and sub-criteria Combination DM1 (0.90, 0.10) (0.75, 0.20) (0.45, 0.50) (0.45, 0.50) (0.90, 0.10) (0.25, 0.70) (0.25, 0.70) (0.75, 0.20) (0.25, 0.70) (0.75, 0.20) (0.75, 0.20) (0.90, 0.10) I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 DMs Table 10 The final weight of Aggregated Criteria and Sub-criteria (ACI) W= ACI1 ACI2 ACI3 ACI4 ACI5 ACI6 ACI7 ACI8 ACI9 ACI10 ACI11 ACI12 DM2 (0.75, 0.20) (0.90, 0.10) (0.75, 0.20) (0.45, 0.50) (0.75, 0.20) (0.10, 0.90) (0.45, 0.55) (0.75, 0.20) (0.45, 0.50) (0.75, 0.20) (0.45, 0.50) (0.90, 0.10) (0.8474, 0.1525, 0.0001) (0.8361, 0.1638, 0.0001) (0.6176, 0.3823, 0.0391) (0.6176, 0.3823, 0.0001) (0.8474, 0.1525, 0.0001) (0.1842, 0.8157, 0.0001) (0.3499, 0.6501, 0.0000) (0.7500, 0.2500, 0.0000) (0.3499, 0.6501, 0.0000) (0.7500, 0.2500, 0.0000) (0.6404, 0.3596, 0.0000) (0.9000, 0.1000, 0.0000) Based on Aggregated Intuitionistic Fuzzy Decsion Matrix (Table 4) and the weightings of criteria and sub-criteria (W) the aggregated weighted intuitionistic fuzzy decision matrix was created, where Eq. 14 and Eq. 15 were used. Advances in Production Engineering & Management 17(4) 2022 463 Patalas-Maliszewska, Łosyk R’ = C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 Table 11 The aggregated weighted intuitionistic fuzzy decision matrix ST (0.874,0.153,0.001) (0.549,0.414,0.037) (0.493,0.519,0.042) (0.617,0.382,0.001) (0.847,0.153,0.000) (0.138,0.862,0.000) (0.229,0.724,0.047) (0.750,0.250,0.000) (0.262,0.737,0.001) (0.750,0.250,0.000) (0.640,0.359,0.001) (0.900,0.100,0.000) TA (0.556, 0.330,0.114) (0.836,0.164,0.000) (0.618,0.382,0.000) (0.415,0.562,0.023) (0.529,0.444,0.027) (0.184,0.816,0.002) (0.349,0.650,0.001) (0.563,0.437,0.000) (0.192,0.773,0.035) (0.750,0.250,0.000) (0.480,0.519,0.001) (0.900,0.100,0.000) OP (0.253, 0.641,0.106) (0.334,0.582,0.084) (0.131,0.728,0.141) (0.082,0.871,0.047) (0.169,0.703,0.128) (0.037,0.935,0.028) (0.166,0.798,0.036) (0.085,0.844,0.071) (0.000,1.000,0.000) (0.224,0.682,0.094) (0.304,0.631,0.065) (0.119,0.814,0.067) In accordance with the division presented in Table 2 the selected criteria belong respectively to the following: J1 = { C1,C2,C6,C7,C8,C9,C10,C11} and J2 = {C3,C5,C12}. T he intuitionistic fuzzy positive-ideal solution and intuitionistic fuzzy negative-ideal solution made by using Eqs. 16 to 20. (0.253,0.641,0.106) (0.836,0.164,0.000) (0.131,0,780,0.089 ) (0.617,0.382,0.001) 𝐴𝐴+ = �(0.847,0.153,0.000) (0.184, 0.816,0.000) (0.166,0.650,0.184 ) (0.750,0.000,0.250)� (0.480,0.250,0.270) 0.847,0.153,0.000 0.640,0.359,0.001) 0.900,0.100,0.000 (0.847,0. 153,0.000) (0.334,0.582,0.084) (0.618,0.382,0.000) (0.082,0.872,0.046) 𝐴𝐴− = �(0.169,0.703,0.128 ) (0.037,0.935,0.028) (0.349,0.650,0.001) (0.085,0.844,0.071) � (0.311,0.623, 0.066) (0.253,0.641, 0.106) (0.024,0.962,0.014) (0.403,0.512,0.085) Measurement of separation between alternatives in the Intuitionistic fuzzy set was made by using normalized Euclidean distance (Eqs. 21 and 22). Then, the relative closeness coefficient to the ideal solution (Eq. 23) was set. The results are presented in Table 12. Table 12 The relative closeness coefficient and separation measures of each level Level of management in company ST TA OP S+ 0.219 0.206 0.305 S0.238 0.227 0.251 Ci* 0.520 0.523 0.451 Rank 2nd 1st 3rd In order to rank the alternatives, the Ci* factor was first calculated and then the alternatives were ranked in decreasing order of Ci*. In the adopted case study, three levels were adopted, which were arranged as follows TA < ST < OP. As a result of calculations, the ST level was accepted as crucial for the examined company. Then, based on the results of the aggregated weighted intuitionistic fuzzy decision matrix (Table 11) key indicators were selected for the SD level by descending order of the μ parameter (Table 13). Rank 1 2 3 4 5 6 7 8 9 10 11 12 Table 13 Key SD objectives for the defined MS level in the context I4.0 Criteria C12 C2 C10 C3 C8 C1 C5 C11 C7 C4 C9 C6 Sub-criteria I14 I3 I12 I4 I9 I10 I1 I6 I13 I8 I5 I11 I7 The results obtained using the F-TOPSIS method represent the key objectives of MS in production enterprises. These objectives should be pursued first, as they form the basis for further activities carried out in the organisation for the benefit of the MS in the context of I4.0. Therefore the values of the key SD objectives set should be determined based on the data included in IT in the I4.0 context (Table 14). 464 Advances in Production Engineering & Management 17(4) 2022 An approach to maintenance sustainability level assessment integrated with Industry 4.0 technologies using Fuzzy-TOPSIS … Table 14 Data source in IT in I4.0 context for the values of the key SD objectives set Rank Criteria Data source 1 C12 ERP 2 C2 ERP 3 C10 MANUALLY 4 C3 ERP 5 C8 ERP 6 C1 ERP 7 C5 ERP 8 C11 ERP 9 C7 MANUALLY 10 C4 MANUALLY 11 C9 MANUALLY 12 C6 MANUALLY 4. Verification and discussion The proposed approach was verified and implemented in five Polish metal companies from the SME sector, in order to verify the usability of applying our model to select SD objectives and to define the needed corrective actions to increase the level of SD in the company. The following company’s activities that are supported by an IT in I4.0 (an ERP system) and its functionality were indicated, namely: Production planning (F1), Cost accounting (F2), Manufacturing execution system (F3), Production technology management (F4), Customer relationship management (F5), Service and repair planning (F6), Personnel management (F7), Warehouse Management (F8), Transport improvement (F9). The following SD indicator values in the analysed company were obtained (Table 15). C C12 C2 C10 C3 S-C I14 I3 I12 I4 Table 15 The base of SD indicator values in the analysed companies Data source ERP ERP MANUALLY EPP Functionality of the ERP system F2 F1 F6 I 640000 kWh over 90 % YES 10 II 38128 kWh over 90 % YES 20 Value III 25000 kWh less than 80 % NO 0 IV 26141 kWh between 80-90 % YES 0 V 41344 kWh less than 80 % YES 16 To determine the reference SD indicators values for a given class of enterprises in a given area the statistical data on a given country, which should be averaged out for a given industry of enterprises should be adopted. Therefore the reference MS indicators values for a given class of enterprises were obtained based on the statistical data in Poland [35] and REACH; ISO 14001; ISO50001; OHSAS 18001 were obtained (Table 16). Table 16 The reference values SD objective C12 C2 C10 C3 SD Indicators I14 I3 I12 I4 Reference values I -5 % over 90 % YES 0 However, to apply our approach to enterprises in other countries, the reference MS indicators values for a given class of enterprises based on the statistical data in the country of the surveyed enterprise should be adopted. Finally, the setting of SD recommendations for the analysed company is possible based on the comparison of the obtained key SD indicator values with the reference values for the SD indicators (Table 17, Table 18). Table 17 Range of values for determining the level of SD MS level Good Medium Low Advances in Production Engineering & Management 17(4) 2022 Compartment < 90-100 % references values < 85-60 % references values > 60 % references values 465 Patalas-Maliszewska, Łosyk Table 18 The base of the obtained SD indicators values in the company compared with the reference values Enterprise I II III IV V Criteria C12 C2 C10 C3 C12 C2 C10 C3 C12 C2 C10 C3 C12 C2 C10 C3 C12 C2 C10 C3 Sub-Criteria I14 I3 I12 I4 I14 I3 I12 I4 I14 I3 I12 I4 I14 I3 I12 I4 I14 I3 I12 I4 Reference values -5 % over 90 % YES 0 -5 % over 90 % YES 0 -5 % over 90 % YES 0 -5 % over 90 % YES 0 -5 % over 90 % YES 0 Obtained values 640000 over 90 % YES 10 38128 over 90 % YES 20 25000 less than 80 % NO 0 26141 between 80-90 % YES 0 41344 less than 80 % YES 16 SD level Check after implementing changes Good Good Low Check after implementing changes Good Good Low Check after implementing changes Low Low Good Check after implementing changes Medium Good Good Check after implementing changes Low Good Low Thanks to the implementation of our model in the analysed company, it is possible to define the key SD objectives: • C12: non-renewable energy consumption • C2: cost of training for maintenance, preventive maintenance time causing downtime • C10: number of innovations carried out related to sustainable maintenance. Moreover, based on Table 18, it is possible to define the needed corrective actions that the company must take to increase its SD level. In the considered case: • reduction of non-renewable energy consumption: e.g., control energy consumption, systematic maintenance and service of machines, use of renewable energy, • staff education: conservation according to the schedule, regular training of maintenance staff, • innovation: intelligent solutions, modern warning systems, automated lubrication, operational diagnostics. The universality of the proposed approach and its adaptability to the specificity of a given company allows it to be employed in different types of enterprises. 5. Conclusion Industry 4.0 technologies and sustainability are popular organizational trends that are vital to increasing sustainable production [36]. However, despite numerous considerations regarding the positive aspects of the implementation of Industry 4.0 technology in the SD concept, further negative effects on the environment are also indicated by throwing outdated equipment [37], and therefore increased greenhouse gas emissions or the production of a large amount of waste [38]. As with all studies, this study owns up to certain limitations that further research should be able to overcome. Firstly, the use of normalized Euclidean distance, which does not take into account the correlation between attributes, and the lack of correlation between criteria and subcriteria are considered limitations of the proposed approach. Secondly, the verification of a model was shown in the example of the Polish companies investigated and all the indicators were measured at the same moment in time; it would, therefore, be useful to provide such research over a longer time period. 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Development of a risk framework for Industry 4.0 in the context of sustainability for established manufacturers, Sustainability, Vol. 11, No. 2, Article No. 384, doi: 10.3390/su11020384. 468 Advances in Production Engineering & Management 17(4) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 4 | December 2022 | pp 469–478 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.4.449 Original scientific paper Optimization of the rhomboidity of continuously cast billets using linear regression and genetic programming: A real industrial study Kovacic, M.a,b,c,*, Zuperl, U.b, Brezocnik, M.d aŠTORE STEEL, d.o.o., Research and Development, Štore, Slovenia of Ljubljana, Faculty of Mechanical Engineering, Laboratory for Fluid Dynamics and Thermodynamics, Ljubljana, Slovenia cCollege of Industrial Engineering, Celje, Slovenia dUniversity of Maribor, Faculty of mechanical engineering, Maribor, Slovenia bUniversity ABSTRACT ARTICLE INFO During the continuous casting of steel billets, several geometrical, inner and surface defects can occur due to the thermomechanical behavior during solidification. One of them is rhombic distortion (i.e. rhomboidity), which can lead to the occurrence of off-corner cracks and twisting of cast billets during further plastic deformation (i.e. rolling). Based on data of 2088 cast batches (64 different hypoeutectoid steel grades), 109,514 billets, produced from January 2022 to September 2022 in Štore Steel Ltd. (Slovenia), chemical composition (content of C, Si, Mn, S, Cr, Mo, Ni and V), casting parameters (average casting temperature, average difference between input and output cooling water, melt level, average cooling water flow and pressure in the first and second zone of secondary cooling) the linear regression and genetic programming were used in order to predict rhomboidity of continuously cast billets. The rhomboidity, in our case defined as relative diagonal difference, was determined using in-house developed computer vision system for measuring of rhomboidity. Based on the modelling results 9 batches (419 billets) of 42CrMos4 were cast in September 2022 with a 10 % higher water pressure in the first zone of secondary cooling (from 2.41 bar to 2.67 bar). The rhomboidity of continuously cast billets improved by 18.18 % (from 1.43 % to 1.21). Keywords: Continuous casting of steel; Casting defects; Rhombic distortion; Rhomboidity; Machine learning; Modelling; Optimization; Prediction; Linear regression; Genetic programming *Corresponding author: miha.kovacic@store-steel.si (Kovacic, M.) Article history: Received 15 June 2022 Revised 19 December 2022 Accepted 22 December 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction Continuous casting, as one of the most important processes in the modern steel industry, takes place when the melt cools rapidly while passing through a copper mould in a horizontal or vertical direction. During primary cooling, the heat from continuously withdrawn strand is taken away by the water-cooled jacket surrounding the mould, and the metal solidifies. Then solidification continues with secondary cooling, where the cast structure is additionally cooled in the air with help of water sprays. During solidification, the solidified shell is exposed to thermomechanical stresses, which can cause many casting defects. In the case of square billets, due to nonuni469 Kovacic, Zuperl, Brezocnik form shell solidification (i.e. nonuniform heat removal in the mould), it can be rhombic distortion (i.e. rhomboidity), which can lead to occurrence of off-corner cracks [1, 2] and twisting of the billets during plastic deformation (i.e. rolling) [3]. Generally, relative diagonal difference is used as a measure of rhomboidity of billets [1]: |𝑑𝑑1 − 𝑑𝑑2 | 𝑑𝑑1 + 𝑑𝑑2 where 𝑑𝑑1 and 𝑑𝑑2 are the lengths of the opposite diagonals of the rhombus. The rhomboidity of the billets is affected by the following parameters [1, 2, 4, 5]: 𝑅𝑅 = 2 (1) • • • • steel chemical composition [6], casting temperature, casting speed, mould (i.e. primary cooling): − chemical composition, − mould thickness [7, 8], − mould tapper [7, 8], − mould support, − water jacket geometry and its alignment [9], − operation (e.g. oscillation, water flow, water quality) [9], • secondary cooling: − water quality, − nozzles geometry, − nozzles assembly, − water pressure. Researches can be divided into measurements and model calculations of the temperature field based on the melt velocity field (e.g. [1, 2]). During the measurements, the rhomboidity and/or temperature of the solidified shell are measured [1, 4, 7, 8, 10]. In this paper the improvement of rhomboidity of continuously cast billets in an industrial environment is presented. A wide range of influencing parameters, not only chemical composition but also casting parameters, have been used to predict of rhomboidity of continuously cast billets for several hypoeutectoid steel grades. Linear regression and genetic programming were used for modelling. At the beginning of the paper, the results of rhomboidity measurements and the influencing parameters are presented. Next, the prediction of rhomboidity of continuously cast billets using linear regression and genetic programming is presented. The results of the optimization of the continuous casting process are also presented and implemented into practice. The casting parameters for 42CrMoS4 steel grade, which is one of the most problematic steel grades in Štore Steel Ltd. in terms of surface defects occurrence, were optimized. Finally, conclusions and future work are highlighted. 2. Materials, methods, and experimental results Štore Steel Ltd. is one of the major flat spring steel producers in Europe. More than 1000 steel grades with different chemical composition are produced. The main steps of the production include the following steps: melting of the scrap using electric arc furnace, tapping, ladle treatment, and continuous casting of the billets. The cooled billets are reheated and rolled in the rolling plant. The rolled bars can be subjected to additionally production operations. Since March 2016, a new two strand continuous casting machine with a radius of 9 m has been in use (Fig. 1). Solidification of the melt takes place during primary cooling in water cooled copper mould, secondary cooling with water sprays, and tertiary radiation in air cooling. Secondary cooling consists of 3 zones. The spray ring in zone 1 is connected directly below the mould support. It consists of 3 rows with spray nozzles which allow a uniform cooling of the 470 Advances in Production Engineering & Management 17(4) 2022 Optimization of the rhomboidity of continuously cast billets using linear regression and genetic programming: A real … billet when it leaves the mould. The upper row is equipped with 8 nozzles, the lower two rows with 4 nozzles. The spray ring system in zone 2 is mounted on the structure in the cooling chamber. It consists of 2 parts – zone 2a and zone 2b. Zone 2a and 2b consist of 8 and 6 rows with spray nozzles, respectively. 5 rows are installed in zone 3. All rows are equipped with 4 nozzles. The continuous casting machine and its cooling zones are schematically presented in Fig. 1. Fig. 1 The continuous casting machine and its cooling zones The company uses in-house developed computer vision system for measurements of rhomboidity. Before entering the cooling bad, each billet is photographed, analyzed, selected features automatically recognized (e.g. billet corners) using computer vision algorithms and finally calculated relative diagonal-difference is stored in the informational system. The in-house developed computer vision system for measurement of rhomboidity of billets is presented in Fig. 2. Fig. 2 In-house developed computer vision system for measurement of rhomoboidity of billets in Štore Steel Ltd. From January 2022 to September 2022, 2088 batches was produced (64 different hypoeutectoid steel grades), and as a result, 109514 billets were cast in Štore Steel Ltd. To reduce the rhomboidity of continuously cast billets following parameters were gathered: Advances in Production Engineering & Management 17(4) 2022 471 Kovacic, Zuperl, Brezocnik • Chemical composition. The content of carbon, silicon, manganese, sulfur, chromium, molybdenum, nickel and vanadium were taking into account. Chemical composition influence on material properties also during solidification (e.g. shrinkage, tensile strength). • Casting parameters were: − Average casting temperature (°C). Casting temperature influences the thermal field in the mould, which influence the heat removal and solidification. − Mould water flow (l/min]. The highest heat removal occurs in the mould, where thermomechanical behavior influences on shell solidification. − Average difference between input and output mould cooling water temperature (°C). This temperature difference is a measure of efficiency of heat removal from the mould (i.e. primary cooling). The mould is cooled with the water. The heating up of the cooling water flowing through the mould indicates the efficiency of heat removal, which influences the thermomechanical behavior during solidification. − Mould metal level (%) expressed as a ratio between operational height of the melt level in the mould and length of the moud (mould is 1 m long copper tube). Delicate melt level movement influences on uniform shell solidification. Nonuniform shell formation leads to rhombic distortion. − The average cooling water pressure (bar) and flow (l/min) in the first (directly below the mould) and the second zone of secondary cooling. The melt primarily solidifies in the mould. After exiting the mould, the strand is cooled by water sprays, where water flux can be automatically set, varying water pressure/flow. Secondary cooling also influences on thermomechanical behavior during solidification. • The rhomboidity of continuously cast billets (%) was determined using in-house developed computer vision system. The average values and standard deviations of gathered influential parameters are presented in Table 1. Table 1 Minimal and maximal values of gathered parameters Parameter Label Average Carbon content (%) C 0.40 Silicon content (%) SI 0.38 Manganese content (%) MN 0.98 Sulfur content (%) S 0.02 Chromium content (%) CR 0.66 Molybdenum content (%) MO 0.06 Nickel content (%) NI 0.21 Vanadium content (%) V 0.06 Average casting temperature (°C) CASTING_TEMPERATURE 1528.71 Mould water flow (l/min) MOULD_WATER_FLOW 1835.71 Average difference between MOULD_WATER_DELTA_TEMPERATURE 7.36 input and output mould cooling water temperature (°C) Mould metal level (%) STEEL_LEVEL 78.09 The average cooling water flow in ZONE1_WATER_FLOW 32.80 the first zone of secondary cooling (l/min) The average cooling water presZONE1_WATER_PRESSURE 2.21 sure in the first zone of secondary cooling (bar) The average cooling water flow in ZONE2_WATER_FLOW 50.72 the second zone of secondary cooling (l/min) The average cooling water presZONE2_WATER_PRESSURE 2.20 sure in the second zone of secondary cooling (bar) Rhomboidity (%) RHOMB 1.36 472 Standard deviation 0.152 0.330 0.270 0.019 0.444 0.067 0.300 0.051 16.978 77.142 0.757 0.932 3.432 0.504 3.981 0.482 1.012 Advances in Production Engineering & Management 17(4) 2022 Optimization of the rhomboidity of continuously cast billets using linear regression and genetic programming: A real … Table 2 Analyzed hypoeutectoid steel grades and number of continuously cast billets Number of continuously Number of continuously Steel grade Steel grade cast billets cast billets 51CrV4 26684 60MnSiCr4 454 C45S 7387 30MnB5 441 16MnCrS5 6694 30CrNiMo8 437 20MnV6 5805 15CrNi6 338 46MnVS5 5442 52SiCrNi5 315 C45 4363 55Si7 265 C50 3880 30NiCrMoV 252 30MnVS6 3542 20NiCrMo2 234 52CrMoV4 3454 37CrV3 230 38B3 3045 100Cr6 166 S355J2 2496 30CrMnV 153 28MnCrB7 2205 65Si7 153 20MnCrS5 1798 50CrMo4 144 16MnCr5 1729 45Mn5S 117 25CrMo4 1346 C35 116 34CrNiMo6 1190 31CrMoV9 110 28MnCrNiB 1115 15NiCr13 106 42CrMoS4 1113 C75 102 42CrMo4 1112 38MnVS5 98 18CrNiMo7-6 1001 50Mn7 97 23MnNiCrMo5-2 985 20NiMoCr6-5 96 61SiCr7 977 36MnVS4 93 38MnVS6 861 70MnVS4 87 20CrMoS5 742 54SiCr6 78 16NiCrS4 640 20MoCrS4 68 31CrV3 588 C15 62 P460NH 516 S235JR 51 C22 516 41CrS4 50 20MnCr5 505 55Cr3 49 18CrMo4 476 60SiMnMoV 47 100Cr6+S 461 25CrMoS4 46 C60 455 S235J2 43 Table 2 shows 64 analyzed hypoeutectoid steel grades and number of continuously cast billets. Fig. 3 shows the average rhomboidity and its standard deviation of continuously cast billets of 20 most problematic hypoeutectoid steel grades. Fig. 3 The average rhomboidity and its standard deviation of continuous cast billets of 20 most problematic hypoeutectoid steel grades Advances in Production Engineering & Management 17(4) 2022 473 Kovacic, Zuperl, Brezocnik 3. Results and discussion Based on the collected data (Table 1), the prediction of rhomboidity of continuously cast billets was conducted. In this paper, two methods are used to support the final decisions more reliably: linear regression approach and the genetic programming evolutionary computational method. The average deviation between predicted and experimental data was selected as the fitness function expressed as: ∆= ′ ∑𝑛𝑛 𝑖𝑖=1�𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖 −𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑖𝑖 � 𝑛𝑛 , (2) In Eq. 1, n is the size of the monitored data, where 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅′ 𝑖𝑖 and 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖 are the actual and the predicted actual rhomboidity of continuously cast billets, respectively. 3.1 Modelling of rhomboidity of continuously cast billets using linear regression Based on the linear regression results, we realized that the model significantly predicts the rhomboidity of continuously cast billets (p < 0.05, ANOVA). Additionally, only 0.048 % of total variances can be explained by independent variables variances (R-square). All parameters are significantly influential except the mould metal level (STEEL_LEVEL), and the average cooling water flow in the first zone of secondary cooling (ZONE1_WATER_FLOW) (p > 0.05). The obtained linear regression model is: RHOMB = −0.426 ∙ C + 0.112 ∙ SI + 0.189 ∙ MN − 1.365 ∙ S + 0.035 ∙ CR + 0.461 ∙ MO − 0.111 ∙ NI − 0.271 ∙ V − 0.002 ∙ CASTING_TEMPERATURE + 0.002 ∙ MOULD_WATER_FLOW − 0.0004 ∙ MOULD_WATER_DELTA_TEMPERATURE + 0.201 ∙ STEEL_LEVEL + 0.010 ∙ ZONE1_WATER_FLOW + (3) 0.168 ∙ ZONE1_WATER_PRESSURE − 0.062 ∙ ZONE2_WATER_FLOW − 0.086 ∙ ZONE2_WATER_PRESSURE + 6.156, The average deviation from experimental data is 6.23 %. The calculated influences of individual parameters on the rhomboidity of continuously cast billets while separately changing individual parameter within the individual parameter range are shown in Fig. 4. While overlooking significant influences, it seems that the mould metal level (STEEL_LEVEL) and the average cooling water flow in the second zone of secondary cooling (ZONE2_WATER_FLOW) are most influential. Fig. 4 The calculated influences of individual parameters on the rhomboidity of continuously cast billets based on linear regression model 474 Advances in Production Engineering & Management 17(4) 2022 Optimization of the rhomboidity of continuously cast billets using linear regression and genetic programming: A real … 3.2 Modelling of rhomboidity of continuously cast billets using genetic programming Genetic programming is a machine learning approach that mimics the natural biological evolution of natural systems. Genetic programming is a general evolutionary optimization method similar to genetic algorithms. Both methods are successfully using to solve very different problems in engineering fields and in many other areas (11-14). In genetic programming, the organisms that undergo adaptation are in fact mathematical expressions (models) of various sizes and contents [15-17]. The content depends on the nature of the problem we are solving. These models consist of the selected and/or defined functions (e.g. mathematical operations of addition, subtraction, multiplication, division) and terminals (e.g. independent input parameters, and random floating-point constants). In the initial generation, random models (i.e. computer programs) of various forms and lengths are generated. In subsequent generations, models are modified by the genetic operations, such as crossover and mutation. After the completion of the variation of the computer programs, a new generation is obtained. During the simulated evolution, each model is evaluated. In most cases, we use experimental data and fitness function for evaluation of models. The iterative process continues until a model that meets the set criteria is obtained. For the purpose of this research, an in-house genetic programming system [18] developed in AutoLISP was used. The following evolutionary parameters were used. The genetic operations of reproduction and crossover were used in the population size of 1000, maximum number of generations was set to 200, probability of reproduction was 0.4, probability of crossover 0.6, and minimum and maximum permissible depth of models in the initial population and after execution of crossover operation was 2 and 6, respectively. For selection of organisms, the tournament method with tournament size 7 was used. One hundred independent runs were caried out. The best mathematical model for prediction of the rhomboidity of continuously cast billets obtained from 100 runs of genetic programming system is: RHOMB = 1 ZONE1_WATER_FLOW 𝐶𝐶 �𝑀𝑀𝑀𝑀 − 𝑆𝑆 − 0.014 � + 𝑆𝑆 + 𝐶𝐶 𝑆𝑆𝑆𝑆 𝑆𝑆 𝐶𝐶 2 𝑆𝑆∙𝑆𝑆𝑆𝑆 �� 𝐶𝐶 𝑀𝑀𝑀𝑀 + ZONE1_WATER_PRESSURE ZONE1_WATER_FLOW �𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶_𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇−𝐶𝐶− �(𝐶𝐶+𝑀𝑀𝑀𝑀+𝑍𝑍𝑍𝑍𝑍𝑍𝑍𝑍1_𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊_𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹) �. 𝐶𝐶2 𝑍𝑍𝑍𝑍𝑍𝑍𝑍𝑍1_𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊_𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 +𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶_𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇−𝑍𝑍𝑍𝑍𝑍𝑍𝑍𝑍1_𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊_𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹+ 𝑀𝑀𝑀𝑀∙𝑆𝑆 𝑆𝑆𝑆𝑆 𝐶𝐶− �+ (4) The average deviation from experimental data produced by the model in Eq. 4 was 5.79 %. The model obtained by genetic programming was 7.52 % better than the one obtained using linear regression. The calculated influences of individual parameters on the rhomboidity of continuously cast billets while separately changing individual parameter within the individual parameter range are shown in Fig. 5. Based on calculated influences it seems that beside chemical composition the average cooling water flow in the first zone of secondary cooling (ZONE1_WATER_FLOW) is most influential. Please mind that content of Cr (CR), Mo (MO), Ni (NI), V (V), average casting temperature (CASTING_TEMPERATURE), mould water flow (MOULD_WATER_FLOW), average difference between input and output mould cooling water temperature (MOULD_WATER_DELTA_TEMPERATURE), mould metal level (STEEL_LEVEL), the average cooling water flow (ZONE2_WATER_FLOW) and pressure (ZONE2_WATER_PRESSURE) in the second zone of secondary cooling are missing in the Eq. 4. Based on this fact, we can conclude that natural selection and crossover operations select the components (i.e. functions or terminals) of mathematical expressions which best describe the collected data. Advances in Production Engineering & Management 17(4) 2022 475 Kovacic, Zuperl, Brezocnik 3% 2,5 % 2% 1,5 % 1% 0,5 % 0% Fig. 5 The calculated influences of individual parameters on the rhomboidity of continuously cast billets based on genetic programming model 3.3 Modelling results and validation 42CrMoS4 steel grade as special structural steel used for highly stressed components for the automotive industry and mechanical engineering (e.g. shafts, connecting rods, crankshafts, screws) is one of the most problematic steel grades in Štore Steel Ltd. in terms of surface defects occurrence. The scrap rate after automatic control line examination of rolled material reaches up to 25 %. As a result, the optimization of the casting parameters was conducted to improve rhomboidity of continuously cast billets. The off-corner cracks and rhomboidity of continuously cast billet of 42CrMoS4 steel grade are presented in Fig. 6. Off-corner cracks at obtuse corners are indicated by arrows. Based on modelling results 9 batches (419 billets) of 42CrMos4 were cast in September 2022 with 10 % higher water pressure in the first zone of secondary cooling (from 2.41 bar to 2.67 bar). The rhomboidity of continuously cast billets improved for 18.54 % (from 1.43 % to 1.21 %). Fig. 6 The off-corner cracks and rhomboidity of continuous cast billet of 42CrMoS4 steel grade 476 Advances in Production Engineering & Management 17(4) 2022 Optimization of the rhomboidity of continuously cast billets using linear regression and genetic programming: A real … The average deviation from experimental data (9 batches, 419 billets of 42CrMoS4 steel grade) of linear regression and genetic programming model for rhomboidity of continuously cast billets are practically the same 0.60 % and 0.59 %, respectively. 4. Conclusions In this paper, the improvement of rhomboidity of continuously cast billets in industrial environment is presented. The wide range of influencing parameters, not only chemical composition but also casting parameters, were used for prediction of rhomboidity of continuously cast billets for several hypoeutectoid steel grades. These are: content of carbon, silicon, manganese, sulfur, chromium, molybdenum, nickel and vanadium, average casting temperature, average difference between input and output cooling water, melt level, average cooling water flow and pressure in the first and second zone of secondary cooling. The in-house developed computer vision system for measurement of rhomboidity of continuously cast billets was used which is installed in the steel plant before cast billets enter the cooling bad. The relative diagonal difference was used as a measure of rhomboidity of billets. To predict the rhomboidity of continuously cast billets, a data of 2088 cast batches (64 different hypoeutectoid steel grades), 109,514 billets, produced from January 2022 to September 2022 in were used. Based on linear regression results all parameters except mould metal level and the average cooling water flow in the first zone of secondary cooling (p > 0.05) are significantly influential. Based on genetic programming results beside chemical composition only the average cooling water flow in the first zone of secondary cooling is influential. 42CrMoS4 steel grade is one of the most problematic steel grades in Štore Steel Ltd. in terms of surface defects occurrence. The scrap rate after automatic control line examination of rolled material reaches up to 25 %. Based on modelling results 9 batches (419 billets) of 42CrMos4 were cast in September 2022 with 10 % higher water pressure in the first zone of secondary cooling (from 2.41 bar to 2.67 bar). The rhomboidity of continuous cast billets improved for 18.54 % (from 1.43 % to 1.21 %). The average deviation from experimental data (9 batches, 419 billets of 42CrMos4 steel grade) of linear regression and genetic programming model for rhomboidity of continuously cast billets are practically the same 0.60 % and 0.59 %, respectively. In the future, secondary metallurgy (i.e. ladle treatment) parameters, refractory material and mould wear-out, strand temperature and other geometrical features of continuously cast billets (e.g. depressions, concavity) will be also taken into account in order to improve the modelling performance. References [1] [2] [3] [4] [5] [6] [7] Patra, P., Tiwari, A., Rathore, P. (2020). In-situ online measurement of rhombic distortion in billets, Engineering Science, Vol. 5, No. 2, 10-16, doi: 10.11648/j.es.20200502.11. Sotnikov, A.L., Strichenko, S.M., Kireev, V.N., Fomenko, Y.V. (2020). State and prospects of upgrading equipment for billet CC machines, Steel in Translation, Vol. 50, 696-706, doi: 10.3103/S0967091220100113. 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China ABSTRACT ARTICLE INFO With the development of commodity market, corporate social responsibility (CSR) has become a topic of widespread concern for both enterprises and society. Cause-related marketing (CRM), as an effective marketing tool for enterprises to fulfill their social responsibility, is rapidly being applied to all stages of the supply chain. However, there is no conclusive evidence on the implementation strategy of CRM for supply chain members. In this paper, we study the decision and pricing strategies of CRM for the manufacturer and the retailer by constructing models for two scenarios: the manufacturer implements CRM, and the retailer implements CRM. We conclude that the donation percentage and the pro-sociality of consumers have a significant impact on the strategic and pricing decisions for supply chain members. The wholesale and selling prices will be higher when the manufacturer implements CRM. Our result also shows that the manufacturer and retailer are profitable in CRM only when the donation amount exceeds a certain percentage. In addition, to maximize profits, the manufacturer is more likely to allow a retailer to implement CRM, and the retailer is only optimally positioned to implement CRM when the pro-sociality of consumers is high or when the donation percentage is high. Keywords: Supply chain management; Cause-related marketing; Corporate social responsibility; Optimal decision; Stackelberg game *Corresponding author: vividyhua@mail.xhu.edu.cn (Duan, H.W.) Article history: Received 22 March 2022 Revised 8 October 2022 Accepted 15 October 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction In a market environment where the price and quality of goods are becoming more and more similar, the single provision of quality products or services can no longer meet the long-term stable development of enterprises [1, 2]. At the same time, with the pursuit of a higher quality experience, consumers are increasingly concerned about the ethical and sustainable conduct of companies [3-5]. Some scholars believe that the social, economic, and environmental behavior of a company is positively related to the profitability of the organization [6-7]. Therefore, the fulfilment of CSR has become one of the key factors indispensable for companies to gain greater competitiveness [8, 9]. As early as 1953, Bowen pointed out that companies should be socially responsible in their business activities and should make corporate decisions based on the goals and values of society. Smith et al. [10] considered corporate responsibility as something that goes beyond economics and law; enterprises also need to focus on politics, education, and welfare. In order to seek better survival and development, it has become a goal for companies to strive to find a marketing method that can balance the acquisition of profit and fulfill social responsibility [11, 12]. Cause-related marketing (CRM), as a combination of CSR and marketing, 479 Xu, Liu, Duan which can not only help firms fulfil their social responsibility and enhance brand image, but also have a positive impact on consumers' willingness to purchase, gradually becomes an effective tool in the marketing area [13]. CSR was introduced in the 1980s and has become one of the major concerns of the business community [14], and CRM is one of the ways in which companies can fulfill their social responsibility. In 1981, American Express partnered with a non-profit organization to link consumers with donations by donating two pennies to the charity for every purchase made with an Express card. The campaign not only generated additional revenue for Express, but also supported the daily operations of the charity. Another example of CRM is the Chinese brand Nongfu Spring, which launched a campaign in 2001, stating that for every mineral water sold, one cent of the proceeds would be donated to support the Olympic bid matters. When a company chooses to engage in CSR, consumers' purchasing decisions may depend not only on the intrinsic value of the product, but also on its social impact. CRM not only builds brand dependence among consumers, and creates higher revenue for the company, but also contributes to society and the environment, creating a win-win situation [15]. It is because of the multiple positive impacts of CRM for businesses that it has become a successful initiative for all types of organizations [1617]. CRM is also widely used in all stages of the supply chain, with upstream suppliers and downstream retailers participating [18]. Supply chain members practice CRM by partnering with non-profit organizations to donate a portion of the proceeds from the sales to the community. At the same time, they will advertise for charity events. A survey shows that most consumers learn about and participate in causes through advertising [19]. In this paper, we analyze the manufacturer's and retailer's decisions and pricing strategies for implementing CRM by constructing a model in the context of the supply chain and discuss the impact of donation percentage and pro-sociality of consumers on the manufacturer's and retailer's decisions. We pose and address the following questions: • How should the price of the manufacturer and retailer price when they implement CRM and how does the donation percentage affect pricing? • How does the donation percentage and the pro-sociality of consumers in the target market to CRM affect the manufacturer's and retailer's decisions? • What kind of marketing strategy should the manufacturer and the retailer develop for the benefit of the supply chain as a whole? We consider a supply chain system consisting of a manufacturer and a retailer who play a Stackelberg game with the goal of maximizing their respective profits. We solve and analyze the optimal and equilibrium solutions of the model by constructing two scenarios, one for the manufacturer and one for the retailer. Our work will provide a suggestion for the implementation of CRM and supply chain management. The remainder of this paper is organized as follows: Section 2 summarizes the previous literature. Section 3 illustrates the notation in this paper and models for the manufacturer and the retailer. In Section 4, we analyze the pricing and CRM decisions, and discuss the effects of donation percentage and consumer’s pro-sociality. Section 5 uses arithmetic examples to validate the analysis in the previous sections. Finally, we draw conclusions in Section 6. All proofs of the paper are in the Appendix. 2. Literature review This paper examines the CRM strategies of supply chain members who fulfill their CSR. Therefore, we build our study on supply chain CSR and CRM. Many scholars have quantitatively analyzed supply chain CSR using empirical methods. Mani et al. [20] found that corporate engagement in CSR promotes mutual benefits among supply chain partners, increases trust to foster long-term trusting relationships. Maloni et al. [21] have studied CSR in the food industry and developed a comprehensive framework for supply chain CSR in this industry. Valdez-Juárez et al. [22] showed that CSR and SCM have a strong interdependence. Many scholars have analyzed the issue of supply chain CSR performance and influenc480 Advances in Production Engineering & Management 17(4) 2022 Cause-related marketing strategy in a supply chain: A theoretical analysis and a case study ing factors by building models. Arya et al. [23] analyzed the situation where the social benefits of a company's CSR strategy have nothing to do with product sales. Raza [24] demonstrated that it is feasible for manufacturers to undertake CSR investments to improve the profitability of their supply chain. Hsueh [8] analyzed the supply chain CSR and concluded that a new revenuesharing contract with corporate social responsibility (RS-CSR) can achieve the goal of improving both performance and total supply chain profitability. Panda et al. [25] explored channel coordination and profit-sharing in socially responsible supply chains, concluding that CSR and its share are key determinants of channel members' net profits, and that supply chain members should pay attention to the CSR practices of other members. Liu et al. [26] concluded that a certain range of government subsidies can promote CSR among supply chain members and improve the overall performance and social welfare. Yan et al. [27] have shown that the retailer with CSR investment practices earns more profits than those without CSR investments. Most of the existing literature has studied CSR in terms of its performance and influencing factors, while little research has been done on the decision-making aspects of supply chain members. In contrast, we combine CRM and supply chain to study the pricing and strategic decisions of supply chain members in fulfilling social responsibility by building a model. In terms of the effectiveness of CRM, Cheng et al. [28] found that consumers are more likely to buy brands that implement CRM. However, Furman et al. [29] argued that not all CRM campaigns are effective in influencing consumer decisions. Arya et al. [23] found by constructing a model that implementing CRM leads to an increase in the price of cause-related products. In contrast, Gao [18] argued that the implementation of CRM results in lower product pricing. There are also some scholars who have given conclusions on the relationship between CRM and consumers. Kraft et al. [30] thought that consumers in the segment have different pro-sociality. Silva et al. [31] concluded that consumers' cause-related identification has a positive impact on their perceived value. Vyravene et al. [32] demonstrated that the product-cause fit affects consumer attitudes toward the brand. A subset of scholars has examined the role of the donation amount. Moosmayer et al. [33] believed that the higher the amount of giving, the better the consumer perception of the CRM campaign. Tsiros et al. [34] considered that both the total amount donated and the method of communication influence consumer response to CRM. Kerr et al. [35] concluded that for individuals with a high perceived need, purchase intentions for the exact donation form are greater when the product-cause fit is low, regardless of the donation form. Grolleau et al. [36] believed the crowding-out effect may be particularly strong if the cause-linked products are targeted at consumers who have provided direct donations. In terms of CRM in the supply chain, Barone et al. [37] thought that consumer perceptions of retailers' motivation to engage in CRM, the affinity of CRM, and the interaction effects associated with the two moderators can have a significant impact on retailer-cause fit. Choi et al. [38] indicated that for the label to be able to convey information to consumers about the fulfillment of CSR, manufacturers should therefore make special designs for the packaging. Heydari et al. [39] proposed a cost-sharing contract and collaboration model when the manufacturer implements CRM and concluded that the collaboration model can increase the profits of channel members. Although Gao [18] explored that decentralized supply chains can generate more social value through CRM, he did not consider the promotional costs of CRM in his study. In summary, previous research has been extremely fruitful, whether from the perspective of consumers or effects for supply chain, but little literature has considered the decision to implement CRM for supply chain members. In addition, while we examine the implementation strategy of CRM, we also consider the cost of promotion during CRM, which has not been addressed in the previous literature. 3. Model formulation and notation In this paper, we consider a supply chain consisting of a manufacturer and a retailer, where both of them are risk-neutral and perfectly rational, making decisions to maximize their profits. The manufacturer is the leader, and the retailer is the follower in the Stackelberg game. The manuAdvances in Production Engineering & Management 17(4) 2022 481 Xu, Liu, Duan facturer has to decide whether to implement CRM himself or to delegate CRM to the retailer, as well as price strategies. The retailer reacts according to the manufacturer's strategy. The manufacturer produces the product at a production cost of 𝑐𝑐 and distributes it to the retailer at a wholesale price of 𝑤𝑤. The retailer sells the product to the consumer at a selling price of 𝑝𝑝. It is assumed that both the manufacturer and the retailer will advertise for their CRM campaign, and therefore incur promotional costs 𝐴𝐴. The cost of promotion will affect consumer utility. Since the utility does not increase indefinitely with the cost, we assume that the additional utility of CRM by the manufacturer or retailer is √𝐴𝐴. Additionally, we denote 𝑣𝑣 by the consumer's perceived value of the product, 𝑣𝑣 serving a uniform distribution between 0 and 1, i.e., 𝑣𝑣~𝑈𝑈[0,1]. Show that in a market of size 1, the price that consumers are willing to pay for this product is uniformly distributed between 0 and 1. At the same time, we use 𝛿𝛿 to denote consumer’s prosociality, i.e., the degree of consumer sensitivity to CRM, and the degree to which the level of CRM donations stimulates consumer buying behavior. We use 𝜂𝜂 to indicate the donation percentage of sales per unit of product, and in other words, it is the donation amount as a percentage of the sales price or wholesale price. Thus, the utility function is 𝑈𝑈 = 𝑣𝑣 − 𝑝𝑝 + 𝛿𝛿𝛿𝛿√𝐴𝐴. And we assume that a consumer will buy the product only if the utility function is greater than zero, i.e., 𝑣𝑣 ≥ 𝑝𝑝 + 𝛿𝛿𝛿𝛿√𝐴𝐴. The number of consumers in a market of size 1 is 1 − 𝑝𝑝 + 𝛿𝛿𝛿𝛿√𝐴𝐴, and the demand function can be obtained as 𝑑𝑑 = 1 − 𝑝𝑝 + 𝛿𝛿𝛿𝛿√𝐴𝐴. The parameters and variables mentioned in the model and their meanings are listed in the table below: Notation 𝑐𝑐 𝑝𝑝 𝑤𝑤 𝛿𝛿 𝜂𝜂 𝐴𝐴 𝜋𝜋𝑚𝑚 𝜋𝜋𝑟𝑟 𝜋𝜋𝑠𝑠 ∙𝑀𝑀 ∙𝑅𝑅 Table 1 Model parameters and decision variables Description The unit production cost of the product The unit sales price of the product The unit wholesale price of the product Consumer sensitivity to cause-related marketing （δ ≥ 0） The proportion of wholesale price or sales price per unit donation amount Promotional costs arising from the implementation of CRM The profit of the manufacturer The profit of the manufacturer Total social welfare The scenario of the manufacturer implementing CRM The scenario of the retailer implementing CRM To avoid a meaningless discussion, we propose the following assumptions: (2−√1+3𝑐𝑐) (1) We assume that 𝜂𝜂 < and 1 − 𝑐𝑐 − 𝜂𝜂 > 0, the profit is guaranteed to be greater than 3 zero when the supply chain members implement CRM and the amount donated is limited by the production cost, which is in line with the real meaning. (2) We assume that 𝛿𝛿 < �2(1−𝜂𝜂) ，it suggests 𝜂𝜂(1−𝜂𝜂) that consumers' sensitivity to CRM is influenced by the percentage of the donation, and that this sensitivity is bounded and does not increase indefinitely as the donation amount increases. (3) Assuming that both the manufacturer and the retailer are equipped to implement CRM and are skilled in CRM techniques. 3.1 The manufacturer implements cause-related marketing In this scenario, the manufacturer implements CRM by donating a percentage of the wholesale price to the charity for each unit of product sold incurring promotional costs for CRM. When the manufacturer implements CRM, the profit functions for the manufacturer and the retailer, as well as the social welfare, are as follows: 𝑀𝑀 (1) 𝜋𝜋𝑚𝑚 = (𝑤𝑤 − 𝜂𝜂𝑤𝑤 − 𝑐𝑐)𝑑𝑑 − 𝐴𝐴 482 𝜋𝜋𝑠𝑠𝑀𝑀 = 𝑀𝑀 𝜋𝜋𝑚𝑚 𝜋𝜋𝑟𝑟𝑀𝑀 = (𝑝𝑝 − 𝑤𝑤)𝑑𝑑 + 𝜋𝜋𝑟𝑟𝑀𝑀 = (𝑝𝑝 − 𝜂𝜂𝜂𝜂 − 𝑐𝑐)𝑑𝑑 − 𝐴𝐴 (2) (3) Advances in Production Engineering & Management 17(4) 2022 Cause-related marketing strategy in a supply chain: A theoretical analysis and a case study Proposition 1: We obtain the optimal solutions when the manufacturer implements CRM as follows: (1 − 𝑐𝑐 − 𝜂𝜂)2 𝛿𝛿 2 𝜂𝜂2 (4) 𝐴𝐴𝑀𝑀∗ = 8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 𝑤𝑤 𝑀𝑀∗ = 𝑝𝑝𝑀𝑀∗ = 4(1 − 𝑐𝑐 − 𝜂𝜂)−𝑐𝑐𝑐𝑐 2 (1 − 𝜂𝜂) (1 − 𝜂𝜂)(8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 ) 2(3 + 𝑐𝑐 − 3𝜂𝜂)−𝑐𝑐𝑐𝑐 2 (1 − 𝜂𝜂) (1 − 𝜂𝜂)(8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 ) From Proposition 1 we can obtain Eqs. 7-9： (1 − 𝑐𝑐 − 𝜂𝜂)2 𝑀𝑀∗ 𝜋𝜋𝑚𝑚 = (1 − 𝜂𝜂)(8 + 𝛿𝛿 2 𝜂𝜂3 − 𝛿𝛿 2 𝜂𝜂 2 ) 4(1 − 𝑐𝑐 − 𝜂𝜂)2 𝜋𝜋𝑟𝑟𝑀𝑀∗ = (1 − 𝜂𝜂)2 (8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 )2 𝜋𝜋𝑠𝑠𝑀𝑀∗ = (1 − 𝑐𝑐 − 𝜂𝜂)2 (12 − 8𝜂𝜂 − 𝛿𝛿 2 𝜂𝜂 2 (1 − 2𝜂𝜂 − 𝜂𝜂 2 )) (1 − 𝜂𝜂)2 (8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂2 )2 (5) (6) (7) (8) (9) We obtain Corollary 1 and Corollary 2 by finding the first-order derivatives of Eqs. 4-9 with respect to 𝜂𝜂. Corollary 1: 𝑑𝑑𝐴𝐴𝑀𝑀∗ 𝑑𝑑𝑑𝑑 > 0, 𝑑𝑑𝑤𝑤 𝑀𝑀∗ 𝑑𝑑𝑑𝑑 > 0, 𝑑𝑑𝑝𝑝𝑀𝑀∗ 𝑑𝑑𝑑𝑑 > 0. Corollary 1 shows that when the manufacturer implements CRM, the pricing strategies are influenced by the donation percentage. Within the constraint, the cost of promotion, the manufacturer's wholesale price, and the retailer's selling price increase with the donation amount. This is because when the manufacturer makes a charitable donation, if the amount of donation is relatively higher, then the wholesale price will also increase, and therefore the retailer will also increase the sales price. At the same time, as the number of donations increases, the manufacturer will also spend more to publicize the behavior. Corollary 2: 𝑀𝑀∗ 𝑑𝑑𝜋𝜋𝑚𝑚 𝑑𝑑𝜋𝜋𝑀𝑀∗ < 0 and 𝑑𝑑𝑑𝑑𝑟𝑟 < 0; 𝑑𝑑𝑑𝑑 𝑑𝑑𝜋𝜋𝑀𝑀∗ 𝑑𝑑𝜋𝜋𝑀𝑀∗ 𝑀𝑀 𝛿𝛿𝑟𝑟𝑀𝑀 < 𝛿𝛿 < 𝛿𝛿𝑚𝑚 , then 𝑚𝑚 < 0 and 𝑟𝑟 > 0; 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝑀𝑀∗ 𝑑𝑑𝜋𝜋𝑚𝑚 𝑑𝑑𝜋𝜋𝑀𝑀∗ �2(1−𝜂𝜂) 𝑀𝑀 𝛿𝛿𝑚𝑚 < 𝛿𝛿 < 𝜂𝜂(1−𝜂𝜂) , then 𝑑𝑑𝑑𝑑 > 0 and 𝑑𝑑𝑑𝑑𝑟𝑟 > (i) If 0 < 𝛿𝛿 < 𝛿𝛿𝑟𝑟𝑀𝑀 , then (ii) If (iii) If Where 𝛿𝛿𝑟𝑟𝑀𝑀 = 2� 2𝑐𝑐 , 𝛿𝛿 𝑀𝑀 𝜂𝜂(1−𝜂𝜂)((3𝜂𝜂+4𝑐𝑐−5)𝜂𝜂+2(1−𝑐𝑐)) 𝑚𝑚 0. 1−𝑐𝑐−𝜂𝜂 . 𝜂𝜂(1−𝜂𝜂)((𝜂𝜂+2𝑐𝑐−2)𝜂𝜂+1−𝑐𝑐) = 2� It is known from Corollary 2 that the profits of the manufacturer and the retailer are jointly affected by the proportion of donation and the pro-sociality of the consumer to CRM. From Corollary 2(i) we are able to obtain that when the pro-sociality of consumer to CRM is less than the threshold value 𝛿𝛿𝑟𝑟𝑀𝑀 , the profits of the manufacturer and the retailer decrease simultaneously with the donation amount; while when the pro-sociality of consumers to CRM is greater than 𝛿𝛿𝑟𝑟𝑀𝑀 𝑀𝑀 , the profits of the manufacturer still decrease, while the profits of the retailer and less than 𝛿𝛿𝑚𝑚 increase with the donation ratio; finally, when the pro-sociality of consumer to CRM is greater 𝑀𝑀 , the profits of the manufacturer and the retailer increase simultaneously. than 𝛿𝛿𝑚𝑚 The Corollary 1 and Corollary 2 show that the profits of the manufacturer and retailer decrease and then increase with the percentage of donations. However, both the manufacturer and the retailer are motivated to implement CRM only if their profits both increase under the influence of the donation amount. At the same time, the manufacturer and retailer’s profits are governed by consumer sensitivity to CRM in the segment. When the manufacturer implements CRM, Advances in Production Engineering & Management 17(4) 2022 483 Xu, Liu, Duan if the segment consumers are relatively low pro-sociality, the donation will have a negative impact on the profits of the manufacturer and retailer, or even reduce the profits; while the target market consumer’s pro-sociality is middle, the donation activities are beneficial for the retailer at this time, but not for the manufacturer; and when the consumer in the target market is more sensitive to public welfare behaviour, the implementation of CRM for the manufacturer can not only increase his own profits, the retailer can also be profitable. 3.2 The retailer implements cause-related marketing In this case, the retailer implements CRM, donating a percentage of the selling price to the charity for each unit of product sold, as well as spending the advertising costs of the CRM. Then, when the retailer implements CRM, the profit functions of the manufacturer and the retailer as well as social welfare are as follows. 𝜋𝜋𝑠𝑠𝑅𝑅 = 𝑅𝑅 𝜋𝜋𝑚𝑚 = (𝑤𝑤 − 𝑐𝑐)𝑑𝑑 𝜋𝜋𝑟𝑟𝑅𝑅 = (𝑝𝑝 − 𝜂𝜂𝜂𝜂 − 𝑤𝑤)𝑑𝑑 − 𝐴𝐴 𝑅𝑅 𝜋𝜋𝑚𝑚 + 𝜋𝜋𝑟𝑟𝑅𝑅 = (𝑝𝑝 − 𝜂𝜂𝜂𝜂 − 𝑐𝑐)𝑑𝑑 − 𝐴𝐴 (10) (11) (12) Proposition 2: We obtain the optimal solutions when the retailer implements CRM as follows. (1 + 𝑐𝑐 − 𝜂𝜂)2 𝛿𝛿 2 𝜂𝜂 2 4(4 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 )2 1 − 𝑐𝑐 − 𝜂𝜂 𝑤𝑤 𝑅𝑅∗ = 2 2 2 (1 2(1 + 3𝑐𝑐 − 3𝜂𝜂)−𝑐𝑐𝑐𝑐 𝜂𝜂 − 𝜂𝜂) − 𝛿𝛿 2 𝜂𝜂2 (1 + 𝜂𝜂 2 − 2𝜂𝜂) = 2(1 − 𝜂𝜂)(4 + 𝛿𝛿 2 𝜂𝜂3 − 𝛿𝛿 2 𝜂𝜂 2 ) 𝐴𝐴𝑅𝑅∗ = 𝑝𝑝𝑅𝑅∗ From Proposition 2 we can obtain Eqs. 16-18： 𝑅𝑅∗ 𝜋𝜋𝑚𝑚 (13) (14) (15) (1 − 𝑐𝑐 − 𝜂𝜂)2 = 2(1 − 𝜂𝜂)(4 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂2 ) (16) 3(1 − 𝑐𝑐 − 𝜂𝜂)2 4(1 − 𝜂𝜂)(4 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 ) (18) 𝜋𝜋𝑟𝑟𝑅𝑅∗ = 𝜋𝜋𝑠𝑠𝑀𝑀∗ = (1 − 𝑐𝑐 − 𝜂𝜂)2 4(1 − 𝜂𝜂)(4 + 𝛿𝛿 2 𝜂𝜂3 − 𝛿𝛿 2 𝜂𝜂 2 ) (17) We obtain Corollary 3 and Corollary 4 by finding the first order derivatives of Eqs. 13-18 with respect to 𝜂𝜂. Corollary 3: 𝑑𝑑𝐴𝐴𝑅𝑅∗ 𝑑𝑑𝑑𝑑 > 0, 𝑑𝑑𝑤𝑤 𝑅𝑅∗ 𝑑𝑑𝑑𝑑 < 0, 𝑑𝑑𝑝𝑝𝑅𝑅∗ 𝑑𝑑𝑑𝑑 > 0. Through Corollary 3, the promotional costs, sales prices, and the manufacturers' wholesale prices are influenced by the proportion of donations in the retailer's donation behaviour. Within the constraint, the advertising cost required for CRM and the retailer's selling price increase with the percentage of donation. That is, when the retailer implements CRM, if he donates a higher amount, it should be equipped with more publicity. Also, to ensure profitability, the retailer’s selling price will increase. In contrast, the manufacturer's wholesale price differs from the previous analysis in that it tends to decrease as the proportion of donations increases. In another words, as long as the retailer implements CRM, the cost he has to spend to obtain the product at the manufacturer will decrease. Corollary 4: (i) If 0 < 𝛿𝛿 < 𝛿𝛿 𝑅𝑅 , then 484 𝑅𝑅∗ 𝑑𝑑𝜋𝜋𝑚𝑚 𝑑𝑑𝑑𝑑 < 0 and 𝑑𝑑𝜋𝜋𝑟𝑟𝑅𝑅∗ 𝑑𝑑𝑑𝑑 < 0; Advances in Production Engineering & Management 17(4) 2022 Cause-related marketing strategy in a supply chain: A theoretical analysis and a case study (ii) If 𝛿𝛿 𝑅𝑅 < 𝛿𝛿 < 𝑅𝑅∗ 𝑑𝑑𝜋𝜋𝑚𝑚 �2(1−𝜂𝜂) , then 𝜂𝜂(1−𝜂𝜂) 𝑑𝑑𝑑𝑑 > 0 and 2(1−𝑐𝑐−𝜂𝜂) . 𝜂𝜂(1−𝜂𝜂)((𝜂𝜂+2𝑐𝑐−2)𝜂𝜂+1−𝑐𝑐) Where 𝛿𝛿 𝑅𝑅 = 2� 𝑑𝑑𝜋𝜋𝑟𝑟𝑅𝑅∗ 𝑑𝑑𝑑𝑑 > 0. Corollary 4 suggests that when retailer practices CRM, profits are equally influenced by consumers' pro-sociality and the percentage of his donations. When consumer’s pro-sociality is below than the threshold 𝛿𝛿 𝑅𝑅 , the profits of both the manufacturer and the retailer decrease as the donation percentage increases; conversely, when consumer’s pro-sociality is above the 𝛿𝛿 𝑅𝑅 , the profits of both the manufacturer and the retailer increase as the donation ratio increases. In the case of a retailer implementing CRM, the benefits to both the manufacturer and the retailer are synchronized, with both tending to decrease and then increase as the percentage of donations increases. This means that when consumers in the target market are relatively less pro-social, the implementation of CRM by the retailer does not help to improve the profitability of both, and it is only when the social awareness of the consumer base is relatively higher that the retailer comes to implement CRM to the benefit of the supply chain. 4. Analysis From the Corollary 1 and 3, pricing strategies as well as promotional cost is not influenced by the pro-sociality of consumers in the segment, but only by the percentage of donations made when they implement CRM. Corollary 5: 𝐴𝐴𝑀𝑀∗ < 𝐴𝐴𝑅𝑅∗ , 𝑤𝑤 𝑀𝑀∗ > 𝑤𝑤 𝑅𝑅∗ , 𝑝𝑝𝑀𝑀∗ > 𝑝𝑝𝑅𝑅∗ . Corollary 5 suggests that when the manufacturer implements CRM, the wholesale prices and sales prices will be relatively high but promotional costs will be less. That is the higher wholesale price will result in a corresponding increase in selling price. In terms of pricing alone, it makes sense for the manufacturer to implement CRM for supply chain members. This is because it costs less and generates more income. Corollary 6: 𝑀𝑀∗ 𝑅𝑅∗ (i) 𝜋𝜋𝑚𝑚 < 𝜋𝜋𝑚𝑚 ; 1 9 (ii) When 0 < 𝜂𝜂 < , if 0 < 𝛿𝛿 < 𝛿𝛿 ′ , then 𝜋𝜋𝑟𝑟𝑀𝑀∗ > 𝜋𝜋𝑟𝑟𝑅𝑅∗ ; if 𝛿𝛿 ′ < δ < 1 9 (iii) When 𝜂𝜂 > , then 𝜋𝜋𝑟𝑟𝑀𝑀∗ > 𝜋𝜋𝑟𝑟𝑅𝑅∗ . Where 𝛿𝛿 ′ = �2(1−𝜂𝜂) , then 𝜋𝜋𝑟𝑟𝑀𝑀∗ 𝜂𝜂(1−𝜂𝜂) < 𝜋𝜋𝑟𝑟𝑅𝑅∗ ; �8��𝜂𝜂−𝜂𝜂� 𝜂𝜂(1−𝜂𝜂) . Corollary 6(i) indicates that the manufacturer can make higher profits when the retailer implements CRM. Even at a lower cost and a higher price, the manufacturer is not more profitable. From Corollary 6(ii) and (iii), for the retailer, the percentage of donations affects the outcome of the decisions. For the retailer, Corollary 6(ii) suggests that it is more advantageous for the manufacturer to implement CRM when both the amount of donation and the pro-sociality of the consumer are lower. However, if the percentage of donations is small but the consumers are more aware of charity, it is more beneficial for the retailer to implement CRM. Conversely, CRM by the manufacturer is more beneficial to the retailer if a larger percentage of donations are made. Since our discussion is focused on the manufacturer as the leader, the manufacturer will choose to maximize its profits by delegating the implementation of CRM to the retailer. It is not that the retailer does not profit from CRM at this point, but it is less profitable than when the manufacturer implements CRM. Corollary 7: If 0 < 𝛿𝛿 < 𝛿𝛿𝑠𝑠 , then 𝜋𝜋𝑠𝑠𝑀𝑀∗ > 𝜋𝜋𝑠𝑠𝑅𝑅∗ ; if 𝛿𝛿𝑠𝑠 < δ < �2(1−𝜂𝜂) , then 𝜋𝜋𝑠𝑠𝑀𝑀∗ 𝜂𝜂(1−𝜂𝜂) Advances in Production Engineering & Management 17(4) 2022 < 𝜋𝜋𝑠𝑠𝑅𝑅∗ . 485 Xu, Liu, Duan Where 𝛿𝛿𝑠𝑠 = 2�2(1−�1−𝜂𝜂+𝜂𝜂2 ) 𝜂𝜂(1−𝜂𝜂) . Corollary 7 illustrates the effect of the pro-sociality of the segment on social welfare. When the pro-sociality of consumers is lower than the threshold 𝛿𝛿𝑠𝑠 , the social welfare of the manufacturer's implementation is higher, but when the sensitivity of the target market to CRM exceeds the threshold 𝛿𝛿𝑠𝑠 , the social welfare of the retailer's implementation of CRM is higher. 5. Numerical examples In this section, we present numerical examples to illustrate the theoretical results. We let the manufacturing cost 𝑐𝑐 = 0.2 and show the effect of the donation percentage on the decision variables, optimal profit, and the pro-sociality of the segment on social welfare in the form of figures. 5.1 Effect of donation percentage on decision variables We plot the effect on the advertising costs, the optimal wholesale price and the optimal sales price of donation percentage 𝜂𝜂 . Fig. 1 Effect of donation percentage on decision variables (𝛿𝛿 = 6) Fig. 1 reflects the effect of the proportion of CRM donations on the decision variables in Corollary 1 and Corollary 3. Fig 1(a) shows that as the donation percentage increases for both the manufacturer and the retailer, the promotional costs and selling price become larger. Further, the retailer's promotional costs are higher when CRM is implemented. As shown in fig. 1(b), for the wholesale price, it decreases with the increase of the donation percentage when the retailer implements the CRM, while the opposite is true when the manufacturer implements the CRM. And when the manufacturer implements CRM, the wholesale price is higher. From Fig. 1(c), we can conclude that the product price increases after the implementation of CRM, and the price increases faster when the manufacturer implements donations. 5.2 Effect of donation percentage on optimal profits We show the effect of the donation percentage on the implementation of CRM strategies by the manufacturer and the retailer at different levels of consumer pro-sociality in the form of arithmetic examples. Through the previous analysis of optimal profit, when the manufacturer implements CRM, we can classify the degree of pro-sociality of the market segment into low, medium and high levels. 486 Advances in Production Engineering & Management 17(4) 2022 Cause-related marketing strategy in a supply chain: A theoretical analysis and a case study Fig. 2 Effect of donation parentage on profit when the manufacturer implements CRM The three images in Fig. 2 represent how the percentage of donations affects the profits of the manufacturer and the retailer when the manufacturer implements CRM for three different magnitudes of consumer’s pro-sociality. As shown in the previous analysis, when the pro-social awareness of consumers is weak, as in Fig. 2(a), these consumers do not care about the public welfare behavior of companies, therefore, they will not be motivated to make purchases by the welfare activities of companies. In this case, the manufacturer only invests the donation amount and the promotion cost but does not obtain the desired effect of revenue. While the wholesale price increases due to the increase of the donation amount, so the profit of the manufacturer and the retailer is in a simultaneous decline in this case. Fig. 2(b) shows the profitability when the manufacturer implements CRM when the consumer’s sensitivity to CRM is at a medium level. As shown in the figure, the manufacturer's profit is still decreasing, but the decreasing trend is slowing down, which means that as the amount of donation increases, the impact of its change on the company's maximum profit is gradually becoming weaker; at the same time, the optimal profit of the retailer increases with the donation percentage, because of higher pro-sociality, the benefits of CRM can already offset the costs and bring additional benefits for the retailer. Fig. 2(c) shows a situation where the consumer base has a high awareness of public goods, and consumers are influenced by CRM to make purchases. At this point, if the manufacturer carries out donation activities, it will benefit both itself and the retailer, and the benefits of both will increase as the donation amount increases. We have used the images above to verify the effect of consumer pro-sociality and donation percentage on the optimal profits when the manufacturer implements CRM, and we will now look at the scenario when the retailer implements CRM. When the retailer implements CRM, we classify the pro-sociality of consumers into two levels. Fig. 3 represents the trend of profitability when the retailer implements CRM. Like the manufacturer's implementation, the optimal profit of the retailer and the manufacturer is affected by the strength of the pro-sociality of the consumers. When this sensitivity is weak, the donation of the retailer will result in losses for both manufacturer and retailer. Conversely, in more prosocial consumer markets, a cause campaign can generate higher returns for both the manufacturer and the retailer, and the higher the amount donated, the greater the return. Below we validate the strategic decisions of the manufacturer and retailer to CRM. In the figure, we show the impact of consumer’s pro-sociality on the CRM decisions of the manufacturer 𝑅𝑅 𝑀𝑀 -𝜋𝜋𝑚𝑚 and the retailer in terms of low and high donation percentages. We use ∆𝜋𝜋𝑚𝑚 to denote 𝜋𝜋𝑚𝑚 𝑅𝑅 𝑀𝑀 and ∆𝜋𝜋𝑚𝑚 to denote 𝜋𝜋𝑟𝑟 -𝜋𝜋𝑟𝑟 . From Fig. 4, we can conclude that the donation strategies are not the same for different donation percentages. Advances in Production Engineering & Management 17(4) 2022 487 Xu, Liu, Duan Fig. 3 Effect of donation parentage on profit when the retailer implements CRM Fig. 4 Effect of consumer’s pro-sociality on optimal profit with different donation percentage As can be seen from the two graphs in Fig. 4, the manufacturer's decision is not influenced by the donation percentage and consumer sensitivity to CRM. Further, the manufacturer receives higher profits whenever the retailer implements CRM, so the manufacturer with the retailer should implement CRM. Differently, the retailer's decision is influenced by both the donation percentage and the consumer's sensitivity. Fig. 4(a) shows that if the donation percentage chosen by the donor is small and the consumer's pro-social awareness is weak, the retailer will not choose to implement CRM; if the consumer's sensitivity is high relatively, it is profitable for the retailer to implement CRM. Fig. 4(b) illustrates that it is more beneficial for the retailer when the manufacturer to implements CRM with a higher donation amount. 5.3 Impact of consumer’s pro-sociality on social welfare In the previous analysis, we obtained that the pro-sociality of consumers in the segment affects the retailer's decision, while the manufacturer's decision is independent of it. In this section, we use images to represent the impact of consumer pro-sociality on the overall profitability of the supply chain, also known as social welfare. We let 𝜂𝜂 = 0.05 . 488 Advances in Production Engineering & Management 17(4) 2022 Cause-related marketing strategy in a supply chain: A theoretical analysis and a case study Fig. 5 Impact of consumer’s pro-sociality on social welfare Fig. 5 analyses the social welfare of the whole supply chain from the point of view of consumer’s pro-sociality. As can be seen from the figure, the sensitivity of consumers to CRM affects the subject of implementing CRM. If the overall pro-social awareness of the consumer group in the market is low, the manufacturer's implementation of CRM is more beneficial to the supply chain as a whole; if the pro-social awareness of the consumer in the target market is high, then the retailer's implementation of CRM is beneficial to the whole supply chain. 6. Conclusion In this paper, we examine the pricing and decision-making issues of implementing CRM by socially responsible supply chain members. We analyze two scenarios of the manufacturer and the retailer’s implementation of CRM and conclude that donation amount and the pro-sociality of consumer groups in the segment are important. We make recommendations for the decisions of the manufacturer and the retailer in CRM and analyze the impact of donation amount and consumer’s pro-sociality on pricing and strategy decisions. In product pricing, we conclude that the retailer incurs higher advertising costs when implementing CRM, while the manufacturer has higher wholesale and selling prices when implementing CRM. In addition, if the retailer implements CRM, the higher the donation amount, the lower the wholesale price required; in other cases, regardless of who implements CRM, an increase in the donation amount will result in higher wholesale and product prices. However, it is not always advantageous for the manufacturer and the retailer to implement CRM. CRM decisions are influenced by a combination of donation amount and consumer’s pro-sociality. Only when the pro-sociality of the segment market exceeds a critical threshold is the implementation of CRM profitable. From the manufacturer's point of view, it is always optimal to entrust the retailer to implement CRM; for the retailer, if the donation amount is small, it is also necessary to consider the pro-sociality of the consumer group: the retailer is willing to implement CRM only when the pro-sociality of the consumer is strong. If the donation percentage is larger, the retailer is the best choice to implement CRM. We also analyzed the problem of the manufacturer and retailer’s decision from social welfare perspective. The implementation of CRM is beneficial for maximizing social welfare for both the manufacturer and the retailer. Again, the pro-sociality of consumers remains an influential factor; if the pro-sociality of the consumer group is low, the manufacturer's implementation of CRM maximizes social welfare; if the pro-sociality of the consumer group is high, the retailer's implementation of public good marketing is optimal. 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The effects of featured advertising and package labeling on sustainability of cause-related marketing (CRM) products, Sustainability, Vol. 10, No. 9, Article No. 3011, doi: 10.3390/ su10093011. [39] Heydari, J., Mosanna, Z. (2018). Coordination of a sustainable supply chain contributing in a cause-related marketing campaign, Journal of Cleaner Production, Vol. 200, 524-532, doi: 10.1016/j.jclepro.2018.07.055. Appendix A Proof of proposition 1: It is easy to obtain Eq. 2 as a concave function with respect to 𝑝𝑝. Making the first order derivative of Eq. 2 with respect to equal to zero yields the reaction function of the selling price as 𝑝𝑝 = (𝛿𝛿𝛿𝛿√𝐴𝐴+𝑤𝑤+1) . 2 Substituting it into Eq. 1, the Hesse matrix of Eq. 1 is obtained as: −(1 − 𝜂𝜂) ⎛ ⎜(1 − 𝜂𝜂)𝛿𝛿𝛿𝛿 ⎝ 4√𝐴𝐴 (1 − 𝜂𝜂)𝛿𝛿𝛿𝛿 ⎞ 4√𝐴𝐴 (𝑤𝑤 − 𝜂𝜂𝜂𝜂 − 𝑐𝑐)𝛿𝛿𝛿𝛿 ⎟ − 𝐴𝐴3/2 ⎠ (A1) 𝛿𝛿𝛿𝛿(1−𝜂𝜂)(𝛿𝛿𝛿𝛿√𝐴𝐴(𝜂𝜂−1)−2(𝜂𝜂𝜂𝜂+𝑐𝑐−𝑤𝑤)) The principal sub formulas of the Hesse matrix are −(1 − 𝜂𝜂) < 0, > 0 , it 16𝐴𝐴 3/2 can be obtained that (A1) is a negative definite matrix. Since Eq. 1 is a concave function with respect to 𝑤𝑤 and A , respectively. Find the first-order derivatives of Eq. 1 to 𝑤𝑤 and A, respectively, and make them equal to zero. Then we give Eqs. 4, 5 and 6. Substituting them into Eqs. 1-3 and simplifying them gives Eqs. 7-9. Proof of Corollary 1: Taking the first order derivative of 𝐴𝐴𝑀𝑀∗ to 𝜂𝜂 . We have 𝑑𝑑𝐴𝐴𝑀𝑀∗ 2𝛿𝛿 2 𝜂𝜂(1 − 𝑐𝑐 − 𝜂𝜂)(𝛿𝛿 2 𝜂𝜂 2 (𝜂𝜂 2 − 2𝜂𝜂 + 2𝑐𝑐𝑐𝑐 − 𝑐𝑐 + 1) + 8(1 − 2𝜂𝜂 − 𝑐𝑐)) = 𝑑𝑑𝑑𝑑 (8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 )3 Advances in Production Engineering & Management 17(4) 2022 (A2) 491 Xu, Liu, Duan Similarly, we can obtain (A2) and (A3) as follows: 𝑑𝑑𝑤𝑤 𝑀𝑀∗ 𝑐𝑐𝛿𝛿 4 𝜂𝜂 4 (1 − 𝜂𝜂)2 + 4𝜂𝜂𝛿𝛿 2 (1 − 𝜂𝜂)(−3𝜂𝜂2 + 5𝜂𝜂 + 2𝑐𝑐 − 2) + 32𝑐𝑐 = 𝑑𝑑𝑑𝑑 (1 − 𝜂𝜂)2 (8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 )2 𝑀𝑀∗ 4 4 2 𝑑𝑑𝑝𝑝 𝑐𝑐𝛿𝛿 𝜂𝜂 (1 − 𝜂𝜂) + 2𝜂𝜂𝛿𝛿 2 (1 − 𝜂𝜂)(9𝜂𝜂 2 − 15𝜂𝜂 + 2𝑐𝑐𝑐𝑐 − 6𝑐𝑐 + 6) + 16𝑐𝑐 = 𝑑𝑑𝑑𝑑 (1 − 𝜂𝜂)2 (8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 )2 (A3) (A4) It is easy to determine (A1), (A2) and (A3) > 0. 𝑀𝑀∗ Proof of Corollary 2: Taking the first order derivative of 𝜋𝜋𝑚𝑚 with respect to 𝜂𝜂 . We obtain (A5): 𝑀𝑀∗ 𝑑𝑑𝜋𝜋𝑚𝑚 2(1 − 𝑐𝑐 − 𝜂𝜂)(𝜂𝜂(1 − 𝜂𝜂)(𝜂𝜂 2 − 2𝜂𝜂 + 2𝑐𝑐𝑐𝑐 − 𝑐𝑐 + 1)𝛿𝛿 2 − 4(1 − 𝜂𝜂 + 𝑐𝑐)) = 𝑑𝑑𝑑𝑑 (1 − 𝜂𝜂)2 (8 + 𝛿𝛿 2 𝜂𝜂3 − 𝛿𝛿 2 𝜂𝜂 2 )2 because of 2 2(1−𝑐𝑐−𝜂𝜂) 2 (1−𝜂𝜂) (8+𝛿𝛿2 𝜂𝜂3 −𝛿𝛿2 𝜂𝜂2 ) (A5) > 0 ，we only need to determine the positive and negative of 𝑑𝑑𝜋𝜋𝑀𝑀∗ 𝑀𝑀 𝜂𝜂(1 − 𝜂𝜂)(𝜂𝜂2 − 2𝜂𝜂 + 2𝑐𝑐𝑐𝑐 − 𝑐𝑐 + 1)𝛿𝛿 2 − 4(1 − 𝜂𝜂 + 𝑐𝑐) . We obtain that if 0 < 𝛿𝛿 < 𝛿𝛿𝑚𝑚 ，then 𝑑𝑑𝑑𝑑𝑚𝑚 < 0； 𝑀𝑀 if 𝛿𝛿𝑚𝑚 < 𝛿𝛿 < 𝑀𝑀∗ 𝑑𝑑𝜋𝜋𝑚𝑚 �2(1−𝜂𝜂) ， then 𝜂𝜂(1−𝜂𝜂) 𝑑𝑑𝑑𝑑 >0. Taking the first order derivative of 𝜋𝜋𝑟𝑟𝑀𝑀∗ to 𝜂𝜂 . We obtain (A6) 𝑀𝑀∗ 𝑑𝑑𝜋𝜋𝑚𝑚 8(1 − 𝑐𝑐 − 𝜂𝜂)(𝜂𝜂(1 − 𝜂𝜂)(3𝜂𝜂 2 − 5𝜂𝜂 + 4𝑐𝑐𝑐𝑐 − 2𝑐𝑐 + 2)𝛿𝛿 2 − 8𝑐𝑐) = 𝑑𝑑𝑑𝑑 (1 − 𝜂𝜂)3 (8 + 𝛿𝛿 2 𝜂𝜂3 − 𝛿𝛿 2 𝜂𝜂 2 )3 Similarly, we can obtain that if 0 < 𝛿𝛿 < 𝛿𝛿𝑟𝑟𝑀𝑀 ， then 𝑑𝑑𝜋𝜋𝑟𝑟𝑀𝑀∗ 𝑑𝑑𝑑𝑑 𝑀𝑀 > 0 . Since 𝛿𝛿𝑟𝑟𝑀𝑀 < 𝛿𝛿𝑚𝑚 , we can proof Corollary 2. 𝑀𝑀∗ 𝑑𝑑𝜋𝜋𝑚𝑚 𝑑𝑑𝑑𝑑 < 0 ；if 𝛿𝛿𝑟𝑟𝑀𝑀 < 𝛿𝛿 < �2(1−𝜂𝜂) 𝜂𝜂(1−𝜂𝜂) (A6) ， then Proof of proposition 2 The Hesse matrix of Eq. 10 is given by −2(1 − 𝜂𝜂) ⎛ ⎜ (1 − 𝜂𝜂)𝛿𝛿𝛿𝛿 ⎝ 2√𝐴𝐴 (1 − 𝜂𝜂)𝛿𝛿𝛿𝛿 ⎞ 2√𝐴𝐴 (𝑝𝑝 − 𝜂𝜂𝜂𝜂 + 𝑤𝑤)𝛿𝛿𝛿𝛿 ⎟ − 4𝐴𝐴3/2 ⎠ Its principal sub formulas are −2(1 − 𝜂𝜂) < 0 , (A7) 𝛿𝛿𝛿𝛿(1−𝜂𝜂)(𝛿𝛿𝛿𝛿√𝐴𝐴(𝜂𝜂−1)−2(𝜂𝜂𝜂𝜂+𝑝𝑝−𝑤𝑤)) 4𝐴𝐴3/2 > 0 respectively. From this we can obtain Eq. 10 as a concave function of 𝐴𝐴 and 𝑤𝑤 . We let the first-order derivative of Eq. 10 with respect to 𝑝𝑝 and 𝐴𝐴 be equal to zero to obtain the reaction function 𝑝𝑝 = 2 𝑤𝑤𝛿𝛿 𝜂𝜂2 (𝜂𝜂−1)−2(𝜂𝜂−𝑤𝑤−1) (1−𝜂𝜂)(4+𝛿𝛿2 𝜂𝜂3 −𝛿𝛿2 𝜂𝜂2 ) , 𝐴𝐴 = 2 (𝜂𝜂+𝑤𝑤−1)2𝛿𝛿 𝜂𝜂2 (4+𝛿𝛿2 𝜂𝜂3 −𝛿𝛿2 𝜂𝜂2 ) 2 . Then we have Eqs. 13-15. Substituting them into Eqs. 10-12 and simplifying them gives Eqs. 16-18. Proof of Corollary 3: Taking the first order derivative of 𝐴𝐴𝑅𝑅∗ to 𝜂𝜂 . We have (A8): 𝑑𝑑𝐴𝐴𝑅𝑅∗ 𝛿𝛿 2 𝜂𝜂(1 − 𝜂𝜂)(𝛿𝛿 2 𝜂𝜂 2 (𝜂𝜂 2 − 2𝜂𝜂 + 2𝑐𝑐𝑐𝑐 − 𝑐𝑐 + 1) + 4(1 − 2𝜂𝜂 − 𝑐𝑐)) = 𝑑𝑑𝑑𝑑 4(4 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 )3 Similarly, we can obtain (A9) and (A10) as follows: 𝑑𝑑𝑤𝑤 𝑅𝑅∗ 1 = 𝑑𝑑𝑑𝑑 2 𝑑𝑑𝑝𝑝𝑅𝑅∗ 𝛿𝛿 4 𝜂𝜂(1 − 𝜂𝜂)(𝛿𝛿 2 𝜂𝜂 3 𝑐𝑐(1 − 𝜂𝜂) + 6𝜂𝜂 2 + 4𝑐𝑐 + 10𝜂𝜂 − 4) + 8𝑐𝑐 = 𝑑𝑑𝑑𝑑 2(1 − 𝜂𝜂)2 (4 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂2 )2 It is easy to obtain (A8), (A9) > 0 and (A10) < 0. (A8) (A9) (A10) 𝑅𝑅∗ Proof of Corollary 4: Taking the first order derivative of 𝜋𝜋𝑚𝑚 to 𝜂𝜂 . We obtain (A11): 492 Advances in Production Engineering & Management 17(4) 2022 Cause-related marketing strategy in a supply chain: A theoretical analysis and a case study 𝑅𝑅∗ (1 − 𝑐𝑐 − 𝜂𝜂)(𝛿𝛿 2 𝜂𝜂(1 − 𝜂𝜂)(𝜂𝜂 2 + 2𝑐𝑐𝑐𝑐 − 𝑐𝑐 − 2𝜂𝜂 + 1)𝛿𝛿 2 − 2(1 − 𝜂𝜂 + 𝑐𝑐)) 𝑑𝑑𝜋𝜋𝑚𝑚 = 𝑑𝑑𝑑𝑑 (1 − 𝜂𝜂)3 (8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 )3 We obtain that if 0 < 𝛿𝛿 < 𝛿𝛿 𝑅𝑅 ， then 𝑑𝑑𝜋𝜋𝑅𝑅∗ 𝑚𝑚 𝑑𝑑𝑑𝑑 > 0 and 𝑑𝑑𝜋𝜋𝑅𝑅∗ 𝑟𝑟 𝑑𝑑𝑑𝑑 𝑑𝑑𝜋𝜋𝑅𝑅∗ 𝑚𝑚 𝑑𝑑𝑑𝑑 < 0 and > 0 . We can proof Corollary 4. 𝑑𝑑𝜋𝜋𝑅𝑅∗ 𝑟𝑟 𝑑𝑑𝑑𝑑 < 0 ；if 𝛿𝛿𝑅𝑅 < 𝛿𝛿 < �2(1−𝜂𝜂) 𝜂𝜂(1−𝜂𝜂) Proof of Corollary 5: we can obtain 𝐴𝐴𝑀𝑀∗ − 𝐴𝐴𝑅𝑅∗ = 𝑤𝑤 𝑀𝑀∗ − 𝑤𝑤 𝑅𝑅∗ = (A12) 𝛿𝛿 2 𝜂𝜂 2 (1 − 𝑐𝑐 − 𝜂𝜂)(2 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 ) 2(4 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 )(8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 ) (A14) 𝑝𝑝𝑀𝑀∗ − 𝑝𝑝𝑅𝑅∗ = (A13) It can be judged that (A12) < 0, (A13) > 0 and (A14) > 0. 𝑀𝑀∗ 𝑅𝑅∗ 𝜋𝜋𝑚𝑚 − 𝜋𝜋𝑚𝑚 = It is easy to get (A15)> 0. 𝜋𝜋𝑟𝑟𝑀𝑀∗ − 𝜋𝜋𝑟𝑟𝑅𝑅∗ = − ， then 𝛿𝛿 4 𝜂𝜂 4 (1 − 𝜂𝜂)(16 + 3𝛿𝛿 2 𝜂𝜂3 − 3𝛿𝛿 2 𝜂𝜂2 ) 4(4 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 )2 (8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 )2 𝜂𝜂(𝜂𝜂(1 − 𝜂𝜂)(𝜂𝜂 2 + 2𝑐𝑐𝑐𝑐 − 𝑐𝑐 − 2𝜂𝜂 + 1)𝛿𝛿 2 + 8(1 − 𝜂𝜂 + 𝑐𝑐)) (1 − 𝜂𝜂)(8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂2 ) Proof of Corollary 6: Since (A11) 𝛿𝛿 2 𝜂𝜂 2 (1 − 𝑐𝑐 − 𝜂𝜂)2 2(4 + 𝛿𝛿 2 𝜂𝜂3 − 𝛿𝛿 2 𝜂𝜂 2 )(8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂2 ) (A15) 𝜂𝜂(1 − 𝑐𝑐 − 𝜂𝜂)2 ((1 − 𝜂𝜂)3 𝛿𝛿 4 𝜂𝜂 3 + 16(1 − 𝜂𝜂)3 𝛿𝛿 2 𝜂𝜂 3 + 64) 4(1 − 𝜂𝜂)2 (4 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 )2 (8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 ) (A16) To determine the positive and negative of (A16). We need to determine the positive and nega1 tive of (1 − 𝜂𝜂)3 𝛿𝛿 4 𝜂𝜂3 + 16(1 − 𝜂𝜂)𝛿𝛿 2 𝜂𝜂3 + 64 , we can solve when 0 < 𝜂𝜂 < 9 , if 𝛿𝛿 ′ < then 𝜋𝜋𝑟𝑟𝑀𝑀∗ < 𝜋𝜋𝑟𝑟𝑅𝑅∗ ; if 𝛿𝛿 ′ < δ < then 𝜋𝜋𝑟𝑟𝑀𝑀∗ > 𝜋𝜋𝑟𝑟𝑅𝑅∗ . �2(1−𝜂𝜂) 𝜂𝜂(1−𝜂𝜂) Proof of Corollary 7: There is 𝜋𝜋𝑠𝑠𝑀𝑀∗ − 𝜋𝜋𝑠𝑠𝑅𝑅∗ = 1 ′ , there is 𝜋𝜋𝑟𝑟𝑀𝑀∗ > 𝜋𝜋𝑟𝑟𝑅𝑅∗ . When 𝜂𝜂 > , there is 𝛿𝛿 > 9 𝜂𝜂(1 − 𝑐𝑐 − 𝜂𝜂)2 (𝛿𝛿 4 𝜂𝜂 3 (1 − 𝜂𝜂)3 − 𝛿𝛿 2 𝜂𝜂(1 − 𝜂𝜂) + 64) 4(1 − 𝜂𝜂)2 (4 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂2 )(8 + 𝛿𝛿 2 𝜂𝜂 3 − 𝛿𝛿 2 𝜂𝜂 2 ) 4 2 �2(1−𝜂𝜂) , 𝜂𝜂(1−𝜂𝜂) �2(1−𝜂𝜂) , 𝜂𝜂(1−𝜂𝜂) (A17) since that when 𝜋𝜋𝑠𝑠𝑀𝑀∗ > 𝜋𝜋𝑠𝑠𝑅𝑅∗ , there is 𝛿𝛿 𝜂𝜂3 (1 − 𝜂𝜂)3 − 𝛿𝛿 𝜂𝜂(1 − 𝜂𝜂) + 64 > 0，then 𝜋𝜋𝑠𝑠𝑀𝑀∗ > 𝜋𝜋𝑠𝑠𝑅𝑅∗ ； when 𝛿𝛿𝑠𝑠 < δ < �2(1−𝜂𝜂) 𝜂𝜂(1−𝜂𝜂) 4 2 ，there 𝛿𝛿 𝜂𝜂3 (1 − 𝜂𝜂)3 − 𝛿𝛿 𝜂𝜂(1 − 𝜂𝜂) + 64 < 0 ，then 𝜋𝜋𝑠𝑠𝑀𝑀∗ < 𝜋𝜋𝑠𝑠𝑅𝑅∗ . Advances in Production Engineering & Management 17(4) 2022 493 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 4 | December 2022 | pp 494–504 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.4.451 Original scientific paper Impact of Cobot parameters on the worker productivity: Optimization challenge Javernik, A.a, Buchmeister, B.a, Ojstersek, R.a,* aUniversity of Maribor, Faculty of Mechanical Engineering, Maribor, Slovenia ABSTRACT ARTICLE INFO In the era of Industry 4.0 and the introduction of new technologies, collaborative workplaces represent the potential to increase the efficiency of manufacturing systems. The presented research focuses on studying the impact of changing the speed and acceleration of a Cobot to the number of finished products at a collaborative workstation, the average assembly time, and the utilization of the Cobot and worker. In a laboratory experiment, it was demonstrated that changing the parameters of the Cobot significantly affects the optimization parameters of the collaborative workstation productivity. The results indicate an increase in production capacity with an increase in the speed and acceleration of the Cobot, while at the same time highlighting the importance of uniform utilization and occupancy of the Cobot and worker. The findings are particularly interesting from the influence of the Cobot’s audio and video effects on worker, when reducing the average assembly time while increasing the Cobot's capabilities. The results and findings presented open up important new areas of research in the field of social, time and financial justification of collaborative workplaces. Keywords: Collaborative robot; Cobot; Collaborative operation; Robot parameters; Worker productivity; Working scenarios; Manufacturing efficiency; Optimization *Corresponding author: robert.ojstersek@um.si (Ojstersek, R.) Article history: Received 10 September 2022 Revised 19 December 2022 Accepted 22 December 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction In the era of Industry 4.0 [1], where the role of making the right decisions in optimizing existing or newly proposed manufacturing system is key to achieving global competitiveness of the company. The optimization of manufacturing systems and its efficiency refers to both machines (technology) and workers (their knowledge and social paradigms) [2, 3]. The correct and equal distribution of occupancy between workers and machines plays a key role in sustainable production systems in terms of social, environmental and financial aspects. Implementing an effective model to acquire new knowledge about technologies that can increase efficiency is crucial [4]. According to the literature [5], classical single-objective approaches do not provide satisfactory solutions, especially when dealing with problems with high market dynamics and continuous optimization trends. Given the global shortage of workers (especially in developed countries), collaborative robots (Cobots) represent a new opportunity for companies willing to invest into new financially feasible technologies. In this case the research question appears: how efficient we can place them into the existing or newly proposed manufacturing system [6]. Proper design of collaborative 494 Impact of Cobot parameters on the worker productivity: Optimization challenge workplaces (cooperation between worker and Cobot) is the main challenge for researchers and engineers who want to increase manufacturing efficiency [7]. In doing so, we encounter the issues of collaboration safety, time and economic justification, and their impact on the entire manufacturing system under consideration [8]. The researchers point out the importance of using simulation modelling methods [9] that allow us to effectively evaluate the time efficiency of collaborative workplaces from the individual optimization parameters of the system [10] in a real-world industrial environment [11]. Different applications of collaborative workplaces [12] require the use of different optimization approaches [13], where we need to ensure safe and efficient parameters of the collaborative machines (Cobot) due to the specificity of the considered cases [14]. In this case, data-driven predictive models [15] prove to be the most reliable methods, where we use numerical and graphical simulation results to investigate the appropriateness of introducing and correctly determining collaborative machines [16]. Collaborative workplaces and their design in manufacturing systems present new challenges also from the ergonomic design point of view [17, 18], where the classical methods of ergonomic studies do not satisfy the criteria of a collected big data at high production dynamics. The impact of collaborative workplaces on the efficiency of the manufacturing systems [19] and the link with adaptive models [20] to monitor the importance of effective implementations are based on the performance of preliminary studies in which researchers compare simulation and real-world data of manufacturing systems [21]. The major limitation of the existing research is in the area of describing how the parameters of the Cobot affect the efficiency of the co-worker, not only from the worker's point of view, but also with respect to the efficiency of the Cobot and the manufacturing system as a combined unit. In this research, we address the research question of whether changing the operating parameters of a Cobot affects the efficiency of the manufacturing system and the occupancy of the worker itself. Based on the results, limitations, and issues of previous research works [19, 21], in this paper, we aim to present an experimental method to study the change of speed and acceleration of a Cobot on the effectiveness of a collaborative workplace. We focus on the multi-objective evaluation of the collaborative workplace optimization parameters with the detailed study of the assembly times, production quantities, and occupancy of the collaborative workplace from the Cobot and worker perspective. 2. Problem description Cobot’s properly set parameters can have a big impact on the efficiency and capacities of the manufacturing system. To set up a proper parameter of robots/machines can be a real challenge, especially when it comes to Cobot’s. It is not necessary that highest working parameters brings the highest number of finished orders, shortest operating times and highest machine utilization. The optimum working parameters depends on the structure of collaborative workplace, application type and defined sequence of tasks [22]. Most integrators/production engineers define Cobot’s working parameters their preference and existing knowledge or based on suggestions from Cobot’s producers. In many cases, parameters are not set up properly or are even set up to the maximum limit of the machine. With higher defined parameters, integrators want to achieve more finished products in less time. In most cases, such a decision leads to positive results as the machine’s operating time is reduced, but is it really only about the machine operating time, or there are also other variables we have overlooked inside the collaborative workplace? At observing of collaborative workplaces and their operations, we noticed that worker movements change or adapt according to parameters of the collaborative device [19, 22]. Such a finding, immediately raised a question of whether the speed and acceleration of the Cobot could have an impact on workers performance indicators (average worker assembly time, number of finished products and worker occupancy)? To determine the correctness or incorrectness of our predictions in the best possible way, we had proposed the design of the collaborative workplace and determine the most suitable type of collaborative application, presented in section three. Advances in Production Engineering & Management 17(4) 2022 495 Javernik, Buchmeister, Ojstersek 2.1 Collaborative workplaces To find out if there is a relation between the parameters of the collaborative robot and the assembly time of the workers, we had to design the structure of the experiment, a collaborative workplace layout and a collaborative operation. In the initial research phase, we had to think about what type of application and type of collaboration between the Cobot and the worker to design. In Fig. 1 four types of collaboration between the Cobot and the worker are presented. The first type is a caged cell. At caged cell type, a collaboration level is zero, the robots are in cages and there is no possible interaction between the worker and the robot. At this type mainly industrial robots are installed. At second type, so called coexistence, the Cobot and the worker work in the same space without fence between them, but they do not share the same workspace. Next type of collaboration is sequential or synchronized. The worker and the Cobot share their workspace but not at the same time, movements needs to be sequential. The last type of collaboration according to literature [23] is cooperation. At this type of work, the level of collaboration is the highest, the worker and the Cobot share the same workspace at the same time. In cooperation type the use of Cobot instead of industrial robot is necessary, because of integrated safety features that allow to work in direct contact. Even that in Cobot safety features are installed, the integrator still needs to perform risk assessment and design the operation as save as possible [24]. To mention, definition of collaboration types differs between the individuals, because the community is still split about their opinions and definitions. But there is not a lot of differences between the sources, mainly in names and small details. 2.2 Manufacturing efficiency Fig. 1 Types of Cobot and worker collaboration Initially, the definition of manufacturing productivity in terms of production is the ratio of output to input in production and is a measure of efficiency. If something is produced, we want to know how long it takes to produce it. While productivity focuses more on increasing the quantity produced, efficiency refers to the quality and effectiveness of the manufacturing system. In our research work we are focused on the collaborative workplace’s efficiency in correlation to its performance parameters. We are focusing on evaluating the ability to do or produce products without wasting material, time, cost, or energy. The efficiency is often expressed as a percentage, with 100 % being the ideal goal so that the product is produced at the lowest average total cost per item at the highest possible workplace occupancy. In presented research work we are measuring efficiency with the parameter of the number of hours of productive quality assembly work divided by the number of minutes available in the experiment run. The optimization methods and workers training can lead to improved manufacturing efficiency. For this purpose, the key performance 496 Advances in Production Engineering & Management 17(4) 2022 Impact of Cobot parameters on the worker productivity: Optimization challenge indicators (KPI) were used to help evaluate Cobot and worker efficiency when the parameters of Cobot speeds and accelerations are changing. In general: if you want to increase manufacturing efficiency, you essentially want to produce more output in the same amount of time. Finding a constant balance between productivity and manufacturing efficiency is critical to keeping your manufacturing running optimally. In Fig. 2 we can see optimization perspectives with which company can achieve high manufacturing system KPI’s. Fig. 2 Manufacturing efficiency, optimization perspectives 3. Experiment description The presented experiment was prepared according to the collaborative workplace standards listed in the literature [7], the research focuses on the reproducibility of the experiment in a laboratory environment, initial simulation model in Siemens software is shown in Fig. 3, where the selected building blocks are standard elements, as presented in subsection 3.1. The experimental environment is presented in detail in the subsections of the collaborative workspace description and the experimental design, where the experiment design is prepared in correlation with different experts from the field of social, medicine and technical sciences. Fig. 3 Collaborative workplace simulation model for laboratory experiments 3.1 Collaborative workplace description The experiment was conducted with the laboratory environment, so the collaborative workplace was adapted to laboratory conditions in terms of size and application type. Collaborative workplace consisted of a worktable ③, a collaborative robot UR3e ⑦, a collaborative gripper Robotiq 2F-85 ⑥, a switch with indicators light in green and red colour ④ and button ⑤, and two types of semi-finished products ① ②. A Lego brick size of 4×2 represented the semi-finished product 1 ① while a brick size of 2×2 represented the semi-finished product 2 ②. The finish product consisted of one semi-finished product ① and two semi-finished products ② assembled together, as shown in Fig. 4. Advances in Production Engineering & Management 17(4) 2022 497 Javernik, Buchmeister, Ojstersek Fig. 4 Layout of the collaborative workplace (left) and the finished product (right) The assembly operation consisted of assembling three semi-finished products into one finished product. The sequence of assembling was predefined to get the most objective results. At the beginning of the collaborative operation, the indicator light glowed red. The red light signalled that the Cobot is working and the worker is not approved to enter the robot area, but the worker can prepare himself. At the beginning, the collaborative robot picked up the semi-finished product and brought it to the collaboration/assembly area. When the robot reached the assembly area, it stopped, the indicator light changed from red to green and the worker was allowed to assemble. After the worker attached two semi-finished products ② to the semi-finished product ①, he or she pressed the button to send the signal about the completed work. The indicator light changed back from green to red and the Cobot moved the finished product into the box. The procedure was repeated until the total time of 30 minutes, for each experiment, was reached. 3.2 Experiment design To test our hypothesis optimal, we decided to design an assembly operation, a collaborative assembly operation, where the Cobot and the worker work sequential. At sequential type, they share the same workspace but at different time intervals. The sequential type of collaboration in our case was ideal because we still provided the contact between them and we could obtain objective results about a relation between the parameters of the robot and the operation time of the worker. In the next phase of experiment planning, we had to determine the structure of the experiment, length of the experiment and Cobot parameters (speed and acceleration). We decided to limit our experiment to 30 minutes and divide it into four phases as seen in Table 1. The experiment was divided into four phases. In the first phase, the Cobot and the worker worked separately. The worker manually assembled the finished products for 5 minutes. The goal of the first phase for the worker was to get used to such a type of the work and to the proximity of the Cobot. After 5 minutes, phase 2 has begun. Phase 2 lasted 10 minutes and consisted of collaborative work. The worker assembled the finished products with the help of the Cobot. The speed and acceleration of the Cobot were set to 60 %. After phase 2, phase 3 had started, it was set up the same way as phase 1, mainly to relax the worker. The worker and Cobot worked separately for 5 minutes. The goal of phase 3 was to release the pressure from the worker from the previous phase in which the worker collaborated with the Cobot. In the last phase of the experiment, phase 4, the worker worked with the Cobot again. Phase 4 lasted the same amount of time as phase 2, but the parameters of the Cobot were set higher, at 100 %. Cobot parameters (Table 2) were define based on attempted test in laboratory, simulation model presented in Fig. 3 and the specifics of the application type. After the experiment was completed, we obtained the results, describing collaborative workplace efficiency from phase 2 and phase 4. Phase No. Phase 1 Phase 2 Phase 3 Phase 4 498 Time length (min) 5 10 5 10 Table 1 Structure of the experiment Description Manual assembly operation Collaborative assembly operation (CR speed and acceleration 60 %) Manual assembly operation Collaborative assembly operation (CR speed and acceleration 100 %) Advances in Production Engineering & Management 17(4) 2022 Impact of Cobot parameters on the worker productivity: Optimization challenge Speed (%) 60 100 4. Results Table 2 Cobot speeds and accelerations Linear movements (mm/s) Acceleration (%) 600 60 1000 100 (mm/s2 ) 1500 2500 add Speed (%) 60 100 Joint movements (°/s) Acceleration (%) 206 60 344 100 (°/s2 ) 310 516 The experiment involved nine participants, both men’s and women’s, aged from 20 to 50 years. Until the end of experiment participants did not know the real goal of the experiment. With unknown, research goal (caning speeds and accelerations of the Cobot), we provided that they could not had an impact on their assembly task. The results in Table 3 show the average assembly time and number of finished products of each participant in two different scenarios corelated to phase 2 and phase 4. In both scenarios, the worker collaborated with the Cobot, but in scenario 1 (S1) the Cobot parameters were set to 60 % meanwhile in scenario 2 (S2) the parameters were set to 100 % of the specified speed and acceleration. Throughout the experiment we focus on next optimization parameters: worker average assembly times, number of finished products and Cobot and worker occupancy. Each worker average assembly times were saved to the time variable of the Cobot data collecting unit. According to the number of finished products and stored assembly times in the time variable, the average assembly time for each scenario was calculated. 4.1 Results of average assembly times and number of finished products From the results seen in Table 3 and Fig. 5, it is clear that with increased Cobot parameters assembly times did shorten. Although the number of participants in our experiment was low, we did not perceive a single longer assembly time while the parameters of the Cobot were increased in comparison with the S1, where Cobot parameters were lower. The average assembly time in S1 was 3.4 s with a standard deviation of 0.81. The number of participants in which the average assembly time was below average was 5 out of 9 participants. In scenario S2, where the speed of the robot was increased to 100 %, the average assembly time decreased to 2.6 s, in this case the standard deviation is lower at 0.66. In S2, 6 out of 9 participants had a shorter average assembly time than the average total time. Increasing the parameters of the Cobot from 60 % to 100 % contributed to the 23.4 % decrease in average assembly time of the worker. The minimum decrease in average assembly time that occurred in our experiment was 8.70 %, while the maximum decrease was 36.90 %. The presented results of the experiment confirm our prediction. Higher define parameters of the Cobot had an impact on the worker and resulted in a higher working speed. Due to the higher working speed, the average assembly time is shorter, and we are able to deliver a higher number of finished products. Using the number of finished products parameters, we see that the total number of products produced in S1 is 497 pieces for nine participants in total. On average, each participant assembled 55.2 pieces in 10 minutes, with a standard deviation of 3.9. A significantly higher number of finished products is seen in S2, where participants assembled a total of 761 pieces in 10 minutes, while each worker assembled an average of 85.5 pieces with a standard deviation of 7.6, as shown in Fig. 6. Table 3 Average assembly times and Number of finished products per participant in S1 and S2 Participants Average assembly Number of finished Average assembly Number of finished time (s) – S1 products (pcs) – S1 time (s) – S2 products (pcs) – S2 1 2.82 58 2.34 87 2 3.00 57 2.42 86 3 2.82 58 1.97 92 4 2.65 59 2.27 88 5 2.48 60 1.70 96 6 3.59 54 2.27 88 7 4.98 48 3.34 76 8 4.24 51 3.45 75 9 4.02 52 3.67 73 Advances in Production Engineering & Management 17(4) 2022 499 Javernik, Buchmeister, Ojstersek Fig. 5 Average assembly times, results comparison (S1 vs S2) Fig. 6 Number of finished products, results comparison (S1 vs S2) 4.2 Results of Cobot and worker occupancy Table 4 shows the occupancy of the collaborative workspace (Cobot and worker time occupancy), where the values are evaluated according to the total assembly time, which is in total 10 minutes for the individual scenario. The results show the three optimization parameters, where the Cobot occupancy indicates the total operating time of the Cobot. The worker occupancy is divided into the assembly and setup time parameters. Notice: the worker's assembly setup time is performed when the robot performs its operations. Participants 500 1 2 3 4 5 6 7 8 9 Table 4 Cobot and worker occupancy in S1 and S2 Cobot occupancy Worker occupancy Cobot occupancy (min) – S1 (min) – S1 (min) – S2 Assembly Setup time time 7.27/10 2.73/10 1.87/10 6.60/10 7.15/10 2.85/10 1.95/10 6.53/10 7.27/10 2.73/10 1.87/10 6.98/10 7.40/10 2.60/10 1.78/10 6.68/10 7.52/10 2.48/10 1.70/10 7.28/10 6.77/10 3.23/10 2.21/10 6.68/10 6.02/10 3.98/10 2.72/10 5.77/10 6.39/10 3.61/10 2.47/10 5.69/10 6.52/10 3.48/10 2.38/10 5.54/10 Worker occupancy (min) – S2 Assembly Setup time time 4.40/10 3.19/10 3.47/10 2.52/10 3.02/10 2.19/10 3.32/10 2.41/10 2.72/10 1.97/10 3.32/10 2.41/10 4.43/10 3.22/10 4.31/10 3.13/10 4.46/10 3.24/10 Advances in Production Engineering & Management 17(4) 2022 Impact of Cobot parameters on the worker productivity: Optimization challenge Fig. 7 Workplace occupancy in S1 Fig. 7 and the results in Table 4 show that in S1, the participating robot is occupied on average 6.92 minutes of the available 10 min total time. The standard deviation of average Cobot occupancy is 4.9. A worker at a collaborative workstation is engaged in assembling operation for an average of 3.08 minutes while spending another 2.11 minutes preparing the parts to be assembled, giving a total time occupancy of 5.18 in the available time of 10 min, where the standard deviation is 4.9. Results of the S2 in Fig. 8 shows, that the Cobot works an average of 6.42 min of the available 10 min. With the parameters S2, the worker is occupied for 3.71 min for the assembly operation and 2.69 min for the setup time, which totals 6.40 min of the available 10 min workplace operation time. For parameters S2, the standard deviation of the Cobot occupancy is 5.7 and for the worker it is 6.3. 5. Discussion Fig. 8 Workplace occupancy in S2 Based on the results shown, we conclude that in total 264 more pieces are produced in S2 at the collaborative workplace than with the parameters representing scenario S1. The average number of finished products at the collaborative workplace in scenario S2 increases by 54.9 %, which significantly increases the number of manufactured products. At the same time, the standard Advances in Production Engineering & Management 17(4) 2022 501 Javernik, Buchmeister, Ojstersek deviation results, which are 3.7 higher for S2, indicate a higher probability of non-constant operation of the collaborative workplace assembly operations when repeated operations are performed in several shifts with several different workers. The results presented indicate that worker workload increases at higher speeds and accelerations of the Cobot. Based on the evaluated optimization parameter of the average assembly time, we find that it is 23.5 % shorter in scenario S2, which is an interesting observation from the justifying the collaborative workplace point of view. The worker changed the work speed (assembling operation) when the Cobot mode of operation changed (the transition of the Cobot parameters from S1 to S2). Obviously, the visual and audio effects presences (perception of the Cobot) had a positive effect on the shorter average assembly time, even though the worker had exactly the same time to assemble the product in both evaluated scenarios (S1 and S2). It is also interesting to analyse the occupancy of the participants (Cobot and worker) in the collaborative workplace. The results show that the occupancy of the Cobot in the S2 scenario decreased by 7.2 % compared to the time occupancy in the S1 scenario. The results prove that the Cobot is able to perform multiple activities simultaneously and possibly participate in more complex activities or collaborate in a workplace with two workers when the operating parameters are increased. In this case, it is useful to study the utilization of the Cobot in detail, because only with a detailed analysis we can ensure the justification for the introduction of such a machine in existing or newly proposed production system. In contrast to the decrease in the time occupancy of the Cobot in S2, the occupancy of the worker in S2 increases, by 23.6 %, the occupancy is higher both during assembly and setup time. With respect to the time occupancy parameter, we find that the importance of consistent collaborative workplace occupancy is critical to the economic and social justification of a collaborative workplace. When introducing new collaborative workstations, the use of simulation techniques is highly justified, assuming that they represent the minimum cost of the initial investment and reduce the risk that the new investment is not justified. As mentioned in the introduction, usually companies start to increase the parameters (speeds and accelerations) of the Cobot to reduce the cycle time of the machine operations to provide enough collaborative workplace capacity. But as our results show, the integrators probably also affect the worker's working speed unconsciously. It is difficult to fully determine the reason for the increased worker operating speed, but a few options emerged during the experiment that may be important contributors. Different speeds and accelerations of the Cobot provide different volumes of noise. The loudness of electro motors in joints could be a factor for faster movements and greater willingness of the worker. The other aspect that should be considered is visualization. In collaborative operation, the worker is constantly in "contact" with the Cobot, as with assembling the products together as at observing the robot's movements. With defined and constant parameters of the Cobot, workers get to use of work sequence and begin to memorize specific positions of the Cobot at specific time frames. If the remembered positions start to differ from previously remembered start to deviate from previous memorized positions, this could trigger some kind of alarm in the worker, whose spontaneous reaction could be an increased working speed. According to the existing literature [19, 21], the presented work highlights the importance of a detailed study of the feasibility of introducing collaborative workplaces, where the setting parameters of the collaborative machine can significantly affect the efficiency of such a workplace. Proper integration of a Cobot affects both economic, time and social justification. The main contribution of the presented work is evident in the results that highlight the study of the importance of the visual and acoustic impact on the worker and consequently on its use. Considering the number of participants considered, the trend of results shown allows further work and extension of the experiment, which must be transferred to a real-world environment where the working hours of the collaborative workplace would be longer. With longer working hours and the evaluation of the collaborative workplace efficiency, the speed and acceleration of the Cobot would have a significant impact on the worker's workload, concentration, and therefore on the quality of the work performed. 502 Advances in Production Engineering & Management 17(4) 2022 Impact of Cobot parameters on the worker productivity: Optimization challenge 6. Conclusions In the research paper, the importance of Cobot parameters on worker productivity is presented. The results of the study provide useful and interesting answers to our research question, but new doubts have also been raised. The results show that the parameters of the Cobot have an impact on the assembly times of the workers. Higher speed and acceleration of the Cobot contribute to a higher working speed of the worker, which leads to shorter assembly times in our study. Despite the positive results, the limit of the Cobot parameters must be considered at different collaborative work operations. The speed and acceleration limit should be set in such a way that it does not affect the correct performance of the Cobot and, most importantly, it does not negatively affect the worker (performance, physical health, mental health, etc.). Future research will focus on the analysis of more participants, different ages, educations and genders. We will focus our research on studying the mental and physical health of workers working with Cobot. Favourable research results will lead to the transfer of the laboratory experiment to a real-world production environment, where the speed and acceleration of the Cobot will have a longer-term effect on the efficiency of the worker and the entire collaborative workplace. When evaluated in a real-world environment, the challenges will enable a more detailed and practical application value of the presented research work, which is crucial in the era of Industry 4.0 and the arrival of new technologies. Cost, time and social justified of the collaborative workplaces certainly represent one of the more attractive research areas from the manufacturing efficiency point of view. Acknowledgement The authors gratefully acknowledge the support of the Slovenian Research Agency (ARRS), Research Core Funding No. P2-0190. 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ABB’s Cobot Portfolio – Customer Presentation, from https://s.sick.com/at-en-robot-roadshow-2022-documents, accessed November 15, 2022. [24] International Federation of Robotics (2020). Demystifying collaborative industrial robots, IFR International Federation of Robotics, Frankfurt, Germany. 504 Advances in Production Engineering & Management 17(4) 2022 Advances in Production Engineering & Management ISSN 1854-6250 Volume 17 | Number 4 | December 2022 | pp 505–513 Journal home: apem-journal.org https://doi.org/10.14743/apem2022.4.452 Original scientific paper Study on scheduling and path planning problems of multi-AGVs based on a heuristic algorithm in intelligent manufacturing workshop Wang, Y.J.a,*, Liu, X.Q.a, Leng, J.Y.a, Wang, J.J.a, Meng, Q.N.a, Zhou, M.J.a aSchool bSchool of Mechanical Engineering, Dalian Polytechnic University, Dalian, P.R. China of Management, Dalian University of Technology, Dalian, P.R. China ABSTRACT ARTICLE INFO In order to solve the scheduling and path planning problems of multi-AGVs in an intelligent manufacturing workshop, it is necessary to consider loading, unloading, and transporting the workpiece of each AGV at the same time. A step task scheduling and path optimization mode of AGV is proposed. The process is as follows: Firstly, a mathematical model algorithm and a material transportation task allocation algorithm based on the urgency degree of workpiece processing were established for the optimization objective, and all workpiece transportation task sequences between shelves and processing equipment were assigned to the corresponding AGV to generate the initial feasible path of each AGV. Then, the AGV collision detection and anti-collision algorithm are designed to plan the global collision-free walking path of multiAGVs in the workshop, and the path can be dynamically adjusted according to the delivery task. The model is solved by a heuristic algorithm ant colony algorithm and MATLAB coding. Finally, an example is given to verify the effectiveness of the method, which can effectively solve the task allocation of multi-AGVs and avoid collision path planning based on the transportation task sequence, and improve the work efficiency of AGV. This research can provide a theoretical basis and practical reference for realizing multi AGVs collaborative scheduling by using AGV automated material transport system in an intelligent production workshop. Keywords: Intelligent manufacturing; Automated guided vehicle(AGV); Multi-AGVs; Task sequence; Task scheduling; Path planning; Heuristic algorithm; Ant colony algorithm; MATLAB *Corresponding author: wangyj@dlpu.edu.cn (Wang, Y.J.) Article history: Received 25 October 2022 Revised 14 December 2022 Accepted 17 December 2022 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction With the rapid development of artificial intelligence, the Internet of Things, 5G, and other innovative technologies, the main direction of the future development of China's manufacturing industry is intelligent manufacturing. The digital workshop of intelligent manufacturing is highly integrated with mechanical equipment, sensor equipment, and other hardware, control, data acquisition, and data processing systems. Automated Guided Vehicle (AGV) is applied to intelligent production workshops, and with its high flexibility and stability, it can help the workshop to realize flexible automatic production [1]. Automatic call, information sensing, and production tempo control functions of AGV can improve workshop efficiency. However, How to design An optimization algorithm for AGV workpiece transportation task scheduling in an intelligent manufacturing workshop and plan the route of AGV for workpiece transportation in the workplace, 505 Wang, Liu, Leng, Wang, Meng, Zhou and AGV can accurately and timely execute and complete the production material transport task, it is an urgent problem to be solved in AGV work of intelligent manufacturing workshop. In the intelligent production workshop based on Manufacturing Execution System (MES), the work of AGV is mainly to load, unload and transport the workpiece, and ensure that the workpiece is delivered to the equipment workbench or the finished workpiece is delivered to the shelf in time, and cooperate with the vehicle equipment to avoid idle mechanical equipment or production delay, and ensure the working efficiency of the equipment. The task scheduling of AGV is aimed at minimizing the total AGV workpiece transportation time, determining the task execution sequence and travel path, and preventing conflicts and collisions in the process of multiple AGVs. There has been much research on AGV scheduling and path planning. Ma et al. [2] applied a tabu search algorithm to solve the vehicle slash-and-drop transportation problem and carried out path planning. Yin et al. [3] applied a tabu search algorithm to solve the path planning problem and solved the problem of excessive energy consumption in the process of vehicle movement. Wang et al. [4] proposed an improved A* algorithm, which solved the problems of redundant points and unsmooth in path planning. Sun et al. [5] proposed a neural network algorithm based on directional constraints, which improved the speed of path planning. Li et al. [6] applied BP neural network to study the path planning and obstacle avoidance problems of robots. Corpuz et al. [7] proposed an improved neural network to solve the problem of slow convergence speed in intelligent vehicle path planning. Sunet et al. [8] solved the problem of complex traps in path navigation based on an adaptive fuzzy neural network. S. Hitam et al. [9] applied an improved genetic algorithm to improve the quality of path planning solutions. Li et al. [10] integrated AGV environmental safety information into a grid map and applied a genetic algorithm to solve the path planning problem. Mousavi et al. [11] applied genetic algorithm and particle swarm optimization algorithm to the AGV task scheduling model. Deepak et al. [12] combined decision theory with stochastic time path planning to schedule and control the optimal path under dynamic and uncertain conditions. Yue et al. [13] proposed a hybrid PSO-GA algorithm to complete the scheduling and planning problem of AGV. Rugalska [14] proposed a new control strategy for cooperative AGVs, in which two AGVs cooperate to achieve specific task objectives. Antakly[15] et al. proposed a task scheduling method based on temporal logic, adding appropriate delay to AGV to avoid collisions between multiple vehicles. Yan et al. [16] proposed an algorithm based on co-evolution to conduct scheduling research on AGV. Shi et al. [17] proposed a multi-objective scheduling model based on total driving distance and waiting time, and used the A* path planning algorithm to search the shortest path of AGV. Zou et al. [18] proposed a multiobjective mixed-integer linear programming model to solve a new automatic guided vehicle scheduling problem with pickup and delivery from the goods handling process in a matrix manufacturing workshop with multi-variety and small-batch production. Yin et al. [19] proposed a decentralized framework of multi-task allocation with attention (MTAA) in deep reinforcement learning. To sum up, most of the literature on AGV path planning focuses on planning AGV anticollision strategies in static environments with known obstacles, which does not apply to intelligent production workshops where multiple AGVs work together. The scheduling algorithm in the existing literature does not apply to intelligent workshops. AGV is necessary equipment for an intelligent workshop to realize intelligent production, but there is little research literature on AGV path planning and collision prevention in an intelligent workshop. Therefore, the problems of workpiece transportation task allocation, task sequencing, path planning, and collision prevention in the multi-AGV system are studied in the intelligent workshop. The paper is organized as follows. The AGV scheduling and path optimization framework is constructed in Section 2. AGV Initial feasible path and AGV collision detection and anti-collision algorithm are described in this section. The case analysis and discussion are reported in Section 3. Finally, in Section 4, the conclusions are reported. 506 Advances in Production Engineering & Management 17(4) 2022 Study on scheduling and path planning problems of multi-AGVs based on a heuristic algorithm in intelligent … 2. AGV scheduling and path optimization framework In the actual production process of the workshop, multiple stations are requiring multiple AGVs to transport the workpiece to each station at the same time. It is necessary to allocate the AGV delivery sequence and optimize the AGV delivery path to make the AGV perform the task of the total transport path shorter, at the same time, to complete the delivery of workpieces for all stations or shelves. Because of AGV path planning and task allocation problems, combined with the manufacturing production line process, a step optimization algorithm model is proposed, as shown in Fig. 1. Task allocation algorithm based on processing urgency AGV task allocation algorithm based on mathematical model AGV task sequence AGV Initial path planning AGV path planning Initial feasible path AGV collision detection and anticollision algorithm Conflict detection and anticollision strategies AGV collision detection and anti-collision Final path Fig. 1 AGV scheduling and path step optimization mode First, using the mathematical model of the algorithm based on minimizing the total delivery time, or the materials transportation task allocation algorithm based on the emergency degree of workpiece processing, all workpiece transport tasks within the planned time between the shelves and the processing equipment shall be assigned to the AGV currently in the idle state according to rules. The current AGV task sequence is dynamically updated, and the initial feasible task transport path for each AGV is generated. Then, the algorithm of AGV collision detection and anti-collision is designed, and the global collision-free walking path of multiple AGVs in the intelligent workshop is planned, and the path can be dynamically adjusted. 2.1 AGV initial feasible path 2.1.1 Generation of AGV transportation task sequence Two algorithms can be used to generate AGV transportation task sequences. (1) AGV task allocation algorithm based on time minimization mathematical model According to the production plan, the workpiece delivery task is assigned to the appropriate AGV, and the task execution sequence is determined. The mathematical model is established with the goal of the shortest time for the AGV to complete all delivery tasks. The relevant settings and assumptions are as follows: • All AGVs are the same, and the transport speed is the same and uniform. • Keep a safe distance during driving, and the waiting time is short and ignored. • Ignore equipment start time. Advances in Production Engineering & Management 17(4) 2022 507 Wang, Liu, Leng, Wang, Meng, Zhou • Each AGV can perform one transportation task at a time. Similarly, only one AGV can perform a transportation task. • No more than two AGVs in each direction on the driving channel to avoid congestion and conflict, and re-plan the route when the capacity exceeds. • AGV runs along the grid, one grid per second, and the statistical distance is calculated according to the broken line distance travelled • When the AGV works, it is powered on continuously and will not fail. • AGV returns to berth after delivery. 𝑃𝑃 The notations used for modelling are described below. represents the transportation set of the workpiece to the equipment for processing and is {1,2, … , 𝑛𝑛}. 𝐷𝐷 represents the task set of transporting the finished workpiece back to the shelf and is {𝑛𝑛 + 1, 𝑛𝑛 + 2, … ,2𝑛𝑛}. 𝑁𝑁 is the set of transporting workpiece, 𝑁𝑁 = 𝑃𝑃 ∪ 𝐷𝐷. 𝐾𝐾 is the set of AGVs, represented as {1,2, … , 𝑚𝑚}, 0 indicates the docking position. 𝐴𝐴 is the set of workshop location points, 𝐴𝐴 = 𝑁𝑁 ∪ 0. 𝐵𝐵𝑖𝑖𝑘𝑘 and 𝐸𝐸𝑖𝑖𝑘𝑘 are the start time and finish time of AGV 𝑘𝑘, 𝑖𝑖 ∈ 𝑁𝑁, 𝑘𝑘 ∈ 𝐾𝐾. (𝑋𝑋𝑖𝑖 , 𝑌𝑌𝑖𝑖 ) represents the position coordinates. The AGV travels one grid per second, so 𝑋𝑋𝑖𝑖 + 𝑌𝑌𝑖𝑖 can represent the travel time. 𝑘𝑘 is the 0-1 variable. When the value is 1, AGV 𝑘𝑘 performs the transport task 𝑖𝑖 and then the 𝑋𝑋𝑖𝑖𝑖𝑖 task 𝑗𝑗, a value of 0 indicates other cases, 𝑖𝑖 ∈ 𝑁𝑁, 𝑗𝑗 ∈ 𝑁𝑁, 𝑘𝑘 ∈ 𝐾𝐾. 𝑡𝑡𝑖𝑖 is the minimum travel time for task 𝑖𝑖. 𝑇𝑇𝑖𝑖𝑖𝑖𝑘𝑘 represents the minimum travel time from the completion position of task 𝑖𝑖 to the start position of task 𝑗𝑗. 𝑃𝑃𝑡𝑡𝑖𝑖 represents the workpiece processing time. 𝑒𝑒𝑖𝑖 represents the planned processing time or planned completion time of the workpiece in the production plan. The mathematical model is constructed to determine the delivery task and execution sequence of AGV. 𝑚𝑚𝑚𝑚𝑚𝑚 𝑍𝑍 = 𝑚𝑚𝑚𝑚𝑚𝑚 𝐸𝐸𝑖𝑖𝑘𝑘 + (𝑋𝑋𝑖𝑖 + 𝑌𝑌𝑖𝑖 ) (1) 𝑘𝑘∈𝐾𝐾,𝑗𝑗∈𝐴𝐴 𝑘𝑘 𝑘𝑘 � 𝑋𝑋0𝑗𝑗 = 1, � 𝑋𝑋𝑖𝑖0 =1 𝑗𝑗∈𝑁𝑁 𝑖𝑖∈𝑁𝑁 � � 𝑋𝑋𝑖𝑖𝑖𝑖𝑘𝑘 = 1 𝑘𝑘∈𝐾𝐾 𝑗𝑗∈𝐴𝐴,𝑗𝑗≠𝑖𝑖 � � 𝑋𝑋𝑖𝑖𝑖𝑖𝑘𝑘 = 1 𝑘𝑘∈𝐾𝐾 𝑖𝑖∈𝐴𝐴,𝑖𝑖≠𝑗𝑗 𝐸𝐸𝑖𝑖𝑘𝑘 ≥ 𝑍𝑍𝑖𝑖𝑘𝑘 (𝐵𝐵𝑖𝑖𝑘𝑘 + 𝑡𝑡𝑖𝑖 ) 𝐸𝐸𝑖𝑖𝑘𝑘 𝑘𝑘 𝐵𝐵𝑛𝑛+𝑖𝑖 ≥ 𝑒𝑒𝑖𝑖 𝐸𝐸𝑖𝑖𝑘𝑘 ∈ {0,1} 𝐵𝐵𝑖𝑖𝑘𝑘 , 𝐸𝐸𝑖𝑖𝑘𝑘 ≥0 ∀𝑖𝑖 ∈ 𝑁𝑁 ∀𝑗𝑗 ∈ 𝑁𝑁 ∀𝑖𝑖 ∈ 𝐴𝐴, 𝑘𝑘 ∈ 𝐾𝐾 ∀𝑖𝑖 ∈ 𝑃𝑃, 𝑘𝑘 ∈ 𝐾𝐾 ≥ + 𝑃𝑃𝑡𝑡𝑖𝑖 𝑘𝑘 𝐵𝐵𝑛𝑛+𝑖𝑖 ≥ 𝑒𝑒𝑖𝑖 𝐵𝐵𝑗𝑗𝑘𝑘 ≥ 𝑋𝑋𝑖𝑖𝑖𝑖𝑘𝑘 (𝐸𝐸𝑖𝑖𝑘𝑘 + 𝑇𝑇𝑖𝑖𝑖𝑖𝑘𝑘 ) 𝑘𝑘 𝑋𝑋𝑖𝑖𝑖𝑖𝑘𝑘 , 𝑍𝑍𝑖𝑖𝑖𝑖 ∀𝑘𝑘 ∈ 𝐾𝐾 𝑖𝑖 ∈ 𝑃𝑃, ∀𝑘𝑘 ∈ 𝐾𝐾 ∀𝑖𝑖 ∈ 𝐷𝐷, 𝑘𝑘 ∈ 𝐾𝐾 ∀𝑖𝑖, 𝑗𝑗 ∈ 𝑁𝑁, 𝑘𝑘 ∈ 𝐾𝐾 𝑖𝑖, 𝑗𝑗 ∈ 𝐴𝐴, ∀𝑘𝑘 ∈ 𝐾𝐾 ∀𝑘𝑘 ∈ 𝐾𝐾, 𝑖𝑖 ∈ 𝐴𝐴 (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Eq. 1 is the objective function. The objective is to minimize the maximum AGV transportation time. Others are constraint conditions. 508 Advances in Production Engineering & Management 17(4) 2022 Study on scheduling and path planning problems of multi-AGVs based on a heuristic algorithm in intelligent … Eq. 2 indicates that AGV starts from the docking position and returns to the docking position after the workpiece arrives. Eqs. 3 and 4 ensure that all delivery tasks are performed. Eqs. 5 and 6 ensure that the execution time of the task is logical, that is, the completion time of task 𝑖𝑖 transporting the workpiece to the machine tool by AGV is later than the sum of the start time and execution time of the task, and cannot be earlier than the planned processing time of the workpiece. In Eqs. 7 and 8, the start time of task 𝑖𝑖 of transporting the finished workpiece to the shelf shall not be earlier than the sum of the processing time and completion time of the task transporting the workpiece to the machine tool, nor shall it be earlier than the planned completion time of the workpiece. Eq. 9 indicates that AGV executes tasks in sequence, and drives to task 𝑗𝑗 by raster after completing task 𝑖𝑖, so the start time of task 𝑗𝑗 cannot be earlier than the time when AGV arrives at the start point of task 𝑗𝑗. Eqs. 10 and 11 represent variable types, which are 0-1 variables and integer variables respectively. (2) AGV transportation task assignment based on processing priority Aiming at the fastest completion of the workpiece according to the production plan, an AGV task allocation algorithm based on the degree of workpiece processing urgency is proposed. Fig. 2 is the algorithm flow. Based on the workpiece processing plan time and completion time set by the intelligent workshop manufacturing execution system, all delivery tasks are sorted according to the urgency of processing to form the whole task sequence. According to the AGV's idle-asallotment rule, the workpiece delivery task is assigned to the AGV that has completed the preorder task and is waiting for task assignment, and the task sequence of the AGV is updated. Repeat the above process until all workpiece delivery tasks are assigned to the corresponding AGV, and the task assignment is stopped. Finally, the workpiece delivery task sequence of each AGV is formed. Start MES of intelligent production workshop Workpiece production plan list AGV set Sort by processing urgency of workpieces AGV task list Arrange AGV k to transport the most urgent processing task t First done, first allocated Update AGV k delivery task sequence Remove task t from task list Y Are there processing tasks that have not been scheduled for delivery? N Delivery task sequence of each AGV End Fig. 2 AGV transportation task assignment based on processing priority 2.1.2 Generation of AGV initial feasible path In order to facilitate path planning and path expression, the intelligent workshop is rasterized, and each functional area is expressed by grids and coded according to the grid position, as shown in Figure 3. Each grid represents a location node, which can be a device or a driving channel for an AGV or a shelf. The grid in front of the equipment and shelves is the AGV operat- Advances in Production Engineering & Management 17(4) 2022 509 Wang, Liu, Leng, Wang, Meng, Zhou ing station, where the AGV completes the feeding and retaking actions. When the AGV is idle, it stops at the docking position. When the task instruction is received, the AGV will transport the workpiece from the current position to the specified grid position according to the task sequence number, and then carry out the operation of material taking or feeding. The AGV will transport the workpiece in the feasible area of the workshop (grid nodes 1-12 in Fig. 3), and complete the loading, unloading, and transportation of the specified workpiece according to the task sequence. In order to ensure the workshop production process stability, AGV drives in the workspace according to the instructions and follows the principle of driving in the workshop grid channel after the first lateral longitudinal to determine the initial path of AGV to perform each task. According to this path, AGV can reduce the collision probability when driving in the workshop grid channel, and efficiently complete the task of workpiece delivery. Transport such as the current task is to carry a workpiece on shelf 2 to equipment 1 for processing, the initial delivery path of AGV is the grid node 7→8→9→4→3. The AGV picks up the workpiece with the specified number on shelf 2 at the starting node 7, then drives to the end node 3 of the grid according to this path, and puts the workpiece in the designated position in front of the machine of equipment 1. According to the assigned task sequence, each AGV forms the initial transport path of all transport tasks, which is expressed by the grid node number in the sequence. Y Shelf3 Node 12 Node 11 Node 10 Shelf2 Node 7 Node 8 Node 9 Shelf1 Node 6 Node 5 Node 4 AGVs Node 1 Node 2 Node 3 Equip ment 4 Equip ment 3 Equip ment 2 Equip ment 1 X Fig. 3 Floor plan of raster intelligent production workshop 2.2 AGV collision detection and anti-collision algorithm The purpose of collision detection is to update the initial AGV transport path in real-time so that there are no two AGVs in the same grid position in the workshop AGV driving area. The current grid position and driving time of AGV in the workshop are represented in the form of , the variables position and time are non-negative integers. The algorithm of AGV collision detection and anti-collision is shown in Fig. 4. The heuristic algorithm ant colony algorithm is a probabilistic algorithm used to find the optimal path. It was proposed by Marco Dorigo in his doctoral dissertation in 1992, and its inspiration comes from the behavior of ants in finding a path in the process of searching for food. This algorithm has the characteristics of distributed computing, positive information feedback and heuristic search, and is essentially a heuristic global optimization algorithm in evolutionary algorithms. The basic idea of applying the ant colony algorithm to solving optimization problems is to use the ant's walking path to represent the feasible solution of the problem to be optimized, and all paths of the entire ant colony constitute the solution space of the problem to be optimized. Ants with short paths release more pheromones. As time goes on, the concentration of pheromones accumulated on the short paths increases gradually, and the number of ants choosing this path also increases. Finally, the whole ant will focus on the best path under the action of positive feedback, and the corresponding is the optimal solution of the problem to be optimized. 510 Advances in Production Engineering & Management 17(4) 2022 Study on scheduling and path planning problems of multi-AGVs based on a heuristic algorithm in intelligent … Start AGV path input Establish AGV initial < position, time > record table Add a stay node to the path AGV performs tasks in turn and updates the record table Calculate the delivery time t for task i Y t earlier than processing time or completion time? add stay node Update record table N Path conflict Collision? N Are there are undetected tasks? Y Y N Adjust the path and update the record table End Fig. 4 AGV collision detection and anti-collision algorithm 3. Example verification The above grid intelligent workshop is still used as the workplace of two AGVs. The model is solved by a heuristic algorithm ant colony algorithm and MATLAB coding. In order to compare the effects of the two task allocation methods in section 2.1, the calculation results are solved and compared respectively, as shown in Table 1. The notation n is the total number of workpiece transportation tasks in the workshop, 𝑝𝑝1 and 𝑝𝑝2 represent the two stages of AGV initial path planning and anti-collision, 𝑡𝑡1 and 𝑡𝑡1 represent the task completion time of each stage, and 𝑑𝑑1 and 𝑑𝑑1 are the corresponding time difference rate. In the AGV initial path generation stage, the total completion time of the AGV initial path calculated by the two task allocation methods is slightly different, and the maximum difference rate is 1.06%. After AGV anti-collision adjustment, the total time calculated by the two scheduling methods is the same. The operation of multiple AGVs in the intelligent workshop is limited by constraints such as conflict and collision. The completion time of the workpiece transportation task should consider the completion time of the delivery task after constraint detection and path adjustment. In this example, the two scheduling methods have the same results after AGV task scheduling allocation and path step-by-step optimization, which can effectively solve the problem of task scheduling and path planning of multiple AGVs in the workshop, and has good practicability. To sum up, since multiple AGVs must consider the impact of collision when driving in the same workshop, the actual completion time of the system depends on the delivery time after collision adjustment, that is, the final result of the second stage. For the small-scale example in this paper, the final results of the two methods are consistent, so the two-stage algorithm (time priority) proposed in this paper can effectively solve small-scale problems. 𝑛𝑛 9 12 15 18 Table 1 Comparison of calculation results Minimum time mathematical model 𝑝𝑝1 43 94 127 153 𝑝𝑝2 52 96 127 155 𝑡𝑡1 16.68 123.57 34.2 216.34 Advances in Production Engineering & Management 17(4) 2022 Processing urgency 𝑝𝑝1 43 95 127 154 𝑝𝑝2 52 96 127 155 𝑝𝑝2 6.84 9.44 9.51 10.51 Difference rate % 𝑑𝑑1 𝑑𝑑2 0 0 1.06 0 0 0 0.65 0 511 Wang, Liu, Leng, Wang, Meng, Zhou 4. Conclusion Aiming at the problems of AGV transportation task scheduling and path planning in the intelligent workshop, according to the corresponding mathematical model established to minimize the maximum delivery task completion time and the workpiece processing urgency, the workpiece delivery task sequence of each AGV is determined and the initial delivery path of AGV is generated. Considering conflict prevention and collision avoidance when multiple AGVs are running, conflict detection and anti-collision strategies are proposed. Finally, an example is given to verify the feasibility and effectiveness of multi AGV task allocation and path planning based on transportation task sequence to avoid conflict and collision. The experiments prove that the multiple collision avoidance strategies proposed in this paper can efficiently complete the delivery tasks according to the production plan while obtaining the collision free path of AGV. In conclusion, this paper schedules the tasks of AGV according to the manufacturing process flow, and plans the path, and avoids collisions of AGV. Finally, the realtime scheduling scheme of the automated material transportation system is obtained, which can provide a reference for intelligent production workshops. In addition, the algorithm proposed in this paper can be extended to other practical application scenarios such as automated terminals and intelligent warehouses using AGV, and has strong practical value. In future research, the non-uniform motion of AGV will be considered. Acknowledgment The research was funded by the Natural Science Foundation of Liaoning province (2019-ZD-0123) and Natural Science Foundation of Liaoning province (No. LJKZ0532). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] 512 Li, G., Zeng, B., Liao, W., Li, X., Gao, L. (2018). A new AGV scheduling algorithm based on harmony search for material transfer in a real-world manufacturing system, Advances in Mechanical Engineering, Vol. 10, No. 3, Article No. 1687814018765560, doi: 10.1177/1687814018765560. Ma, H.W., Fan, F.W., Hu, X.X. (2016). 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Advances in Production Engineering & Management 17(4) 2022 513 Calendar of events • 7th International Conference of Computational Methods in Engineering Science, November 24-26, 2022, Zamosc, Poland. • 14th International Conference on Mechatronics and Manufacturing, February 10-12, 2023, Royal Princess Larn Luang, Bangkok, Thailand. • 7th International Conference on Material Engineering and Manufacturing, April 7-10, 2023, Chiba University, Japan. • 51th North American Manufacturing Research Conference, June 12-16, 2023, Rutgers University, New Brunswick, New Jersey, USA. 514 Advances in Production Engineering & Management 17(4) 2022 Notes for contributors General Articles submitted to the APEM journal should be original and unpublished contributions and should not be under consideration for any other publication at the same time. 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. 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APEM Advances in Production Engineering & Management journal Chair of Production Engineering (CPE) University of Maribor APEM homepage: apem-journal.org Volume 17 | Number 4 | December 2022 | pp 397-516 Contents Scope and topics 400 Verification of intelligent scheduling based on deep reinforcement learning for distributed workshops via discrete event simulation Yang, S.L.; Wang, J.Y.; Xin, L.M.; Xu, Z.G. 401 Demand prediction and optimization of workshop manufacturing resources allocation: A new method and a case study Wan, J. 413 Monte Carlo Tree Search improved Genetic Algorithm for unmanned vehicle routing problem with path flexibility Wang, Y.D.; Lu, X.C.; Song, Y.M.; Feng, Y.; Shen, J.R. 425 End-of-line delivery vehicle routing optimization based on large-scale neighbourhood search algorithms considering customer-consumer delivery location preferences Niu, X.Y.; Liu, S.F.; Huang, Q.L. 439 An approach to maintenance sustainability level assessment integrated with Industry 4.0 technologies using Fuzzy-TOPSIS: A real case study Patalas-Maliszewska, J.; Łosyk, H. 455 Optimization of the rhomboidity of continuously cast billets using linear regression and genetic programming: A real industrial study Kovacic, M.; Zuperl, U.; Brezocnik, M. 469 Cause-related marketing strategy in a supply chain: A theoretical analysis and a case study Xu, G.Y.; Liu, H.; Duan, H.W. 479 Impact of Cobot parameters on the worker productivity: Optimization challenge Javernik, A.; Buchmeister, B.; Ojstersek, R. 494 Study on scheduling and path planning problems of multi-AGVs based on a heuristic algorithm in intelligent manufacturing workshop Wang, Y.J.; Liu, X.Q.; Leng, J.Y.; Wang, J.J.; Meng, Q.N.; Zhou, M.J. 505 Calendar of events 514 Notes for contributors 515 Published by CPE, University of Maribor ISSN 1854-6250 9 771854 625008 apem-journal.org