ISSN 1854-6250 APEM journal Advances in Production Engineering & Management Volume 19 | Number 4 | December 2024 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 Smetanova ulica 17, SI – 2000 Maribor, Slovenia, EU Desk Editor Website Technical Editor desk1@apem-journal.org desk3@apem-journal.org Martina Meh Lucija Brezocnik 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 Changsong Ma, Geely University of China, China 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 and Innovation 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 further 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 advertisements. 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Advances in Production Engineering & Management is indexed and abstracted in the WEB OF SCIENCE (maintained by Clarivate): 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 19 | Number 4 | December 2024 | pp 411–542 Contents Scope and topics A bi-objective Genetic Algorithm for flexible flow shop scheduling: A real-world application in the electrical industry 414 415 Reducing scrap in long rolled round steel bars using Genetic Programming after ultrasonic testing 435 Optimizing electric vehicle charging strategies using multi-layer perception-based spatio-temporal prediction of charging station load 443 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility 460 An algorithmic review of the technological progress and milestones in resource-constrained project planning 489 Integrated production and maintenance policy for manufacturing systems prone to products' quality degradation 512 Integrating simulation modelling for sustainable, human-centred Industry 5.0: ESG-based evaluation in collaborative workplaces 527 Calendar of events Notes for contributors 539 541 Escobar, D.; Chivata, B.; Nino, K. Kovacic, M.; Zupanc, A.; Zuperl, U.; Brezocnik, M. Wang, Y.N.; Zhang, Z.J.; Ping, A.; Wang, R.J.; Gong, D.Q. Siwiec, D.; Gawlik, R.; Pacana, A. Pourhejazy, P.; Ying, K.-C.; Cheng, C.-Y. BouAbid, H.; Dhouib, K.; Gharbi, A. Ojstersek, R.; Javernik, A.; Buchmeister, B. Journal homepage: apem-journal.org ISSN 1854-6250 (print) ISSN 1855-6531 (on-line) Published by CPE, University of Maribor. Scope and topics Advances in Production Engineering & Management (APEM journal) is an interdisciplinary refereed international academic journal published quarterly by the Chair of Production Engineering at the University of Maribor. The main goal of the APEM journal is to present original, high quality, theoretical and application-oriented research developments in all areas of production engineering and production management to a broad audience of academics and practitioners. In order to bridge the gap between theory and practice, applications based on advanced theory and case studies are particularly welcome. For theoretical papers, their originality and research contributions are the main factors in the evaluation process. General approaches, formalisms, algorithms or techniques should be illustrated with significant applications that demonstrate their applicability to real-world problems. Although the APEM journal main goal is to publish original research papers, review articles and professional papers are occasionally published. Fields of interest include, but are not limited to: Additive Manufacturing Processes Advanced Production Technologies Artificial Intelligence in Production Assembly Systems Automation Big Data in Production Block Chain in Manufacturing Computer-Integrated Manufacturing Cutting and Forming Processes Decision Support Systems Deep Learning in Manufacturing Discrete Systems and Methodology e-Manufacturing Evolutionary Computation in Production Fuzzy Systems Human Factor Engineering, Ergonomics Industrial Engineering Industrial Processes Industrial Robotics Intelligent Manufacturing Systems Joining Processes Knowledge Management Logistics in Production 414 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 19 | Number 4 | December 2024 | pp 415–434 Journal home: apem-journal.org https://doi.org/10.14743/apem2024.4.516 Original scientific paper A bi-objective Genetic Algorithm for flexible flow shop scheduling: A real-world application in the electrical industry Escobar, D.a, Chivata, B.a, Nino, K.b,* aSchool of Exact Sciences and Engineering, Sergio Arboleda University, Bogotá, Colombia Engineering Program, Universidad Militar Nueva Granada, Bogotá, Colombia bIndustrial ABSTRACT ARTICLE INFO The electrical sector forces manufacturing companies of electrical solutions to continually innovate and implement new processes for greater efficiency. The growing demand for electrical energy, as well as the need to adapt to hybrid operations that combine multi-project operation models with continuous production models, requires efficient workflow management. Accordingly, this article proposes a Genetic Algorithm (GA) approach for solving the scheduling problem in a Flexible Hybrid Flow Shop (FHFS) environment considering a transfer batch approach to minimize makespan and total tardiness. The approach is inspired by a real-world application in the electrical industry and also accounts for unrelated parallel machines, precedence, release times, and due dates for jobs at each production center as key constraints. Three real-data scenarios were generated and evaluated. In the first scenario, a 7 % improvement in makespan was observed compared to real execution times. In Scenario 2, the makespan improved significantly by 33 %, and only 17.4 % of jobs were delayed, compared to 96 % in the real data. Likewise, GA showed a lightly better performance over Tabu Search (TS) in 3.01 % for makespan while the delayed jobs found by GA were 25 % below those obtained by TS. These results highlight the potential of the proposed method to improve overall production efficiency, not only in the electrical sector but also in similar industries. Keywords: Production scheduling; Flexible flow shop; Genetic algorithm; Makespan; Tardiness; Transfer batch; Electrical sector *Corresponding author: karen.nino@unimilitar.edu.co (Nino, K.) Article history: Received 7 October 2024 Revised 21 December 2024 Accepted 23 December 2024 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 rapidly evolving electrical sector, manufacturing companies face continuous challenges to innovate and implement new processes aimed at enhancing efficiency. The growing demand for electrical energy, driven by the increasing interconnectivity of devices through the Internet of Things (IoT) and emerging technologies, necessitates a shift toward hybrid operational models that blend multi-project frameworks with continuous production systems. This trend underscores the urgent need for effective workflow management and highlights the complexities of production processes. As the sector increasingly adopts electronic equipment and the infrastructure required for its operation, planning, scheduling, and production control have become critical to ensuring competitiveness and success. Companies are tasked with not only meeting rising production demands but also adapting to the customization requirements of their customers in an ever-changing market. This dynamic environment compels firms in the electrical sector to consistently align their operations with the rapid pace of technological advancements and evolving customer expectations. 415 Escobar, Chivata, Nino Consequently, the production processes within these companies must navigate the dual challenge of enhancing efficiency while accommodating the growing demand for tailored solutions. This delightful balance is essential for maintaining relevance and achieving long-term sustainability in a sector characterized by constant change. Accordingly, the literature during the last decades has been describing a great amount of research focused on solving these kinds of problems from both real applications and theory points of view. Thus, this work made a review on this literature focus the search mainly on scheduling problems considering flexible production systems, one of the most used metaheuristics known as Genetic Algorithm and application on several industries, especially in electrical sector. Initially, the flexible production systems, also known as Hybrid Systems (HS) or Flexible Hybrid Flow Shop Systems (FHFS), are defined as the scheduling of n jobs across m processing stages that consider a specific objective function, as determined by the production sequence of the job according to Xu et al. [1]. The scheduling problem in FHFS is known for its high combinatorial complexity. The allocation of resources to perform different operations in the production process results in a combinatorial complexity problem that must be optimized. In other words, the number of possible sequences and production route combinations can grow exponentially with the number of jobs and workstations; therefore, scheduling problems in an FHFS system are considered NP-Hard according to Gupta et al. [2]. Similarly, the objective functions considered are mainly the minimizing of total production time (makespan) [1, 4, 6-12, 14-17], followed by total tardiness [3, 5, 8, 12-13], productivity [1, 4-5, 7, 14, 16-17], among others. The inherent flexibility of a flexible hybrid system implies the system must dynamically adapt to changes in demand, machine failures, or new work orders [1, 3, 5-7, 9-12, 16]. Optimization under these changing conditions requires algorithms that can handle uncertainty and variability, which is inherently complex and difficult to solve in polynomial time [1-17]. Most problems in an FHFS do not have a single objective [5, 8-9, 11-12, 15]. Generally, there are multiple objectives in conflict, such as minimizing production time, maximizing machine utilization, and minimizing costs, meaning that optimizing multiple objectives is even more complex. For example, Hasani et al. [15] proposed solving a bi-objective scheduling problem in a flexible Flow Shop with unrelated parallel machines, minimizing makespan and total production cost; authors introduced an approximate solution method based on a Non-dominated Sorting Genetic Algorithm (NSGA-II). Also, Jeen and Rajkumar [4] implemented a modified genetic algorithm in a Flow Shop production environment to minimize the makespan. In addition, considering the approaches addressed to solve the FHFS scheduling problem, the Genetic Algorithm, which is nature-inspired, is one of the most used metaheuristics for this problem. For instance, Espitia and Mendoza [11] developed a scheduling methodology based on the use of a genetic algorithm as a solution method to minimize makespan and tardy jobs. Similarly, Salazar and Sarzuri [3] Considered a FSF environment with anticipatory sequencedependent setup times, applying a genetic algorithm to minimize total tardiness by using dispatching rules for the initial population of EDD (Earliest Due Date). They also considered an IP neighbourhood search to enhance the performance of the proposed genetic algorithm. Likewise, Xu et al. [1] presents a case study where they develop a mathematical model aimed at minimizing the maximum completion time for a mixed flow shop scheduling problem, using a genetic algorithm to solve the problem. Najarro et al. [6] analysed the effect of including various constraints that negatively impact scheduling in a real Flow Shop environment, introducing an efficient genetic algorithm combined with a variable neighbourhood search, minimizing makespan. Han. and Lee [17] explored HFS pro-duction management based on an improved Genetic Algorithm (GA), proposing several assumptions for the multi-objective optimization problem of HFS production management. They introduced new constraints to the problem, such as multi-period control and job transport time, achieving efficiency in the experiments. As well, López et al. [16] selected a textile company as their case study and, through the coding of a simple genetic algorithm, developed a production scheduling methodology for Flexible Hybrid Flow Shop configurations, successfully reducing makespan. 416 Advances in Production Engineering & Management 19(4) 2024 [8] Tian, X. K. et al. (2019) [7] Bedhief, A.O and Dridi. N. (2019) [6] Najarro, R. et al. (2017) In summary, Table 1 shows the consolidation of the main research reviewed, highlighting the different objectives, approaches, and research methodologies for solving production planning problems. Thus, one of the relevant findings is the predominant interest in makespan (𝐶𝐶max ) and tardiness �𝑇𝑇𝑗𝑗 � minimization. Thus, this paper describes a Genetic Algorithm (GA) approach for solving the scheduling problem in a Flexible Hybrid Flow Shop (FHFS) environment, inspired by a real-world application in the electrical industry, the results show an important improvement on the current performance of production system resulting in a valuable tool in decision making for company. Advances in Production Engineering & Management 19(4) 2024 O O O O O O O LS O O TS O EA O ICA O O O NEH NQ-L NSGAII Heuristic and Metaheuristic methods O SPEA 2 O MOGA x x x x x x x x x x x x x x x x x x x x x x x Cmax Tj Energy Tt Cost Objective Function x x x x x x SP x x x x x x x x x x x x x x x x x x Approach x Table 1 Classification of articles by production types x x ST Stages Hybrid Lots Approach AG: Genetic Algorithm; LS: Local Search; TS: Tabu Search; EA: Evolutionary Algorithm; ICA: Imperialist Competitive Algorithm; NEH: Nawaz, Enscore, Ham NSGAII: Non-dominated Sorting Genetic Algorithm; NQ-L: Reinforcement Learning Method; SPEA2: Strength Pareto Evolutionary Algorithm MOGA: Multi-Objective Genetic Algorithm SP: Scheduling Problem; ST: Setup Time; Cmax: Makespan; Tj: Total Tardiness; Tt: Tardy Jobs [17] Han, J.H. and Lee, J.Y. (2023) [16] López, J.C. et al. (2014) [15] Hasani, A. et al. (2022) [14] Ren, J.F. et al. (2021) [13] Ištoković, D. et al. (2021) [12] Chen, D. and Zhao, X.R. (2021) [11] Espitia, J.A. and Mendoza, G.L. (2021) [10] Waraporn, F. et al. (2020) O O O [4] Jeen, R and Rajkumar R. (2017) [5] Kazemi, H. et al. (2017) O O AG [3] Salazar, E. and Sarzuri R. (2015) [1] Xu, W. et al. (2022) Articles Flow Shop [9] Shijin, W. et al. (2019) Method A bi-objective Genetic Algorithm for flexible flow shop scheduling: A real-world application in the electrical industry 417 Escobar, Chivata, Nino The remaining content of this work is as follows. Section 1 provides a clear introduction to the problem being addressed, along with a literature review focused on the main topics, particularly in electrical industry applications and scheduling solution approaches. Section 2 presents the characterization of the production process for the real case. Sections 3 and 4 detail the problem definition and the proposed solution method, respectively. Section 5 explains the real instance of the production process in the case study as well as presents the results and analysis of the evaluated scenarios. Finally, Section 6 addresses the conclusions and potential ways for future research. 2. Description of production process The electrical company specializes in the design and manufacturing of customized solutions under an Engineering to Order (ETO) production scheme. Its operation is divided into two key phases: the project-based model and the production-based model. The first phase encompasses all related from sales to the availability of materials, managing each project individually. This stage includes subprocesses such as sales, project management, engineering, procurement, logistics, and storage, where opportunities are identified, contractual aspects are managed, technical designs are developed, and necessary materials are ensured. The second phase, focused on productive execution through a Flexible Flow Shop approach, primarily concentrates on production processes, where raw materials are transformed, and the final product is assembled. This model allows manufacturing to be adapted to the specifications of each project, addressing several challenges in a structured manner. Mainly, the scheduling approach of this research is focusing only on the stages of the process that are directly related to product manufacturing. Thus, the set of production and project jobs merged from project-based model phase. Table 2 describes, for the project-based model, only the electrical and mechanical engineering stages, while the production-based model includes the production centres, and the stages required for the transformation of raw materials and assembly. Production-based model Project-based model Phase Production center Electrical engineering Mechanical engineering Manufacturing Assembly Table 2 Grouping of production and project tasks Cod RITM ECU L090 EPA APRB PED APRD LME LMV PCN FMC FMD SOL TPI FBC EME EEL EBC PRU 2.1 Production centre capacity Description Information review Equalization meeting with the client – Tecnichal clarifications List of electrical materials with delivery time greater than 90 days Development of basic engineering for client approval Approval of basic engineering by the client Detailed electrical engineering by the client Approval of detailed engineering by the client List of mechanical materials for structures List of various mechanical materials and cooper vbars CNC programing Cutting and punching of steel metal Bending of sheet metal Welding Treatment and painting Manufacturing of cooper bars Mechanical assembly Electrical assembly Assembly of cooper busbars Testing The capacity of the production centres is defined in terms of the amount of work each can perform within a specific time; it is measured in effective working hours for the context of this research. Each centre’s capacity is determined by the number of personnel and/or the effective 418 Advances in Production Engineering & Management 19(4) 2024 A bi-objective Genetic Algorithm for flexible flow shop scheduling: A real-world application in the electrical industry availability of the machines it comprises. The total capacity of the centre is obtained by adding up these individual capacities, expressed in terms of available working hours. Table 3 provides a detailed breakdown of the production centres (CP1, CP2, and CP3), which includes the production stages, the duration of each stage of 9 hours, the work shifts, and the required human resources, equipment, or machines. CP1 includes the electrical and mechanical engineering stages, each requiring six human resources. Meanwhile, CP2 focuses on manufacturing processes such as CNC programming, cutting, bending, welding, treatment, and copper bar fabrication, with personnel needs varying between one and four human resources, in addition to the use of machines. Finally, CP3 is dedicated to assembly, where the stages require between two and eight human resources. The distribution of work capacity among the various production centres illustrates the complexity and specialization of each stage in the production process. As manufacturing progresses, it is essential to consider both resource availability and process efficiency, as these factors will impact on the total production capacity and, ultimately, the timely delivery of the final products. According to capacity determined in each production centre (CP1, CP2 and CP3), as well as the work centres into them, the production times were established and shown in Table 4; this table provides a comprehensive overview of the processing time required (in days) for various products across different production centres and stages of the process, organized into families and specific items. The columns "Family" and "Item" indicate the type of product being manufactured, where each "Family" represents a broader category, such as Medium Voltage (MT), which includes products designed for electrical solutions in installations ranging from 1 to 57.7 kV, and Low Voltage (BT), which encompasses solutions for electrical installations below 1 kV. Each "Item" specifies a product within that category, such as the Motor Control Centre (CCM) or the Auxiliary Services Panel (TSA). In addition, the table highlights the time required for each process—engineering, manufacturing, and assembly—across the production centres (CP1, CP2, and CP3). For example, the "Power Distribution Centre" (CDP) requires approximately 3.94 days for electrical engineering (CP1), 0.76 days for bending (CP2), and 4.68 days for testing (CP3). This detailed breakdown is essential for understanding production timelines and efficiently managing resource allocation. Table 3 Production centre capacity Description Duration (hrs) A Electrical engineering 9 CP1 B Mechanical enginering 9 C CNC programming 9 D Cutting and punching 9 E Bending 9 CP2 F Welding 9 G Treatment and painting 9 H Cooper busbar fabrication 9 I Mechanical assembly 9 J Electrical assembly 9 CP3 K Cooper busbar assembly 9 Quality control and electrical L 9 testing HR: Human resources; CE: Computer equipment; M: Machines Production center Stage Work shifts 1 1 1 1 1 1 1 1 1 1 1 1 Human resources 6 6 1 2 2 4 2 2 4 8 2 4 Description HR + CE HR + CE HR + CE HR + M HR + M HR + M HR + M HR + M HR + CE HR + CE HR + CE HR + CE The result of data shown in Table 4, is the production system is settled as the diagram described in Fig. 1. At the top of the diagram, the general production centres are identified: CP1 (Engineering), CP2 (Manufacturing), and CP3 (Assembly). In the next level, the stages of the process are located, while the subsequent level details, the available resources, whether human or machine. The arrows represent the different routes the product can take through the various production centres and stages for its manufacturing. Thus, the production process is considered Advances in Production Engineering & Management 19(4) 2024 419 Escobar, Chivata, Nino as a flexible flow shop model. Each box shows the number of machines and the consecutive id to identify it into the model. For example, the CP1 production centre has in total six (6) machines which are the first machines from the total list of resources which has in total 43 machines. Table 4 Time required (days) 5 6 7 8 9 MT 10 11 12 13 14 A. IE M1 (1) M2 (2) M3 (3) CP1 VVB 3.94 Low voltage distribution panel TDB Medium voltage secondary switchgear 24 kV Medium voltage secondary switchgear 36 kV Medium voltage primary switchgear 17.5 kV Medium voltage primary switchgear 36 kV Primary medium voltage GIS switchgear Medium voltage variable frecuency drives Medium voltage soft starters B. IM M1 (7) M2 (8) M3 (9) M4 (10) M6 (6) M6 (12) M5 (11) C. PCN M1 (13) TCP CMS2 3.94 2.95 6.89 2.95 2.54 2.40 2.91 2.40 2.40 0.19 0.19 0.19 0.19 0.39 0.44 0.86 0.42 0.38 0.38 0.28 0.77 0.50 0.58 0.50 12 0.67 0.39 0.64 1.70 2.98 0.94 4.68 0.41 0.38 0.39 1.23 1.91 0.21 2.76 0.40 0.57 0.97 0.42 0.89 0.45 0.41 0.38 0.42 0.30 0.22 0.13 0.81 1.93 0.56 1.75 0.44 1.28 0.39 1.23 0.11 0.89 0.15 0.78 4.25 4.46 3.93 1.91 6.38 1.91 1.02 5.78 0.79 4.82 0.68 0.21 0.19 0.31 4.04 2.76 6.80 2.27 CMS3 3.94 3.20 0.39 0.28 0.79 0.29 0.13 0.16 1.35 2.34 0.34 2.59 CMP1 4.92 3.20 0.39 0.51 0.88 0.67 0.39 0.64 2.07 5.38 0.94 4.68 CMP3 4.92 3.20 0.39 0.58 0.92 0.78 0.56 0.68 2.14 5.38 1.20 4.68 VVMT 5.90 4.00 0.39 0.42 0.76 0.67 0.39 0.64 1.70 3.83 0.85 4.68 CMPG ASMT D. FMC 4.92 5.90 CP2 E. FMD M1 (14) M1 (16) M2 (15) M2 (17) 4.00 4.00 F. SOL 0.39 0.39 0.58 0.36 G. TPI 0.93 0.65 H. FBC M1 (18) 1.29 0.86 0.57 0.33 I. EME M1 (26) M2 (19) M1 (22) M1 (24) M2 (27) M3 (20) M2 (23) M2 (25) M3 (28) M4 (21) M4 (29) 0.34 2.53 0.55 1.45 CP3 J. EEL M1 (30) M2 (31) M3 (32) M4 (33) M5 (34) M6 (35) 5.54 3.32 K. EBC 0.71 0.72 4.68 4.68 L. PRU M1 (40) M1 (38) M2 (41) M2 (39) M3 (42) M4 (43) M7 (36) Fig. 1 Flow diagram of the production process 420 11 PRU-Testing 0.50 10 EBC-Cu busbar assembly 0.38 0.66 9 EEL-Electrical assembly 0.19 2.95 0.31 8 EME-Mechanical assembly 2.40 TSA 0.39 7 SOL-Welding 0.76 3.20 6 FMD-Bending 0.42 Low voltage variable frecuency drives Control and protection panel FMC-Cutting and punching 0.39 4.92 M4 (4) M5 (5) 2.40 CCM ASB 5 3.94 CDP Motor control center Low voltage soft starters 4 FBC-Cu busbar fabrication 4 3 CP3 – Assembly TPI-Treatment and painting Auxiliary services panel 2 PCN-CNC programing 3 1 CP2 – Manufacturing Mechanical engineering Power distribution center Time required by process (days) CP1 – Enginnering Electrical engineering 1 2 BT Description Type of solution Item Family Description of products M8 (37) Advances in Production Engineering & Management 19(4) 2024 A bi-objective Genetic Algorithm for flexible flow shop scheduling: A real-world application in the electrical industry 3. Construction of the HFS scheduling model This study addresses the scheduling and permutation of tasks in a project planning environment within a Flexible Hybrid Flow Shop (HFS) production system. This system includes three production centres with unrelated parallel machines, dedicated to the fabrication, transformation, and testing of semi-finished and finished products for industrial electrical equipment projects. Key variables such as processing times, release times, and due dates are directly influenced by the production centre assigned. The objective functions considered are makespan and total tardiness, as main constraints are related to transfers lots, unrelated parallel machines, setup times. Accordingly, to Graham et al. [21], notation, the problem addressed is: 𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚 / 𝑅𝑅𝑚𝑚 , 𝑟𝑟𝑗𝑗 , 𝑆𝑆𝑗𝑗𝑗𝑗 , 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ(𝑏𝑏) / 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 , ∑𝑇𝑇𝑗𝑗 The Hybrid Flow Shop (HFS) manufacturing environment presents complex scheduling challenges, involving the coordination of multiple jobs across various processing stages [1]. This problem is classified as strongly NP-Hard, meaning exact methods become infeasible for large instances, as confirmed by prior studies like those of Gupta et al. [2]. To address this complexity, metaheuristic algorithms, specifically Genetic Algorithms (GA), from mathematical model, is performed to provide approximate solutions. In this study, a GA algorithm is adapted to optimize the scheduling process by minimizing makespan, total tardiness, and the number of delayed jobs in the HFS system; it means it is necessary to determine the optimal assignment of jobs 𝑗𝑗 to machines 𝑘𝑘, within a sequence of production centres 𝑙𝑙, in such makespan (𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 ) and total tardiness (∑ 𝑇𝑇𝑗𝑗 ) are minimized. In addition, the developed algorithm does not consider dynamic inputs, which means that production orders arriving continuously or in real-time during the execution of the plan are not included; so, all production orders are predefined, and their characteristics are known at the beginning of the process due to this information is given by Planning and Production control Department of the company. Thus, the proposed Hybrid Flow Shop (HFS) production model is developed considering the following assumptions: • Each machine can process only one job at a time. • Each job is processed by only one machine at any given time. • Jobs follow a fixed sequence of production centres (e.g. CP1, CP2, and CP3). • Once started, a job is processed to completion without interruptions. • The number of jobs and their processing times are deterministic. • Setup times are considered negligible to simplify the model. • Jobs can only be processed if the corresponding production centre is available. • Transportation times between machines depend on the predefined sequence. • Jobs can be assigned to any available machine within their respective set. • Maintenance schedules are predefined and occur outside production times. • Materials and inputs required are guaranteed to be continuously available throughout the scheduling process. To establish a mathematical model for the HFS scheduling problem for electrical companies, the following notation is defined: 𝑗𝑗 𝑙𝑙 𝑁𝑁𝑖𝑖 𝐾𝐾 𝑇𝑇𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝑃𝑃𝑙𝑙 𝑑𝑑𝑗𝑗 Set of jobs to be processed on the machines {1,2, … , 𝑛𝑛} where 𝑛𝑛 is the total number of jobs, (𝑗𝑗 ∈ 𝐽𝐽, for every job) Set of production centres {1, 2, … , 𝐿𝐿} where 𝐿𝐿 is the total number of production centres, (𝑙𝑙 ∈ 𝐿𝐿, for every production centre) Set of operations per job {1,2, … , 𝑛𝑛𝑖𝑖 }, where 𝑛𝑛𝑖𝑖 is number of operations for job 𝑗𝑗, (𝑗𝑗 ∈ 𝑁𝑁𝑖𝑖 , for every operation) Set of machines {1,2, … , 𝑘𝑘}, where k is the total number of machines, (𝑘𝑘 ∈ 𝐾𝐾, for every machine) Processing time of job 𝑗𝑗 assigned to machine 𝑘𝑘 in production center 𝑙𝑙 Time capacity in production centres Due date of job 𝑗𝑗 Advances in Production Engineering & Management 19(4) 2024 421 Escobar, Chivata, Nino 𝑃𝑃𝑗𝑗𝑗𝑗𝑗𝑗 𝜔𝜔𝑗𝑗 𝑟𝑟𝑗𝑗 𝑋𝑋𝑗𝑗𝑗𝑗𝑗𝑗 𝐶𝐶𝑗𝑗𝑗𝑗𝑗𝑗 𝑇𝑇𝑗𝑗𝑗𝑗𝑗𝑗 𝑇𝑇𝑗𝑗 𝑇𝑇𝑘𝑘𝑘𝑘 𝛽𝛽𝑘𝑘 𝑇𝑇𝑛𝑛𝑛𝑛 𝐶𝐶max Duration of job 𝑗𝑗 on machine 𝑘𝑘 in production center 𝑙𝑙 Weighting factor Release time of job 𝑗𝑗 Binary variable equal to 1 if job 𝑗𝑗 is processed by machine 𝑘𝑘 in production center 𝑙𝑙, and 0 otherwise 𝑋𝑋𝑗𝑗𝑗𝑗𝑗𝑗 for 𝑋𝑋𝑗𝑗𝑗𝑗𝑗𝑗 = 0, 1 𝑗𝑗 = 1, 2…, 𝑛𝑛, 𝑘𝑘 = 1, 2…, 𝑛𝑛, 𝑙𝑙 = 1, 2…, 𝑛𝑛 Completion time of job 𝑗𝑗 on machine 𝑘𝑘 in production center 𝑙𝑙 Star time of job 𝑗𝑗 on machine 𝑘𝑘 in production center 𝑙𝑙 Job 𝑗𝑗 tardiness Start time of machine 𝑘𝑘 in production center 𝑙𝑙 Total number of jobs assigned to machine 𝑘𝑘 Start time of operation 𝑛𝑛 of job 𝑗𝑗 Makespan, the maximum completion time of all processes in the last production centre The bi-objective function, denoted as Z, seeks to minimize both the weighted total production time 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 and the weighted total tardiness 𝑍𝑍𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 . Thus, a unique objective function is defined using a weight ω𝑗𝑗 which works as ponderator obtaining as a result the following equations. (1) 𝑀𝑀𝑀𝑀𝑀𝑀 𝑍𝑍 = ωj · 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + �1 − ωj � · 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 0≤w≤1 where: 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑗𝑗 (𝑚𝑚𝑚𝑚𝑚𝑚𝑙𝑙 (𝐶𝐶𝑗𝑗𝑗𝑗𝑗𝑗 ) (2) 𝑍𝑍𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = � 𝑛𝑛 𝑗𝑗=1 𝑇𝑇𝑗𝑗 In this way, the objective function is obtained as follows: Subject to: 𝑍𝑍 = (𝜔𝜔1 · 𝑧𝑧𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ) + (𝜔𝜔2 · 𝑧𝑧𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 ) � 𝑁𝑁 𝑗𝑗,𝑘𝑘 𝑋𝑋𝐽𝐽𝐽𝐽𝐽𝐽 · 𝑇𝑇𝑃𝑃𝑗𝑗𝑗𝑗𝑗𝑗 ≤ 𝐶𝐶𝑃𝑃𝑙𝑙 ∀ 𝑙𝑙 ∈ L � � 𝑛𝑛 𝑘𝑘 𝑘𝑘 𝑗𝑗=1 𝑛𝑛 𝑋𝑋𝑗𝑗𝑗𝑗𝑗𝑗 = 1, ∀ 𝑗𝑗, 𝑙𝑙 𝑋𝑋𝑗𝑗𝑗𝑗𝑗𝑗 ≤ 1, ∀ 𝑘𝑘, 𝑙𝑙 � 𝑋𝑋𝑗𝑗𝑗𝑗𝑗𝑗 = 𝛽𝛽𝑘𝑘 ∀ 𝑘𝑘, 𝑙𝑙 𝑗𝑗 𝐶𝐶𝑗𝑗𝑗𝑗𝑗𝑗 = 𝑇𝑇𝑗𝑗𝑗𝑗𝑗𝑗 + 𝑃𝑃𝑗𝑗𝑗𝑗𝑗𝑗 (3) (4) (5) (6) (7) (8) (9) 𝑇𝑇𝑗𝑗 = max (0, 𝐶𝐶𝑗𝑗𝑗𝑗𝑗𝑗 − 𝑑𝑑𝑗𝑗 ) (10) 𝑃𝑃𝑗𝑗𝑗𝑗𝑗𝑗 ≥ 0, ∀ 𝑗𝑗, 𝑘𝑘, 𝑙𝑙 (13) 𝑇𝑇𝑛𝑛𝑛𝑛 ≥ 𝑇𝑇𝑘𝑘𝑘𝑘 + 𝑃𝑃𝑗𝑗𝑗𝑗𝑗𝑗 · �1 − 𝑋𝑋𝑗𝑗𝑗𝑗𝑗𝑗 � ∀ 𝑗𝑗, 𝑘𝑘, 𝑙𝑙 𝐶𝐶𝑗𝑗𝑗𝑗 ≤ 𝑑𝑑𝑗𝑗 ∀ 𝑗𝑗, 𝑙𝑙 𝛽𝛽𝑘𝑘 ≥ 0, ∀ 𝑘𝑘 𝑇𝑇𝑗𝑗𝑗𝑗𝑗𝑗 > 0, ∀ 𝑗𝑗 𝐶𝐶𝑗𝑗𝑗𝑗 ≥ 0, ∀ 𝑗𝑗, 𝑙𝑙 (11) (12) (14) (15) (16) The set of constraints (Eqs. 1 to 16) describes mathematical model. Eqs. 1 to 4 refer to objective function. Likewise, constraint Eq. 5 corresponds to the capacity constraint associated with the processing times of the jobs; constraint Eq. 6 ensures that each job (j) is assigned to exactly one machine (k) in the production centre (l); constraint Eq. 7 limits the number of jobs assigned to a specific machine (k) and production centre, ensuring that no more than one job is assigned in each case. Meanwhile, constraint Eq. 8 ensures that the total number of jobs (j) assigned and 422 Advances in Production Engineering & Management 19(4) 2024 A bi-objective Genetic Algorithm for flexible flow shop scheduling: A real-world application in the electrical industry not assigned to each machine and production centre is balanced; constraint Eq. 9 calculates the completion time of the jobs; constraint Eq. 10 guarantees that jobs are completed within their deadlines and penalizes any delays; constraint Eq. 11 ensures that an operation cannot begin until the machine to which it has been assigned is available and until its predecessor has been completed. Constraint Eq. 12 guarantees that job (j) is not completed after its due date. Finally, constraints Eqs. 13 to 16 correspond to non-negativity constraints, ensuring that the initial and final times are greater than 0. It is worth to mention that, not only this approach could be focusing on electrical sector manufacturing production process, but also it could be easily applicable to production environments with similar structures, particularly those that operate with production centres and stages, processing products in a defined sequence using parallel machines. It is especially suitable for systems where production times at each stage are known in advance, enabling planning and process optimization. This latter is possible because of the algorithm is constructed modularly and sequentially in stages, allowing for modifications to the network structure of the proposed production model. Thanks to this design, machines can be added or removed at each stage, and the processing times of products can be dynamically adjusted at every stage. 4. Genetic algorithm for scheduling in a flexible hybrid flow shop (FHFS) Based on the mechanisms of artificial selection, the Genetic Algorithm (GA) combines the concept of fittest survival among solutions with a structured random exchange of information, and the creation of offspring [18]. The Genetic Algorithm repeats the processes of evaluation, selection, crossover, and mutation after initialization until the stopping condition is reached. The GA is inherently parallel and exhibits implicit parallelism [19], which means that it does not evaluate and improve a single solution but rather analyses and modifies a set of solutions simultaneously. Fig. 2 describes the flowchart of the GA addressed in this study. Fig. 2 GA approach flowchart (Adapted from Jeen and Rajkumar [4]) Advances in Production Engineering & Management 19(4) 2024 423 Escobar, Chivata, Nino 4.1 Parameters The encoding of each solution alternative for the Flexible Sequential Hybrid Flow (FSHF) problem is represented by a vector of size n, where each position 𝑘𝑘 of the vector indicates the job that will be performed in the 𝑘𝑘 𝑡𝑡ℎ place [6]. The population (set of solutions) is created from a specific number of chromosomes, which each one represents the sequence that jobs will be scheduled. To ensure the validity of the chromosome, no job should be repeated, ensuring that all of them are completed and the total completion time and total tardiness of all jobs can be calculated. Fig. 3 shows the composition of the vector for a chromosome for 8 jobs. 7 1 5 6 2 3 8 4 Fig. 3 Vector – representation of job order Regarding the initial population, according to the study by López et al. [16], a binary matrix of size 𝑖𝑖 𝑥𝑥 𝑘𝑘 was used to represent jobs and machines, where each row is a chromosome. In the study by Najarro et al. [6], the initial population is generated randomly, and its size varies depending on the number of jobs (𝑛𝑛) and machines (𝑚𝑚), where 𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑛𝑛 ∗ 𝑚𝑚. The initial population is created by repeating the chromosome generation process as many times as the population size is set. The genetic algorithm in this study involves several key steps to optimize task scheduling by minimizing makespan and weighted tardiness, as is shown in Fig. 4. The fitness function evaluates everyone in the population, assigning a value that reflects the quality of the task sequence in meeting the scheduling objectives [3]. A lower fitness value indicates a superior solution. About selection is performed using the tournament selection method, which balances exploration and exploitation [19]. In this study, individuals compete in tournaments, with the best-performing ones proceeding to genetic operations. A tournament size of three is used, allowing for quicker algorithm convergence compared to methods like roulette wheel selection. Fig. 4 Process cycle in genetic algorithm Likewise, the Double Point Crossover (DPX) operator is applied to combine genetic material from two parent solutions, with repair mechanisms preventing duplicate jobs in the offspring [20]. After crossover, the offspring's fitness is evaluated, and the best individuals are selected for the next generation. Regarding, mutation is performed using a two-point mutation technique, where two positions in the offspring's sequence are randomly selected, and the segment between them is re-versed. This probabilistic process generates new solutions, which are evaluated for fitness, with the best-performing solutions advancing to the next generation [20]. In addition, the replacement process ensures the evolution of the population by selecting individuals from the current generation to create the next, based on their fitness. Finally, the algorithm employs stopping criteria that prevent infinite runs, including a maximum number of generations and stopping after several generations without improvement. 424 Advances in Production Engineering & Management 19(4) 2024 A bi-objective Genetic Algorithm for flexible flow shop scheduling: A real-world application in the electrical industry 5. Results and discussion This section explains how the instances were created with real data from electrical sector. In addition, three scenarios were created and performed, and the obtained results of each are discussed. Likewise, the GA algorithm is compared to TS (Tabu Search) method to evaluate its performance and results obtained are also argued. Finally, Computational time behaviour of all tests was analysed to evaluate the functioning of the model. 5.1 Real instance of the production process Delivery date Previously, in the planning process at the company, a dedicated department handles production planning and control, conducted daily with the support of an expert professional using Excel. The planning process varies depending on project complexity, often leading to delays in both planning and production. The production area receives a schedule, which includes project details, task numbers, product references, and start and delivery dates. Based on this information, production management is expected to allocate resources effectively to meet delivery deadlines, heavily relying on staff experience. Fig. 5 shows the behaviour of deliveries in the evaluated period. The red line illustrates the planned deliveries, and the black line identifies the actual behaviour of the same. An analysis of a six-month period for 27 tasks revealed a 96 % non-compliance rate, with 25 tasks delivered late. The planned makespan was 370 days, but the actual execution took 538 days, a 31 % increase, resulting in a weighted tardiness of 102.96 days. 09/03/2024 30/11/2023 22/08/2023 14/05/2023 1 3 5 7 9 11 13 15 17 19 21 23 25 27 Job P. delivery date 5.2 Test instances Real delivery date Fig. 5 Actual delivery performance – 6-month period Based on the results obtained during the data analysis, changes are proposed to focus on the number of jobs to be processed. This involves adjusting quantities to create more efficient transfer batches that provide effective solutions in the transformation and execution processes within each production centre based on the research made by Kazemi et al. [5]. A set of three simulations was managed considering the number of jobs to be performed and the number of available machines, referred to as scenarios 1, 2, and 3. Additionally, the Genetic Algorithm (GA) parameters were adjusted for each scenario to achieve more efficient results closer to the optimal. The scenarios included three production centres with a total of 43 machines; the only difference between them lies in the number of jobs: scenarios 1, 2, and 3 have 27, 46, and 87 jobs, respectively. These jobs are divided into transfer batches, which are scheduled independently. To illustrate the distribution of these transfer batches, Table 5 shows how the distribution of jobs is planned. The Gantt charts show the job distribution, and the convergence graphs confirm that the algorithm reached solutions close to the optimum. To ensure job precedence in each scenario, the difference between due dates and completion times is compared for each task. The results of the best sequencing in Production Centre 1 (CP1) determine the start times for each job in Production Centre 2 (CP2), and in turn, the results from CP2 establish the release times for Production Centre 3 (CP3). Once the simulation for CP3 is complete, the results are used to evaluate the performance of each scenario and transfer batch. Advances in Production Engineering & Management 19(4) 2024 425 Escobar, Chivata, Nino Job 1 Project Product Proj. # 1 CMP1 T. batch size 27 5.3 Results of Scenario 1 Table 5 Transfer batch – Scenarios 1, 2 and 3 Job 1 2 3 4 5 Project Product Proj. # 1 CMP1 CMP1 CMP1 CMP1 CMP1 T. batch size Job 5 5 6 6 2 3 4 5 6 7 8 9 5 Project Product 1 CMP1 Proj. # 1 CMP1 CMP1 CMP1 CMP1 CMP1 CMP1 CMP1 CMP1 T. batch size 3 3 3 3 3 3 3 3 3 Fig. 6 presents the results obtained for this scenario. Gantt charts are divided into three production centres, each showing the behaviour of jobs in terms of sequencing, indicating the completion time of each task and the makespan for each centre, highlighting the best sequencing solutions. The analysis reveals that in Production Centre 1 (CP1), Task 27 is the last to finish, with a makespan of 243.1 days. In Production Centre 2 (CP2), Task 26 is the last to finish, with a makespan of 262.9 days. Finally, in Production Centre 3 (CP3), Task 1 is the last to complete the process on the last machine, with a total time of 502 days. Fig. 7 shows the convergence behaviour of the algorithm in each phase of the production process. Thus, in the first 10 generations, the convergence is slow; after that, the best fitness value decreases until it reaches optimal convergence around 40 generations. Likewise, Fig. 8 describes the difference between the delivery dates of the real execution and those obtained with the GA algorithm. On average, it is seen that the GA finds earlier delivery dates for jobs, which results in better tardiness performance. These results suggest a slight improvement in reducing delayed tasks across the different production centres, which may be related to the large number of jobs assigned to each project. However, there are still high delay values that require further analysis to optimize task planning and sequencing. Fig. 6 also details the behaviour of the genetic algorithm in this first scenario. Upon analysing the results, a 26.3 % increase is observed compared to the planned makespan of 370 days, while there is a 6.7 % reduction when compared to the actual makespan of 538 days. 426 Fig. 6 Gantt chart – Transfer batch 1 – PC 1, PC 2, PC 3 – 27 jobs Advances in Production Engineering & Management 19(4) 2024 A bi-objective Genetic Algorithm for flexible flow shop scheduling: A real-world application in the electrical industry In conclusion, although the genetic algorithm has proven to be more effective than the real instance, it has not yet reached the efficiency needed to surpass the company's planned objectives. These findings emphasize the importance of continuing to investigate and adjust the algorithm’s parameters to improve its performance in future production scenarios. Here is where transfer batch approach gets importance into the model. Delivery date Fig. 7 Convergence graph – Transfer batch 1 – PC 1, PC 2, PC 3 – 27 jobs 18/04/2024 09/03/2024 29/01/2024 20/12/2023 10/11/2023 01/10/2023 22/08/2023 13/07/2023 03/06/2023 24/04/2023 15/03/2023 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Job P. delivery date 5.4 Results of Scenario 2 AG Delivery date - 27 Job Fig. 8 Real delivery performance vs GA – 27 jobs In this scenario, 46 jobs were evaluated with the aim of improving production through batch transfers. Project 26, initially composed of 27 jobs, was divided into smaller batches. As a result, makespan was reduced by 2.4 % compared to the previous scenario. At the same time, delayed jobs decreased, and only 17.4 % of the jobs missed their deadlines. Among the results obtained, it was observed that in CP1 and CP2, job 32 had the greatest delay, with 99.1 and 104.2 days, respectively. In CP3, the job with the greatest delay was job 23, with 91.5 days, processed on machine 40 and at stage L. Advances in Production Engineering & Management 19(4) 2024 427 Escobar, Chivata, Nino Figs. 9, 10 and 11 show the sequencing behavior found by the G.A in this scenario. The results show that the use of transfer batches and genetic operators in this scenario achieved significant improvements in delivery times. The makespan was reduced to 361.29 days, compared to the actual makespan of 538 days, and the number of delayed jobs decreased from 46 to 8. Additionally, the weighted tardiness was reduced to 6.27 days. These results highlight the effectiveness of the genetic algorithm in achieving the planned completion time of 370 days, improving the efficiency of the production system in this second scenario. Fig. 9 Gantt chart – Transfer batch 2 – PC 1, PC 2, PC 3 – 46 jobs 428 Fig. 10 Convergence graph – Transfer batch 2 – PC 1, PC 2, PC 3 – 46 jobs Advances in Production Engineering & Management 19(4) 2024 Delivery date A bi-objective Genetic Algorithm for flexible flow shop scheduling: A real-world application in the electrical industry 10/12/2023 31/10/2023 21/09/2023 12/08/2023 03/07/2023 24/05/2023 14/04/2023 05/03/2023 24/01/2023 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 Jobs P. delivery date 5.5 Results of Scenario 3 A.G Delivery date - 46 Job Fig. 11 Real delivery performance vs GA – 46 jobs This scenario involved 87 jobs and revealed a compact distribution of tasks due to uniform processing times, which led to efficient sequencing. However, the larger number of machines required more computational resources, and the high number of delays (peaks) indicated that this approach was less effective for higher work volumes. Figs. 12, 13, and 14 present the distribution and sequencing of the solution found by the genetic algorithm. They illustrate how the use of the largest number of available machines has been optimized at each stage of the process, and they also allow the convergence process to be identified. The results indicate that this scenario presents significantly high delay values. Although the number of delayed jobs was reduced by 52 % compared to the initial 87 jobs, this percentage is not substantial enough to be considered effective for implementation in the production plant. When compared to other scenarios, the obtained makespan of 443 days represents a 19.7 % increase over the planned makespan of 370 days. However, compared to the actual makespan of 538 days, there is a 17.7 % reduction, and relative to scenario 1 (502 days), there is an 11.8 % decrease. Finally, when analysing the difference with scenario 2 (361.29 days), there is an 18.4 % increase. Fig. 12 Gantt chart – Transfer batch 3 – PC 1, PC 2, PC 3 – 87 jobs Advances in Production Engineering & Management 19(4) 2024 429 Escobar, Chivata, Nino Fig. 13 Convergence graph – Transfer batch 3 – PC 1, PC 2, PC 3 – 87 jobs Delivery date This third scenario demonstrates that, although the transfer batch approach has potential, its effectiveness significantly decreases with a substantial increase in the number of jobs. The high delay values suggest that further adjustments in planning and the configuration of the genetic algorithm are necessary to efficiently handle larger workloads. 28/02/2024 19/01/2024 10/12/2023 31/10/2023 21/09/2023 12/08/2023 03/07/2023 24/05/2023 14/04/2023 05/03/2023 24/01/2023 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 Jobs P. delivery date A.G Delivery date - 87 Job Fig. 14 Real delivery performance vs GA – 87 jobs 5.6 Genetic Algorithm vs. Tabu Search for HFS The Genetic Algorithm approach was compared with another well-studied method known as Tabu Search (TS). TS is a metaheuristic based on local search, whose primary objective is to escape local optima and efficiently explore the solution space through adaptive memory, known as the tabu list [10]. By applying Tabu Search to the case study and comparing it with GA, Scenario 2, previously described, was evaluated. This scenario had previously demonstrated the best performance using the Genetic Algorithm in terms of execution time (makespan) and total tardiness. Fig. 15 430 Advances in Production Engineering & Management 19(4) 2024 A bi-objective Genetic Algorithm for flexible flow shop scheduling: A real-world application in the electrical industry shows the sequencing of jobs in the production centers in a Gantt chart. After analysing the data obtained through TS, slight differences were identified at each stage of Scenario 2. For example, in Production Centre 1 (CP1), the execution time (makespan) was reduced by 8.57 %, while total tardiness and the number of delayed jobs increased by 20.71 % and 9.09 %, respectively, compared to GA. Likewise, a reduction was observed compared to GA in the completion time (makespan), total tardiness, and the number of delayed jobs by 6.4 %, 47 %, and 44.44 %, respectively. For Production Centre 3 (CP3), the data is particularly significant, as it evaluates how closely the planned in Production Centre 2 (CP2), completion time of 370 days is achieved. In this centre, an increase of 3.01 % in the makespan was observed when employing the TS method. Additionally, 12 delayed jobs were recorded compared to the 8 delayed jobs obtained using GA. Table 6 provides a summary of the results obtained through both methods, highlighting the differences in their performance and showcasing the behaviour of TS as an effective alternative for solving the problem under study. Metrics Makespan Weighted Tardiness Number of Delays AG 290,09 13,04 24 Table 6 Results of scenario 2, AG and TS Scenario 2 CP1 CP2 TS AG TS 267,2 300 282,9 15,74 19,56 9,19 0 27 12 AG 361,29 6,27 8 CP3 TS 372,5 5,13 12 Fig. 15 Gantt chart – Transfer batch 2 – PC 1, PC 2, PC 3 – 46 jobs – TS A comparative analysis of the two methods reveals very similar behaviour. As shown in Fig. 16, jobs tend to meet the planned delivery dates. However, in both methods, there are jobs that exceed the planned times. It is determined that the GA meets the planned makespan constraint Advances in Production Engineering & Management 19(4) 2024 431 Escobar, Chivata, Nino of 370 days and results with a lower number of delays. Nevertheless, the results obtained with Tabu Search (TS) demonstrate it can be considered like an alternative approach for achieving positive outcomes in FHFS production environments. Fig. 16 TS vs GA performance – 46 jobs 5.7 Evaluation of robustness under disruptive production environments In the context of production planning in real-world environments, it is common to face significant disruptions that hinder the achievement of objectives within the planned time horizon. These disruptions include machine failures or shutdowns and the introduction of new orders with tight delivery schedules. To evaluate the performance and robustness of the Genetic Algorithm (GA) under these conditions, modifications to the algorithm were introduced, and two test instances were generated using the transfer batch from Scenario 2. In the first instance (AG-1), machines were randomly selected across different production centres, simulating their inactivity. In the second instance (AG-2), eight new jobs with various products, delivery times, and release times were added. The corresponding simulations were conducted, consolidating the results in Table 7, which allowed for analysing the impact of these disruptions on the algorithm's performance. The results obtained show that disturbances in the evaluated scenarios have a significant impact on makespan and total tardiness, especially in more complex environments such as Production Centre 3 (CP3). It is observed that, in general, both indicators tend to increase in the disturbed scenarios (AG-1 and AG-2) compared to the baseline scenario (AG). Table 7 Results of scenario 2, different environments Makespan Total Tardiness Number Delays CP 1 CP 2 CP 3 AG 290.1 AG - 1 339.9 AG - 2 325.0 AG 300.0 AG - 1 350.8 AG - 2 345.2 AG 361.3 AG - 1 421.0 436.5 13.04 32.98 16.34 19.56 40.62 33.92 6.27 25.46 44.75 24 5.8 Computational time 27 24 27 33 26 8 18 AG - 2 20 Based on the data in Table 8, a growing trend in CPU time is observed as the number of jobs increases. In Scenario 1, with 27 jobs, CPU time ranges between 22 and 72 minutes, being the lowest compared to the other scenarios. In Scenario 2, with 46 jobs, CPU time progressively increases from 62 to 142 units as the stages advance. Finally, in Scenario 3, with 87 jobs, the highest CPU times are recorded, rising from 76 to 304 minutes. Likewise, there is a correlation between CPU time and makespan; as the makespan increases, CPU time also tends to grow. This is clear in Scenario 3, Stage 3, where the makespan reaches 443.0, and CPU time registers its highest value (304 minutes). In conclusion, the number of jobs and the computational load required in later stages significantly increase CPU time. This sug432 Advances in Production Engineering & Management 19(4) 2024 A bi-objective Genetic Algorithm for flexible flow shop scheduling: A real-world application in the electrical industry gests that the Genetic Algorithm (GA) solution demands greater computational time as the size and complexity of the problem increase. Solution Actual (empirical) AG Scenario * 1 2 3 Table 8 Performance metrics and CPU time in FHFS Stage * 1 2 3 1 2 3 1 2 3 Flexible Flow Shop Scheduling Makespan 538 243 263 502 290 300 361 366 379 443 F.O (Z) * 124.93 134.5 262.5 151.6 159.8 183.8 206 228.2 254.8 T. Tardiness 1.933 6.8 6.1 23.1 13.0 19.6 6.3 45.6 88.8 34.1 Jobs 27 27 27 27 46 46 46 87 87 87 N° Delays CPU Time 25 5040 13 22 12 43 10 72 24 62 27 97 8 142 50 76 78 186 45 304 6. Conclusion The results of this research demonstrate that the proposed model for production scheduling, sequencing, and control achieves significant reductions in both makespan and tardiness. In Scenario 2, a makespan of 361.29 days was achieved, representing a 32.85 % improvement compared to the 538 days of the current model. Similarly, tardiness was reduced from 96 % to 17.4 %, significantly enhancing customer satisfaction and operational efficiency. In addition, the comparative analysis between the GA and TS (Tabu Search) methods reveals similar behaviours in job scheduling. Regarding the planned completion time of 370 days, the GA achieved a 2.41 % reduction, while the TS showed a 0.54 % increase. Furthermore, 8 delays were observed with the GA compared to 12 with the TS. Based on these results, the GA method is identified as the most suitable tool for addressing scenarios like the one presented in the case study. Also, it was observed that CPU time is directly influenced by the number of jobs, the size of the makespan, and the number of machines at each stage. This suggests that, as the size and complexity of the problem increase, the solution based on the Genetic Algorithm requires more computational time. A key advantage of the model is the substantial reduction in scheduling time when using the Genetic Algorithm (GA) compared to manual methods using transfer batches. Results showed this approach improves resource allocation, ensures more efficient deliveries, and has proven to be robust, adapting to various production scenarios. Additionally, it offers flexibility to meet the specific needs of other production systems, allowing customization based on the characteristics of the environment, such as product types, machine capacities, and operational constraints. This makes it applicable to various production models, including hybrid flow shops, assembly lines, cellular manufacturing systems, and batch production configurations. Finally, as an opportunity for future research, the development of algorithms that allow dynamic inputs for real-time decision-making is proposed. The incorporation of variables such as maintenance, inventory, and logistics could significantly expand the applicability of the model to different industrial sectors. References [1] [2] Xu, W., Sun, H.Y., Awaga, A.L., Yan, Y., Cui, J.Y. (2022). Optimization approaches for solving production scheduling problem: A brief overview and a case study for hybrid flow shop using genetic algorithms, Advances in Production Engineering & Management, Vol. 17, No. 1. 45-56, doi: 10.14743/apem2022.1.420. Gupta, J.N.D., Krüger, K., Lauff, V., Werner, F., Sotskov, Y.N. (2002). 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Advances in Production Engineering & Management 19(4) 2024 Advances in Production Engineering & Management ISSN 1854-6250 Volume 19 | Number 4 | December 2024 | pp 435–442 Journal home: apem-journal.org https://doi.org/10.14743/apem2024.4.517 Original scientific paper Reducing scrap in long rolled round steel bars using Genetic Programming after ultrasonic testing Kovacic, M.a,b,c,*, Zupanc, A.a, Zuperl, U.d, 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 At Štore Steel Ltd., continuously cast billets (180 mm × 180 mm) are reheated and rolled after cooling to room temperature. Hot-rolled bars are controlled as they cool to room temperature in specially designed cooling chambers, minimizing residual stresses and the development of pre-existing surface and internal defects. The bar ends can be additionally covered with insulating material. The cooled, rolled bars undergo examination using automated control lines to detect surface and internal defects, which primarily originate from the casting process. Internal defects are identified using ultrasonic testing. Between January 2022 and June 2023, 1550.0 tons of 61SiCr7 rolled bars, with diameters ranging from 53 mm to 72 mm and lengths from 7010 mm to 7955 mm, were examined using ultrasonic testing. The scrap was 109.6 tons (7.07 %). After collecting data on chemical composition (C, Si, Mn, Cr, Mo, Ni content), the casting process (casting temperature, cooling water pressure and flow in the first, second, and third zones of secondary cooling, as well as the temperature difference between input and output mould cooling water), and rolled bar geometry (diameter, length), scrap modelling after ultrasonic testing was carried using genetic programming. The genetic programming model suggested reducing the length of the rolled bar. Due to length multiplication, it was possible to reduce the rolled bar length from the initial lengths of 7010-7955 mm to the current lengths of 4558-6720 mm in June 2023. Based on this adjustment, a new production of rolled bars was established. By August 2024, 1251.9 tons of 61SiCr7 rolled bars were produced with the mentioned length adjustments. These rolled bars were subsequently examined using ultrasonic testing. The scrap was reduced by nearly 14 times, amounting to only 8.1 tons (0.64 %). Keywords: Steel industry; Rolling; Long bars; Ultrasonic testing; Scrap; Defects; Modelling; Genetic programming *Corresponding author: miha.kovacic@store-steel.si (Kovacic, M.) Article history: Received 2 September 2024 Revised 5 December 2024 Accepted 9 December 2024 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 steel industry, the solidified steel is usually cooled to room temperature, additionally heated and hot deformed. Warm deformation is usually conducted during rolling. Rolled material is often further processed, either through heat treatment or mechanical methods. Consequently, the quality of the cast semi-finished product directly impacts the quality of the rolled and subsequently processed material. Thermo-mechanically induced defects, which may arise during or after plastic deformation and originate from the solidification process, can be minimized or eliminated either by addressing their root causes (e.g., melt preparation, casting parameters) [1-3] or reducing the 435 Kovacic, Zupanc, Zuperl, Brezocnik consequences of the post-processed material (e.g., reduction of residual stresses, heat treatment, appropriate deformation during deformation) [4-7]. A review of the literature reveals that research on the deformation of cast semi-products with surface and internal defects, as well as their post-processing, has been ongoing for several decades [6-8]. However, investigating the behaviour of surface and internal defects in cast semi-finished products during and after deformation, particularly in industrial environments, continues to be a significant priority. The authors in [7] analysed the influence of the orientation of surface and internal defects of continuously cast steel ingots on occurrence of defects on rolled material. Smooth flat rolls were used for the deformation process. They found that with an optimal orientation angle of the internal defects, their complete elimination is achievable. Similarly, in [9], the authors analysed the influences of previously deformed continuously cast billets of chromium steel grades on the structure and properties of seamless pipe produced with radial-shear rolling in Pervoural’sk New Pipe Plant JSC. Their analysis of the cast macrostructure and the seamless pipe microstructure revealed that grain refinement depends on the preliminary deformation and the resulting changes in the cast macrostructure, which can be further adjusted through heat treatment. Accordingly, the required properties of seamless pipe can be achieved. The authors in [8] describe the optimization of groove geometry, which influences the occurrence of ductility cracks during hot rolling of the remaining brittle dendritic macrostructure from the solidification process. Based on finite element simulations, the changes of the groove geometry have been made to reduce strains and stresses that promote crack openings. As a result, ductility cracks were no longer occurred. A similar approach was used in [10], where the 3D finite element method was used to analyze the effect of stresses occurring during the three-roll planetary rolling process on existing internal voids and newly formed internal cracks. Furthermore, experimental rolling of bismuth-containing austenitic stainless steel bars was performed. The study found that the most important parameters were rolling elongation and temperature. Rolling elongation is primarily influenced by discontinuous contact between the rolls. The article [11] investigates cross-wedge rolling of Inconel 718 for aero-engine blades to reduce internal defects. The grain size, heating temperature and rolling speed were monitored. The study found that defects nucleate at the interface between carbide particles and the matrix, subsequently propagating along chain carbides or grain boundaries. Based on sulphur addition, the grain size was reduced, the heating temperature was selected to range from 950 °C to 1020 °C, and the rolling speed was increased. The individual influences of gathered parameters were also calculated and the optimal values selected. The authors of the study [12] attempted to analyse the occurrence of lamination during forming of seamless tube or pipe. Lamination is essentially a subsurface or surface defect that affects the inner or outer diameter of tube. Lamination can cause additional crack propagation. These types of defects are not easily detected through nondestructive testing. The recrystallization temperature, soaking time, furnace temperature, process parameters and mechanical properties were monitored to predict the surface quality of the final product. Analytical models were used. It was found that process parameters have a significant impact during production of seamless tube. The influence of process parameters on the occurrence of asymmetrical camber defects during hot rough rolling of plate shapes was studied in [13]. The serial production data from the Xichang Steel was analysed. An Interpretable Prediction Model and Shapley additive explanation models were used to predict the occurrence of asymmetrical camber defects for two steel grades (Q335B and ST12). The theoretical analyses were consistent with the obtained models. The authors also prepared a detailed process optimization plan. In [14], an attempt to reduce surface cracks during hot charging of high-strength, low-alloy steel thick plates is presented. Hot charging is the processes in which hot cast products (e.g., billets, slabs) are directly transported (without cooling down and reheating) from the steel plant to the rolling mill. Laboratory reports indicated that the presence of austenite in the microstructure significantly increased the size of recrystallized austenite grains, contributing to grain size nonuniformity. Based on the data on microstructure, charging temperature, and recrystallized 436 Advances in Production Engineering & Management 19(4) 2024 Reducing scrap in long rolled round steel bars using Genetic Programming after ultrasonic testing austenite content, it was determined that the root cause of surface cracks was the presence of recrystallized austenite. As a result, the hot charging process was optimized. Based on the effort applied, the surface cracks were reduced from 7.38 % to 0.12 %. The paper [15] presents the evolution of surface cracks that were already present on the cast semi-finished product during the rolling of heavy plates made of carbon-manganese steel. Cut samples of both the cast semi-finished product and the heavy plates were used for microstructural analysis. Additionally, electron microscopy was employed. All analyzed defects exhibited decarburization, indicating that they were present on the cast semi-finished product prior to rolling. To reduce the propagation of existing defects and prevent the occurrence of additional defects, a change in processing parameters was proposed. This article presents an attempt to reduce the formation of internal defects or the development of defects originating from the casting process using genetic programming. The article begins with an overview of the production and rolling of 61SiCr7 rolled bars, ranging from a diameter of 53 mm to 72 mm and a length of 7010 mm to 7955 mm. After collecting data on chemical composition, casting process, and rolled bar geometry, the article describes in detail the modelling of scrap after ultrasonic testing using genetic programming. Following the modelling results, efficient practical implementations are presented, and future work is suggested in the conclusion. 2. Materials and methods 2.1 Materials and experimental setup Production at Štore Steel plant starts with the scrap melting in an electric arc furnace, tapping, ladle treatment (i.e. secondary metallurgy) and continuous casting of billets (180 mm × 180 mm). The billets can be additionally heat-treated or control cooled under hoods. The cast billets are then reheated and rolled in the rolling plant using three rolling stands. The first two stands are duo reversible stands (800 mm and 650 mm diameter rolls), and the final continuous rolling line (460 mm diameter rolls) consists of 6 horizontal and 4 vertical stands. The cooling bed is equipped with the hoods that are adjusted according to the steel grades and the geometry of the rolled bars. The bars can be stacked individually or in pairs in cooling bed. After leaving the cooling bed, the rolled bars are cut according to the customer requirements and automatically bonded in the bundle. The bundles are transported by overhead cranes to additional cooling chambers. When the bars enter the cooling chamber, the temperature of the material is at least 500 °C. The bar ends are additionally covered with insulation material. After at least 24 hours of cooling in the chambers, the bars can be straightened, examined for internal soundness and surface quality, cut, sawed, chamfered, drilled, and peeled. Rolled round bars can be examined (internal and surface control) using an automatic control line. Internal defects are detected using the Karl Deutsch ECHOGRAPH Ultrasonic Flaw Detector. The root causes of internal defects are typically shrinkage porosity, centre porosity, and segregations, which are linked to the solidification process – in our case, the continuous casting process. The introduction of additional stresses (e.g., bar end cutting, straightening, cooling, heating) and the presence of residual stresses increase the likelihood of internal cracking in the rolled bars. Fig. 1 shows rolled round bars with insulating material (cloths) in a cooling chamber. The ends of the three longer bars in Fig. 1 are not covered with insulating material, increasing the risk of thermally induced cracking during cooling in the chamber. 61SiCr7 is commonly used for heavy-duty springs (e.g., flat, round, and helical), as well as stabilizers and torsion bars. Between January 2022 and June 2023, 1550 tons of 61SiCr7 rolled bars, with diameters ranging from 53 mm to 72 mm and lengths from 7010 mm to 7955 mm, were inspected using an automatic control line and the Karl Deutsch ECHOGRAPH Ultrasonic Flaw Detector. A total of 152 instances were recorded, where the inspected quantity of an individual product varied from 0.8 tons to 37 tons. The scrap rate varied from 0 % to 100 %. The total scrap amount was 109.6 tons, accounting for 7.07 % of the total. To reduce the occurrence of internal defects of 61SiCr7 steel, several parameters were gathered: Advances in Production Engineering & Management 19(4) 2024 437 Kovacic, Zupanc, Zuperl, Brezocnik • Chemical composition: Content of carbon (C), silicon (Si), manganese (Mn), chromium (Cr), molybdenum (Mo) and nickel (Ni) (%). • Casting parameters: - The average temperature of the melt in tundish (TEMP) (°C). - The average difference between input and output mould cooling water temperature (DELTAT) (°C). - The average cooling water pressure (bar) and flow (l/min) in the first (directly below the mould) (Z1P, Z1Q), second (Z2P, Z2Q) and third zone (Z3P, Z3Q) of secondary cooling. • Rolled bar diameter (DIA). • Rolled bar length (LONG). • Scrap ratio after ultrasonic testing using Karl Deutsch ECHOGRAPH Ultrasonic Flaw Detector (i.e. ratio between scrap and examined material quantity). Based on gathered data, a correlation between influential parameters and the scrap ratio using genetic programming was established. Fig. 1 The rolled round bars with insulation material (cloths) in the cooling chamber 2.2 Used methods The scrap ratio after ultrasonic testing with Karl Deutsch ECHOGRAPH Ultrasonic Flaw Detector was predicted using genetic programming, a method belonging to the field of evolutionary computation. Evolutionary computation is inspired by natural evolutionary processes such as selection, crossover, and mutation. Two of the most well-known methods in evolutionary computing are genetic algorithms and genetic programming. Genetic algorithms focus on finding optimal solutions by simulating evolutionary processes, where solutions evolve over generations. Genetic programming is an extension of this, where computer programs (i.e., predictive models for description of the studied system) themselves are generated and evolved to solve specific tasks. These methods are highly versatile and can be applied across various fields, including optimization, machine learning, prediction, engineering, and data analysis, as they allow for the discovery of solutions to complex problems without the need for predefined solutions [19-22]. In genetic programming, the computer programs (e.g., predictive models) consist of genes that can be selected functions (e.g., essential arithmetical functions), selected input variables, and random constants. For more details on genetic programming, please refer primarily to sources [1618]. Based on selected genes, random mathematical expressions are built at the beginning of the simulated evolution. For this research, basic arithmetic operations (i.e., addition, subtraction, multiplication, and division) were utilized as functions. Selected input variables (parameters) 438 Advances in Production Engineering & Management 19(4) 2024 Reducing scrap in long rolled round steel bars using Genetic Programming after ultrasonic testing included factors such as carbon content (C), the average difference between the input and output mould cooling water temperatures (DELTAT), rolled bar diameter (DIA), etc. A comprehensive list of variables is provided in Subsection 2.1 (since they are now considered as variables, they are presented in italics). Predictive models are constantly being modified with genetic operations during several generations. In the research, we used crossover and mutation operations to modify organisms. The reproduction operation was incorporated as a standard mechanism to enhance the probability of higher-fitness organisms progressing to subsequent generations. After the completion predictive models’ modification, a new generation is obtained. All predictive models are evaluated using the fitness function. In this study, the average of absolute differences between the actual and predicted scrap ratio was chosen as the fitness function. The process is repeated until the termination criterion is fulfilled. For this research, the termination criterion was defined as reaching the maximum prescribed number of generations. 3. Results and discussion We developed a general-purpose genetic programming system to model predictive models [2326]. This self-developed system was designed to handle a wide range of tasks, enabling the effective evolution of models tailored to specific prediction needs. After performing 100 runs of the genetic programming system, we analysed the results and obtained the best predictive model for predicting the scrap ratio after ultrasonic testing. The resulting model is as follows. DIA DIA − Z1P �DIA − ⎛ LONG Cr Z3P ⎜ �Mo + + 2 Si + Z2P + Z3P + � Mo − DELTAT DIA (DELTAT + Z2Q) ⎜ −Cr + ⎜ Ni ⎝ LONG Mo DELTAT Z3P �−DELTAT + Mo + Ni + Si + Z3P� �⎞ DELTAT LONG � 𝐶𝐶 �TEMP + DELTAT Ni − Z2Q ⎟ ⎟ ⎟ ⎠ (1) The average of absolute differences between the actual and predicted scrap rate is 5.96 %. Additionally, it is necessary to note that the genetically developed model does not contain the following parameters: Z1Q (average cooling water flow in the first zone of secondary cooling), Z3Q (average cooling water flow in the first zone of secondary cooling) and Mn (manganese content). Similarly, while checking the developed models from other runs obtained using genetic programming, it can be concluded that the LONG (rolled bar length) is one of the top 5 (out of 16) parameters which were not excluded from the developed models. The number of excluded parameters is presented in Fig. 2. 40 35 30 25 20 15 10 5 0 Fig. 2 The number of excluded parameters from 100 genetically developed models Advances in Production Engineering & Management 19(4) 2024 439 Kovacic, Zupanc, Zuperl, Brezocnik Additionally, the influences of individual parameters can be calculated using a genetic programming model. When changing the values within the actual interval of individual parameters, the values of the other parameters remained the same. The results of the genetic programming model are shown in Fig. 3. The length of the rolled bars (parameter LONG) appears to be the most influential factor, with scrap rates ranging from 93.81 % to 100.05 %. Based on the technical delivery conditions, required chemical composition, rolled bar diameter, post-rolling treatment in cooling chambers, the number of parameters extracted from 100 genetically developed models, and the calculated effects of individual parameters using genetic programming, the only viable option was to change the length of the rolled bars. It should be emphasized that length multiplications were possible. For informational purposes, in this phase of the research, we envisioned shorter rolled bar lengths from 4558-6720 mm (until now, we have been producing bars with lengths of 7010-7955 mm) to be used with the obtained genetic programming model. Other parameters gathered from January 2022 to June 2023 remained the same. The genetically developed model predicted that the scrap rate would be 0.00 % (currently 7.07 %) if shorter bars were used. Fig. 3 The calculated influences of individual parameters using genetic programming model Validation of modelling results Based on the modelling results and the length multiplications, the rolled bar lengths were reduced from the initial range of 7010-7955 mm to 4558-6720 mm for all orders starting from June 2023. By August 2024, a total of 1251.9 tons of 61SiCr7 rolled bars with adjusted lengths had been examined using ultrasonic testing. As a result, scrap was reduced by nearly 14 times, amounting to only 8.1 tons (0.64 %). This result clearly demonstrates that with relatively simple measures, we can reduce the carbon footprint in the steel processing industry and thus contribute to environmental sustainability. 4. Conclusion This paper examines the use of genetic programming to reduce internal defects in 61SiCr7 steel bars originating from the casting process. The billets are reheated, rolled, and cooled in a controlled cooling bed, followed by further treatment in cooling chambers. After cooling, the bars are inspected, straightened, and cut. Internal defects, such as porosity and segregations, are detected using the Karl Deutsch ECHOGRAPH Ultrasonic Flaw Detector. A total of 1550 tons of 61SiCr7 bars were examined, with a scrap rate ranging from 0 % to 100 %, resulting in 109.6 tons of scrap (7.07 %). Data on chemical composition, casting conditions, and bar geometry were used to develop a genetic programming model to predict the scrap rate. The model achieved an average error of 5.96 %, and the most influential parameter was the bar length (LONG). Shortening the rolled bars from 7010-7955 mm to 4558-6720 mm resulted in a predicted reduction in scrap to 0.00 %. 440 Advances in Production Engineering & Management 19(4) 2024 Reducing scrap in long rolled round steel bars using Genetic Programming after ultrasonic testing Since June 2023, all orders have been produced using shorter bar lengths, as suggested by the research, leading to a significant reduction in scrap by nearly 14 times. By August 2024, a total of 1251.9 tons of bars had been examined, and only 8.1 tons (0.64 %) of scrap were produced, demonstrating the effectiveness of the length adjustments in minimizing waste. This approach also significantly improves the carbon footprint, contributing to a greener and more sustainable production process. Future plans include optimizing the cooling processes in continuous casting to improve internal quality and exploring the potential for shortening bars for other steel grades and shapes. 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Modelling and optimization of sulfur addition during 70MnVS4 steelmaking: An industrial case study, Advances in Production Engineering & Management, Vol. 16, No. 2, 253-261, doi: 10.14743/apem2021.2.398. 442 Advances in Production Engineering & Management 19(4) 2024 Advances in Production Engineering & Management ISSN 1854-6250 Volume 19 | Number 4 | December 2024 | pp 443–459 Journal home: apem-journal.org https://doi.org/10.14743/apem2024.4.518 Original scientific paper Optimizing electric vehicle charging strategies using multi-layer perception-based spatio-temporal prediction of charging station load Wang, Y.N.a, Zhang, Z.J.a, Ping, A.a,*, Wang, R.J.a, Gong, D.Q.a a School of Economics and Management, Beijing Jiaotong University, Beijing, P.R. China ABSTRACT ARTICLE INFO The production and sales of electric vehicles have been increasing in line with the gradual adaptation of consumers to electric vehicles, driven by various government policies and subsidies over the past decade. As a result, the deployment of charging facilities, which are essential for supporting electric vehicles, has also been extensive. However, despite the rapid development in scale, charging facilities face challenges such as low utilization during off-peak hours and excessive congestion during peak hours, leading to resource wastage and a diminished user charging experience. To address these issues, this study proposes a spatio-temporal prediction model for charging station load. The model introduces a global spatial enhancement module to simultaneously learn shortrange and long-range spatial dependencies in the data, resulting in improved prediction accuracy. The aim of this research is to provide practical guidance in terms of conserving charging resources and enhancing user charging experience based on spatio-temporal prediction effectiveness. Keywords: Electric vehicles; Spatio-temporal prediction; Charging station load; Multi-layer perception (MLP) *Corresponding author: 23111184@bjtu.edu.cn (Ping, A.) Article history: Received 6 August 2024 Revised 5 December 2024 Accepted 12 December 2024 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 increasing awareness of environmental protection and the increasing preciousness of fossil energy, Electric Vehicle (EV) has gradually become a key to address the issues of environmental pollution and energy shortage due to its clean and low-carbon features [1]. Hence, it is evident that the electric vehicle industry has garnered substantial attention and support worldwide. Numerous governments have implemented a range of policy measures to facilitate the development of electric vehicles. The Chinese government, in particular, has demonstrated a high level of commitment to the electric vehicle industry. In recent years, the National Development and Reform Commission, the Ministry of Finance, the Ministry of Industry and Information Technology, and other relevant departments have jointly issued the Notice on Financial Subsidies for the Promotion and Application of New Energy Vehicles (Caijian [2020] No. 86) [2]. With incentives such as financial subsidies, tax incentives and quotas for vehicle purchase targets, the production and sales of electric vehicles have continued to rise in the domestic market. According to the China Association of Automobile Manufacturers (CAAM), the production and sales of new energy vehicles in 2022 were completed at 7,058,000 and 6,887,000 units, respectively, representing year443 Wang, Zhang, Ping, Wang, Gong on-year growth of 96.9 % and 93.4 %. In the development plan for the future, the Energy Saving and New Energy Technology Roadmap of the China Society of Automotive Engineering expects that by 2025, China's new energy vehicle production and sales will reach 8 million units. In the next five years, the market size of new energy vehicles will grow even more rapidly and is expected to reach 15 million units by 2030 [3]. In addition, the promotion of electric vehicles is a key initiative to promote the development of green transformation in the global power and transportation sectors, and to achieve the strategic goals of carbon peaking and carbon neutrality (dualcarbon), and the Paris Agreement has set a target of 100 million electric vehicles in the world by 2030. This indicates that the number of electric vehicles worldwide has exploded in recent years and will continue to grow in the coming years. Therefore, electric vehicle charging infrastructure, which is the energy supply for electric vehicles, will develop rapidly under the trend of growth in the number of electric vehicles. To meet the increasingly diverse charging demands of electric vehicle drivers, governments and enterprises at all stages have invested in the construction of charging piles, charging stations and other facilities. However, some issues need to be resolved while the number and scale of charging facilities are expanding. First, ‘no pile for vehicles, no vehicle for piles’ means that the layout and distribution of electric vehicle charging facilities are not reasonable enough, and the situation has gradually revealed itself. In some regions, the supply of charging piles at charging stations is well below the demand of electric vehicles, and the symptom of charging difficulty has appeared [4]. Simultaneously, in other regions, charging stations are overbuilt with a large number of charging piles lying idle, which is a severe waste of resources. This situation reflects the mismatch between the construction of charging facilities and EV ownership. Moreover, the generally low utilization rate of charging infrastructure is accompanied by the phenomenon of peak congestion. Due to the uneven distribution of charging facilities and the volatility of EV users' charging demand, there are obvious peaks and troughs in the utilization of many charging facilities. Underutilization not only wastes resources, but also reduces the experience of EV users during peak congestion, which in turn affects the acceptance of EVs in the EV consumption market. This study finds that the centrepiece of the above issues is the result of the uneven spatial and temporal spread of EV charging station loads that is specifically evident [5]. A possible solution is to analyse the spatial and temporal distribution patterns of loads at EV charging stations and use them as a basis for predicting the spatial and temporal distribution of loads [6]. The main contributions of this study are summarized as follows: • We built the model structure with higher prediction performance for loaded spatio-temporal data. • In the spatio-temporal prediction model, we innovatively built a global spatial enhancement module, which enables the model to learn global spatial information directly. Compared with the traditional convolutional learning method that gradually improves the sensory field by stacking, the global spatial reinforcement module improves the model's learning effect on the spatial-dependent features of charging station loading over long distances. • In terms of prediction model accuracy, the model we built is better than the baseline model in comparison tests, as quantified by two evaluation metrics, with 10.2 % and 7.3 % improvement, respectively. 2. Literature review 2.1 Charging selection behaviour The charging choice behaviour of electric vehicle users is quite different from the traditional refuelling behaviour of fuel vehicle users. Therefore, the study of EV users' charging choice behaviour has begun to receive extensive attention from both the academic and technical communities. Li et al. revealed that range uncertainty has a significant impact on users' charging behaviour [7]. When the range uncertainty is high, users will have a greater tendency to charge their EVs when the remaining power is high, in order to reduce the contingencies caused by insufficient power. 444 Advances in Production Engineering & Management 19(4) 2024 Optimizing electric vehicle charging strategies using multi-layer perception-based spatio-temporal prediction of … Therefore, its subsequent study proposed an ordered probability distribution model and suggested that the availability of charging facilities, distance and charging time are important influences on users' charging behaviour [8]. Meanwhile, Yang et al. studied charging behaviour selection optimization by using a bi-level optimization model and found that EV drivers are influenced by a variety of factors in charging and route selection, including charging facility availability, distance, charging time, and charging price, etc. [9]. Latinopoulos and Sivakumar found that there is also a close relationship between charging location, driving distance, and range anxiety. The above studies reveal that the charging choice behaviour of EV users is influenced by a variety of factors including availability of charging facilities, distance, charging time, price, remaining charge [10], and battery range. 2.2 Charging station load capacity and influencing factor The load of charging station comes from the selection and interaction behaviour of users with charging station, so the charging selection behaviour of users influences the distribution and change rule of charging station load. Al-Kandari and Soliman in 2003 proposed a load prediction model that integrates the consideration of multi-source information and the adjustment of users' decision-making, and the study considered the influence of users' behavioural patterns and decisionmaking strategies on the prediction effect [11]. Sani’s team also conducted a study on the robust integration of electric vehicle charging loads in smart grid capacity expansion planning [12], to improve the robustness and reliability of grid operation. The study focuses on the impact of user behaviour on the planning and integration process, where user behaviour includes uncertainty in charging demand, user's charging time period selection, and fluctuation in charging behaviour. The EV charging station load in this study is defined as the number of charging piles working at a charging station at a given point in time is equal to the number of EVs undergoing charging operations. If the number of EVs in a charging station is close to or equal to the maximum charging load limit of the current charging station, queuing and congestion occurs at that charging station, i.e., the charging station is overloaded. If the number of EVs being charged is significantly less than the maximum charging position limit of the current charging station, this represents a more relaxed idle state of the current charging station. Therefore, the influencing factors affecting the charging station load and its spatio-temporal distribution is a relatively complex dynamic problem [13]. First, regarding the charging price factor, two scholars proposed a data-driven approach based on using conditional random field modelling in order to perform a spatio-temporal price elasticity analysis of public charging demand for EVs [14]. Meanwhile, Wang et al. proposed an integer hybrid planning model in which a vehicle-to-grid (V2G) model is implemented by analysing spatiotemporal electricity prices and grid load profiles, which integrates electric vehicles into the grid for energy delivery and exchange through battery swapping, thus acting as a peak-shaving and valley-filling agent for electricity [15]. Second, geographic factors: The location of charging stations and the characteristics of the surrounding environment are also an important factor affecting the spatial and temporal distribution of charging station loads. Both factors can affect the utilization rate and charging capacity of charging stations. Bian found that the planning of EV fast charging stations should be based on point-of-interest segmentation, functional zones, and multiple spatio-temporal features [16]. Points of interest (POIs) help identify potential charging needs, functional zones enhance services and functions for charging stations, and multiple spatio-temporal features further optimize the planning and layout of charging stations. Zhang et al. proposed an EV charging demand prediction method considering the fine division of functional zones based on the characteristics of the functional zones of the city, which are divided into different functional zones, such as residential, commercial, and industrial zones [17]. The time factor is a key influence on charging station loads, with effects from factors such as morning and evening peak hours, weekends, holidays, and seasons impacting the spatial and temporal distribution of charging station loads. Bayram and Galloway focused on pricing strategies and distributed control for fast EV charging stations operating in cold climates [18]. Research has shown that cold weather can affect battery performance, leading to reduced charging efficiency, increased charging time, and influencing user charging behaviour decisions to some extent. Louie Advances in Production Engineering & Management 19(4) 2024 445 Wang, Zhang, Ping, Wang, Gong modelled the time series of EV charging station loads. By analysing the data of EV charging station loads, it was found by Louis that the loads exhibit distinct time series characteristics, including random fluctuations, multiple periodicities, and long-term trends [19]. Additionally, Bampos et al. developed a predictive model for the electric vehicle load curve (EVLC) [20]. Seasonal variations in the predicted performance are explored, deepening the importance of the impact of seasonal characteristics on research in this field. Spatial factors also play a role in influencing charging station loads. This is because the loads between adjacent charging stations may affect each other, depending on factors such as their distance, number, capacity, type, usage patterns, and demand. In areas with high charging station density, stations may compete with each other, leading to uneven loads. Conversely, in more dispersed layouts, users may consider additional factors when selecting a station, reducing mutual impact. Huang and Kockelman developed a network equilibrium model and considered the elasticity of demand for EV charging and congestion at charging stations [21]. It was found that the location selection of charging stations should consider the spatial and temporal distribution of EV charging demand, the congestion of charging stations, and the interaction between charging stations. In particular, an excessive number of charging stations on a regional scale can lead to intense competition between charging stations and network congestion, thus reducing the efficiency of the entire charging network. The travel demand and charging demand of EV users can also be affected by special circumstances such as holiday periods and participation in large events. Unterluggauer proposed a shortterm load prediction model for EV charging stations using a multivariate multi-step short-term memory approach [22]. The effect of holidays was used as one of the input variables of the model in the study, this is because the researcher found that holidays may have a significant effect on the load of EV charging stations. For example, during holidays, people's travel patterns and charging needs may be very different from normal working days, which may lead to results such as higher load fluctuations at charging stations. 3. Research methodology 3.1 Multi-source data In this study, the data types of multi-source dataset are used to cover the business data of EV users' charging behaviours at charging stations in Shanghai, the equipment information data of EV charging stations, the POI basic information data, the weather data, holidays, and other environmental data. Table 1 shows a brief introduction of the data names and contents. The total amount of data on charging behaviour at charging stations for the period of August 30, 2020 to February 28, 2021 for the specific data involved in this study is approximately 117.6 million. The total number of data items is 64 columns. The number of data pieces totals 1,095,889. By processing the business data and equipment data of charging stations, based on the latitude and longitude location of the charging stations, we get the specific allocation of the relevant charging stations shown in Fig. 1. Data name Operational data Charging station facility data Road network data Points of interest data Weather data Holiday data 446 Table 1 Detailed introduction of data source and data content Data content Data source Operational data generated by users during charging Shanghai charging station online platform Charging station facility information and geographic Shanghai charging station online location platform Shanghai's road location and road property OpenStreetMap open-source dataset POI name, type and geographic location Gaode Map API Temperature, precipitation, wind, etc. of the day National meteorological data sharing platform The dates of national legal holidays State council website announcement Advances in Production Engineering & Management 19(4) 2024 Optimizing electric vehicle charging strategies using multi-layer perception-based spatio-temporal prediction of … Fig. 1 Distribution diagram of charging station Fig. 2 Visualization of Shanghai road network data classification Meanwhile, by using the Shanghai road network data from the OpenStreetMap open source road information database, we simplified the road types in the data structure of the open source database for the convenience of the study. First, according to the TYPE-Road Type attribute, highway and urban expressway are grouped into A and B road types, which represent the roads that need to be connected to the road network A, which represents the type of road that requires the user to drive faster across the spatial distance per unit of time. Second, urban main roads and urban secondary roads are grouped together as B roads, which represent a road type that requires users to cross a moderate distance per unit of time while driving. Finally, urban branch roads and rural roads are categorized as C roads, which represent a type of road that crosses a slower distance per unit of time when the user is driving. The road network visualization of the above three road types is shown in Fig. 2. 3.2 Time distribution characteristics The patterns of change in charging station loadings in the time dimension include short-term patterns of change, multiple periodicities, long-term trends, and the effects of special events. Fig. 3 shows the short time variation of the load of the charging station. The results indicate that the load at a specific time of day is influenced by the load values from the preceding neighbouring hours. Analysing the daily load trend reveals a consistent pattern, characterized by gentle upward and downward fluctuations. Figs. 4 and 5 show the multiple periodicities characterising the variation of the charging station load values. Multiple periodicity refers to the presence of several cycles with different lengths in the load values. The charging station loads at a specific time are influenced by loads spanning Advances in Production Engineering & Management 19(4) 2024 447 Wang, Zhang, Ping, Wang, Gong multiple previous cycles. The periodic effects observed include the same hour of previous days as well as the same hour of the corresponding days from previous weeks, which affect the charging station load at the target time. This pattern is derived from the results of the autocorrelation function method. Fig. 3 Diagram of daily charging load variation at a charging station in Shanghai Fig. 4 Change in load capacity of charging station within one week Fig. 5 Loading capacity of charging station varies continuously for multiple weeks As shown in Fig. 6, this represents a long-term trend in the values of charging station loads. By changing through time, the charging station loads will have an overall trend of increasing in fluctuation. This regularity is reflected according to the results of the exponential smoothing method. The pattern of change in the value of the charging station load is affected by some special effects, including legal holidays (Fig. 7) and special weather such as rainy and snowy days. This feature is analysed by multiple linear regression method. 448 Fig. 6 Smoothing result of charging station load index Advances in Production Engineering & Management 19(4) 2024 Optimizing electric vehicle charging strategies using multi-layer perception-based spatio-temporal prediction of … Fig. 7 Trend of load changes during the National Day holiday(seven-day time period) Despite holidays, weather should also be considered as a factor that affects the time series trend of charging station loads. This is because special weather, such as rain, fog, and snow, can affect the travel decisions and charging decisions of electric vehicle users. Similar to the method of observing the effect of legal holiday factors on the time series of charging station loads, the study compares the trends of the hourly granularity of loads within an average single day under four types of weather, namely, rainy day, snowy day, foggy day, and normal. It is found that the charging station loads in rainy, snowy, and foggy days are overall smaller than the charging station loads under normal days in all hours. This study attempts to find a linear function such that the dependent variable can be explained by a weighted combination of the independent variables. In this case, 𝑌𝑌 is the dependent variable, 𝑋𝑋1 to 𝑋𝑋𝑘𝑘 are independent variables, 𝛽𝛽0 is the intercept, 𝛽𝛽1 to 𝛽𝛽𝑘𝑘 are the regression coefficients, and ε is the error term. 𝑌𝑌 = 𝛽𝛽0 + 𝛽𝛽1 𝑋𝑋1 + 𝛽𝛽2 𝑋𝑋2 + ⋯ + 𝛽𝛽𝑘𝑘 𝑋𝑋𝑘𝑘 + 𝜀𝜀 (1) The study in this paper uses four dummy variables to represent weather conditions (holiday, rain, snow, and fog). Each dummy variable is a binary indicator variable that takes the value of 0 or 1. Such variables can help in understanding the effect of different weather conditions on loadings. Thereafter, least squares regression was used and statistical information such as estimates of regression coefficients, t-statistics, and p-values were obtained. This information helps to understand the relationship between the independent and dependent variables. For example, the regression coefficient indicates the amount of change expected in the dependent variable when the independent variable is increased by one unit. The p-value helps to determine whether the relationship is significant or not. In the data of this paper, it was found that holidays have a significant positive effect on loadings at the p < 0.01 level, while rainy and snowy days have a negative effect on loadings at the p < 0.05 level, and foggy days have a non-significant effect on loadings, as detailed in the analyses shown in Table 2. Special time Legal holidays Rainy days Snowy days Foggy days Table 2 Multiple linear regression results with special time effects Coefficient t value 14.25 7.476 -3.49 -1.828 -6.52 -3.417 -4.50 -2.361 3.3 Spatial distribution characteristics p value 0.004** 0.039* 0.045* 0.077 This study defines charging stations with straight line distance between charging stations within 3 km and road form distance within 5 km as relatively close charging stations. Others are defined as relatively distant charging stations. There are three patterns of influence of charging station loads in the spatial dimension. Firstly, a charging station with saturated charging load will transmit the excess charging demand in the area to the close charging station. This means that when a charging station reaches saturation charging load, it will transfer a portion of the load to neighbouring charging stations, causing the loads of the neighbouring charging stations to rise This phenomenon is particularly common during peak periods. As well, there is competition between neighbouring charging stations that have not yet saturated their loads. Because they need to share limited resources, if the load of a charging station that has not yet saturated increases, it will affect Advances in Production Engineering & Management 19(4) 2024 449 Wang, Zhang, Ping, Wang, Gong the load of neighbouring charging stations, as shown in Fig. 8. Secondly, high-load charging stations near points of special interest, such as commercial centres, tend to cluster. This is because charging stations located near commercial centres attract more electric vehicles (EVs), leading to an increase in charging demand at multiple stations in the surrounding area. In this study, the effect of point-of-interest factors on EV mobility patterns and charging load distribution is considered. Charging stations within 2 km from the point of interest are defined as charging stations around the point of interest. Using multiple linear regression and least squares method, the study quantitatively assesses the degree of influence and the confidence level of different types of points of interest on charging station loads. The details are shown in Table 3, where the coefficients represent the degree and direction of the influence of the point of interest feature on the load of the surrounding charging stations, and the p-value represents the confidence level of whether an influence exists. p < 0.05 means that there is a confidence in the influence of the corresponding point of interest feature, and p < 0.01 represents a higher level of confidence. Fig. 8 Influence of saturated charging stations on adjacent charging stations Table 3 Multiple linear regression results of the influence of interest points POI Regression coefficient p value Transportation facilities 6.35 0.022* Commercial zone 4.37 0.032* Official zone 2.72 0.047* Residential zone -8.64 0.009** Recreation 2.48 0.015* The results of the multiple linear regression with point of interest as a variable show that transportation facilities, such as train stations, bus stations, and subway stations, lead to an increase in the load of nearby charging stations. Commercial areas lead to a smaller increase in the load of nearby charging stations. Office areas likewise increase the load on nearby charging stations to some extent, especially during peak commuting hours. Residential areas may have relatively low loads on nearby charging stations, and recreational areas, such as movie theatres, parks, and restaurants, can lead to an increase in loads on nearby charging stations, especially during legal holidays. As a third pattern, there is also a relationship between charging stations that are farther apart where loads affect each other, mainly due to user behaviour. This is because user charging needs migrate to more distant areas with their individual driving behaviour. Therefore, the spatial dependency of long distances should also be considered. 3.4 Models construction The objective of this paper is to predict the spatial distribution of charging loads at the target time 𝑋𝑋𝑡𝑡+1 based on the historical data { 𝑋𝑋𝑡𝑡 ∣ 𝑡𝑡 = 0,1, ⋯ , 𝑛𝑛 − 1 } of the spatial and temporal distribution of electric vehicle electric loads within a single city. Each time period is a matrix containing the load values of all EV charging stations for the current time period. The relative position of each charging station is also reflected in the number of rows and columns of each value in the matrix. 450 Advances in Production Engineering & Management 19(4) 2024 Optimizing electric vehicle charging strategies using multi-layer perception-based spatio-temporal prediction of … On top of the historical data on the spatial and temporal distribution of loads, the influence of multiple sources of factors is also considered and their information is introduced into the prediction model, including relevant road network characteristics, point-of-interest characteristics, legal holidays, and weather characteristics. Fig. 9 Model framework Fig. 9 shows the model architecture developed in this paper. The architecture consists of 4 parts, which are historical feature inputs, residual structure, global spatial enhancement module, and multi-layer perceptron with the introduction of time vectors. In a single round of model training, weekly-level periodicity, daily-level periodicity, short-term variations, road network information, and point-of-interest data from the historical dataset must be stacked together. A convolution operation is then performed to reduce the number of channels in the feature map through channel fusion, while keeping the feature map size unchanged. This operation aims to reduce the network's parameters and computational complexity while maintaining its performance. The result of the convolution operation is fed into the residual neural network, which undergoes an activation function, a global spatial reinforcement module, a second activation function, and this convolution operation to produce a final output of the matrix with the number of channels as one. At the same time, information about rainy days, snowy days, legal holidays, and other special times is input into the multi-layer perceptron in the form of vectors. The perceptron outputs a matrix with the same structure as the residual structure output matrix. These matrices are fused to produce the predicted value. The predicted value is then evaluated using a loss function to calculate the loss value for the current round of training. This loss value quantifies the degree of fit between the predicted value and the true value. Finally, the backpropagation method is used to calculate the gradient of the loss value, enabling the weights and biases of the network to be updated accordingly. The historical characteristics of the inputs in the model include time-varying and stationary characteristics. The temporal variation characteristics change with the forecast target time change, and it includes weekly periodic information, daily periodic information and short time variation information, the support for introducing this information comes from the temporal characterization in Section 3.2 of this paper, and their model equations are as follows: 𝑋𝑋𝑖𝑖𝑤𝑤 = �𝑋𝑋𝑖𝑖−𝑙𝑙𝑤𝑤 , 𝑋𝑋𝑖𝑖−(𝑙𝑙𝑤𝑤−1) , ⋯ , 𝑋𝑋𝑖𝑖−𝑤𝑤 � (2) 𝑋𝑋𝑖𝑖ℎ = �𝑋𝑋𝑖𝑖−𝑙𝑙ℎ , 𝑋𝑋𝑖𝑖−(𝑙𝑙ℎ −1) , ⋯ , 𝑋𝑋𝑖𝑖−1 � (4) 𝑋𝑋𝑖𝑖𝑑𝑑 = �𝑋𝑋𝑖𝑖−𝑙𝑙𝑑𝑑 , 𝑋𝑋𝑖𝑖−(𝑙𝑙𝑑𝑑−1) , ⋯ , 𝑋𝑋𝑖𝑖−𝑑𝑑 � (3) It is assumed that the length of the selected time period is 1 hour (𝑎𝑎 = 24 hours). The weeklevel periodicity information 𝑋𝑋𝑖𝑖𝑤𝑤 represents the information about the spatial distribution of the Advances in Production Engineering & Management 19(4) 2024 451 Wang, Zhang, Ping, Wang, Gong charging station loadings on the same day and at the same hour in the same week w weeks prior to the target time i that needs to be predicted. For example, if the target time to be predicted is 17:00 on March 15, 2021 (Monday), the information of 𝑋𝑋𝑖𝑖𝑤𝑤 is the spatial distribution matrix of charging station loads at 17:00 on March 8, March 1, and so on for the previous 𝑤𝑤 Mondays. The day-level periodicity information 𝑋𝑋𝑖𝑖𝑑𝑑 represents the information on the spatial distribution of the charging station loadings at the same hour on the 𝑑𝑑 previous day 𝑖𝑖 to the target time to be forecasted. For example, if the target time to be predicted is 17:00 on March 15, 2021, the information of 𝑋𝑋𝑖𝑖𝑑𝑑 is the spatial distribution matrix of charging station loadings at 17:00 on March 14 at 17:00, March 13 at 17:00, and so on for the previous 𝑑𝑑 days. The short time variation information 𝑋𝑋𝑖𝑖ℎ represents the spatial distribution information of the charging station loadings for the ℎ hours before the target time 𝑖𝑖 to be predicted. For example, if the target time to be predicted is March 15, 2021 at 17:00, the information of 𝑋𝑋𝑖𝑖ℎ is the spatial distribution matrix of charging station loadings for the ℎ hours before March 15 at 16:00, March 15 at 15:00, etc. Fixed features, on the other hand, do not change with the predicted target time. It includes point of interest and road network information. The support for introducing this information comes from the spatial characterization in 3.3. The equations are as follows: 𝑋𝑋 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = [𝑋𝑋𝐴𝐴1 , 𝑋𝑋𝐴𝐴2 , 𝑋𝑋𝐵𝐵1 , 𝑋𝑋𝐵𝐵2 , 𝑋𝑋𝐶𝐶1 , 𝑋𝑋𝐶𝐶2 ] 𝑋𝑋 𝑃𝑃𝑃𝑃𝑃𝑃 = [𝑋𝑋𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 , 𝑋𝑋𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 , 𝑋𝑋𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 , 𝑋𝑋𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 , 𝑋𝑋𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 ] (5) (6) 𝑋𝑋𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 consists of 6 layers of matrix stacking. Each layer represents the spatial distribution information of different types of roads. The corner symbols in the Eq. 5 are explained as follows. 𝐴𝐴1 𝐴𝐴2 𝐵𝐵1 𝐵𝐵2 𝐶𝐶1 C2 Unidirectional road of fast road type Bidirectional road of fast road type Unidirectional road of medium-speed road type Bidirectional road of medium-speed road type Unidirectional road of slow road type Bidirectional road of slow road type 𝑋𝑋 𝑃𝑃𝑃𝑃𝑃𝑃 consists of a stack of 5 layers of matrices, with each layer representing the spatial distribution information of different types of points of interest. The corner symbols in the equation are explained as follows. 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 Transportation facilities Commercial area Official area Residential area Recreational area The rationale for introducing this information is that points of interest can have varying degrees of impact on the charging station loadings in their neighbourhoods. The charging station load prediction model built in this paper will stack the data mentioned above and feed it together into a convolutional layer. It is hoped that the model will establish connections between different times in this way as a way of extracting time-dependent information from the data. A residual neural network is a framework for deep convolutional neural networks. The core idea of residual neural networks is to introduce residual connections into the model. These residual connections make it easier for the network to learn by skipping certain layers and passing information directly. Specifically, assuming that the input to a certain layer is 𝑋𝑋. It is desired that the model learns a mapping of 𝐹𝐹(𝑋𝑋). In the residual module, the mapping is actually learned as 𝐹𝐹(𝑋𝑋) − 𝑋𝑋,which is the residual mapping. After that the input 𝑋𝑋 needs to be added with the residual mapping to get the final output𝐹𝐹(𝑋𝑋) = 𝐹𝐹(𝑋𝑋) − 𝑋𝑋 + 𝑋𝑋. This process can be represented by the following equation: 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 = 𝐹𝐹(𝑋𝑋) + 𝑋𝑋 452 (7) Advances in Production Engineering & Management 19(4) 2024 Optimizing electric vehicle charging strategies using multi-layer perception-based spatio-temporal prediction of … Compared to traditional convolutional neural networks, this jump connection makes it easier for gradients to circulate during back-propagation, thus alleviating the problems of gradient vanishing and gradient explosion, and allowing the network to be trained deeper as well as more easily. In the study of this paper, the residual unit that performs a single loop can be expressed as: 𝑦𝑦 = 𝐹𝐹(𝑥𝑥, {𝑊𝑊}) + 𝑥𝑥 (8) 𝐹𝐹(𝑥𝑥, {𝑊𝑊1, 𝑊𝑊2}) = 𝑊𝑊2 ∗ 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅(𝑊𝑊1 ∗ 𝑥𝑥) (9) where 𝑥𝑥 represents input, 𝑦𝑦 is output, 𝐹𝐹(𝑥𝑥, {𝑊𝑊}) is a function with a set of weights {𝑊𝑊}. It represents a series of convolutional layers and activation functions. The result of the computation 𝐹𝐹(𝑥𝑥, {𝑊𝑊}) is added to the input 𝑥𝑥 to get the output 𝑦𝑦. In a practical implementation, two or more convolutional layers may be included in 𝐹𝐹(𝑥𝑥, {𝑊𝑊}), as shown below: Here, 𝑊𝑊1 and 𝑊𝑊2 are the weights of the convolutional layers. ReLU is the nonlinear activation function chosen for this model. Substituting this equation into the residual unit equation gives the final: 𝑦𝑦 = 𝑊𝑊2 ∗ 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅(𝑊𝑊1 ∗ 𝑥𝑥) + 𝑥𝑥 (10) As shown in Fig. 10, the global spatial enhancement module we have created can extract the spatial dependency relationships at long distances within the network structure. The global spatial enhancement module first separates a portion of the channels from the regular convolution. These channels undergo global average pooling to reduce the number of parameters before entering the fully connected layer. The fully connected layer is designed to capture the long-range spatial dependency patterns between each pair of charging stations. Its output is added to the synchronous convolution output to provide the global spatial dependency parameters learned from the convolution output. This approach ensures that the global spatial enhancement module can output data of the same shape as the output of the regular convolution operation and can be used as input for the residual unit in the next loop. Fig. 10 Global space enhancement module Fig. 11 Multi-layer percepton Advances in Production Engineering & Management 19(4) 2024 453 Wang, Zhang, Ping, Wang, Gong In this model, the medium for learning special fixed-time features such as rainy or snowy weather and statutory holidays is a time vector introduced into the entire model through a multilayer perceptron. The time vector in the model is a vector of length α + 7 + 12 + 1 + 2, where each component takes on the value of 0 or 1. The vector encodes the month to which the predicted target time belongs, the day of the week, the time interval within a day, whether it is a statutory holiday, and whether there is rainy or snowy weather on that day. Among them, the part of the time vector with a length of α encodes all time intervals within a day. If 1 hour is chosen as the time interval, then α = 24. The part with a fixed length of 7 encodes the 7 days of the week. The part with a fixed length of 12 encodes the 12 months of the year. The part with a length of 1 indicates whether it is a statutory holiday. The part with a length of 2 indicates two types of weather found in the data that have a significant impact on the spatial-temporal distribution of the load. The data format of the time vector is not a grid-like data graph that is passed between the structures of the model, so convolutional neural networks cannot be directly used to extract information from it. Therefore, a multi-layer perceptron is used here to learn the vector data and transform it into the same data shape as the output of other parts of the model. A multi-layer perceptron is a type of feed-forward neural network where each layer is fully connected, enabling it to learn complex relationships between input features. In this model, the structure of the multi-layer perceptron is shown in Fig. 11. The time vector inputted is first dimensionally increased in the first fully connected layer, then goes through an activation function to enhance the model's non-linear expressive power. It then goes through additional fully connected layers to reach the desired data dimension 𝐻𝐻 × 𝑊𝑊, which is the matrix shape used for extracting the spatial distribution features of the charging stations in this study. Finally, after reshaping the data shape, it matches the output of the residual unit, and the two are added together to generate the prediction data. 4. Result and discussion 4.1 Modelling effectiveness evaluation The evaluation metrics used in this study include Root Mean Square Error (RMSE) and the previously mentioned MAE. RMSE and MAE directly assess the error between predicted values and true values, facilitating an objective observation of the magnitude of deviations. Here, 𝑋𝑋𝑖𝑖 represents the true value, and 𝑋𝑋�𝑖𝑖 represents the predicted value. The specific equation for RMSE is as follows: 𝑇𝑇 1 2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = � � ∥𝑋𝑋𝑖𝑖 − 𝑋𝑋�𝑖𝑖 ∥2 𝑇𝑇 (11) 𝑖𝑖=1 Consistent with the loss function, 𝑋𝑋𝑖𝑖 and 𝑋𝑋�𝑖𝑖 represent the actual data and predicted data for the 𝑖𝑖 time interval, respectively. 𝑇𝑇 is the total number of samples in the test data. After four-stages ablation experiments, as shown in Table 4, the smaller the value of the evaluation metric, the smaller the deviation between the predicted values and the actual values, indicating a better model performance. It can be observed from the evaluation metric data that gradually introducing the global spatial enhancement module, road network and point-of-interest information, legal holidays, and special weather information into the model leads to a gradual improvement in the overall model effectiveness. This demonstrates that incrementally adding new components to the model during its construction can optimize the accuracy of the model predictions. 𝑡𝑡ℎ Table 4 Results of ablation experiment Modelling stage Base model Base model + global space enhancement module Base model + global spatial enhancement module + road network & points of interest Full model 454 RMSE 5.87 5.49 MAE 3.54 3.41 5.27 3.28 5.34 3.32 Advances in Production Engineering & Management 19(4) 2024 Optimizing electric vehicle charging strategies using multi-layer perception-based spatio-temporal prediction of … Table 5 presents the performance of the model constructed in this study compared to other baseline models in terms of evaluation metrics. It also compares the performance of models with different parameters. The parameter selection for the number of time periods within a day is set to 24 hours, representing the division of a day into 24 time periods, each lasting 1 hour. The parameter selection of 48 hours represents dividing a day into 48 time periods, each lasting 30 minutes. The best performance in terms of evaluation metrics is highlighted in bold in the table. In the evaluation results, it was observed that the performance of various models with a time period length of 30 minutes was better than the performance with a time period length of 1 hour. Additionally, the model proposed in this paper outperformed the best-performing baseline model, which was a Residual Neural Network model, in two evaluation metrics. When compared to the Residual Neural Network model, the proposed model achieved a 10.2 % decrease in RMSE and a 7.3 % decrease in MAE. This indicates that the proposed model exhibits good performance in predicting the spatial-temporal distribution of electric vehicle charging station loads. Table 5 Baseline model comparison results Model 1 hour RMSE MAE Historical Average Model 10.17 6.59 Auto-regressive Integrated Moving Average Model 9.88 6.51 (ARIMA) Recurrent Neural Network (RNN) 9.12 5.86 Long Short-Term Memory Network (LSTM) 8.79 5.83 Convolutional Long Short-Term Memory Network 7.32 4.22 (ConvLSTM) Graph Convolutional Neural Network (GCN) 7.87 4.28 Residual Neural Network (ResNet) 7.05 4.02 The model proposed in this paper 6.35 3.71 4.2 Predictive results analysis 30 minutes RMSE MAE 9.24 6.02 8.19 5.69 6.02 3.85 6.97 6.81 6.23 5.87 5.27 4.28 4.13 3.99 3.54 3.28 In this section, to demonstrate the predictive effectiveness of the model in real-world applications, the predictive results of the model are visualized. In the specific process, two charging stations are randomly selected from the dataset, and the actual load variations from Monday to Friday within a single week are extracted. The real data variations are then compared with the predicted data variations. The comparisons are illustrated in Figs. 12 and 13. From the comparison between the predicted values and the actual values, it can be seen that the spatiotemporal load forecasting model in this paper can accurately predict the trends and magnitudes of load variations for each charging station. While the model successfully predicts the general trends of load increase and decrease for the majority of cases, there are discrepancies in predicting the specific numerical values of load peaks and valleys, especially in complex and variable real-world scenarios. Overall, the predictive performance of the model is in line with expectations. Fig. 12 Comparison between predicted and actual load values of a charging station A Advances in Production Engineering & Management 19(4) 2024 455 Wang, Zhang, Ping, Wang, Gong Fig. 13 Comparison between the predicted and actual load values of a charging station B 4.3 Parameter impact analysis In the global spatial enhancement module, to capture long-distance spatial dependencies, some channels of the convolutional neural network are allocated to the fully connected layer. The role of the fully connected layer is to learn global spatial information. Fig. 14 illustrates the impact of the number of channels allocated to the fully connected layer on the model's predictive performance while keeping the total number of channels constant at 128. The graph shows that as the number of channels allocated to the fully connected layer increases from 0 to 1, the model immediately benefits, indicating that learning long-distance spatial dependencies in the dataset is meaningful for prediction. The model performs better with 24 separate channels, but performance decreases with more separate channels. This suggests that both short-distance spatial dependencies and long-distance spatial dependencies are significant and cannot be ignored. The impact of the total number of channels in the convolutional neural network on the prediction results is shown in Fig. 15. The evaluation covers a range of total channels from 16 to 128. The results indicate that as the number of channels increases, the computational cost also increases, and the model's predictive performance benefits from the increase in the number of channels. However, the rate of improvement decreases gradually with the increase in the number of channels. An increase in the total number of channels leads to diminishing returns in the model's predictive performance. Therefore, we clearly defined the predictive goals for the spatiotemporal distribution of electric vehicle charging station loads and proposed a multi-feature fusion prediction model based on residual neural networks. This model learns the short-term variations, multiperiodicity, long-term trends, and special time influences of electric vehicle charging station loads in the time dimension. In the spatial dimension, it integrates road network information, charging station location information, and various points of interest locations, enabling the model to learn the spatial distribution patterns of electric vehicle charging station loads. Additionally, spatial dependencies are categorized into short-distance and long-distance categories, and a global spatial enhancement module is designed to help the model focus on long-distance spatial dependencies while retaining some channels for learning short-distance spatial dependencies. Fig. 14 The effect of the number of channels in the full connection layer on the results 456 Advances in Production Engineering & Management 19(4) 2024 Optimizing electric vehicle charging strategies using multi-layer perception-based spatio-temporal prediction of … Fig. 15 Influence of amount of all channels In the training process, the loss function MSE and relevant parameters in the model are defined. During the model evaluation phase, RMSE and MAE are used as evaluation metrics, and ablation experiments and comparative experiments are conducted. Ablation experiments involve gradually adding key components to observe the prediction errors, showing that the introduction of each component significantly enhances the model's predictive performance. In comparative experiments, the proposed model's superior performance in predicting the spatio-temporal distribution of electric vehicle charging station loads is demonstrated by comparing RMSE and MAE metrics, with reductions of 10.2 % and 7.3 %, respectively, compared to existing baseline models in the field. 4.4 User demand analysis To avoid queuing at congested charging stations, users currently rely on real-time information provided by charging station operation platforms and map-based navigation applications to determine which charging stations still have available spaces. However, the rapid fluctuations in the load and availability of charging stations make the information on the saturation status of charging stations outdated by the time users arrive at the station or during their journey. This lag in information may lead to discrepancies between users' expectations and the actual situation when making charging station selection decisions based on outdated information, such as arriving at a station only to find it fully occupied, necessitating a waiting queue. User decisions on charging station selection heavily rely on the saturation status information of charging stations, but the uncertainty stemming from the time lag in this information has become a major pain point in the chain of electric vehicle charging behaviour for users. Currently, the pain point primarily lies in the fact that electric vehicle users need to plan their charging station selections along the route in advance before embarking on long-distance drives. However, since the arrival times at each charging station along the long-distance route vary, the pre-queried saturation status information of charging stations also varies in terms of time lag based on the different arrival times. Due to the varying time lag of the real-time saturation status information that users rely on, planning a rational strategy for selecting multiple charging stations before a long-distance journey becomes challenging. This strategy requires accurate prediction of the saturation status information at multiple charging stations in the future, serving as deterministic information to support decision-making. 4.5 Charging station selection strategy support The electric vehicle charging station load spatial-temporal prediction model established in this paper can output predicted values of load levels at multiple charging stations across various time intervals and locations in the future. By combining the predicted load data with the actual saturation levels of the charging stations, it is possible to determine which stations will experience queue congestion or excessive idleness at specific times in the future. In a specific process, defining the saturation load level of a particular electric vehicle charging station as 𝐿𝐿𝑚𝑚𝑚𝑚𝑚𝑚 and the predicted load level at a future time as 𝐿𝐿𝑖𝑖 , queue congestion coefficient as 𝛼𝛼, and idleness coefficient as 𝛽𝛽, where 𝛼𝛼 > 𝛽𝛽. Based on the comparison between the load levels 𝐿𝐿𝑚𝑚𝑚𝑚𝑚𝑚 and 𝐿𝐿𝑖𝑖 of a charging station Advances in Production Engineering & Management 19(4) 2024 457 Wang, Zhang, Ping, Wang, Gong at a specific time in the future, the load saturation status of any charging station at any time and location in the future can be defined. The load saturation status can be categorized into the following three states: Queue Congestion State (C): 𝐿𝐿𝑖𝑖 ≥ 𝛼𝛼 ∗ 𝐿𝐿𝑚𝑚𝑚𝑚𝑚𝑚 Excessive Idle State (L): 𝐿𝐿𝑖𝑖 ≤ 𝛽𝛽 ∗ 𝐿𝐿𝑚𝑚𝑚𝑚𝑚𝑚 Normal Load State (N): 𝛽𝛽 ∗ 𝐿𝐿𝑚𝑚𝑚𝑚𝑚𝑚 < 𝐿𝐿𝑖𝑖 < 𝛼𝛼 ∗ 𝐿𝐿𝑚𝑚𝑚𝑚𝑚𝑚 Based on the three divisions of load saturation states, the distribution of load saturation states for various charging stations at multiple future time points can be obtained. The schematic diagram of the load saturation states of each charging station in Shanghai at a single time point is shown in Fig. 16. Fig. 16 Influence of amount of all channels 5. Conclusion and outlook On this paper, the load capacity prediction model helps users to predict the load saturation state of charging stations at different locations within a certain range at different times. To help users identify charging stations where queuing is expected to occur at the target time for circumvention, it also helps users to identify charging stations with a large number of idle charging posts at the target time to minimize the risk of congestion. This provides users with relatively more accurate real-time predictive information for both one-time temporary charging station selection decisions and long-term charging plan development. 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Advances in Production Engineering & Management 19(4) 2024 459 Advances in Production Engineering & Management ISSN 1854-6250 Volume 19 | Number 4 | December 2024 | pp 460–488 Journal home: apem-journal.org https://doi.org/10.14743/apem2024.4.519 Original scientific paper Sustainable design of products: Balancing quality, life cycle impact, and social responsibility Siwiec, D.a, Gawlik, R.b,c,*, Pacana, A.d aFaculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Rzeszow, Poland of Public Economy and Administration, Krakow University of Economics, Krakow, Poland cNWU Business School, North-West University, Potchefstroom, South Africa dFaculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Rzeszow, Poland bCollege ABSTRACT ARTICLEINFO The shift towards sustainable mobility has increased the demand for energyefficient and environmentally friendly vehicles, such as Hybrid Electric Vehicles (HEVs). However, designing HEVs that simultaneously meet high product quality, minimize environmental impact, and adhere to social responsibility standards remains a complex challenge. This study presents a decision-making model aimed at integrating these key sustainability criteria into the design and improvement of HEVs. The model combines three indices: the Aggregated Quality Index (AQI), Environmental Impact Index (EII) based on Life Cycle Assessment (LCA), and Social Responsibility Index (SRI), to assess and compare different HEV prototypes. By processing customer expectations, environmental impacts, and social responsibility considerations, the model predicts the optimal prototype that balances quality, environmental sustainability, and social standards. The findings demonstrate that applying this model can significantly enhance decision-making in sustainable vehicle development and support the creation of HEVs that better align with global sustainability goals. This approach has practical implications for automotive manufacturers aiming to innovate responsibly in the green mobility sector. Keywords: Hybrid Electric Vehicle (HEV); Eco-innovation; Product quality; Sustainable development; Life Cycle Assessment (LCA); Multiple Criteria Decision-Making (MCDM); Mechanical engineering; Public management *Corresponding author: remigiusz.gawlik@uek.krakow.pl (Gawlik, R.) Article history: Received 27 October 2024 Revised 18 December 2024 Accepted 19 December 2024 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 diversity of considerations in product design reflects efforts towards achieving sustainable development. Actions in this area should simultaneously address quality, environmental impact, and social responsibility [1, 2]. This approach aligns with modern solutions that prioritize designing products satisfying customer needs, social acceptance, and environmental friendliness throughout their life cycle [3]. Integrating these considerations during product design sets milestones but also presents challenges due to the multitude and diversity of necessary decision-making criteria [4]. This process requires involving various decision-makers to establish comprehensive priorities across different application areas [5, 6]. However, research on sustainable product development often lacks equivalent and comprehensive analysis of these considerations, typically focusing on one or two aspects [1], as noted by 460 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility authors in [7]. For instance, Life Cycle Assessment (LCA) methods continue to neglect product design and development (PDD) [8]. Considering all aspects collectively is challenging due to the interdisciplinary nature and scarcity of studies that address all sustainable development criteria – economic growth, social well-being, and environmental protection – simultaneously [9, 10]. Despite the development of several methods and tools supporting sustainable product design, there is still a lack of unified consensus, including clear frameworks, methods, and standards for supporting prospective design for sustainable product development that integrates quality, environmental, and social responsibility aspects. Critically discussed conceptual design processes providing analysis of current products and alternative product solutions (prototypes) in a multidimensional evaluation process considering sustainable development criteria (quality, environmental, and social responsibility) are notably absent, and therefore were identified as our research gap. The main research question of this research is: "How to support the process of improving current products based on possible design prototypes in a multidimensional approach that integrates product quality (customer satisfaction), environmental impact of the product life cycle, and social responsibility compliance?" We assumed that it can be answered by developing a model that provides three separate indexes: i) quality, ii) environment, and iii) social responsibility, subsequently aggregated into a coherent decision-making indicator, used to rank the product design and improvement for their compatibility with sustainable development criteria. This research aims to develop a decision-making model to anticipate the direction of improving current products based on prototypes (production alternatives) methodically verified in a multidimensional approach encompassing key aspects of sustainable development: quality, life cycle environmental impact, and social responsibility compliance. The model is primarily dedicated to managerial decision-making in product design and production management, aiming to support private individuals, companies, and public entities in sustainable product development decisions, focusing on achieving socially responsible production engineering that also ensures high-quality offered products and environmental friendliness. 2. Literature review A literature review was conducted on product design and improvement concerning sustainable development aspects: quality, environmental impact throughout the life cycle, and social responsibility. Due to the limited popularity of simultaneously combining these aspects, the review was conducted in three stages, analysing works that address: i) customer satisfaction with product quality while reducing negative environmental impact throughout the entire life cycle; ii) customer satisfaction with product quality considering social responsibility; iii) product LCA considering social responsibility. All analysed works came from the Web of Science (WoS) international database. The literature review was conducted in March 2024 within a specified timeframe. Works were categorized based on title, abstract, and keywords. The identified works included: i) LCA, product design, and customer (10 out of 28 works); ii) socially responsible design, product (7 out of 82 works); iii) LCA, product design, quality, and social responsibility (0 works). Initially, a preliminary selection was based on publication abstracts, resulting in a lower number of works analysed compared to those identified. In total, 17 relevant works were identified, including 12 scientific articles and 5 conference papers. The selected works were further analysed for their distribution, as depicted in Fig. 1. Next, the keywords included in the selected papers were analysed using the WordArt software "Word Cloud" tool. The word cloud visually presents the frequency of individual keywords, with larger font sizes indicating higher frequency of occurrence (Fig. 1). Advances in Production Engineering & Management 19(4) 2024 461 Siwiec, Gawlik, Pacana (a) (b) Fig. 1 Analysis of: (a) publication trends and future developments in the research area of QESR decision-making for sustainable product design and improvement; (b) word cloud for Web of Science database metasearch keywords The first publication dates from year 2005, but no publications were revealed be-tween 2006 and 2013. Search keywords emerged from 2014 onwards, with only up to two publications per year until 2023, where a slightly higher number (5 publications) was noted. These findings suggest that the selected research area is in a developmental phase, characterized by numerous research gaps, making it an area worthy of further investigation. Keyword analysis revealed that across the 17 reviewed studies, there were a total of 162 unique keywords (including those provided by authors and indexed in WoS). The most frequently occurring keyword (12 times) was "LCA" (including variations like “life cycle assessment”). Following closely were: "corporate social responsibility" (6), "design" (6), "QFD" (6), "decision making" (5), and "sustainability" (4). Keywords related to "eco-design" (3), "impact" (3), and "quality" (3) appeared slightly less frequently. The remaining keywords appeared twice (11 words) or once (92 words). The high-frequency keywords related to the analysed thematic area and resulted from the search scope used in the selection of works in WoS. Subsequently, mutual citation analysis was conducted to identify the most frequently cited studies critical to the development of the analysed research area. This analysis was supported by the Gephi 0.10.1 software. Initially, a network of connections was established among the 17 reviewed publications. Subsequently, the focus was narrowed down to the primary citations occurring among these works (Fig. 2). Fig. 2 Mutual connections among the key publications in content analysis in the Gephi 0.10.1 software, based on the metasearch of the Web of Science database 462 Advances in Production Engineering & Management 19(4) 2024 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility The 17 analysed studies collectively contained 585 citations (bibliographic entries). When examining their mutual citations, inconsistency was observed both among the studies and within the cited works. This inconsistency may stem from the limited number of studies addressing the chosen thematic area, as well as the previously identified low level of development in this research domain. Among all references, only four most frequently cited works were identified, namely [1114]. These studies encompassed LCA, decision support, and customer expectation processing using the Quality Function Deployment (QFD) method, acknowledging these issues as integral to sustainable product design. All selected works underwent synthetic content analysis. It was observed that the most frequently proposed solutions for assessing product quality and environmental impact in the life cycle involved combining QFD for processing customer expectations and LCA for environmental impact assessment [15-18]. Besides combining results from QFD and LCA methods, other approaches were also employed, such as: integrating Failure Mode and Effects Analysis (FMEA), Theory of Inventive Problem Solving (TRIZ), and Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS) to develop product criteria rankings indicating the most favourable prototypes for existing products [14]; conducting surveys to gather customer expectations regarding product quality and subsequently processing them considering LCA results for different product materials [19]; developing decision support processes during the design phase by modelling LCA outcomes based on customer demand for alternative design solutions [9]; analysing customer sensitivity towards recyclable products [20]. Initial attempts at comprehensive integration of product quality assessment during development phase with environmental impact assessment of product solutions were presented, for example, in [21, 22]. Existing studies on socially responsible design focus on ensuring environmentally friendly products by analysing: • Customer reactions to eco-labels in the context of their awareness and perceptions of corporate social responsibility [23]; • Social effects following technological support in the product life cycle, demonstrating that sustainable social development impacts sustainable environmental and economic development [24]; • Business social responsibility in the light of customer demand factors determining the expected level of eco-friendliness of new products [25]; • Changing roles and responsibilities of designers in environmentally conscious product design [26]; • Opportunities for implementing the Cradle to Cradle (C2C) approach in conceptual product design focusing on environmental and social benefits [27]; • Motivations of designers in making socially responsible decisions, indicating that the interaction of designer beliefs depends on business feasibility levels, and proper management should focus not only on social but also environmental aspects in product development [28]; • Characteristic product criteria and customer perceptions to align them with CSR [29]. Table 1 summarizes the results of the literature analysis. Following conclusions were drawn from the literature review: • A limited number of studies (17) focus on product design considering quality (customer satisfaction), environmental impact in LCA, and social responsibility; • The selected research area is not widely studied and is still in a developmental phase since 2005, with slow predicted growth in subsequent years, indicating significant research gaps; • The most frequently discussed topics among the analysed works were LCA, corporate social responsibility, product design, QFD, and decision-making; • Common proposed solutions for assessing product quality and environmental im-pact in the life cycle typically involve combining QFD for processing customer expectations and LCA for environmental impact assessment; Advances in Production Engineering & Management 19(4) 2024 463 Siwiec, Gawlik, Pacana • Existing studies on socially responsible design aim to ensure environmentally friendly products, often overlooking the aspect of achieving customer-desired product quality. Critically discussed conceptual design processes providing analysis of current products and alternative product solutions (prototypes) in a multidimensional evaluation process considering sustainable development criteria (quality, environmental, and social responsibility) are notably absent, and therefore were identified as our research gap. Research Area Product quality assessment and environmental life cycle assessment (LCA) Ensuring socially responsible design and environmentally friendly products 464 Table 1 Summary of literature analysis results Description Methods Acquiring and processing cusQFD and LCA tomer requirements for prodCustomer survey and LCA uct quality and environmental Customer demand data, impact assessment in product LCA life cycle Analysis of customer sensitivity to recyclable products in their life cycle Acquiring and processing cusQFD, LCA, FMEA, TRIZ, tomer requirements for prodFTOPSIS uct quality and environmental impact assessment in product life cycle; analysis of product nonconformities and identification of product innovations Combining product quality asCustomer surveys, TOPIS, sessment with environmental LCA impact assessment in product design Customer reactions to product CSR, customer expectations eco-labels in the context of for product eco-labels their awareness and motives for perceiving corporate social responsibility Assessment of social impacts LCA, sustainable developin the case of technological ment criteria, CSR support in the product life cycle Modelling customer demand Game theory, ethical operafor the level of environmental tions, CSR friendliness of new products Identification of customer exCSR, analysis of customer pectations for product criteria expectations for their compatibility with the CSR Analysis of changes in product Focus groups with product roles and responsibilities in designers the field of conscious ecological product design Examining designers' motivaSocially responsible design tions in socially responsible (SRD), CSR product design decisions Assessment of implementation C2C, analysis of qualitative potential of the C2C approach and quantitative experiin conceptual product design ments for environmental and social benefits Examples of studies [15, 16, 18, 30] [19] [9] [20] [31] [21 22] [23] [24] [25] [29] [26] [28] [27] Advances in Production Engineering & Management 19(4) 2024 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility 3. Model design The research framework, including the developed model, is illustrated in Fig. 3. It involves determining the development direction of the current product by considering design alternatives (prototypes) in the context of sustainable development. The model primarily operates during the conceptual phase, translating and transforming the functional requirements of the product, its environmental impacts, and social acceptability into design parameters. Stage 1 Start Stage 2 Choice of the reference product and determination of the research goal Determination of the Aggregated Quality Index (AQI) Step 2.1 Identi�ication of the quality criteria Stage 3 Determination of the Environmental Impact Index (EII) in the life cycle Step 3.1 De�inition of goals and scope Step 3.2 Step 2.2 Gathering of customers’ expectations Step 2.3 Processing of customers’ expectations AQI Stage 5 Inventory analysis Step 3.3 Impact assessment Step 3.4 Interpretation EEI Stage 4 Determination of the Social Responsibility Index (SRI) Step 4.1 Identi�ication of the social responsibility criteria Step 4.2 Grading of the social responsibility criteria Step 4.3 Evaluation of the degree of accordance with social responsibility standards SRI Calculation of the aggregated Quality Social -Environmental indicator (QESR) QESR Indicator No QESR values for the product and its prototypes between 0 and 1?" Yes Stage 6 Elaboration of a product ranking under the aggregated QESR Indicator Stop Fig. 3 Research design: model development for products enhancement with use of design prototypes within the context of sustainable development Advances in Production Engineering & Management 19(4) 2024 465 Siwiec, Gawlik, Pacana The design parameters are both quantitative and qualitative, encompassing multidimensional aspects of the product and its prototypes in terms of meeting customer quality expectations, environmental impact throughout their life cycle, and fulfilling social responsibility criteria. This process involves a comprehensive and detailed analysis and prioritization of various sustainable development parameters. It integrates customer expectations and insights from interdisciplinary expert teams. Within the developed model, each key aspect (quality, environment, and society) can be considered independently or simultaneously using designated decision-making indicators. This ensures the model's versatility and flexibility in adapting to changing market demands. Based on the aggregated decision-making indicator, the model predicts the most favourable development direction for the product, aiming to simultaneously enhance customer satisfaction with product quality, reduce the product's negative environmental impacts throughout its entire life cycle, and achieve acceptable levels of social responsibility fulfilment. Consecutive stages of model’s application are presented below. 3.1 Stage 1: Choice of the reference product and determination of the research goal The selection of the product falls within the purview of the entity utilizing the model. This choice can be justified based on numerous factors, including the product's development stage (favouring the maturity phase), customer expectations, or the entity's individual preferences. The chosen product should be widely recognized and used, thereby increasing the efficiency of its analysis in subsequent stages of the model. This product serves as a reference product, representing a generalization of products of a particular type [32]. In accordance with the selected product, the entity defines the research objective using the SMARTER method (Specific, Measurable, Achievable, Relevant, Time-bound, Evaluate, and R Reevaluate or Risks) [33]. It is assumed that the objective will involve determining the most favourable direction for enhancing the product using proposed alternative production solutions (prototypes), while simultaneously considering their: i) quality, ii) environmental impact throughout the life cycle, and iii) fulfilment of social responsibility criteria. 3.2 Stage 2: Determination of the Aggregated Quality Index (AQI) The Aggregated Quality Index (AQI) is estimated for the current product and its prototypes. This index can be considered an aggregated measure due to its analysis of compliance and non-compliance (coverage) for all analysed quality criteria. It is considered based on two approaches: i) user-centred, where quality is the degree to which the product meets or exceeds customer requirements, and ii) production-driven, where quality is conformity to standards and design specifications [34, 35]. Following the works of [35-37], it is assumed that the assessment of product quality (and its alternatives) should be conducted using a multidimensional measure of product quality. This multidimensionality refers to the inclusion of various numbers and types of component dimensions (criteria or quality indicators) related to the product, such as performance, durability, or functionality [38]. Insights from an extensive literature review presented in [39] indicate that previous studies have focused on one-dimensional measures of product quality or provided quality assessments based on selected quality metrics. Therefore, aiming to fill this gap, original methodological frameworks for multidimensional assessment of product quality (and its alternatives/prototypes) have been developed. The proposed method includes assessing the importance of product criteria (as determined by customers) and assessing the fulfilment of customer expectations regarding the quality of these criteria (while simultaneously considering customer expectations and expert team requirements). The product and its prototypes quality index are determined sequentially, as outlined in steps 2.1-2.3. • Step 2.1. Identification of the quality criteria Quality criteria relate to customer satisfaction with product usage. These criteria can be perceived as external (e.g., brand, price, country of origin) or internal [39]. In the proposed approach, product quality criteria refer to an internal conceptualization of quality perception [40]. This implies that modifying product criteria changes the nature of the product, thus affecting the perception of 466 Advances in Production Engineering & Management 19(4) 2024 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility quality both objectively and subjectively. As stated in [41], objective quality determines whether a product fulfils its functions as expected by customers. Objective quality also encompasses engineering design, where product criteria are measured to shape perceived quality as objectively recognized by experts. On the other hand, subjective quality concerns customers' perception of product quality and serves to conceptualize it [39, 42]. Product quality criteria can be selected according to the ISO/IEC 25010 standard, which includes criteria such as functional suitability, performance, compatibility, usability, reliability, security, maintainability, and portability [43]. Additionally, the selection of criteria can be based on foundational research in this area, such as [34, 37] and aligned with other works from a literature review [35, 39, 44]. Based on these sources, the proposed model focuses on internal quality criteria. Criteria should be chosen that relate to the target product (the subject of the study). However, reducing the analysis to criteria that meet all quality indicators is impractical and inefficient for assessing overall product quality. As mentioned in [45], identifying numerous product criteria, most of which are insignificant in the holistic perception of product quality, is unnecessary. Therefore, following [45], it is advisable to limit the criteria to key factors that have the greatest impact on customer satisfaction with product usage [46]. The selection of criteria is carried out by an expert team, chosen based on their knowledge and qualifications relevant to the study and analysis. Methodical selection of expert teams is outlined in [47, 48]. According to literature reviews, a sufficient number of experts can range from six to eight [49], four to fifteen [50], or, as proposed in [51], an optimal team size could be ten experts. Following [52], experts may include employees of companies manufacturing the selected product, assuming that this product is interpreted as a reference product (products of varied brands differing in specifics but serving the same purpose and belonging to the same type). Delegating decision-making to an expert team, including employees of manufacturing companies, reflects current practices of well-functioning organizations where employees participate in participatory practices and teamwork, and interdisciplinary or multifunctional teams are key assets in the improvement process [53]. This expert team can effectively select criteria, basing their choices on the specificity, usefulness, and often ambiguity of the criteria. The selection of criteria is carried out according to the product catalogue (specification), which includes key product criteria in terms of customer usage. To efficiently select the main criteria, it is recommended to utilize teamwork and decision-making methods [52], such as Preliminary Criteria Reduction (PCR) [54]. The total number of quality criteria should be below 10, adhering to the principle of a minimum number of 7±2 [46]. Since quality criteria have different parameters (measures, specifications), it is necessary to characterize them for further evaluation. This characterization involves defining the parameters of the criteria, such as those used to measure their quality, e.g., parameters in the product catalogue (specification). The magnitude of these parameter measures should be expressed in international metric units, such as value, value range, or a verbal description of the criterion's state. It is assumed that the current (marketed) product is characterized according to its specification, meaning that the criteria are expressed in their current state, as in the product catalogue. The model concept assumes that the direction of product improvement will be determined based on a multidimensional assessment of various modifications of this product, referred to as design solution alternatives (product prototypes). These prototypes are developed as modifications of the current product's quality criteria. The number of prototypes should adhere to the principles of effective comparison, so the total number of prototypes along with the reference product should not exceed 15 [55], where the minimum number should meet the 7±2 principle [46]. Prototypes are developed as modifications of the current state of the reference product's criteria. Modifying current criteria to hypothetical ones is done according to the Pareto principle [21 ,56, 57], meaning that various modifications of quality criteria, changing their characteristic values (parameters), are proposed by increasing or decreasing them by 20 % in a sequential manner. Decisions regarding these modifications are made by the previously selected expert team. Advances in Production Engineering & Management 19(4) 2024 467 Siwiec, Gawlik, Pacana • Step 2.2. Gathering of customers’ expectations To assess the quality of the product and its prototypes, obtaining customer expectations is essential. Customers express their expectations regarding the importance (weights) of product criteria and their satisfaction with the quality fulfilment of these criteria. At this stage, the expert team plays a crucial role in supporting the assessment process of quality criteria fulfilment. Incorporating the Voice of Customer (VoC) [58] and expert opinion is important because customers tend to express their satisfaction through overall ratings or perceptions of product quality, rather than objective measures of criteria compliance with technical standards [35, 59]. Meanwhile, the expert team can verify these assessments by analysing their alignment with customer requirements, for example, through focus groups [51]. Customer expectations are gathered through exploratory research, with survey research being the most popular method used in customer satisfaction studies [60]. If the survey responses are imprecise, in-depth interviews may be necessary. The recruitment strategy for survey participants should be well-planned to ensure high-quality results and sample representativeness. It is expected that the database will be built on real customer experiences with the product, with customers participating in the survey having used the studied product for at least a month [61]. The representative sample size of customers can be estimated using the method from [57]. During the survey, customers rate the importance (weights) of the product's quality criteria, including its prototypes. The importance rating reflects the significance of these criteria in terms of their utility in the product. The ratings are given on a 5-point Likert scale [62], where 1 represents a criterion that is insignificant, and 5 represents a criterion that is significantly important. Additionally, customer satisfaction with the fulfilment of these criteria is assessed during the survey. This assessment indicates the extent to which each criterion meets customer expectations regarding the product's utility. Satisfaction ratings are also provided on a Likert scale [62], where 1 represents a criterion that does not meet the expected quality, and 5 represents a criterion that significantly meets the expected quality. An advantage of the proposed model is its ability to compare the i-th product criterion against the j-th product alternative, ensuring increased precision in the assigned ratings. This approach involves a pairwise comparison of the same criteria across different solution variants, which is effective in multi-criteria decision-making [12]. • Step 2.3. Processing customers’ expectations After obtaining customer expectations regarding the importance of criteria, the next step is to rank the criteria's importance to form them into groups distinguished by the significance of these criteria to customers. Due to the assumption regarding the total number of quality criteria (7±2) [46] and the adopted five-point scale for rating the im-portance of these criteria, the criteria weights are calculated as the arithmetic mean of the criteria importance ratings [55, 57]. Subsequently, the assessment of product and its prototypes quality is conducted. To maintain the multidimensionality of this assessment corresponding to a varying number of criteria across different component dimensions (criteria or quality indicators) of the product [38], an expert assessment of quality is proposed, which applies to calculating the level of multi-aspect quality for any products or processes that may be in the design, production, or operational phase. For this purpose, Eq. 1 is utilized to calculate the AQI: ∑ 𝑤𝑤𝑖𝑖𝑖𝑖 𝑞𝑞𝑖𝑖𝑖𝑖 (1) ∑ 𝑤𝑤𝑖𝑖𝑖𝑖 where: i – product or prototype; j – criterion, j, i = 1, 2,…, n; wij – weight of the j-th criterion for the i-th product or prototype; qij – quality of the j-th criterion for the i-th product or prototype. 𝐴𝐴𝐴𝐴𝐴𝐴𝑖𝑖 = AQI pertains to customer satisfaction with the utility of the product (and its pro-posed alternatives). It enables the development of a product ranking based on customer satisfaction with their quality. The maximum value of the AQI corresponds to the most favourable product. 468 Advances in Production Engineering & Management 19(4) 2024 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility 3.3 Stage 3: Determination of the Environmental Impact Index (EII) in the life cycle The model assumption is, that the direction of product improvement will be considered regarding the environmental impact of its prototypes throughout their life cycle. To achieve this, an Environmental Impact Index (EEI) for the product (and its prototypes) over the entire life cycle has been developed. This indicator is determined using results obtained from the LCA method. It is a structured, comprehensive, and internationally standardized method that quantitatively assesses important emissions and resources, including environmental and societal impacts, resource depletion, and other issues arising throughout the life cycle of any product (as well as processes or services). LCA is recognized as an effective decision-support method that, when supplemented with other tools, contributes effectively to more environmentally sustainable consumption and production practices. LCA is often applied in the area of product design (including improvement) as a specialized method dedicated to strategic assessments of new concepts [63]. It is most often conducted in accordance with ISO 14040 [64], which includes phases such as defining goals and scope, inventory analysis, impact assessment, and interpretation [61] (Fig. 4). 1 Definition of goals and scope, and among others goal of LCA functional unit system boundaries data quality requirements     2 Inventory analysis data collection calculation method for the quantification of system inputs and outputs standardization of data for their comparison as part of settling them for the same amount with the functional unit    3    4    Impact assessment assignment of inventory data to impact categories (classification) modelling of inventory data in the area of impact categories aggregation of results in exceptional situations and if relevant Interpretation validation for a specific input withing the quantity materiality indicator for product environmental weighting, where environment is the criterion for evaluating and prioritizing verbal and argumentative assessment for category without using the results for further calculations Fig. 4 LCA in ISO 14040 norm [63] Advances in Production Engineering & Management 19(4) 2024 469 Siwiec, Gawlik, Pacana In our model, the existing product is compared with existing products (prototypes, modified products within the framework of the current/real product). The challenge of using LCA in this approach is conditioned by the lack of complete definitions and data for estimation during the design process, where the concept and architecture of prototypes are developed. Consequently, the use of LCA is focused on answering environmental protection questions, such as "Which of the proposed design solutions is more environ-mentally favourable?" The ability to answer this question accurately lies with specific experts, ideally environmental experts [63]. The full and detailed scope of an LCA system begins with the extraction and pro-cessing of materials, continues through production, usage, and ends with the product's end-of-life stage, adhering to the fundamental cradle-to-grave approach for life cycle assessment [65]. LCA involves analysing each stage of material transformation, including intermediate states, culminating in the synthesis of the final product [66, 67]. LCA application can be supported by software, e.g.: OpenLCA, SimaPro, Gabi [68, 69]. For less rigorous LCA applications, it is preferable to use Level 1 LCA or Level 2 LCA [70]. These levels were deemed adequate for the proposed model. LCA should be conducted for the reference product (current and commercially available), resulting in a single EII > 0 value, such as for carbon footprint, which has a measurable, numerical nature. After evaluating the reference product, a prospective life cycle assessment (LCA) of its prototypes – alternative products modified according to quality criteria parameters and specifications – is conducted. LCAs for prototypes still in the design phase face inherent limitations due to incomplete data, which can result in compilation challenges and an increased risk of errors [63]. Traditionally, scenario analysis has been employed to conduct LCAs for products during the design phase [71, 72]. Our research, however, seeks to advance this process by more comprehensively integrating results from various model stages, addressing qualitative, environmental, and social aspects. To this end, we propose a novel approach that predicts environmental impact changes in prototypes relative to the quality levels of the reference product. This method utilizes simplified modelling of LCA value changes, aligning with quality parameter modifications, and adheres to the Pareto principle [73]. For instance, if the current quality level of a product results in a particular LCA outcome, a 20 % increase in quality level is expected to produce a corresponding 20 % increase in the LCA result, as previously tested in [21, 56]. The prospective and simplified LCA for product prototypes is conducted following Eq. 2 [21]: 𝐸𝐸𝐸𝐸𝐸𝐸𝑖𝑖 = 𝐸𝐸𝐸𝐸𝐸𝐸 (1 + 𝑝𝑝) (2) where: EII – reference product in its life cycle, 𝑝𝑝 – percentage change of EII represented in decimal form; i – prototype, i = 1, 2,…, n. Obtained EII enables the ranking of products, and their prototypes based on their environmental impact in LCA. The top position in the ranking corresponds to the minimum EII value, where a lower EII value indicates a smaller negative environmental impact. 3.4 Stage 4: Determination of the Social Responsibility Index (SRI) Research design assumes that product improvement will also consider the fulfilment of social responsibility standards. This derives from the concept of sustainable enterprise development, where it is essential for companies to take actions based on a shared understanding of social responsibility. Social responsibility according to ISO 26000 [74] is defined as the impact of a company's decisions and actions on society through transparent and ethical behaviours across seven core areas: organizational governance, human rights, labour practices, environment, fair operating practices, consumer issues, and community involvement and development. Various approaches exist in our fields of research (management, production engineering), e.g.: social innovation design [75], which emphasizes the role of designers, or transformation design [76], focusing on designing within social transformation in a local context. These approaches confirm that designers can directly and indirectly encompass social responsibility in their products, processes, and services. Social responsibility within products is derived from individual ethical 470 Advances in Production Engineering & Management 19(4) 2024 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility values of designers [77], as well as customer needs, including engagement of other enterprise stakeholders, e.g., through Corporate Social Responsibility (CSR) [78]. In our model, social responsibility specifically pertains to Socially Responsible Design (SRD) [79]. SRD focuses on alleviating societal problems to improve the quality of life through intentional design. During socially responsible design, it is necessary to address macro-social issues (e.g., health, governance, education, crime, fair trade, social inclusion, and economic policy) and macroenvironmental requirements (poverty, energy, climate change, rapid population growth, etc.) [78]. For manufacturing enterprises, decisions involving social responsibility should be made as early as possible in the product engineering process, ideally during product design – to increase the likelihood of cost reduction and efficiency. This is achieved by understanding the societal impacts of offered products and how changes in these products can contribute to sustainable production [77 ,80]. In this regard, we propose the Social Responsibility Index (SRI) for products and their prototypes, calculated through steps 4.1-4.3 described below and conducted by team of experts. They are selected independently [47, 48]. The number of experts vary from 6-8 [49], 4-15 [50], or 10 [51] experts. According to [81], fewer experts in the team are beneficial because a collective opinion leads to fewer socially responsible decisions resulting from an increase in the moral leeway of their opinions. Experts should also come from various disciplines (interdisciplinary collaboration) [77] and include: i) de-signers from the model applicating enterprise; ii-a) CSR experts from the company, or, in a more ambitious approach, ii-b) experts in Sustainable Development Goals (SDGs) from relevant NGOs. Such a team composition assures a socially responsible approach to business, including defining a sustainable development perspective and supporting sustainable production and consumption analyses [75-77, 79]. • Step 4.1. Identification of the social responsibility criteria The model design focuses on evaluating products and their prototypes by assessing the importance and feasibility of social responsibility criteria. These criteria are selected by a team of experts and are based on six areas specified in ISO 26000, excluding the environmental area as it is addressed in the third stage of the model [74]: i) Organizational governance; ii) Human rights (due diligence; human rights situations at risk; avoidance of complicity; resolving grievances; discrimination and vulnerable groups; civil and political rights; economic, social, and cultural rights); iii) Labour practices (employment and working relationships; working conditions and social protection; social dialogue; occupational health and safety; employee training and development); iv) Fair operating practices (anti-corruption measures; responsible political engagement; fair competition; promoting social responsibility in value chains; respect for property rights); v) Consumer issues (fair marketing, factual and impartial information, and fair contractual practices; consumer health and safety protection; sustainable consumption; customer service, support, complaint resolution, and dispute settlement; consumer data protection and privacy; access to basic services; education and awareness); vi) Community involvement and development (community engagement; education and culture; job creation and skills development; development and access to technology; wealth and income creation; health; social investments). Analysing all social responsibility criteria is inefficient, as many may be irrelevant to the overall assessment of a product's or prototype's social responsibility [45]. Therefore, the selected social criteria should specifically relate to the target product (research subject) and establish a strong connection to fulfilling social responsibility objectives [46]. The selection process for these criteria is carried out by an expert team using methods such as focus groups or alternative approaches like PCR [54]. To ensure consistency in the criteria analysis throughout the model, the total number of social responsibility criteria should ideally fall within the range of 7±2 [46], aligning with the number of qualitative criteria used in Stage 2. • Step 4.2. Grading of the social responsibility criteria The social responsibility criteria selected in Step 4.1 are subjected to significance grading. Experts evaluate these criteria based on their relevance to overall customer satisfaction with the product. Advances in Production Engineering & Management 19(4) 2024 471 Siwiec, Gawlik, Pacana The importance of each criterion is rated using a five-point Likert scale [62], where: 1 – criterion irrelevant, 5 – most important criterion. The weight (gi) of each social responsibility criterion is then calculated as the arithmetic mean of the importance ratings assigned to that criterion. • Step 4.3. Evaluation of the degree of accordance with social responsibility standards The analysed product and its prototypes are assessed for their compliance with social responsibility standards. Ratings are assigned by an expert team using a scale from 0 to 1 [82], where: 0 indicates the criterion does not meet social expectations; 1 indicates full satisfaction of social expectations; and 0.7 denotes acceptable fulfilment of social expectations [55, 57]. Focus groups [51] are often employed for assigning these ratings. The evaluation is conducted based on the social responsibility criteria identified in Step 4.1. Simultaneously, analysing the qualitative criteria parameters (from Stage 2 of the model) that may influence the social responsibility fulfilment of the product and its prototypes is beneficial. Assessing socially responsible products is inherently linked to uncertainty, including epistemic uncertainty regarding actual consequences and ethical uncertainty concerning the purpose of the evaluation [77, 80]. This ambiguity arises from questions about whether the outcomes of socially responsible products will be desirable, particularly if they introduce potential disadvantages for stakeholders, such as increased prices or reduced usability compared to alternative solutions. To reduce this uncertainty, the proposed model incorporates an analysis of the potential negative effects of social responsibility initiatives [77, 80]. Expert assessments of social expectation fulfilment can be supported by supplementary questions, such as those proposed in [83, 84]. Achieving a comprehensive assessment of social responsibility fulfilment in verified products and prototypes requires ethical conduct by the expert team. Additionally, the process encourages the integration of sustainable design practices—an ongoing global challenge [82]. After assessing the social responsibility fulfilment, the SRI is determined for the product and its prototypes, considering the importance of social responsibility criteria (identified in Step 4.2.). The SRI index is based on the concept proposed in [43], adopting the Coverage of Fulfilment method. This method distinguishes between fulfilment coverage for different social criteria and total coverage for these criteria across the analysed products and prototypes. Initially, the Total Coverage for each social criterion (OP) is calculated for the product and its prototypes, considering the importance of these criteria (Eq. 3): 𝑝𝑝𝑝𝑝𝑖𝑖 𝑂𝑂𝑂𝑂𝑖𝑖 = � 𝑔𝑔𝑖𝑖 (3) 𝑟𝑟𝑟𝑟𝑖𝑖 where: psi – the number of positive grades (value = 1) of fulfilment of social responsibility standards for per criterion; rsi – the total number of all grades per criteria within the fulfilment of social responsibility standards; gi – criterion weight; i – product or prototype, i = 1, 2,…, n. Subsequently, the SRI is determined for a given product and prototype (Eq. 4): 𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖 = � 𝑂𝑂𝑂𝑂𝑖𝑖 (4) where: OPi – total coverage for social criteria of the i-th product or its prototype; i – product or prototype, i = 1, 2,…, n. The SRI allows to create a ranking of products or their prototypes in terms of accordance with social responsibility standards. Higher SRI values indicate a more favourable level of this index. 3.5 Stage 5: Calculation of the aggregated Quality-Environment-Social-Responsibility Indicator (QESR) The model aims to determine the most favourable direction for product development, considering its quality, environmental impact throughout the life cycle, and fulfilment of social responsibility standards. Therefore, at this stage of the model, the AQI, EII, and SRI are aggregated into a single composite Quality-Environment-Social-Responsibility Indicator (QESR). 472 Advances in Production Engineering & Management 19(4) 2024 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility It is assumed that each index determined within the model, AQI, EII, and SRI, is a normalized index. This is necessary to standardize these index values into a unified and comparable measure [85], given the inability to standardize the values of an LCA index, where the value does not have an upper boundary limit. Therefore, this relativization (normalization) is necessary and consequently requires appropriate actions on the quality and social indices. The proposed relativization is applicable if the total number of analysed products meets the principle of a minimum of 7±2 products [46]. Initially, the normalized AQI for the i-th product or prototype is calculated (Eq. 5): 𝐴𝐴𝐴𝐴𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚 − 𝐴𝐴𝐴𝐴𝐴𝐴𝑖𝑖 𝐴𝐴𝐴𝐴𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚 − 𝐴𝐴𝐴𝐴𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚 (5) 𝑊𝑊𝑠𝑠𝑠𝑠 = 𝐸𝐸𝐸𝐸𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚 − 𝐸𝐸𝐸𝐸𝐸𝐸𝑖𝑖 𝐸𝐸𝐸𝐸𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚 − 𝐸𝐸𝐸𝐸𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚 (6) 𝑤𝑤𝑝𝑝𝑝𝑝 = 𝑆𝑆𝑆𝑆𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑆𝑆𝑆𝑆𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚 (7) 𝛼𝛼𝑤𝑤𝑗𝑗𝑗𝑗 + 𝛽𝛽𝑤𝑤𝑠𝑠𝑠𝑠 + 𝛾𝛾𝑤𝑤𝑝𝑝𝑝𝑝 𝛼𝛼 + 𝛽𝛽 + 𝛾𝛾 (8) 𝑤𝑤𝑗𝑗𝑗𝑗 = where: wji – normalized AQI for the i-th product or prototype; AQImax – highest quality; AQImin – lowest quality (both max and min can be calculated with any method, but consequently the same throughout the whole QESR application); i – product or prototype, i = 1, 2,…, n. Then, the normalized EII is calculated (Eq. 6): where: wsi – normalized EII for the i-th product or prototype; EIImax – highest LCA value; EIImin – lowest LCA value; i – product or prototype, i = 1, 2,…, n. Then, the normalized SRI is calculated (Eq. 7): where: wpi – normalized SRI for the i-th product or proto-type; SRImax – highest SRI value, SRImin – lowest SRI value; i – product or prototype, i = 1, 2,…, n. Then, the aggregated QESR indicator is calculated as in Eq. 8: 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑖𝑖 = where: α – relevance of the quality component; β – relevance of the environment component; γ – relevance of the social responsibility component; wji – normalized AQI; wsi – normalized EII; wpi – normalized SRI; i – product or prototype, i = 1, 2,…, n. Then, considering the normalized indexes, their weights can be adjusted in the process of calculating the aggregated index. The weights of each aspect are assigned collectively by experts from teams selected in stages 2, 3, and 4 of the model. It is possible to establish such weights [55, 86, 87], e.g. α = 7, β = 3, γ = 2. In such a case the Eq. 9: α:β:γ:δ=7:3:2 (9) It should be noted that the change of adopted ratios between the indexes would result in changes in the final hierarchy of decision alternatives. Hence, the model is sensitive to the weights of normalized indexes. The total weight sum does not have to equal 1, allowing for considerable flexibility in determining the weight proportions. The aggregated QESR indicator is calculated with use of Eq. 10: 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑖𝑖 = 1 − �0.083�7𝑤𝑤𝑗𝑗𝑗𝑗 + 3𝑤𝑤𝑠𝑠𝑠𝑠 + 2𝑤𝑤𝑝𝑝𝑝𝑝 �� (10) where: wji – normalized AQI; wsi – normalized EII; wpi – normalized SRI; i – product or prototype, i = 1, 2,…, n. The QESR indicator is interpreted as follows: i) from a qualitative perspective, it represents the level of customer satisfaction with using the product; ii) from an environmental perspective, it indicates the potential for achieving a product that is environmentally friendly throughout its lifecycle, depending on the analysed environmental impacts; iii) from a social perspective, it signifies the fulfilment of societal expectations within the product. A higher QESR indicator value reflects a closer-to-perfect level of the three analysed aspects simultaneously. Advances in Production Engineering & Management 19(4) 2024 473 Siwiec, Gawlik, Pacana 3.6 Stage 6: Elaboration of a product ranking under the aggregated QESR Indicator Based on the Quality-Environment-Social-Responsibility (QESR) indicator, a ranking of products (or their alternatives) is created. Products should be ordered from highest to lowest QESR value. A higher QESR value indicates a more favourable index and higher customer satisfaction level. Therefore, the top position in the ranking corresponds to the maximum QESR value and represents the product that is most desired in terms of quality, environmental impact, and social responsibility. The verbal interpretation of the QESR indicator is conducted on a relative scale (Fig. 5). The QESR indicator can help improving products, i.e. a prototype with the maximum QESR value will best meet customer expectations in terms of quality, while also having a minimal negative environmental impact in its entire life cycle, at the same time keeping the social responsibility standards. Class discriminants bad critical unvaforable unsatisfactory suf�icient imperfection moderate satisfactory distinctive excellent bene�icial normality perfection 0.95 0.85 0.75 0.65 0.55 0.45 0.35 0.25 0.15 0.05 index 0 1 2 3 4 5 6 7 8 9 decision 0.5 0.4 0.3 0.2 0.1 class Uniform states scale 0.6 very unfavorable 0.7 unfavorable 0.8 average 0.9 bene�icial very bene�icial 1.0 increase of customer satisfaction Fig. 5 Interpretation scale of the QESR indicator: customer satisfaction with the products in terms of quality, environmental impact, and social responsibility [51, 60]. 4. Results Light Passenger Vehicles (LPVs) of a global manufacturer were employed as study subject. They are pivotal in mitigating climate change due to their energy efficiency and reduced environmental impact during use [88]. The analysis focused on a Hybrid Electric Vehicle (HEV) [89], which proves to be a promising solution for fuel savings, moderating fuel costs for consumers, and aiding in pollution reduction while meeting environmental regulations. The key advantage of HEVs lies in their drivetrain, which re-duces fuel consumption through an electric motor (EM) to achieve the required vehicle power. The electric motor utilizes energy from a battery or regenerative braking to power auxiliary systems and minimize engine idling [90]. A detailed characterization of HEVs is presented, for instance, in [91]. Moreover, hybrid vehicles are widely recognized and utilized globally, thus meeting model assumptions. Due to the research's specificity, the analysed HEV is seen as a reference vehicle, or a generalization of vehicles of this type [32]. For Stage 1 of the model, the research goal was established for the selected subject of study: determining the most favourable direction for improving HEVs through proposed manufacturing alternatives (prototypes), considering their: i) quality, ii) environmental impact throughout their lifecycle, and iii) meeting the social responsibility standards. In Stage 2 a team of five experts undertook the task of defining a quality index for HEV and its prototypes. Initially, quality criteria were established to internally conceptualize quality perception. The selection process was guided by broad categories of quality criteria outlined in ISO/IEC 474 Advances in Production Engineering & Management 19(4) 2024 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility 25010 [43], the HEV catalogue (specification), and quality criteria proposed by other authors (e.g., [90-93]. The primary quality criteria chosen for verification included: total mass (kg), maximum engine power (kW), maxi-mum speed (km/h), battery range (km), battery charging time (hours), vehicle colour, vehicle dimensions (mm), equipment, fuel consumption (average), and drivetrain. The assumptions regarding the number of quality criteria, with a maximum of 10 and a minimum of 5 [46], were met. Subsequently, all criteria were characterized based on their descriptive measures. For the reference HEV, the catalogue (specification) and current parameters of these criteria were utilized. Six design solution prototypes for the reference HEV were pro-posed. These prototypes were developed as modifications of the current states of the analysed HEV criteria. According to the proposed model concept, the Pareto-Lorenz principle (20/80) was applied in this process. Seven design solutions were obtained (the current solution and its six modifications/alternative design solutions), as shown in Table 2. Table 2 Characteristic of reference HEV criteria and its prototypes Alternative C1 C2 C3 C4 C5 Ref. product 1815 140 200 1195 ≈30 min Prototype 1 2178 84 220 1434 > 30 min to 3 h Prototype 2 2541 112 240 1673 > 3 h to 6 h Prototype 3 2904 168 260 1912 > 6 h to 9 h Prototype 4 3267 196 180 2151 > 9 h to 12 h Prototype 5 1452 224 160 956 > 12 h to 15 h Prototype 6 1089 252 140 717 > 15 h Alternative C6 C7 C8 C9 C10 Ref. Product white pearl 4630 × 1780 × 1435 basic 4.40 front axis Prototype 1 clean white 5556 × 2136 × 1722 advanced 5.28 rear axis Prototype 2 light grey 6482 × 2492 × 2009 full 6.16 AWD Prototype 3 dark grey 7408 × 2848 × 2296 advanced 7.04 4×4 Prototype 4 black 3704 × 1424 × 1148 basic 7.92 front axis Prototype 5 red 2778 × 1068 × 861 full 3.52 rear axis Prototype 6 white pearl 1852 × 712 × 574 basic 2.64 4×4 C1: total mass (kg); C2: maximum engine power (kW); C3: maximum speed (km/h); C4: battery range (km); C5: battery charging time (hours); C6: vehicle colour; C7: vehicle dimensions (mm); C8: equipment; C9: fuel consumption (average) (l); C10: drivetrain. To assess the quality of HEV and its prototypes, customer expectations were gathered through a survey conducted as a pilot study to verify the proposed model concept. The survey was conducted in March and April 2024 among 116 randomly selected customers who use LPVs. Pilot studies [94, 95] proved this sample size to be sufficient. The survey was administered electronically through Microsoft Forms. The response rate for the survey was 100 %, and the collected data complete. This resulted from the form of pilot studies, which were conducted in a targeted (nonrandom) manner to specific customers who had previously expressed a willingness to participate in the survey. Additionally, the studies were carried out in-depth by utilizing direct communication techniques with customers. This involved obtaining surveys during direct interviews, which aimed to identify potential difficulties in completing the survey (understanding the survey questions). Simultaneously, the use of a computer tool aided in avoiding mistakes regarding skipping a question or a required response. In the survey, customers rated the importance of selected vehicle criteria on a Likert scale and evaluated the quality fulfilment of these criteria based on the proposed design alternatives. Based on the acquired ratings of criterion weights for the reference HEV, the im-portance and quality of criteria were determined by calculating the arithmetic mean of these ratings. Following the developed model, Eq. 1 was utilized to calculate the AQI for reference vehicle and its prototypes (Table 3). Advances in Production Engineering & Management 19(4) 2024 475 Siwiec, Gawlik, Pacana No. C2 C4 C5 C9 C3 C7 C8 C10 C1 C6 Table 3 Relevance of the quality criteria for the HEV and ranking of HEV Quality criteria Criterion Quality of criteria for HEV and its prototypes weight Ref. P1 P2 P3 P4 P5 3.6 maximum engine power (KM) 4.09 2.07 2.76 3.75 4.06 4.33 6 3.3 battery range (km) 4.18 3.71 4.00 4.33 4.47 2.46 7 4.5 battery charging time (h) 4.09 3.83 2.76 2.24 1.81 1.46 7 fuel consumption (average) 4.4 4.21 4.11 3.61 3.19 2.98 4.63 (l) 7 3.9 maximum speed (km/h) 3.86 4.17 4.27 4.28 3.33 2.70 7 3.5 vehicle dimensions (mm) 3.43 3.23 2.92 2.75 3.60 3.34 1 3.3 equipment 3.84 4.44 4.70 4.44 3.31 4.44 1 3.9 drivetrain 3.85 3.82 3.84 4.64 3.99 3.82 9 3.6 total mass (kg) 2.95 3.36 3.09 2.74 2.36 3.34 6 3.8 vehicle colour 2.74 3.56 3.75 3.97 4.42 3.39 2 3.8 AQI 3.64 3.58 3.65 3.43 3.39 1 Ranking 1 3 4 2 5 6 P6 4.33 2.04 1.30 4.68 2.33 2.86 3.31 4.64 2.90 2.49 3.12 7 AQI ranks the utility of the reference HEV and its prototypes. It was observed that the reference vehicle performed best. However, the ranking may be reversed in further stages of model application, when considering environmental impact and social responsibility. In Stage 3, the EEI of the HEV throughout its life cycle was determined. A second level LCA was conducted under ISO 14040 rigor [64], utilizing GREET v1.3.0.13991 software data [96], covering material extraction and processing, production, usage, and recycling. The functional unit was defined as the vehicle traveling 150,000 km [89, 97, 98]. This unit allowed for data normalization to facilitate comparison with vehicle prototypes. However, the functional unit could vary, e.g. [99] proposes 200,000 km. The system boundaries were set within the timeframe of 2021-2024 and data from the GREET model. The first phase of LCA included carbon dioxide (CO2) from material extraction and processing in vehicle component construction, involving extraction, smelting, beneficiation, and refining [100]. Following [101], CO2 emissions in this initial phase are calculated with Eq. 11: 𝐶𝐶𝑀𝑀 = ��𝐶𝐶𝑥𝑥,𝑓𝑓 + 𝐶𝐶𝑥𝑥,𝑒𝑒 � ⎧ 𝑥𝑥 ⎪ ⎪ 𝐶𝐶𝑥𝑥,𝑓𝑓 = 𝑚𝑚𝑥𝑥 � �𝐸𝐸𝑥𝑥,𝑛𝑛 � 𝜔𝜔𝑥𝑥,𝑛𝑛,𝑘𝑘 𝛼𝛼𝑘𝑘 � ⎨ 𝑛𝑛 𝑘𝑘 ⎪ 𝐸𝐸𝑥𝑥,𝑛𝑛 𝜔𝜔𝑥𝑥,𝑛𝑛,𝑒𝑒 ⎪ 𝐶𝐶𝑥𝑥,𝑒𝑒, = 𝑚𝑚𝑥𝑥 � � � 3600 ⎩ 𝑛𝑛 (11) where: Cx,f – CO2 emission from fuel consumption at material production; Cx,e – CO2 emission from electricity consumption at material production; x – material; m – weight (kg); n – production process; Ex,n – energy consumption per material unit in its production process (kJ/kg); k – fuel; 𝜔𝜔𝑥𝑥,𝑛𝑛,𝑘𝑘 – share of fuel consumption in Ex,n; 𝜔𝜔𝑥𝑥,𝑛𝑛,𝑒𝑒 – share of electricity consumption in Ex,n; 𝛼𝛼𝑘𝑘 – CO2 emission factor from fuel consumption (CO2 kg⁄kJ). Main materials in HEV production were identified, excluding low mass materials. Emissions during the processing of these materials were specified according to the literature [102] (Table 4). Data from the GREET model and [100, 101] results allowed us to adopt the energy consumption coefficient for material production and the CO2 emission factor for energy consumption in the 476 Advances in Production Engineering & Management 19(4) 2024 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility entire life cycle. In this way, CO2 emissions from the material extraction and processing phase for the analysed reference vehicle were calculated (Table 4). The total CO2 emissions during the material extraction and processing phase for the HEV amounted to 623.19 kJ = 0.623 MJ. It was inferred that fuel consumption emissions contributed significantly more to the total CO2 emissions during the first LCA phase. Material Steel Iron Cast aluminium Wrought aluminium Copper Glass Plastic Rubber Table 4 Main materials in HEV production and CO2 emissions Material Emission factor of CO2 emission CO2 emission (kg) material production from fuel from electricity (CO2/kg) consumption consumption 899.80 2.00 403.28 0.10 77.20 0.55 0.10 0.00 67.50 2.62 86.95 0.08 27.60 5.92 57.90 35.80 148.80 23.40 2.35 1.62 3.05 3.62 76.15 25.20 1.95 16.19 403.28 Total CO2 emission 0.07 0.02 0.00 0.02 0.10 403.38 0.11 87.02 76.22 25.22 1.95 16.21 403.38 Next, emissions resulting from vehicle and component production were analysed. This analysis focused on emissions during the processing and assembly of key com-ponents, with the possibility of additionally considering emissions during their distribution [100]. Following the methodology presented in [101], CO2 emissions were calculated using Eq. 12: 𝐸𝐸𝑉𝑉𝑉𝑉 ⎧𝐶𝐶𝑉𝑉𝑉𝑉 = ��𝐶𝐶𝑦𝑦,𝑓𝑓 + 𝐶𝐶𝑦𝑦,𝑒𝑒 � + 3600 ⎪ ⎪ 𝑥𝑥 𝐶𝐶𝑦𝑦,𝑓𝑓 = � �𝐸𝐸𝑦𝑦,𝑞𝑞 � 𝜔𝜔𝑦𝑦,𝑞𝑞,𝑘𝑘 𝛼𝛼𝑘𝑘 � (12) ⎨ 𝑞𝑞 𝑘𝑘 ⎪ 𝐸𝐸𝑦𝑦,𝑞𝑞 𝜔𝜔𝑦𝑦,𝑞𝑞,𝑒𝑒 𝐶𝐶𝑦𝑦,𝑒𝑒, = � � � ⎪ 3600 ⎩ 𝑞𝑞 where: Cva – CO2 emission from vehicle components production; Cy,f – CO2 emission from fuel consumption at component production; Cy,e – CO2 emission from electricity consumption at component production; y – vehicle component (part); Eva – electricity consumption at vehicle assembly; q – production process; Ey,q – energy consumption per component in its production process (kJ); 𝜔𝜔𝑦𝑦,𝑞𝑞,𝑘𝑘 – share of fuel consumption in Ey,q; 𝜔𝜔𝑦𝑦,𝑞𝑞,𝑒𝑒 – share of electricity consumption in Ey,q; 𝛼𝛼𝑘𝑘 – CO2 emission factor from fuel consumption (CO2 kg⁄kJ). GREET data and detailed characteristics of the vehicle production process allowed us to estimate the energy consumption and CO2 emission levels when producing components for the reference HEV (Table 5). The assembly of the main components is assumed to consume approximately 862 MJ of energy. A crucial component of an HEV is the battery. In this analysis, a lithium-ion (Li-Ion) battery was examined, consisting of elements such as the cathode, anode, separator, electrolyte, packaging, and battery management system. Based on the GREET model and [98, 103, 104], a material list for this type of battery was assumed. Table 5 Energy consumption and CO2 emissions in the production process of an LPV Production process Energy (MJ) CO2 (kg) material transformation 22912.60 1261.73 machining 1163.40 66.34 vehicle painting 4936.75 317.51 HVAC & lighting 3951.06 266.56 heating 3684.50 231.02 material handling 817.46 54.50 welding 1089.95 73.45 compressed air 1634.92 110.18 Advances in Production Engineering & Management 19(4) 2024 477 Siwiec, Gawlik, Pacana Additionally, based on studies presented in [98, 103, 104] and data from the GREET model, the energy consumption during the production of the Li-Ion battery was determined. The assembly of a Li-Ion battery consumes approximately 2.67 MJ/kg, resulting in about 1002 MJ for the entire battery. With Eq. 12, CO2 emissions during the production and assembly of HEV components (including the battery) are estimated to be around 43,572.18 MJ. Subsequently, an analysis of energy consumption and carbon emissions during the vehicle's usage phase, which constitutes the third phase of the life cycle, was conducted. This phase includes fuel consumption and vehicle maintenance [100]. Eq. 13 was applied [101]: 𝑑𝑑𝐹𝐹𝑘𝑘 (13) (𝜌𝜌 𝛼𝛼 𝐿𝐿𝐿𝐿𝑉𝑉𝑘𝑘 + 𝐶𝐶𝑘𝑘 ) 100 𝑘𝑘 𝑘𝑘 where: Cvu – CO2 emission from vehicle exploitation; d – total distance driven (km); Fk – combustive fuel consumption (l/100 km); 𝜌𝜌𝑘𝑘 – fuel viscosity; k – fuel; 𝐿𝐿𝐿𝐿𝑉𝑉𝑘𝑘 – lower calorific value of fuel (kJ/kg); Ck – CO2 emissions per k unit of fuel production. The lifespan of an HEV is around 150,000 km [97], we assumed the use of PB 98 gasoline within standard specifications. Based on the manufacturer’s characteristics, the average fuel consumption of the HEV is assumed 4.4 L/100 km, and the total driving range with a full tank and hybrid drive is up to 1000 km. Using Eq. 13, CO2 emissions during the reference phase of HEV over its lifespan are estimated to be ap-proximately 470,969 MJ. Next, an analysis of emissions during the recycling of selected HEV components was conducted. This pertains to the fourth phase of LCA — recycling, disposal, and reuse [99]. This phase includes disassembly, separation, and purification of metals and other non-metallic materials. Metals are recycled, while other materials like plastics and glass are typically landfilled or incinerated. For Li-Ion batteries, the recycling process includes cooling the battery, cutting, and shredding, separating, and sorting shredded material, converting lithium to lithium carbonate (or lithium oxide), neutralizing electrolytes to stable compounds, and, if applicable, recovering cobalt from lithium cobalt oxide [105]. CO2 emissions in the fourth phase of LCA are estimated using Eq. 14 [101]: 𝐶𝐶𝑉𝑉𝑉𝑉 = 𝐶𝐶𝑅𝑅𝑅𝑅 = 𝐶𝐶𝑟𝑟𝑟𝑟,𝑓𝑓 + 𝐶𝐶𝑟𝑟𝑟𝑟,𝑒𝑒 𝐶𝐶𝑟𝑟𝑟𝑟,𝑓𝑓 = � �𝑚𝑚𝑥𝑥 𝐸𝐸𝑟𝑟𝑟𝑟,𝑥𝑥 ��𝜔𝜔𝑟𝑟𝑟𝑟,𝑥𝑥,𝑘𝑘 𝛼𝛼𝑘𝑘 �� 𝐶𝐶𝑟𝑟𝑟𝑟,𝑒𝑒 = � 𝑥𝑥 𝑘𝑘 𝐸𝐸𝑣𝑣𝑣𝑣 𝐸𝐸𝑟𝑟𝑟𝑟,𝑥𝑥 𝜔𝜔𝑟𝑟𝑟𝑟,𝑥𝑥,𝑒𝑒 + � �𝑚𝑚𝑥𝑥 �� 3600 3600 (14) 𝑥𝑥 where: CRE – CO2 emissions from vehicle recycling; Cre,f – CO2 emissions from fuel consumption during vehicle recycling; Cre,e – CO2 emissions from electricity consumption during vehicle recycling; Ere,x – energy consumption per unit of material x in the recycling phase (kJ/kg); x – recycled material; 𝜔𝜔𝑟𝑟𝑟𝑟,𝑥𝑥,𝑘𝑘 – share of fuel consumption in Ere,x; 𝜔𝜔𝑟𝑟𝑟𝑟,𝑥𝑥,𝑘𝑘 – share of electricity consumption in Ere,x; m – weight (kg); Evd – energy consumption during vehicle disassembly. GREET data implies an assumption, that CO2 emissions during the recycling of an HEV include approximately 630 kWh of electricity for disassembly, and for recycling the remaining components: 1114 kWh of electricity, 8.4 kWh of natural gas, and 10 kg of coal. Based on these assumptions and using Eq. 15, CO2 emissions in the final phase of the LCA for the reference HEV are estimated to be 6608 MJ. The total environmental impact in the LCA for the reference HEV was calculated with Eq. 15: 𝐸𝐸𝐸𝐸𝐸𝐸 = 𝐶𝐶𝑀𝑀 + 𝐶𝐶𝑉𝑉𝑉𝑉 + 𝐶𝐶𝑉𝑉𝑉𝑉 + 𝐶𝐶𝑅𝑅𝑅𝑅 (15) where: EII – EEI of the reference HEV in its entire life cycle; CM – CO2 emission from material extraction and processing; Cva – CO2 emission from vehicle components production; Cvu – CO2 emission from vehicle exploitation; CRE – CO2 emission from vehicle recycling. The estimated CO2 emissions over the life cycle of the analysed reference HEV are approximately 520,150 MJ. It was observed that the largest emissions occur during the vehicle's usage 478 Advances in Production Engineering & Management 19(4) 2024 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility phase, followed by component production, recycling, and the smallest amount during material extraction and processing. After assessing the reference HEV, an LCA of its prototypes was conducted under the assumptions of the model, i.e. using simplified modelling to reflect changes in LCA values based on changes in the parameters of HEV quality criteria, following the Pareto principle [73]. The prospective and simplified LCA of HEV prototypes was carried out using Eq. 5. The results are presented in Table 6. Alternative Ref. product Prototype 1 Prototype 2 Prototype 3 Prototype 4 Prototype 5 Prototype 6 Table 6 Prospective LCA of HEV prototypes EII [MJ] 520150 624180 728210 832240 936270 416120 312090 Ranking 3 4 5 6 7 2 1 Aggregated EII was obtained for the reference HEV and its prototypes over their life cycle. Vehicles were ranked, with Prototype 6 securing the top position, which anticipates its least negative total environmental impact. Next, the SRI for the reference HEV and its prototypes was obtained, with participation of a multidisciplinary team of four experts, including CSR specialists and the authors of the article. Initially, HEV – relevant social responsibility criteria were selected from those presented in Step 4.3 of our model. Ultimately, nine main criteria belonging to six areas indicated in ISO 26000 were chosen: (CC1) fair competition – assessment of the possibility of applying fair (including unfair) competition by using very distant or remarkably similar product solutions as another manufacturer; (CC2) promoting social responsibility in the value chain – assessment of the ap-plication of a solution that can shape social attitudes; (CC3) access to essential services – assessment of the product or prototype functionality in terms of selected usability criteria; (CC4) technology development and access – assessment of the advancement and accessibility for customers of selected technological features; (CC5) social investment – assessment of the degree of implementation of pro-social investments in terms of usability criteria of the product or its prototype; (CC6) community involvement – assessment of differences between the product and prototypes in terms of initiating pro-social behaviours for the common good; (CC7) wealth and income creation – assessment of differences in basic technological features of the product and prototypes that affect the increase in customer satisfaction level from owning a given product/prototype compared to others; (CC8) sustainable consumption – assessment of the environmental-consumption balance in the form of achieving satisfaction from the most sustainable product solution or its prototypes; (CC9) education and awareness – assessment of the possibility of providing ap-propriate product or prototype solutions as a result of customer education and awareness. Subsequently, the relevance of these criteria was assessed in terms of accordance to social responsibility standards. The highly relevant criteria (g1) were: fair competition (CC1), promoting social responsibility in the value chain (CC2), access to essential ser-vices (CC3), technology development and access (CC4), and sustainable consumption (CC8). The moderately relevant criteria (g2) were: community involvement (CC6), wealth and income creation (CC7), and social investments (CC5). The less important criterion (g3) was: education and awareness (CC9). Fixed weights were assigned to these criteria in the ratio 50:10:1 [55, 57]. Then, the reference HEV and its prototypes were evaluated for social responsibility compliance. The evaluations were conducted by a team of experts using a 0-1 scale, where scores equal to or above 0.7 indicated an acceptable level of compliance. The social responsibility compliance scores were then processed into binary values (0 - does not comply, 1 - complies). The results are presented in Table 7. Advances in Production Engineering & Management 19(4) 2024 479 Siwiec, Gawlik, Pacana Table 7 Social responsibility compliance of reference HEV and its prototypes Alternative Level of social responsibility compliance by the decision criteria (0-1) CC1 CC2 CC3 CC4 CC5 CC6 CC7 CC8 CC9 Ref. product 0.5 0.8 0.9 0.6 0.6 0.6 0.8 0.6 1.0 Prototype 1 0.6 0.7 0.8 0.8 0.6 0.7 0.5 0.5 0.9 Prototype 2 0.5 0.6 0.9 0.9 0.9 0.9 0.7 0.5 0.8 Prototype 3 0.7 0.5 0.9 0.8 0.9 0.7 0.5 0.5 0.7 Prototype 4 0.8 0.4 0.7 0.7 0.7 0.6 0.6 0.4 0.6 Prototype 5 0.5 0.9 0.6 0.7 0.6 0.8 0.9 0.8 0.5 Prototype 6 0.6 1.0 0.5 0.6 0.7 0.5 0.9 0.9 0.5 Alternative Fulfilment of social responsibility standards by the decision criteria (0 or 1) CC1 CC2 CC3 CC4 CC5 CC6 CC7 CC8 CC9 Ref. product 0 1 1 0 0 0 1 0 1 Prototype 1 0 1 1 1 0 1 0 0 1 Prototype 2 0 0 1 1 1 1 1 0 1 Prototype 3 1 0 1 1 1 1 0 0 1 Prototype 4 1 0 1 1 1 0 0 0 0 Prototype 5 0 1 0 1 0 1 1 1 0 Prototype 6 0 1 0 0 1 0 1 1 0 (CC1) fair competition; (CC2) promoting social responsibility in the value chain; (CC3) access to essential services; (CC4) technology development and access; (CC5) social investment; (CC6) community involvement; (CC7) wealth and income creation; (CC8) sustainable consumption; (CC9) education and awareness. After assessing social responsibility compliance, an aggregated SRI was deter-mined for the reference HEV and its prototypes with use of Eq. 6 and Eq. 7 (Table 8). The calculated SRI allowed to establish a ranking of the reference HEV and its prototypes in terms of social responsibility compliance. Prototype 3 secured the top position, with Prototype 5 closely following. The reference product performed the worst among the assessed models, though these results may vary depending on expert opinions. Finally, an aggregated QESR indicator was determined (model – stage 5). This in-volved combining the quality (AQI), environmental (EII), and social responsibility (SRI) indexes into a single QESR indicator. The three abovementioned indexes indices were normalized with respect to the reference HEV and its prototypes, using Eq. 8, Eq. 9, Eq. 10. Eq. 11, Eq. 12, Eq. 13 served for the estimation of the aggregated QESR indicator, which resulted in a ranking of the reference HEV and its prototypes. The ranking proves Prototype 3 being the most favourable and Prototype 6 the least favourable. For a verbal interpretation of the results, a further analysis was conducted (Stage 6). A verbal relative scale was used for this purpose, with the final model results and in-depth analysis presented in Table 9. Alternative Ref. product Prototype 1 Prototype 2 Prototype 3 Prototype 4 Prototype 5 Prototype 6 Alternative Ref. product Prototype 1 Prototype 2 Prototype 3 Prototype 4 Prototype 5 Prototype 6 480 Table 8 SRI for the reference HEV and its prototypes SRI 12.33 17.89 14.56 19.00 17.78 18.89 13.33 Ranking 7 3 5 1 4 2 6 Table 9 Aggregated QESR indicator for the reference HEV and its prototypes Normalized Normalized Normalized QESR Interpretation weighted AQI weighted EII weighted SRI 0.00 2.00 2.00 0.67 satisfactory 1.72 1.50 0.33 0.70 beneficial 2.33 1.00 1.33 0.61 satisfactory 1.62 0.50 0.00 0.82 distinctive 3.86 0.00 0.37 0.65 satisfactory 4.26 2.50 0.03 0.44 sufficient 7.00 3.00 1.70 0.03 bad Ranking 3 2 5 1 4 6 7 Advances in Production Engineering & Management 19(4) 2024 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility Prototype 3 was identified as the most suitable in terms of quality, environmental, and social responsibility aspects. It is then rational to guide accordingly the design of the reference HEV. Should Prototype 3 not be financially viable for the company, the ranking points at the next highest-ranked product, i.e. Prototype 1. A comprehensive comparison of the results obtained at each stage of model application is summarized in Table 10. It was observed that Prototype 3, identified as the most advantageous, ranked second in the quality index (AQI), first in social responsibility (SRI), and sixth in environmental impact (EII). The final development decisions were influenced by the as-signed weights to each aspect (quality, environment, social responsibility) in the ratios of 7:3:2 [55]). It was noted that quality and environmental impact had a greater influence on the final ranking, with a smaller contribution of social responsibility. This phenomenon is evident in the case of the reference product, which ranked third according to the QESR indicator. The in-depth analysis of the impact of model indexes on the final product ranking was verified through a sensitivity analysis presented in the Discussion section of the article. Alternative Ref. product Prototype 1 Prototype 2 Prototype 3 Prototype 4 Prototype 5 Prototype 6 5. Discussion Table 10 Comparison of model indexes and resulting prototype rankings AQI and prototype EII and prototype SRI and prototype Final QESR indicator ranking ranking ranking and prototype ranking 3.81 1 520150 3 2.00 7 0.67 3 3.64 3 624180 4 0.33 3 0.70 2 3.58 4 728210 5 1.33 5 0.61 5 3.65 2 832240 6 0.00 1 0.82 1 3.43 5 936270 7 0.37 4 0.65 4 3.39 6 416120 2 0.03 2 0.44 6 3.12 7 312090 1 1.70 6 0.03 7 The research aimed to develop a multicriteria decision-making model for predicting the improvement direction of current products based on methodically verified prototypes (alternative production solutions) through a multidimensional framework encompassing key sustainable development aspects: product quality (customer satisfaction), environmental impact throughout the product's life cycle, and compliance to social responsibility standards. These aspects, whether considered separately or in combination, have already been subjects of previous research [11, 12, 14, 15, 17]. The proposed approach integrates three respective indicators (AQI, EII, SRI) into a single Quality-Environmental-Social-Responsibility (QESR) indicator, providing a comprehensive assessment method. This integration represents the model's primary originality and its contribution to the field of management, sustainable development and production engineering, as corroborated by [4, 5, 9, 118], which responds to the ongoing challenges in sustainable product design. The developed QESR indicator aims to guide product development through personalized rankings of product prototypes, which remains a valuable approach for exploring new product opportunities or enhancing existing ones [106-109; 119-120]. The model's effectiveness was tested using HEV as a case study. The resulting prototype rankings aligned with the outcomes of each stage of the model, confirming the appropriateness of the chosen methodology. Consequently, a sensitivity analysis of the model was deemed necessary. This analysis aimed to verify the significance of the quality (AQI), environmental impact (EII), and social responsibility (SRI) indexes on the aggregated QESR indicator. The sensitivity analysis was conducted using machine learning in Statistica 13.3 software. The input variables (independent) were the AQI, EII, and SRI values obtained from the model test for the reference HEV and its prototypes. The sensitivity analysis was performed twice: a) for unweighted relativized values, and b) for weighted relativized values, to additionally verify the impact of aspect weights on the final QESR ranking. The sensitivity analysis was conducted using machine learning tools, specifically regression analysis, suitable for quantitative data. Random sampling was applied, with the following sample Advances in Production Engineering & Management 19(4) 2024 481 Siwiec, Gawlik, Pacana sizes: 70 % for training, 15 % for testing, and 15 % for validation [110, 111]. The initial value of the random generator was set to 1000. The search focused on identifying a Multilayer Perceptron (MLP) network with a minimum of 3 and a maximum of 10 hidden layers. Twenty networks were trained, retaining the five with the most favourable learning parameters each time. For processing the relativized (unweighted) model indexes in the neural network, the most optimal set of networks was generated, from which the MLP 3-10-1 network was selected. This network had three input neurons, ten hidden layer neurons, and one output neuron. In contrast, for processing the relativized weighted model indexes, the MLP 3-6-1 network was chosen, featuring three input neurons, six hidden layer neurons, and one output neuron. Based on the developed neural network models and the specified input and output data, a global sensitivity analysis was conducted. Global sensitivity analysis for the analysed model indicators for unweighted normalized indexes were: AQI=7.609, EII=24.641, SRI=8.999, and for weighted normalized indexes were: AQI=1.997, EII=8.7675, SRI=4.857. The interpretation of global sensitivity analysis results boils down to identifying input variables with values above 1, indicating significant influence on the output variable (including model quality) [112]. It was observed that in both cases, all analysed indicators AQI, EII, and SRI significantly impacted the aggregated QESR indicator. In the global sensitivity analysis for unweighted relative indicators, the pre-dominant influence on the final QESR indicator (including the final product ranking) was the EII indicator (24.641). Subsequently, the SRI indicator (8.999) had a significant but notably smaller impact, followed by the AQI indicator (7.609). Sensitivity analysis for weighted relative indicators revealed the impact of weights assigned to these indicators on the final ranking (including QESR), leading to approximate alignment of model indicator values. The conducted sensitivity analysis demonstrated that all ana-lysed indicators significantly influenced the final model outcome, confirming the validity and effectiveness of the developed model and research methodology. It was shown that weighting qualitative, environmental, and social aspects significantly affects the final model indicator (QESR), and consequently, the final ranking of products and their prototypes. Therefore, these weights should be thoughtfully assigned based on the needs of the model user, business development strategies, legal regulations, or market dynamics. The main limitation of the model is the lack of direct consideration of customer preferences in the decision-making process at the environmental impact assessment stage in the product lifecycle, as well as in the assessment of social responsibility compliance. Nevertheless, it is justified to conduct these assessments by a competent and qualified expert team [49, 52, 53]. Another significant limitation is the limited access to data or the lack of assurance of comparability of results obtained from LCA – which is a widely known and discussed issue of LCA methodology [113,114]. Despite this limitation we still decided to employ LCA in our model, as it is currently considered to be the most popular and most efficient method for estimating the environmental impact of products throughout their life cycle [115-117]. Another limitation is the potential for divergent interpretations of social responsibility (not always synonymous with CSR), which also concern the diversity of socially responsible business practices, leading to varying model outcomes depending on the country or region of application. Consequently, this limits the comparability of model results when applied in culturally diverse markets. Future research aims to consider incorporating customer feedback at the environmental impact analysis stage. Additionally, the model structure allows for further development with other indicators and sustainable development criteria. Addressing the model limitations, efforts will be made to establish assumptions enhancing the accuracy and reliability of environmental impact assessment. Further studies will also involve other products to ensure the universality of the developed model. 6. Conclusion In the era of dynamic customer expectations, including concerns about global warming, adapting products to market and societal needs is crucial. However, achieving sustainable product development remains challenging. Therefore, the aim of this re-search was to develop an MCDM model for predicting the direction of improving cur-rent products towards prototypes (alternative 482 Advances in Production Engineering & Management 19(4) 2024 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility production solutions) methodically verified in a multidimensional approach covering key aspects of sustainable development: quality, environmental impact throughout the life cycle, and social responsibility. The model was tested for a specific type of LPVs the HEVs. Initially, the AQI was determined, requiring the identification of the vehicle's main quality criteria: total mass, maximum engine power, maximum speed, battery range, battery charging time, vehicle colour, vehicle dimensions, equipment, fuel consumption, and drivetrain. These criteria were modified by proposing six alternative design solutions (prototypes). Through survey research, expectations from 116 customers were obtained and processed, resulting in the AQI. According to this index, the reference product and its prototypes were ranked, with Prototype 1 deemed the most favourable in terms of quality. Next, the EII throughout the life cycle was determined. This involved conducting an LCA "from cradle to grave" according to ISO 14040 and using data from the GREET v1.3.0.13991 software. LCA results were employed for the prospective environmental impact assessment of the reference HEV and its prototypes, resulting in the EII index, which formed the basis for ranking these products. Prototype 6 showed the least negative environmental impact. Subsequently, the SRI was determined. Selected social criteria from the ISO 26000 set were: fair competition, promoting social responsibility in the value chain, access to essential services, technology development and access, social investment, community involvement, wealth and income creation, sustainable consumption, education, and awareness. These criteria were assessed on a Likert scale for the reference HEV and its prototypes for relevance and social responsibility compliance. SRI resulted in a ranking, with Prototype 3 on top. Finally, AQI, EII and SRI were aggregated into a single QESR indicator, considering their relativization and weighting. The indices were interpreted qualitatively and quantitatively on a relative scale. Ultimately, Prototype 2 was selected as possibly the most favourable in terms of quality, environment, and social responsibility aspects. In line with the model concept, it provides a good basis for determining the development direction of the reference HEV. Thus, the model test confirmed its effectiveness in prospectively deter-mining product development directions in accordance with the principles of sustainable development. The model is dedicated to managerial decision-making in product design and production management. Therefore, it can support individuals, companies, and public entities in sustainable product development decisions, aiming to achieve socially re-sponsible production engineering that also ensures high product quality and environ-mental friendliness. Acknowledgement The publication presents the result of research financed from the subsidy granted to the Krakow University of Economics within the Support for Publishing Activities 2024 (Wsparcie Aktywności Publikacyjnej 2024) programme. References [1] [2] [3] [4] [5] [6] [7] Wang, S., Su, D. (2022). 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A combined genetic algorithm and A* search algorithm for the electric vehicle routing problem with time windows, Advances in Production Engineering & Management, Vol. 18, No. 4, 403-416, doi: 10.14743/apem2023.4.481. 488 Advances in Production Engineering & Management 19(4) 2024 Advances in Production Engineering & Management ISSN 1854-6250 Volume 19 | Number 4 | December 2024 | pp 489–511 Journal home: apem-journal.org https://doi.org/10.14743/apem2024.4.520 Original scientific paper An algorithmic review of the technological progress and milestones in resource-constrained project planning Pourhejazy, P.a,*, Ying, K.-C.b,*, Cheng, C.-Y.c aDepartment of Industrial Engineering, UiT – The Arctic University of Norway, Narvik, Norway of Industrial Engineering and Management, National Taipei University of Technology, Taipei, Taiwan cTaiwan Semiconductor Manufacturing Company (TSMC) Limited, Hsinchu City, Taiwan bDepartment ABSTRACT ARTICLE INFO Engineering, procurement, and construction projects are time-intensive and subject to resource constraints. Modern project planning software requires optimization algorithms to schedule tasks while considering resource availability. A comprehensive review of the optimization algorithms used in project planning has not yet been conducted. This study seeks to bridge the gap through an algorithmic review of the Resource-constrained Project Scheduling Problems (RCPSPs) literature and investigates the following research questions: What are the milestones on the main development trajectory of optimization algorithms for solving RCPSPs? How might this influence future advancements in the field? To answer these questions, the Main Path Analysis (MPA) method is employed to review the development trajectory and milestones from over 1100 project scheduling articles published between 1980 and 2024. Cluster Analysis (CA) complements the investigations by identifying the prevalent research themes, mathematical features, and solution algorithms. Recommendations for future research directions, supported by the systematic review, conclude the study. This review provides a reference for project management researchers focused on industrial applications of project scheduling problems. Keywords: Project management; Task scheduling; Resource constraint; Multi-objective optimization; Evolutionary computation; Swarm intelligence; Metaheuristics; Main path analysis; Cluster analysis *Corresponding authors: pourya.pourhejazy@uit.no (Pourhejazy, P.) kcying@ntut.edu.tw (Ying, K.-C.) Article history: Received 27 October 2024 Revised 6 December 2024 Accepted 17 December 2024 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 Modern project planning must account for the rapid changes in the resources [1]. Traditionally, project managers use planning tools based on the Critical Path Method (CPM) and the Program Evaluation and Review Technique (PERT) to schedule tasks and predict project progress, milestones, and completion times. These methods are predominantly based on operative and predictive models [2]; they overlook resource availability, requiring schedules to be adjusted each time a task is delayed due to the lack of resources. As the scope and complexity of projects increase, such tools, although powerful, cannot provide dependable solutions that are both optimal and robust. Mathematical models and solution algorithms are required for optimal project planning, taking into account various practical constraints. The Resource-Constrained Project Scheduling 489 Pourhejazy, Ying, Cheng Problem (RCPSP) is an advanced planning alternative that optimizes resource allocation while sequencing project tasks. The primary investigation shows that research on project scheduling has grown steadily since 1995, reaching a peak of 107 published articles in 2021. The early works focused on developing priority rules for resource‐constrained project scheduling [3]. More recent studies evolved towards developing advanced heuristics and metaheuristics. Among the seminal works, Debels et al. [4] developed a hybrid Scatter Search/Electromagnetism algorithm for project scheduling. Kolisch and Hartmann [5] contributed an experimental analysis of heuristic algorithms for resource-constrained project scheduling. Van Peteghem and Vanhoucke [6] developed a Genetic Algorithm for solving preemptive and non-preemptive multi-mode RCPSPs. Most recently, several constructive heuristic algorithms were developed by Nekoueian et al. [7] for selecting and scheduling alternative subgraphs in resource-constrained projects. Melchiors et al. [8] conducted an experimental analysis comparing the performance of priority rules for dynamic stochastic RCPSPs. Servranckx et al. [9] proposed a Genetic Algorithm integrated with a Boolean satisfiability solver to solve RCPSP with alternative subgraphs. Identifying the main development trajectory of RCPSP sheds light on scientific progress and milestones in project planning. There are several reviews of the literature on project scheduling, three of which are recent and relevant. Gomez et al. [10] reviewed multi-project scheduling problems as one of the several variants of RCPSP. Aghileh et al. [11] contributed a more focused literature review focusing on multi-project scheduling problems under uncertainty and resource flexibility. These articles investigated specific variants of RCPSP. The most relevant study, Hartmann et al. [12] surveyed the prominent extensions of RCPSP. They considered a theoretical lens, focusing solely on mathematical features; solution methods for solving RCPSP were not investigated. Moreover, their review scope covered only articles published between 2010 and 2020. Most importantly, the existing surveys are based on a traditional literature reviews, i.e. manual reading of articles, which is subjective and cannot trigger big-picture thinking. To the authors’ best knowledge, the present study is the first algorithmic review (see [13]) of the project planning literature using mathematical methods. Main Path Analysis (MPA) and Cluster Analysis (CA) are used to analyze the literature published between 1980 and 2024. The objective is to explore the following research questions: What are the milestones on the development trajectory of RCPSP solution algorithms? How might this influence future advances in the field? This article continues in three more sections. The research methods are first described in Section 2. MPA results are presented in Section 3, followed by discussions on the outcomes of CA and keyword analysis. This research concludes in Section 4, where directions for future studies are suggested. 2. Research framework The Web of Science (WoS) database serves as the data collection source in this study. WoS comprises six index databases, namely Emerging Sources Citation Index (ESCI), Science Citation Index Expanded (SCIE), Social Sciences Citation Index (SSCI), Arts & Humanities Citation Index (A&HCI), Book Citation Index (BCI), and Conference Proceedings Citation Index (CPCI). Compared to other databases such as Google Scholar and Scopus, WoS strictly controls the quality of its collections, and only includes peer-reviewed documents of high quality. Step 1. Data collection The keyword TS = (Resource-Constrained Project Scheduling) was considered the primary term for the search. "AND" and "*" operators were used for keyword searches to reduce the chances of missing relevant documents: TS = (Resource-Constrained) AND TS = (project*) AND TS = (scheduling*). The search was conducted on April 25, 2024, covering the period FPY = (19802023). Initial investigations showed that 1,264 documents fall within the defined research scope considering the articles’ titles, abstracts, and keywords. The manual screening was then conducted to remove irrelevant records from the analysis; 1,189 documents remained in the database. Next, 32 retrospective articles were excluded to ensure their high citation count would not 490 Advances in Production Engineering & Management 19(4) 2024 An algorithmic review of the technological progress and milestones in resource-constrained project planning influence the path analysis procedure. Finally, the main path analysis software, MainPath 480, identified 42 isolated documents that neither cited other articles nor were cited by others; these were also removed from the database. A total of 1,130 documents were considered for further investigations. The accuracy index Precision in Eq. 1, and the Digital Object Identifier percentage DOI in Eq. 2 were used to check whether the database is representative of the entire literature; values greater than 0.7 are considered a green flag for MPA and CA analysis [14, 15]. The former index compares the number of articles before and after the removal of isolated points. In this study, the numbers of articles before and after excluding isolated points were 1,174 and 1,130, respectively. The search accuracy was 0.96, which is pretty high. Additionally, a high DOI percentage confirms the representativeness of the database. The total citation count of the topic is 43,550 while the DOI Total is 32,301 times, accounting for 0.74, which is acceptable and indicates that the database can be used for further analysis. Precision = Network Size × 100 % Number of Articles in the Original Database DOI ratio = DOI Total × 100 % Citation Record Step 2. Data processing using MPA, CA, and keyword analysis (1) (2) The database must be converted into a citation network to establish the basis for data processing. This network categorizes documents into source (where knowledge dissemination begins), intermediate (where knowledge is transferred from one node to another), or sink (where knowledge dissemination ends). The citation relationships within the network are represented by directed arrows, indicating knowledge diffusion. The analysis continues by calculating the weights of the arrows, taking into account all possible citation chains from source to sink. MPA uses these weights to identify the backbone of the citation network. Search Path Count (SPC; from all source nodes to all sink nodes of the network), Search Path Link Count (SPLC; all the ancestors of a tail node for a specific link), or Search Path Node Pair (SPNP; all the ancestors and descendants of a specific link) methods can be used to calculate and assign weights to the network links. SPLC best represents the knowledge dissemination process in academic literature [16] and is therefore used in the analysis. The weighted network forms the basis for identifying the main path and the key development branches. Using the weighted network as input, the MPA function of MainPath480 considers all possible citation chains and selects the one with the largest overall SPLC as the main path. The Global Main Path setting is used to identify the major citation chain over the entire literature period, i.e. from sink to source nodes. The Key-route Main Path is further used to identify the main path while including top-cited references; this study uses Key-route 10, which ensures that the top ten contributions are included in the analysis. The same database is also used for the data-driven categorization of articles using the CA [17] function of MainPath480. A three-step procedure organizes articles based on their similarities (the shortest path between all the node pairs, calculating edge credit using Eq. 3, and removing the edge(s) with the highest score to isolate groups of articles). Additionally, similar terms are merged to identify the cluster containing the most frequently used words. Edge_Credit = (1 + � Incoming Edge Credit) × Score of Destination Score of Start (3) Step 3. Literature content analysis The literature content analysis will explore the advances in solution algorithms for solving RCPSPs. A three-field notation, 𝛼𝛼|𝛽𝛽|𝛾𝛾 is used to characterize the reviewed RCPSPs; the problem characteristics are treated as an influencing factor in the advances in project scheduling algorithms. In the notation system, 𝛼𝛼 specifies the process type; 𝛽𝛽 identifies the practical features Advances in Production Engineering & Management 19(4) 2024 491 Pourhejazy, Ying, Cheng and characteristics considered in the studied RCPSP; and 𝛾𝛾 represents the objective function. Tables 1-3 define the notations used in the three sections, respectively. Notation PS MPS 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 𝛼𝛼1 = 0 𝛼𝛼1 = 1 𝛼𝛼1 =m 𝛼𝛼2 = 0 𝛼𝛼2 = 1 𝛼𝛼2 = 𝑇𝑇 𝛼𝛼2 = 1𝑇𝑇 𝛼𝛼2 = 𝜐𝜐 𝛼𝛼3 = 0 𝛼𝛼3 = 𝜐𝜐𝜐𝜐 𝛼𝛼3 = 𝑎𝑎� 𝛼𝛼3 = 𝜐𝜐𝑎𝑎� 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 − 𝑀𝑀𝑀𝑀 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 − 𝑀𝑀𝑀𝑀𝑀𝑀 − 𝐷𝐷𝐷𝐷 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 − 𝑃𝑃𝑃𝑃 𝑀𝑀𝑀𝑀 − 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 − 𝐶𝐶𝐶𝐶 𝑀𝑀 − 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 𝑀𝑀𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 𝑀𝑀𝑀𝑀 − 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 𝑀𝑀𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 𝐶𝐶𝐶𝐶𝐶𝐶𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 Notation 𝑝𝑝𝑗𝑗 = 1 𝑝𝑝𝑗𝑗 = 𝑠𝑠𝑠𝑠𝑠𝑠 𝑑𝑑 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎, 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖, 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜, 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝛽𝛽1 𝛽𝛽1 𝛽𝛽1 𝛽𝛽2 𝛽𝛽2 =0 = 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 − 𝑟𝑟𝑟𝑟𝑟𝑟 =0 = 𝑐𝑐𝑐𝑐𝑐𝑐 𝛽𝛽2 = 𝑚𝑚𝑚𝑚𝑚𝑚 𝛽𝛽2 = 𝑔𝑔𝑔𝑔𝑔𝑔 𝛽𝛽2 = 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 492 Table 1 Process type-related notations, 𝛼𝛼 Definition General project scheduling. Multi-mode project scheduling. General project scheduling considering 𝑚𝑚 resources, 𝜎𝜎 units of available resources, each activity requiring at most 𝜌𝜌 units of the resources. Multi-mode project scheduling with 𝑚𝑚 renewable and 𝜇𝜇 non-renewable resources; 𝜎𝜎 and 𝜏𝜏 units of renewable and non-renewable resources with each activity requiring at most 𝜌𝜌 and 𝜔𝜔 units of the renewable and non-renewable resources, respectively. No resource types are considered. One resource type is considered. The number of resource types is equal to m. Absence of any resource type specification. Renewable resources; availability is specified for a time unit. Non-renewable resources, the availability of which is specified for the entire project horizon T. Both renewable and non-renewable resources are considered. Partially (non-)renewable resources the availability of which is renewed in specific periods. (Partially) Renewable resources available in constant amounts. (Partially) Renewable resources available in variable amounts. Stochastic resource availability with constant value over time. Stochastic resource availability with variable values over time. RCPSP with Multiple Routes. Integrated RCPSP and material ordering with discounted cash flows. RCPSP with a model-endogenous decision on the project structure. Multi-Skill Resource-Constrained Project Scheduling Problem. Multi-mode Integrated RCPSP with Contractor Selection. Multi-objective Multi-mode RCPSP. Multi-mode, Multi-project RCPSP. Multi-skill Multi-modal RCPSP. Resource-constrained multi-project scheduling problem. Resource-constrained project scheduling with critical chain. Table 2 Process characteristics-related notations, 𝛽𝛽 Definition All processing times are equal to one. Stochastic processing times. Deadline for project duration. Precedence constraints between activities. Precedence relations between activities are specified. General temporal constraints, given the minimum and maximum start-start time lag between activities. No preemption is allowed. Preemptions of the preempt-resume type are allowed. Preemptions of the preempt-repeat type are allowed. No precedence constraints. Strict finish-start precedence constraints with zero time lag, as used in the basic PERT/CPM model. Precedence diagramming constraints of the types start-start,finish-start, start-finish, and finish-finish with minimal time lags. Generalized precedence relations of the types start-start, finish-start, start-finish, and finish-finish with both minimal and maximal time lags. The activity network is of probabilistic type where the evolution of the corresponding project is not determined in advance. Advances in Production Engineering & Management 19(4) 2024 An algorithmic review of the technological progress and milestones in resource-constrained project planning 𝛽𝛽3 = 0 𝛽𝛽3 = 𝜌𝜌𝑗𝑗 𝛽𝛽4 = 0 𝛽𝛽4 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝛽𝛽4 = (𝑑𝑑𝑗𝑗 = 𝑑𝑑) 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 𝛽𝛽5 = 0 𝛽𝛽5 = 𝛿𝛿𝑗𝑗 𝛽𝛽5 = 𝛿𝛿𝑛𝑛 𝛽𝛽6 = 0 𝛽𝛽6 = 𝜐𝜐𝜐𝜐 𝛽𝛽6 = 𝑟𝑟̃ 𝛽𝛽6 = 𝜐𝜐𝑟𝑟̃ 𝛽𝛽6 = 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝛽𝛽6 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝛽𝛽6 = 𝑖𝑖𝑖𝑖𝑖𝑖 𝛽𝛽7 = 0 𝛽𝛽7 = 𝑚𝑚𝑚𝑚 𝛽𝛽7 = 𝑖𝑖𝑖𝑖 𝛽𝛽8 = 0 𝛽𝛽8 = 𝑐𝑐𝑗𝑗 𝛽𝛽8 = 𝑐𝑐̃𝑗𝑗 𝛽𝛽8 = 𝑐𝑐𝑗𝑗+ 𝛽𝛽8 = 𝑝𝑝𝑝𝑝𝑝𝑝 𝛽𝛽8 = 𝑠𝑠𝑠𝑠ℎ𝑒𝑒𝑒𝑒 𝛽𝛽9 = 0 𝛽𝛽9 = 𝑠𝑠𝑗𝑗𝑗𝑗 Table 2 (Continuation) All ready times are zero. Ready times differ per activity. Activities have arbitrary integer durations. Activities have arbitrary continuous durations. All activities have a duration equal to d units. The activity durations are stochastic. No deadlines are assumed in the system. Deadlines are imposed on activities. A project deadline is imposed. Constant discrete resource requirements. Variable discrete resource requirements. Stochastic constant discrete resource requirements. Stochastic discrete variable resource requirements. The requirements are a discrete function of the activity duration. The requirements are a continuous function of the activity duration. The requirements are expressed as an intensity or rate function. Activities must be performed in a single execution mode. Activities have multiple prespecified execution modes. Activities are subject to mode identity constraints. No cash flows are specified in the project scheduling problem. Activities have an arbitrary cash flow. Cash flows are stochastic. Activities have an associated positive cash flow. Periodic cash flows are specified for the project. Both the amount and the timing of the cash flows are determined. No change-over (transportation) times. Sequence-dependent change-over times. � 𝑐𝑐𝑗𝑗𝐹𝐹 𝛽𝛽 𝐶𝐶𝑗𝑗 Table 3 Objective function-related notations, 𝛾𝛾 Definition Net present value. � 𝑐𝑐𝑘𝑘 𝑚𝑚𝑚𝑚𝑚𝑚 𝑟𝑟𝑘𝑘 (𝑆𝑆, 𝑡𝑡) Resource investment. Notation � 𝑐𝑐𝑘𝑘 𝑓𝑓(𝑟𝑟𝑘𝑘 (𝑆𝑆, 𝑡𝑡)) 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 = 𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 = 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 = 𝐹𝐹̄ = 𝐿𝐿𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑇𝑇𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒/𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑛𝑛 𝑇𝑇 𝛾𝛾 = � 𝑠𝑠𝑠𝑠. 𝑑𝑑𝑑𝑑𝑑𝑑. 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 𝛾𝛾 = 𝑎𝑎𝑎𝑎 = 𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝑛𝑛𝑛𝑛𝑛𝑛 = 𝐸𝐸[⋅] = 𝑐𝑐𝑐𝑐𝑐𝑐 = 𝑐𝑐𝑐𝑐 = 𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 𝐸𝐸𝐸𝐸𝐸𝐸 = 𝐸𝐸𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 = 𝐶𝐶𝐶𝐶 = 𝑇𝑇𝑇𝑇 = 𝑇𝑇𝑇𝑇 Resource leveling. The performance measure is any early completion (regular) measure. The performance measure is any free completion (non-regular) measure. Minimize the project makespan. Minimize the average flow time across all sub-projects or activities. Minimize the project lateness. Minimize the project tardiness. Minimize the weighted earliness-tardiness of the project. Minimize the number of tardy activities. The sum of squared deviations of the resource requirements from the average. Minimize the resource availabilities to meet the project deadline. Minimize the resource availability costs. Determine the complete time/cost trade-off curve. Maximize the net present value of the project. Optimize the expected value of a performance measure. Determines the cumulative density function of the project realization date. Determines the criticality index of an activity or a path. Determines the most critical path(s) or activities based on the criticality index. Different objectives are weighted or combined. Multi-criteria functions. Minimizes the expected project duration. Expected makespan. Minimize the carbon footprints. Minimize the Total cost. Minimize the Total Duration. Advances in Production Engineering & Management 19(4) 2024 493 Pourhejazy, Ying, Cheng Step 4. Dissemination The outputs of MainPath480 consist solely of character results. The results were further processed using Pajek 5.18 (http://mrvar.fdv.uni-lj.si/pajek/) and VOSviewer 1.6.18 [18] for dissemination. A satellite-like view, which illustrated the major knowledge diffusion paths is used to visualize the findings. 3. Results and discussions 3.1 Main development trajectory of solution algorithms A total of 27 articles formed the main development trajectory of RCPSPs. The contributions predominantly fall under at least one of the following categories: new solution algorithms or optimization models, new datasets, and benchmarking or organizing the available methods. The trajectory is shown in Fig. 1, which is followed by an elaboration on the scientific progress and milestones. RahmanSCVE2022 AsadujjamanRCR2022 AsadujjamanRCR2021b AsadujjamanRCR2021a ChakraborttyRR2020 BirjandiM2019 TaoD2018 SonmezG2016 Duc-hoctranCC2016 ChengDW2014 Zamani2013a CoelhoV2011 VanpeteghemV2010 VanhouckeD2008 KolischH2006 VallsBQ2005 VallsBQ2004 Hartmann2002 HartmannK2000 Hartmann1998 BruckerKST1998 KolischS1997 KolischD1996 KolischSD1995 SampsonW1993 BellH1991 BellP1990 Fig. 1 The main development trajectory of RCPSPs As the starting point of the main development trajectory, Bell and Park [19] studied 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and developed the A-STAR search method to solve it, which operates by identifying active nodes that violate resource restrictions and prioritizing them to reduce resource conflicts. Bell and Han [20] proposed a new heuristic to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . The algorithm first generates an initial solution and uses a procedure inspired by the Hill Climbing method to improve the solution. They used Patterson’s dataset to compare their algorithm with six traditional heuristic rules. Sampson and Weiss [21] developed several local search techniques to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and used Patterson's 110 datasets to test their performance, comparing it with the as-is situation in a hypothetical problem. 494 Advances in Production Engineering & Management 19(4) 2024 An algorithmic review of the technological progress and milestones in resource-constrained project planning Kolisch et al. [22] developed a new dataset for the problems of 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡, and a multi-objective variant of the two. Experimental analysis showed that some of the smallscale instances from their test bank can be solved in polynomial time under certain circumstances. Kolisch and Drexl [23] developed an Adaptive Search Procedure with new sorting rules and random search techniques for 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They used the 308 instances of Geninstances to show that the algorithm can effectively limit the solution space and compared it with four other heuristics coded using different programming languages. Kolisch and Sprecher [24] referred to the ProGen system to develop the new database, Project Scheduling Problem Library (PSPLIB) for RCPSPs. Their platform generated instances of different sizes for minimizing the overall project completion time and considers the number of activities, single-mode and multi-mode activity execution modes, activity duration, and resource constraints. Brucker et al. [25] developed a new Branch and Bound algorithm for solving 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝛽𝛽6 = 𝜊𝜊 , 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . Kolisch’s PSPLIB test bank was used to test the algorithm comparing it with the best solutions found by Demeulemeester and Herroelen [26]. Hartmann [27] developed a Competitive Genetic Algorithm for 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and used the PSPLIB database to compare its performance with other variants of the Genetic Algorithm. Hartmann and Kolisch [28] compared the Genetic Algorithm, Tabu Search, and Simulated Annealing for 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and the PSPLIB dataset. They analyzed the impact of different sorting rules, computational mechanisms, problem size, and resource limitations on algorithm performance. Hartmann [29] introduced the self-adapting Genetic Algorithm to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and used the PSPLIB database to compare its performance with Simulated Annealing, Tabu Search, and several variants of the Genetic Algorithm. Valls et al. [30] proposed a Four-Phase-Based procedure that uses the Convex Search Algorithm to generate the initial solution and the Homogeneous Interval Algorithm to improve the initial solution. The algorithm was compared with state-of-the-art heuristics using randomly generated instances for solving 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . Valls et al. [31] proposed a heuristic with several justification techniques for solving 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They used the ProGen test bank to compare their algorithm with 22 different heuristics. Kolisch and Hartmann [5] used the PSPLIB test bank to evaluate many of the algorithms commonly used to solve RCPSPs and analyzed their characteristics to speculate on the reasons for their performance. Vanhoucke and Debels [32] explored the impact of practical characteristics, such as activity duration, task splitting, and fast-tracking on the total lead time and improved the Branch and Bound method to solve RCPSPs. Van Peteghem and Vanhoucke [6] proposed the bi-population Genetic Algorithm to address 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝛽𝛽1 = 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 − 𝑟𝑟𝑟𝑟𝑟𝑟|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They used the PSPLIB database to evaluate the solution algorithm’s performance with and without preemption. Coelho and Vanhoucke [33] introduced the AND-OR network for the project structure of 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 , 𝛼𝛼2 = 1𝑇𝑇�𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and compared hybrid algorithms based on Tabu Search and Non-dominated Sorting Genetic Algorithms (NSGA) -I and -II using the PSPLIB database. Zamani [34] proposed a Magnet-Based Genetic Algorithm to solve 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 , 𝛼𝛼2 = 1𝑇𝑇�𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and used the PSPLIB database to compare their algorithm with baseline Genetic Algorithms. Cheng et al. [35] proposed the Fuzzy Clustering Chaotic-based Differential Evolution to minimize the project duration in 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and used a case study from the construction sector to demonstrate the practical implications of implementing their optimization method. Tran et al. [36] developed a new hybrid solution method based on the Artificial Bee Colony and Differential Evolution algorithms to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They used PSPLIB as a benchmark set to compare their algorithm with improved versions of the Genetic Algorithm, Particle Swarm Optimization, Artificial Bee Colony and Differential Evolution algorithms. Sonmez and Gürel [37] developed the Harmony Search Algorithm to solve 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and used PSPLIB to evaluate its performance against two improved Genetic Algorithms, as well as Particle Swarm and Ant Colony Optimization algorithms. Tao and Dong [38] studied the problem of 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 and developed an improved hybrid method based on the Tabu Search Advances in Production Engineering & Management 19(4) 2024 495 Pourhejazy, Ying, Cheng and NSGA-II to solve it. They used the PSPLIB to compare the solution algorithm’s performance with two basic versions of NSGA-II. Birjandi and Mousavi [39] proposed a Cluster-based Tabu Search integrated with the Particle Swarm Optimization algorithm to solve 𝑀𝑀𝑀𝑀𝑀𝑀 − 𝑀𝑀𝑅𝑅𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐. The new algorithm was evaluated using random test instances and compared with basic versions of Particle Swarm Optimization and Genetic Algorithms. Chakrabortty et al. [40] developed Variable Neighborhood Search-based Local Search Heuristic algorithms to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 , 𝛽𝛽6 =𝜊𝜊 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 , 𝛽𝛽6 = 𝜐𝜐𝜐𝜐�𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They considered six different priority rules and analyzed the algorithms’ performance using random test instances in dynamic environments. Asadujjaman et al. [41] developed the Immune Genetic Algorithm for the problem of 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽5 = 𝛿𝛿𝑛𝑛 |𝑛𝑛𝑛𝑛𝑛𝑛 and benchmarked its performance against the Lagrangian relaxationbased forward-backward improvement heuristic and the Scatter Search using the database from [42]. Asadujjaman et al. [43] proposed 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 − 𝑀𝑀𝑀𝑀𝑀𝑀 − 𝐷𝐷𝐷𝐷�𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽5 = 𝛿𝛿𝑛𝑛 |𝑛𝑛𝑛𝑛𝑛𝑛, 𝑝𝑝𝑝𝑝, which integrated an RCPSP with a material ordering problem. The author used the Immune Genetic Algorithm to solve the problem considering random test instances and comparing the results with those of the basic Genetic and Immune algorithms. Asadujjaman et al. [44] proposed a multioperator version of the Immune Genetic Algorithm to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐|𝑛𝑛𝑛𝑛𝑛𝑛. They used 17,280 different instances from the database of Vanhoucke [42] to evaluate and compare the algorithm’s performance against the Branch & Cut algorithm as the baseline. The last study on the main development trajectory, Rahman et al. [45], proposed the Genetic Algorithm-based Memetic Algorithm to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝑇𝑇𝑇𝑇, 𝐶𝐶𝐶𝐶, considering Carbon Footprints as one of the optimization objectives. They developed a new test set to compare the performance of their algorithm with the basic Genetic and Memetic algorithms, as well as the basic and enhanced versions of NSGA-II. Overall, early studies developed exhaustive solution methods and decision trees suitable for solving small-scale problems with low computational complexity. Studies evolved after 2006, incorporating practical constraints to bridge the gap between scheduling theory and practice. The precedence condition is a prime example. The optimization models and algorithms shifted from single-objective to multi-objective optimization after 2016. Initial works focused on minimizing project completion time, but later studies considered optimization objectives such as Resource Utilization Rate, total project cost, net present value, and environmental factors. 3.2 Key branches in the development of solution methods Different values for the key-route parameter, i.e. 5, 10, 15, 20, 25, 30, 35, 40, and 45, are considered to find the most reasonable setting for the literature analysis. The key-route value of 30 is deemed suitable, resulting in a total of 51 articles: 2 sources, 2 sinks, and 47 intermediate nodes, including the articles on the main path. The key branches are shown in Fig. 2, followed by a review of the articles that emerged from the main path. The first source node, Patterson et al. [46], proposed a Backtracking Algorithm to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛼𝛼2 = 1, 𝛼𝛼2 = 𝑇𝑇|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and confirmed its efficiency through numerical experiments while considering different problem characteristics. The second source, Bell and Park [19], is present on the main development path; this study was later cited by Bell and Han [20], and was followed by Sampson and Weiss [21], both of which are main path articles. Sprecher et al. [47] explored the active, semi-active, and non-delay schedules in the context of RCPSPs. They used small illustrative examples to explain the applicability and implications of their method. This article was later cited by Kolisch and Drexl [23], which is considered a main path article. Kolisch and Drexl [48] explored 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛼𝛼2 = 1, 𝛼𝛼2 = 𝑇𝑇|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and proposed a new local search technique to find feasible solutions as well as a neighborhood search method to improve it. The authors used the test bank generated by ProGen to compare results with two general non-preemptive algorithms developed by Drexl and Gruenewald [49]. 496 Advances in Production Engineering & Management 19(4) 2024 An algorithmic review of the technological progress and milestones in resource-constrained project planning 2. 3. Analyze and compare existing methods for solving RCPSP. Use heuristic algorithms to solve (mostly Makespan). BellP1990 DemeulemeesterH1992 BellH1991 KolischSD1995 SampsonW1993 Kolisch1996 SprecherKD1995 BruckerKST1998 KolischS1997 KolischD1996 Schirmer2000 Hartmann1998 KolischD1997 Hartmann2002 HartmannK2000 VallsBQ2004 MerkleMS2002 VallsBQ2005 PalpantAM2004 KolischH2006 DebelsDLV2006 VanhouckeD2008 VallsBQ2008 DeblaereDH2011a VanpeteghemV2010 DeblaereDH2011b CoelhoV2011 HuWPWLD2015 Zamani2013c ZhengWZ2017 KellenbrinkH2015 ChengDW2014 MyszkowskiOLS2018 TaoD2017 Duc-hoctranCC2016 MyszkowskiLNS2019 TaoD2018 SonmezG2016 LaszczykM2019b BirjandiM2019 Nemati-lafmejaniDN2019 ChakraborttyRR2020 ChaleshtartiSKFP2020 AsadujjamanRCR2021a YuanYLG2021 AsadujjamanRCR2021b ChuLGCPC2023 AsadujjamanRCR2022 YuraszeckMCCR2023 RahmanSCVE2022 2. PattersonTSW1990 Minimize project duration time. 1. Green environmental problem. Net present value problem 1. Multi-mode resource constraint project scheduling problem. 2. Multi-skill resource restriction project scheduling problem. Fig. 2 The key development branches from the main path The middle path constitutes many references from the main path, i.e. Kolisch et al. [22], Kolisch and Sprecher [24], Hartmann [27], and Hartmann and Kolisch [28]. Demeulemeester and Herroelen [50] developed a new Branch-and-Bound method suitable for addressing PERT/CPM problems with preconditions and solving 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽1 =𝜊𝜊 |𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 ; they used Patterson's test bank to evaluate its performance, comparing it with the Branch-and-Bound method developed by Stinson et al. [51]. Kolisch [52] investigated the limitations of the serial and parallel scheduling methods; they put forward new strategies that were tested using the PSPLIB databases in comparison to well-known priority rules, including the most total successors, latest start time, latest finish time, minimum slack, and the greatest rank position weight. Merkle et al. [53] developed an Ant Colony Optimization algorithm to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . This algorithm was tested on the PSPLIB instances and compared with the lower bounds using a critical path heuristic. Palpant et al. [54] developed the neighborhood search algorithm with exact resolution of sub-problems to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and considered Patterson’s 110 easy instances, along with some other datasets, to evaluate its performance by comparing the results with the best-known solutions at that time. Debels et al. [4] introduced the hybrid Scatter Advances in Production Engineering & Management 19(4) 2024 497 Pourhejazy, Ying, Cheng Search Electromagnetism algorithm to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and used PSPLIB to showcase its superiority over self-adaptive and robust Genetic Algorithms, Tabu Search, and Simulated Annealing. Valls et al. [55] proposed a hybrid Genetic Algorithm to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They used ProGen's instances and performed extensive comparisons with several versions of the Genetic Algorithm, Tabu Search, and solution methods based on network decomposition. After the studies of Van Peteghem and Vanhoucke [6], Coelho and Vanhoucke [33], and Zamani [34], which are considered on the main path, Kellenbrink and Helber [56] explored the problem of model-endogenous decisions on the project structure in RCPSPs, and developed a novel Genetic Algorithm with a module that adjusts the activity structure of inter-project activities to improve the solutions; the authors extended the ProGen generator and compared the results with those of CPLEX. Tao and Dong [57] introduced a new AND-OR network, proposed a new mathematical formulation for 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 , and adjusted the Simulated Annealing algorithm to solve the problem. They designed a new instance set to evaluate the algorithm’s performance, comparing it with an exact solver and several variants of the same algorithm. These studies also considered stochastic activity restrictions. The study of Zamani [34] was continued along the main path by Cheng et al. [35], Tran et al. [36], and Sonmez and Gürel [37]. The next seven articles were reviewed in the main path section, namely: Tao and Dong [38], Birjandi and Mousavi [39], Chakrabortty et al. [40], Asadujjaman et al. [41], Asadujjaman et al. [43], Asadujjaman et al. [44], and Rahman et al. [45]. These articles focused on green operational factors and multi-skill RCPSPs. The left path in Fig. 2 includes Brucker et al. [25], Hartmann [29], Valls et al. [30], Valls et al. [31], Kolisch and Hartmann [5], and Vanhoucke and Debels [32], all of which are part of the main path. Schirmer [58] incorporated the Case-Based Reasoning, which is a learning method, into adaptive search algorithms to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛼𝛼2 = 1, 𝛼𝛼2 = 𝑇𝑇|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . The authors focused on developing a mechanism for selecting algorithms based on the problem characteristics and used PSPLIB to confirm the practicability of the method. Deblaere et al. [59] proposed a new execution strategy for the stochastic RCPSPs, 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛼𝛼3 = 𝜐𝜐𝑎𝑎�|𝛾𝛾 = 𝐸𝐸[⋅]. They used PSPLIB to compare their Simulation-based Descent Algorithm with the general heuristic developed by Van de Vonder et al. [60]. Deblaere et al. [61] explored 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and extended the Iterative Deepening A-STAR algorithm that is equipped with a module to repair the disrupted schedules. They considered the PSPLIB project scheduling library to compare the algorithm with different dominance rules as well as different search strategies, including the regular Branch-and-Bound and one integrated with Tabu Search. Hu et al. [62] proposed an Outer-Inner Fuzzy Cellular Automaton for the Dynamic Uncertainty Multi-Project Scheduling Problem, 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝛾𝛾 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐, 𝛾𝛾 = 𝑅𝑅𝑅𝑅𝑅𝑅. They considered the PSPLIB database for performance comparison with a Bee Swarm Optimization that utilizes forward-backward interchange and a hybrid Genetic Algorithm. Zheng et al. [63] developed the Teaching–Learning-Based Optimization algorithm to solve 𝑀𝑀𝑀𝑀 − 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They used the iMOPSE database to compare the results obtained by their method with those from the Hybrid Ant Colony Optimization algorithm. Myszkowski et al. [64] developed a Hybrid Differential Evolution and Greedy Algorithm for 𝑀𝑀𝑀𝑀 − 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 and considered the iMOPSE database to compare its performance with Hybrid Ant Colony Optimization algorithm that utilizes Greedy Randomized Adaptive Search Procedure (GRASP). Myszkowski et al. [65] introduced the iMOPSE platform for the 𝑆𝑆 − 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 variant of RCPSPs. The software includes test instances, visualization tools, and other material. Laszczyk and Myszkowski [66] developed the Nondominated Tournament Genetic Algorithm to solve 𝑀𝑀𝑀𝑀 − 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝛾𝛾 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐. The authors considered the iMOPSE dataset to evaluate the effectiveness of the algorithms, comparing the results with those of NSGA-II and Differential Evolution hybridized with Greedy Algorithm. Nemati-Lafmejani et al. [67] developed dual-objective optimization methods, NSGA-II, and Multi-Objective Particle Swarm Optimization to solve 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 − 𝐶𝐶𝐶𝐶�𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝛾𝛾 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐, 𝛾𝛾 = 𝑇𝑇𝑇𝑇, and compared them using the PSPLIB test set. Chaleshtarti et al. [68] developed a Hybrid 498 Advances in Production Engineering & Management 19(4) 2024 An algorithmic review of the technological progress and milestones in resource-constrained project planning Genetic and Lagrangian Relaxation Algorithm to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 , 𝛼𝛼2 = 𝑇𝑇�𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . Yuan et al. [69] developed a Hybrid Cooperative Co-evolution Algorithm to solve 𝑀𝑀 − 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝛾𝛾 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐. The algorithm performed exceptionally well in terms of robustness when compared to the Genetic Algorithm, Particle Swarm Optimization, and hybrid multi-objective version of the Estimation of Distribution Algorithm. Chu et al. [70] introduced a metaheuristic recommendation model to address 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 , which can select the most suitable solution algorithm based on the problem characteristics. The authors used PSPLIB as the testbed to evaluate the performance of the developed solution method, considering various practical scenarios. Yuraszeck et al. [71] proposed a new constraint programming model to address the problem of 𝑀𝑀 − 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . The authors considered a total of 321 test instances from five earlier studies and compared the results with the best-found lower bounds reported by Dauzère-Pérès et al. [72]. Overall, the key branch articles focused primarily on developing case-specific project scheduling variants. Multi-mode RCPSPs and the differentiation between renewable and nonrenewable resources became prevalent in the key branches. The most recent studies explored multi-skill RCPSPs and project scheduling that considers green factors. Hybridization played a significant role in key development branches of RCPSP algorithms. 3.3 Major thematics Fig. 3 provides an overlay view of the most frequently occurring keywords over time. Larger nodes represent words with higher frequencies of occurrence. The closer the connection between the two nodes is, the stronger their correlation. Nodes with more recent occurrences appear in brighter colors, with yellow indicating the most recent ones. This visualizes the shift in focus within the literature over time. Fig. 3 Overlay visualization of the keywords network CA indicates that the literature on RCPSPs can be divided into 23 themes. The top three themes will be considered for further analysis. Each theme is identified based on the proportion of keyword occurrences in the associated cluster. The first theme is priority rules and heuristic Advances in Production Engineering & Management 19(4) 2024 499 Pourhejazy, Ying, Cheng algorithms, which include 191 articles. This research theme experienced significant growth between 1995 and 2015. Methods for modeling and solving multi-mode RCPSPs, with 99 articles, constitute the second major research theme. The cluster began in 1993 and continued to grow until 2017. The first two clusters are currently in the saturation stage. Algorithms for RCPSPs with random activity durations constitute the third major theme, highlighting its practical relevance with 93 articles. This research theme received recognition only after 2010 and is now in the final years of the growth stage. The growth forecast trends and keyword proportions of these clusters are presented in Table 4. This is followed by a brief analysis of the seminal literature within each cluster. Cluster Count Cluster A: priority rules and heuristic algorithms /191 Table 4 Major research themes Keyword – Occurrence Ratio Rule – 0.178 PSPLIB – 0.115 Representation – 0.109 Parameter – 0.104 Network – 0.094 Duration – 0.083 Cluster B: multi-mode RCPSPs /99 Experiment – 0.263 Computational result – 0.172 Parameter – 0.162 Multiple execution mode – 0.152 Type – 0.152 Efficiency – 0.132 Cluster C: RCPSPs with random activity durations /93 Baseline schedule – 0.28 Stochastic resource – 0.24 Robustness – 0.2 Cost – 0.19 Computational experiment – 0.17 Heuristic – 0.17 Growth trend 3.3.1 Priority rules and heuristics for RCPSPs Fig. 4 illustrates the primary development trajectory within the first cluster. Among the 23 articles recognized as significant development progress in developing priority rules and heuristic algorithms, only four articles are absent from the main path and the key development branches. 500 Advances in Production Engineering & Management 19(4) 2024 An algorithmic review of the technological progress and milestones in resource-constrained project planning BellP1990 BellH1991 SampsonW1993 KolischSD1995 KolischD1996 Kolisch1996 KolischS1997 BruckerKST1998 Hartmann1998 HartmannK2000 Hartmann2002 VallsBQ2004 VallsBQ2005 KolischH2006 MobiniRARR2009 Zamani2010a Zamani2012 Zamani2013a ChengDW2014 ElsayedSRC2017 LiuLSL2020 LiuHYD2022 LiuHLJCO2023 Fig. 4 Progress in the development of priority rules and heuristics for RCPSPs From the remaining articles, Mobini et al. [73] improved the Scatter Search algorithm to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . Using the PSPLIB database, the algorithm was compared with the basic Scatter Search, the hybrid of Genetic Algorithm and Tabu Search with path relinking, and several other versions of Genetic Algorithms. Zamani [74] developed an Accelerating Two-Layer Anchor Search algorithm to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 , and used the PSPLIB database to compare its performance with the Local Search algorithm integrated with subproblem exact resolution. Zamani [75] introduced the Polarized Adaptive Scheduling Scheme for 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 , which dynamically adjusts the priority of activities in the project. He used the PSPLIB database and Local Search with subproblem exact resolution to evaluate the performance of the new scheme. Elsayed et al. [76] proposed a consolidated optimization algorithm, which combines GA and the Multi-operator Differential Evolution to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . Using the PSPLIB databases, they showed that their algorithm outperforms 11 algorithms, including the decompositionbased Genetic Algorithm, the hybrid of Ant Colony Optimization and Scatter Search, Particle Swarm Optimization, Bee Colony Algorithm, and an improved version of the Shuffled Frogleaping Algorithm. This research theme dominated scientific progress in the early development stages of RCPSPs. These studies are mainly focused on testing the developed rules and heuristics on simple RCPSPs and establishing the foundations for solution modeling and representation. 3.3.2 Multi-mode resource-constrained project scheduling algorithms Fig. 5 shows the main development trajectory of solution algorithms to solve multi-mode RCPSPs. In contrast to the first theme, this group of studies did not contribute much to the main development trajectory. The progress in this specific category shows the wide real-world applications of multi-mode RCPSPs. Considering the increase in the scale and complexity of problems, the articles under this theme are focused on improving the efficiency of solution algorithms and calibrating the parameters. Advances in Production Engineering & Management 19(4) 2024 501 Pourhejazy, Ying, Cheng Boctor1993 Hartmann2001 ZhangTL2006 JarbouiDSR2008 DrexlG1993 KolischD1997 JózefowskaMRWW2001 AlcarazMR2003 BuddhakulsomsiriK2006 LovaTCB2009 VanpeteghemV2010 WangF2012 VanpeteghemV2014 Geiger2017 FernandesmuritibaRD2018 ChakraborttyAR2020 ChenLHC2022 PengLPS2023 Fig. 5 Progress in multi-mode resource-constrained project scheduling algorithms Boctor [77] proposed several effective heuristic rules for 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛼𝛼2 = 1𝑇𝑇|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . He randomly generated 240 test problems to compare them with 18 other heuristics. Drexl and Gruenewald [49] proposed a novel stochastic scheduling method for the general class of nonpreemptive RCPSPs. They used randomly generated test problems to compare their method with the min LF method, which was the state-of-the-art deterministic search method at the time. Kolisch and Drexl [48] cited both source nodes and is recognized as one of the key branch articles. Hartmann [78] extended the Genetic Algorithm to optimize 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . Their experiments confirmed that the improved algorithm outperforms both Simulated Annealing and Branch and Bound algorithms. Józefowska et al. [79] introduced a new Simulated Annealing algorithm to optimize 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 , and used PSPLIB to confirm its effectiveness with and without a penalty function. The results were compared with the Genetic Algorithm developed by Hartmann. Alcaraz et al. [80] proposed the Multi-Mode Two-Point Forward-Backward Crossover Genetic Algorithm for 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . The algorithm performed better than those developed by Hartmann [78], Kolisch and Drexl [48], and the Genetic Algorithm developed by Ozdamar [81]. Buddhakulsomsiri and Kim [82] improved Hartmann's Branch and Bound algorithm and adjusted it so that the activities can be split in 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . The algorithm was used to compare the project performance in various practical scenarios. Zhang et al. [83] proposed the Multimode Particle Swarm Optimization to solve 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 , and compared the algorithm with the current best algorithms such as SA, BB, and so on. The results confirm its superior performance. Jarboui et al. [84] extended the Particle Swarm Optimization algorithm with a new local search method for 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They used PSPLIB to test it and showed that the algorithm outperforms the Simulated Annealing Algorithm, and the algorithm proposed by ZhangTL2006. Lova et al. [85] proposed a multi-mode Hybrid Genetic Algorithm for 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They considered the instances generated by the project generator ProGen to compare their algorithm with the Simple Genetic Algorithm as a baseline, as well as those developed by Hartmann [78], Kolisch and Drexl [48], Ozdamar [81], and Bouleimen and Lecocq [86]. Van Peteghem an Vanhoucke [6] proposed the Bi-Population Genetic Algorithm for solving 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽1 = 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽1 = 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 − 𝑟𝑟𝑟𝑟𝑟𝑟|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . The algorithm outperformed the Hybrid Genetic Algorithms developed by Lova et al. [85] and Alcaraz et al. [80], the extended Particle Swarm Optimization of Jarboui et al. [84], and the Hybrid Scatter Search of Ranjbar et al. [87]. Wang and Fang [88] adapted the Estimation of Distribution Algorithm to optimize 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝛾𝛾 = ∑ 𝑠𝑠𝑠𝑠. 𝑑𝑑𝑑𝑑𝑑𝑑. Experimental results based on PSPLIB instances showed that the average percentage deviation of this algorithm is smaller than that of the Simulated Anneal502 Advances in Production Engineering & Management 19(4) 2024 An algorithmic review of the technological progress and milestones in resource-constrained project planning ing of Józefowska et al. [79], the Genetic Algorithms of Alcaraz et al. [80], Van Peteghem and Vanhoucke [6], the Hybrid Scatter Search of Ranjbar et al. [87], the Artificial Immune System of [89], and the Hybrid Genetic Algorithm of Lova et al. [85]. Vanpeteghem and Vanhoucke [90] introduced the Multi-Mode Library, which is a new database for Multi-mode RCPSPs. They compared MMLIB and PSPLIB using different metaheuristics to verify the new instances. Geiger [91] studied 𝑀𝑀𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 , 𝛼𝛼2 = 1𝑇𝑇�𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . He combined Variable Neighborhood Search with the Iterated Local Search algorithm for a Multi-Threaded Local Search Algorithm to solve it. Using the MMLIB database, it was shown that the new algorithm outperforms several state-ofthe-art metaheuristics, including those developed by Hartmann [78], Lova et al. [85], VanpeteghemV2010, and the Differential Evolution algorithm by Damak et al. [92]. Fernandes Muritiba et al. [93] proposed a Path-Relinking algorithm to explore the solution spaces of 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛼𝛼2 = 1𝑇𝑇|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . Experimental results confirmed that its performance is better than the competing methods proposed earlier, such as the Genetic Algorithms of Lova et al. [85], Vanpeteghem and Vanhoucke [6], the Differential Evolution algorithm by Damak et al. [92], and the Estimation of Distribution Algorithms of Wang and Fang [88], among others. Chakrabortty et al. [94] proposed a modified Variable Neighborhood Search Heuristic algorithm for 𝑀𝑀𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 , 𝛼𝛼2 = 1𝑇𝑇�𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽1 =𝜊𝜊 |𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They used PSPLIB to confirm its effectiveness against adopted versions of the Simulated Annealing, Genetic Algorithm, Particle Swarm Optimization and its discrete variant, Differential Evolutionary Algorithm, Estimation of Distribution Algorithm, and Ant Colony Optimization algorithm. Chen et al. [95] developed a Hybrid Genetic Algorithm that combines different priority rules, as well as the series and parallel scheduling methods to solve 𝑀𝑀𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 , 𝛼𝛼2 = 1𝑇𝑇�𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . The experimental results show that this algorithm is particularly effective in reducing the construction period while evaluating the integration with various priority rules. Finally, Peng et al. [96] introduced the Hybrid Quantum Particle Swarm Optimization to solve 𝑀𝑀𝑀𝑀 − 𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌;𝜇𝜇,𝜏𝜏,𝜔𝜔 , , 𝛼𝛼2 = 1𝑇𝑇�𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝|𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . The authors used PSPLIB to test, and the experimental results show that the algorithm provides more accuracy and better convergence than the baseline Particle Swarm Optimization algorithm. Genetic Algorithms have been the cornerstone of the developments in multi-mode resourceconstrained project scheduling. Nearly all seminal studies under this research theme included different versions of the Genetic Algorithms in their numerical experiments. 3.3.3 Integrating stochasticity into RCPSPs The last major theme constitutes the integration of stochasticity into RCPSPs. Fig. 6 shows the backbone of scientific progress in this research theme, where the studies are predominantly concerned with uncertain time parameters and resource availability. Developing robust solution methods to minimize the expected project completion time and makespan has been at the center of attention in the development of this theme. LeusH2004 TsaiG1998 VandevonderDHL2006 ChtourouH2008 GolenkoginzburgG1997 Ballestin2007 BallestinL2009 AshtianiLA2011 DeblaereDH2011b LiW2015 RostamiCL2018 ChenDBG2018 ZamanESEC2021 ChenDZLJQ2022 SallamCR2021 ChenZLDQ2022 PengLL2023 Fig. 6 Scientific progress in the integration of stochasticity into RCPSPs Advances in Production Engineering & Management 19(4) 2024 503 Pourhejazy, Ying, Cheng Golenko-Ginzburg and Gonik [97], Tsai and Gemmill [98], and Leus and Herroelen [99] are the source articles in the development trajectory of this research theme. Golenko-Ginzburg and Gonik [97] proposed a heuristic method for 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝛾𝛾 = 𝐸𝐸𝐸𝐸𝐸𝐸 and tested it by considering various possibility terms. Tsai and Gemmill [98] developed a Tabu Search algorithm to enhance the computational performance when solving 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They tested the method by considering various combinations of heuristics. Leus and Herroelen [99] proposed a resource allocation model for 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They used the RanGen platform to generate test instances and improved the Branch and Bound algorithm developed by Demeulemeester and Herroelen [50] to test their method, comparing it with insertion techniques for both online and offline RCPSPs. Vandevonder et al. [100] developed a new heuristic method to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = ̃ 𝑑𝑑𝑗𝑗 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . The instances used in their numerical experiment were generated using RanGen software to analyze the impact of the weighting parameter, the number of activities, the order strength, buffer sizes, and the resource constraints. Ballestín [101] developed an adaptive Genetic Algorithm to study 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . The performance of the developed algorithm was compared with Simulated Annealing and Tabu Search algorithms using the ProGengenerated question bank. Chtourou and Haouari [102] developed the Two-Stage Priority RuleBased Algorithm for investigating 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝛾𝛾 = 𝑎𝑎𝑎𝑎, mentioning the stability of the project schedule as the main motivation. They conducted a simulation analysis based on the instances of Kolisch et al. [103]. Ballestín and Leus [104] developed the GRASP algorithm to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝛾𝛾 = 𝐸𝐸𝐸𝐸𝐸𝐸. Using instances from PSPLIB, they compared this algorithm with the Genetic Algorithm developed in an earlier study, Ballestín [101]. Ashtiani et al. [105] introduced a novel scheduling policy, namely the Preprocessor Polic for 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝛾𝛾 = 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . Using instances generated by the ProGen data generator and RanGen, they compared this policy with an activity-based (priority) policy using Genetic Algorithms. Li and Womer [106] developed an Approximate Dynamic Programming algorithm with Hybrid Backward and Forward Approximation for 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝛾𝛾 = 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . This type of solution algorithm is particularly useful for scheduling highly uncertain and variable projects. The authors tested their method using Patterson’s benchmark and PSPLIB instances and compared the algorithm with the GRASP algorithm developed by Ballestín and Leus [104]. Rostami et al. [107] proposed a new strategy and a new two-stage heuristic algorithm for 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝛾𝛾 = 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . Instances from the PSPLIB library were used to compare the two-phase metaheuristic procedure with the Estimation of Distribution algorithm by Wang and Fang [88], the Genetic Algorithm of Ashtiani et al. [105], as well as the GRASP method of Ballestín and Leus [104]. Chen et al. [108] developed five new priority rules and compared them with twelve from the literature while solving 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝛾𝛾 = 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They considered instances from PSPLIB with three different probability distribution functions for activity durations. Zaman et al. [109] developed the Scenario-based Combined Optimization Algorithm by integrating the Multi-operator Genetic Algorithm with the Multi-operator Differential Evolution to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝛾𝛾 = 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . The algorithm was compared with Genetic Algorithm of Ballestín [101], GRASP of Ballestín and Leus [104], the Two-phase Genetic Algorithm of Ashtiani et al. [105], and the Estimation of Distribution Algorithm of Fang et al. [110], while using PSPLIB instances. Sallam et al. [111] developed a Reinforcement Learning-Based Multi-Method Approach, which is a hybrid of the Multi-Objective Genetic Algorithm and Differential Evolution, to solve 𝑃𝑃𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝛾𝛾 = 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They considered three different industrial cases along with instances from the PSPLIB to showcase its effectiveness compared with the enhanced local search heuristic of Chakrabortty et al. [94], the Genetic Algorithm of Ballestín [101], the GRASP of Ballestín and Leus [104], the Two-phase Genetic Algorithm of Ashtiani et al. [105], and the Approximate dynamic programming of Li and Womer [106], and the optimization algorithm developed by Zaman et al. [109]. This is a seminal work on applications of machine learning in project scheduling. 504 Advances in Production Engineering & Management 19(4) 2024 An algorithmic review of the technological progress and milestones in resource-constrained project planning Chen et al. [112] proposed a Hierarchical Hybrid Filtering Genetic Programming method that regulates the scope and attributes of priority rules to solve 𝑀𝑀𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They used the test instances from PSPLIB and considered a set of traditional priority rules to showcase the superiority of their algorithm. Chen et al. [113] developed a Hyper-heuristic-based Two-Stage Genetic Programming Framework to solve 𝑀𝑀𝑀𝑀𝑀𝑀𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They considered a benchmark of 1,000 instances based on PSPLIB to compare their method, using SPEA2 and NSGA-II as the evaluation methods, as well as the traditional priority rules as the baseline. Peng et al. [114] introduced the Proactive-Reactive Scheduling Algorithm, which combines a novel scheduling strategy with CPM to study 𝐶𝐶𝐶𝐶𝐶𝐶𝑆𝑆𝑚𝑚,𝜎𝜎,𝜌𝜌 �𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝛽𝛽4 = 𝑑𝑑̃𝑗𝑗 �𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 . They used the datasets J30, J60, and J120 from the PSPLIB to evaluate their algorithm against the Approximate Dynamic Programming algorithm of Li and Womer [106] under various settings. Overall, studies under this cluster paid special attention to establishing a balance between computational stability, efficiency, and solution quality, especially when dealing with the randomness of activity durations, interruptions, and other uncertainty issues. Robust solution algorithms were at the center of scientific progress under this research theme. 4. Concluding remarks and future research This study comprehensively reviewed the resource-constrained project scheduling articles published between 1980 and 2024. The development paths and milestones in knowledge dissemination in project planning research were analyzed systematically. It was found that the impactful research directions gradually shifted from basic scheduling models and priority rules to multimodal, multi-objective problems considering practical research constraints. The most recent focus shift of RCPSPs is towards dynamic scheduling. Practical aspects of resource uncertainty and multi-project coordination have also gained attention in recent years. Research on RCPSPs has risen steadily, reaching a record high in published articles in 2021 (see Fig. 7a). Investigating the past development trajectory, including the maximum records, the starting point of the growth curve, and the turning point from growth to saturation indicates continuing growth until the late 2030s (see Fig. 7b). a) The historical trend on the scientific progress of RCPSPs b) An estimation of the future growth Fig. 7 Historical trends and an estimation of the future development trend using a Logistic model Advances in Production Engineering & Management 19(4) 2024 505 Pourhejazy, Ying, Cheng The less tangible patterns of development in the literature on RCPSPs were also explored. It was found that solution methods based on network structure analysis and dynamic programming approaches have received limited attention and therefore require further development. Overall, project planning requires a fresh multidisciplinary perspective to enrich task scheduling and extend mathematical applications by incorporating real-life needs and features into RCPSPs. More specific suggestions follow for future research directions. • Process mining and dynamic scheduling. This allows for real-time adjustment of tasks, considering changes in both tangible parameters and intangible operational patterns. • Changes in resource availability driven by machine failures, maintenance, and employee shiftwork require more attention. Additionally, resource conflicts and multi-agent systems in multi-project management require new coordination strategies. • Standard datasets considering multiple heterogeneous projects and projects with dynamic resource allocation are needed to provide a more diverse test platform for advances in solution algorithms. • Learning from large datasets to improve the search in solution spaces. Machine learningbased solution algorithms are required to balanced computational efficiency and solution quality. • Interactive multi-objective optimization schemes to balance conflicting objectives in realtime. 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Advances in Production Engineering & Management 19(4) 2024 511 Advances in Production Engineering & Management ISSN 1854-6250 Volume 19 | Number 4 | December 2024 | pp 512–526 Journal home: apem-journal.org https://doi.org/10.14743/apem2024.4.521 Original scientific paper Integrated production and maintenance policy for manufacturing systems prone to products' quality degradation BouAbid, H.a, Dhouib, K.b, Gharbi, A.c,* aLMPE Laboratory, Mechanical Engineering & Production Department, École Nationale Supérieure d’Ingénieurs de Tunis (ENSIT), University of Tunis, Tunis, Tunisia bRIFTSI Laboratory, Mechanical Engineering & Production Department, École Nationale Supérieure d’Ingénieurs de Tunis (ENSIT), University of Tunis, Tunis, Tunisia cC2SP Laboratory, Systems Engineering Department, École de Technologies Supérieure (ÉTS), Montréal, Canada ABSTRACT ARTICLE INFO This paper proposes an integrated production planning and preventive maintenance strategy for manufacturing systems prone to quality degradation. The production planning focus on the regulation of production rates and the sizing of finished product’s safety stock to meet costumer’s demand. The safety stock is built to palliate shortages when the manufacturing operation begins generating non-conforming products and is shutdown to perform restoration action. In the other hand, preventive maintenance activities are also planned to minimise the quantity of non-conforming products. Mathematical models are proposed and consider all sub-policies and scenarios contingent on the production control policy as well as the entire range of possible values for the safety stock level. A numerical procedure has been established to ascertain the optimal integrated policy, aiming to minimize the total accrued cost per time unit along an infinite horizon. A simulation model has also been created to check and validate the analytical results. Finally, a comparative analysis is presented to prove that the proposed joint policy outperforms other strategies considered in the literature and practice and can result in substantial economic gains. Keywords: Production planning; Stock control; Preventive maintenance; Quality degradation; Hedging point policy; Analytical modelling; Simulation analysis *Corresponding author: Ali.Gharbi@etsmtl.ca (Gharbi, A.) Article history: Received 12 December 2023 Revised 1 December 2024 Accepted 15 December 2024 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, quality, and maintenance management play an essential role to improve efficiency, profitability, competitiveness as well as sustainability of today's industrial companies affected by the technical developments of Industry 4.0 [1, 2]. Manufacturing businesses are becoming more and more concerned with producing high-quality goods in a sustainable way which establishes the basis for Quality 4.0 [3, 4]. As equipment maintenance, at a level which can produce an appropriate quality product is essential for keeping them operating, sustainable quality products cannot be produced unless they are subject to efficient maintenance [5]. The Growing adherence to Industry 4.0 proposes a novel framework that links the different facets of industrial systems supervision: production, inventory, maintenance, and quality. In general, the main objective is to reduce operating costs and to increase business opportunities which 512 Integrated production and maintenance policy for manufacturing systems prone to products' quality degradation can only be achieved when production, maintenance and quality strategies are jointly addressed. The integration of these aspects leads to important improvement of the system’s performance, especially the significant growing of the industrial profit which can be increased up to 40 % [6]. In a recent study, this joint consideration allows a reduction in overall production cost of up to 44 % [7]. However, more efforts must be made to propose mutual production, maintenance, and quality policies according to the multiple industrial environments and to their own specificities [8, 9]. In this situation, production control is closely associated with inventory management and particularly the safety stock. The majority of researchers do not consider all potential value ranges of security stock capacity. and focus only on high levels ignoring possible optimal solutions related to middle security stock level (i.e. low value of repair time) or to zero-stock strategy (i.e. expensive stock cost). This reflection often leads to the identification of suboptimal policies and implies excessive costs. This paper studies the combined optimization of production, stock, and maintenance strategy for industrial systems prone to quality degradation. We propose a multi-model framework and a broad holistic strategy that considers all potential security stock value ranges. Mathematical models are developed studying all sub-policies and scenarios that my raise based on the production control policy, level of security stock, and the moment when the system moves into the ‘out-ofcontrol state’. A simulation model is also designed to validate mathematical models. In next Section, a literature review covering integrated production and preventive maintenance policies for industrial systems prone to quality degradation is provided. The system synopsis, dynamic behaviour, and notations are stated in Section 3. Section 4 proposes analytical models for the generated sub-policies and associated scenarios according to all potential security stock value ranges. Section 5 presents a numerical procedure to determine the optimal combined policy. A simulation model is designed to validate analytical models. The beneficial effect of the suggested combined policy is then demonstrated through numerical examples and a comparison analysis involving various control policies drawn from the literature and implemented in practice. Conclusions are finally reported in Section 6. 2. Literature revue During the last decades, several contributions have been proposed integrating production, inventory, maintenance and quality in production planning and control. These contributions can be classified according to several criteria; mainly, the production control policy, the degree of integration, and the industrial context. Production control focus on the regulation of the production rate to respond to a continuous demand. Several control policies have been considered in the literature [10, 11]. In their pioneer paper, Akella and Kumar [10] introduce the Hedging Point Policy for systems prone to failures and subject to corrective maintenance and prove its optimality. The HPP policy entails to build a security stock to reduce the impact of breakdowns on demand satisfaction. The basic HPP policy has been extended by several authors to palliate against the negative impact of random failures using reserve resources [12], outsourcing [13] and preventive maintenance [14]. Other researchers have extended these models to consider the quality degradation of produced items. Some authors studied the specific case of perishable products [15]. Several works consider inspection policies to evaluate the quality of produced items [16]. These works have been extended by integrating static and dynamic sampling plans [7, 9] where the manufacturing system is prone to operation-dependent degradations [17]. The majority of preceding research assumes that industrial systems are prone to failures and that the produced quantity of non-conforming items depends on the equipment age; thus, the quality degradation is correlated with the degradation of the equipment reliability. But several researchers consider that the degradation of product quality is not correlated with the aging of the manufacturing equipment. Therefore, the production system can transit to the ‘out-of-control’ state and starts generating a proportion of non-conforming parts, according to a probability distribution, [18-30]. Advances in Production Engineering & Management 19(4) 2024 513 BouAbid, Dhouib, Gharbi Pandey et al. [18] propose an analytical model to jointly optimize the production scheduling, quality and maintenance in a one-machine industrial system that produces identical batches. Other researchers dealt mainly with the joint consideration of the economic production quantity, product quality degradation, and preventive maintenance policies [19-25]. A combined production-maintenance policy is suggested by Chelbi et al. for single-machine systems that generates items that comply as well as those that don't [26]. The presented model aims to determine the optimum lot size and preventive maintenance plan. Colledani and Tolio developed an analytical approach for mutually optimizing control charts and production parameters for unreliable multi-stage transfer lines. The control policy is based on a kanban system [27]. Dhouib et al. considered a joint production/maintenance strategy for systems subject to quality degradation [28]. Bahria et al. investigate the problem of the assimilation of production planning and the design of control charts [29]. This work has been extended to involve a preventive maintenance policy [30]. These studies, dealing with the one-product single-machine production systems, focus only on high levels of the safety stock, ignoring low levels which can result in non-optimal policies involving excessive incurred costs. In the other hand, these works do not proceed to the validation of analytical results and limit this important step in the modelling methodology to a sensitivity analysis based on the variation of some parameters. This study addresses the problem of building stochastic analytical models for the combined optimization of production rate control and PM schedule for manufacturing systems prone to quality degradation. The proposed approach allows addressing all possible security stock value ranges. The primary contributions include: i) Combined control of production, inventory, and maintenance for systems prone to quality degradation; ii) Multi-model approach according to potential security stock value ranges; iii) Resolution of complex stochastic mathematical models via numerical procedure; iv) Dynamic-stochastic simulation model to validate the analytical results; v) Proposed approach outperforms strategies examined in the literature and put into practice. 3. Manufacturing cell description, dynamic behaviour, and notations 3.1 System description and dynamics The system subject to this study is an automatic one-machine cell devoted to make and inspect one product type to respond to a constant and ongoing demand (d) (Fig. 1). The equipment, representing an aggregation of several machines, is prone to random quality degradation during the production phase. Initially, it starts in an ‘in-control’ situation, generating good products. The duration of this ‘incontrol’ situation is a stochastic variable (τ) characterized by a general probability distribution having a density (cumulative) function f (τ) (F(τ)) with a mean time within ‘in-control’ state (MTIC). After that, the cell may move to an ‘out-of-control’ situation, manufacturing non-conforming products with a proportion (α). Preventive maintenance interventions are scheduled during the in-control period to decrease the shift frequency to the ‘out-of-control’ situation. They obey to an age maintenance policy (AMP), planned at age (T), and allow to recover the system to an ‘as-good as-new’ condition. After a situation becomes out of control, a Logistic Delay Period (LDP) is required ensuing the switch to an out-of-control condition to organize total essential resources (both human and material) for the restoration procedure. To guarantee that the demand is met during the LDP, the machine keeps manufacturing. Then, the production process is aborted to undergo restoration which brings the system to the ‘as-good as-new’ condition, and then starts again generating good products. The delay of the restoration is a r.v. (tr) defined by a general probability distribution having a density (cumulative) function h(tr) (H(tr)) with a mean time to restore (MTTR). 514 Advances in Production Engineering & Management 19(4) 2024 Integrated production and maintenance policy for manufacturing systems prone to products' quality degradation Production Control (u(t),Umax) Preventive Maintenance Restoration Activity (LDP) (MTTR) (MTIC) (PM) (T) On-line Inspection Good items Warehouse (SS) Raw Material Customer Demand (d) Non-conforming items (α) Manufacturing Cell Fig. 1 Manufacturing system dynamics Throughout the production phase, a reserve of good products is established to address demand and avoid shortages throughout the restoration period. Only after the available inventory runs out can production resume, at which point a setup action is initiated. If a shortage is observed after the restoration, the necessary quantities are not supplied during a period of scarcity; these are seen as penalty costs for missed demand. The manufacturing process is managed across time through a unified policy governing production, inventory, and maintenance, according to HPP policy. The main aim is to determine the optimal production rates, the level of safety stock, and the preventive maintenance schedule. It aims to minimize the overall incurred cost per time unit over the long range, encompassing costs related to setup, quality, preventive maintenance, restoration, inventory holding, and shortages. According to the HPP plan, the production cell runs at maximum rate (Umax) until the safety stock is built (SS). After then, it lowers its production rate (u(t)) to match the demand. A deep analysis of the manufacturing system dynamics has shown different behaviours depending on the value of the safety stock level. In fact, this control strategy, which permits the production of nonconforming goods during LDP while the safety stock is built, leads to three joint control sub-policies, each having a distinct scenario, depending on the many conceivable value ranges of SS: • Sub-Policy I: HPP and zero-inventory policy (SS = 0) (Fig. 2). Scenario 1 s(t) Next Cycle d (0) SS=0 T 2T 3T ….. d(1+α) (0) d (0) 0 (-d) T τΤ ….. t Shortage situation LDP Production phase 2T Restoration phase Fig. 2 Inventory level evolution under joint Sub-Policy I • Sub-Policy II: HPP and stock policy SS < SLDP (middle level of security stock) (Fig. 3). This policy is characterized by the safety stock threshold SLDP (Eq. 1); SLDP is the number of compliant items places in the security stock during LDP. Advances in Production Engineering & Management 19(4) 2024 515 BouAbid, Dhouib, Gharbi 𝑆𝑆𝐿𝐿𝐿𝐿𝐿𝐿 = 𝐿𝐿𝐿𝐿𝐿𝐿(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 (1 − 𝛼𝛼) − 𝑑𝑑) (1) This crucial threshold signifies that the preparations for restoration conclude upon the completion of constructing the safety stock SS. So, and like sub-policy I, non-conforming item manufacture is carried out also during LDP. s(t) SLDP SS d (0) Umax (Umax(1-α)-d) d(1+α) (0) Scenario 1 Scenario 2 (U ma x -d ) 0 (-d) U ma x Next Cycle T 2T 3T ..... τT LDP Next Cycle τT t LDP Production phase Shortage situation Restoration phase Production phase Restoration phase Fig. 3 Inventory level evolution under joint Sub-Policy II • Sub-Policy III: HPP and stock policy SS ≥ SLDP (high-security stock) (Fig. 4). Unlike Sub-Policies I and II, the accomplishment of the preparation action's planning may be achieved prior to the construction of the safety stock SS (Scenario 1). In agreement with Sub-policy III, the production of non-compliant goods can extend for a period greater than LDP. s(t) SS d(1+α) (0) d (0) Scenario 1 Scenario 2 Scenario 3 Umax (Umax(1-α)-d) SLDP ma x -d ) 0 (-d) ma x (U Next Cycle U Next Cycle T 2T 3T ...τT τT LDP τT LDP Production phase Production phase Production phase Next Cycle t LDP Restoration phase Shortage situation Restoration phase Restoration phase Fig. 4 Inventory level evolution under joint Sun-Policy III 516 Advances in Production Engineering & Management 19(4) 2024 Integrated production and maintenance policy for manufacturing systems prone to products' quality degradation 3.2 Notations In this paper, we consider the following notations, where indices j and i denote a specific scenario (j = 1, 2, 3) in the sub-policy (i = I, II, III). Additional notations are defined in the text. ni s(t) τT Eij(τT) Eij (tr) Prij PrHij (PrSij) Number of scenarios associated with the sub-policy i (i = I, II, III). Inventory level at instant t. Random instant to transit to the ‘out-of-control’ situation according to the AMP. Mean duration of residence in control situation associated to sub-policy i-scenario j. Anticipated restoration delay while scarcity case associated to sub-policy i-scenario j. For sub-policy i, Probability of falling into scenario j. Probability of experiencing an excess inventory (scarcity) condition for sub-policy i, following the occurrence of scenario j. Expected length of the production/restoration cycle in an excess inventory (scarCLHij (CLSij) city) condition for sub-policy i, following the occurrence of scenario j. ����� 𝐼𝐼𝐼𝐼𝚤𝚤𝚤𝚤 Average stock level held during the production phase for sub-policy i, in scenario j. PPICij Expected Inventory holding cost incurred during Production Phase associated to sub-policy i, following the occurrence of scenario j. Cost of Non-Compliant parts for sub-policy i, scenario j . NCCij Mean number of Preventive Maintenance interventions for sub-policy i, in scenario j. NbPMij PMCij Cost of Preventive Maintenance for sub-policy i, in scenario j. Anticipated cost accrued through the Production Phase associated to sub-policy iPPCij scenario j. ������� 𝐼𝐼𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅 Average inventory kept during restoration phase for sub-policy i, in scenario j. RPICij Expected Inventory holding cost incurred during Restoration Phase associated to sub-policy i, following the occurrence of scenario j. Expected amount of Missing Demand for sub-policy i, in scenario j. NbLDij SCij Expected Shortage cost for sub-policy i, in scenario j. RPCHij (RPCSij) Anticipated cost accrued through the Restoration Phase in an excess (lack) circumstance for sub-policy i-scenario j. Overall Expected cost associated with the joint sub-policy i. TCi 4. Modelling joint control policies To model the behaviour of the proposed joint control policies, the cycle of the studied system is divided into two phases: the production phase, during which the cell is producing, and the phase of restoration following the shutdown of the manufacturing cell. The machine transits, cyclically, from ‘operating’ to ‘shutdown’ and from ‘shutdown’ to ‘operating’ state. Figs. 2, 3, and 4 show that each cycle starts and ends with an empty stock. Based on these observations, we are certain that the system dynamics is a renewal process since cycles are independent of one another. Therefore, 'the elementary renewal theorem' [31] can be employed to calculate the mean value of any KPI per time unit beyond an infinite time span (TC, WIP, preventive actions number, Amount of nonconforming items, etc.). The global cost for sub-policy i (i = I, II, III) is assessed by Eq. 2. It consists of the expenses paid both during manufacturing and restoration stages whether there is excess or lack of inventory, weighted by corresponding probability of scenario. 𝑇𝑇𝑇𝑇𝑖𝑖 = 𝑖𝑖 ∑𝑛𝑛𝑗𝑗=1 ��𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖 + 𝑅𝑅𝑅𝑅𝑅𝑅𝐻𝐻𝐻𝐻𝐻𝐻 �Pr𝐻𝐻𝐻𝐻𝐻𝐻 + �𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖 + 𝑅𝑅𝑅𝑅𝑅𝑅𝑆𝑆𝑆𝑆𝑆𝑆 �Pr𝑆𝑆𝑆𝑆𝑆𝑆 � Pr𝑖𝑖𝑖𝑖 𝑖𝑖 ∑𝑛𝑛𝑗𝑗=1 �𝐶𝐶𝐶𝐶𝐻𝐻𝐻𝐻𝐻𝐻 Pr𝐻𝐻𝐻𝐻𝐻𝐻 + 𝐶𝐶𝐶𝐶𝑆𝑆𝑆𝑆𝑆𝑆 Pr𝑆𝑆𝑆𝑆𝑆𝑆 �Pr𝑖𝑖𝑖𝑖 (2) The production phase cost comprises the expenses due to setup (CSU), non-compliant items, inventory holding, and preventive maintenance activities (Eq. 3). 𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖 = 𝐶𝐶𝑆𝑆𝑆𝑆 + 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖 + 𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖𝑖𝑖 + 𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖 Advances in Production Engineering & Management 19(4) 2024 (3) 517 BouAbid, Dhouib, Gharbi The inventory keeping cost is computed by multiplying the cost of an item held in stock per time unit (CH) with the average quantity seized in the safety stock (Eq. 4). 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖 = 𝐶𝐶𝐻𝐻 ����� 𝐼𝐼𝐼𝐼𝚤𝚤𝚤𝚤 (4) The non-conforming items expense includes the costs of raw material (CRM) and operating of the manufacturing cell per time unit (CMCO). The preventive maintenance charge is determined by multiplying the expense of a preventive activity (CPM) with the anticipated number of performed preventive interventions (Eq. 5). 𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖 = 𝐶𝐶𝑃𝑃𝑃𝑃 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖𝑖𝑖 (5) The restoration phase cost comprises, in case of surplus, the inventory holding and the restoration cost (CR) (Eq. 6). In scarcity situation, it also includes the unit shortage expense (CS) multiplied by the non-delivered parts (Eqs. 7 and 9). 𝑅𝑅𝑅𝑅𝑅𝑅𝐻𝐻𝐻𝐻𝐻𝐻 = 𝐶𝐶𝑅𝑅 + 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖 (6) 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖 = 𝐶𝐶𝐻𝐻 ������� 𝐼𝐼𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅 (8) (9) 𝑅𝑅𝑅𝑅𝑅𝑅𝑆𝑆𝑆𝑆𝑆𝑆 = 𝐶𝐶𝑅𝑅 + 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖 + 𝑆𝑆𝑆𝑆𝑖𝑖𝑖𝑖 where and (7) 𝑆𝑆𝑆𝑆𝑖𝑖𝑖𝑖 = 𝐶𝐶𝑆𝑆 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖𝑖𝑖 The cycle length equals the mean time to transit to ‘out-of-control’ condition under an AMP policy, the LDP while reaching SS, and the MTTR in a situation of a shortage or the delay to consume all the safety inventory in instance of excess inventory. 4.1 Sub-policy I: HPP and zero-inventory policy If a zero-stock policy is required based on production parameters (SS = 0), the production control sub-policy can be expressed by Eq. 10. 𝑑𝑑 𝑑𝑑(1 + 𝛼𝛼) 𝑢𝑢(𝑡𝑡) = � 0 If the cell is producing in the ‘in control’ state If the cell is producing during 𝐿𝐿𝐿𝐿𝐿𝐿 alternatively (10) The progression of the stock level is presented in Fig. 2, where shortage situation is inevitable; in fact, only one scenario can occur according to Sub-Policy I (nI = 1). Fig. 2 also indicates the production and the inventory construction/depletion rates during production and restorations phases. The global accrued cost TCI is assessed by Eq. 2, where: • PrI1 = 1, PrHI1 = 0, and PrSI1 = 1. • The cycle length is calculated using Eq. 11. 𝐶𝐶𝐶𝐶𝑆𝑆I1 = 𝐸𝐸I1 (𝜏𝜏 𝑇𝑇 ) + 𝐿𝐿𝐿𝐿𝐿𝐿 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 (11) 𝐸𝐸I1 (𝜏𝜏 𝑇𝑇 ) is the expected time to move to ‘out-of-control’ condition beneath a T-age AMP policy (Eq. 12), and MTTR is calculated by Eq. 13. 𝐸𝐸I1 (𝜏𝜏 𝑇𝑇 ) = � ∞ 𝑘𝑘=0 (𝑘𝑘+1)𝑇𝑇 𝑅𝑅(𝑇𝑇)𝑘𝑘 � ∞ 𝑘𝑘𝑘𝑘 𝜏𝜏 𝑓𝑓(𝜏𝜏 − 𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 = � 𝑡𝑡𝑟𝑟 ℎ(𝑡𝑡𝑟𝑟 )𝑑𝑑𝑡𝑡𝑟𝑟 0 (12) (13) • PPC I1 can be assessed with Eq. 3, with PPIC I1 is 0 as no stock building is allowed (Fig. 2). NCC I1 and PMC I1 costs can be assessed by Eqs. 14 and 5, respectively, where NbPMI1 is given by Eq. 15. 𝑁𝑁𝑁𝑁𝑁𝑁I1 = 𝛼𝛼 𝐿𝐿𝐿𝐿𝐿𝐿 �𝑑𝑑 𝐶𝐶𝑅𝑅𝑅𝑅 + 518 1 𝐶𝐶 � 1 + 𝛼𝛼 𝑀𝑀𝑀𝑀𝑀𝑀 (14) Advances in Production Engineering & Management 19(4) 2024 Integrated production and maintenance policy for manufacturing systems prone to products' quality degradation 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁I1 = � ∞ 𝑘𝑘 𝑅𝑅(𝑇𝑇)𝑘𝑘 𝐹𝐹(𝑇𝑇) 𝑘𝑘=0 • RPCS I1 is given by Eq. 7; RPIC I1 is 0 and SC I1 is expressed with Eq. 9, where: ∞ 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁I1 = 𝑑𝑑 � 𝑡𝑡𝑟𝑟 ℎ(𝑡𝑡𝑟𝑟 )𝑑𝑑𝑡𝑡𝑟𝑟 0 4.2 Sub-policy II: HPP and the stock policy SS < SLDP (15) (16) When mandatory security stock quantity is fewer than SLDP based on production parameters (middle level), the production control sub-policy will be described by Eq. 17. 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 𝑑𝑑 𝑢𝑢(𝑡𝑡) = � 𝑑𝑑(1 + 𝛼𝛼) 0 If 𝑠𝑠(𝑡𝑡) < 𝑆𝑆𝑆𝑆 If 𝑠𝑠(𝑡𝑡) = 𝑆𝑆𝑆𝑆 where the cell is ‘in control’ state If 𝑠𝑠(𝑡𝑡) = 𝑆𝑆𝑆𝑆 where the cell is ‘out of control’ state alternatively (17) In the production phase, the system may exist in one of two scenarios (nII = 2) contingent on the shift instant (𝜏𝜏 𝑇𝑇 ) to the ‘out-of-control’ condition (Fig. 3). Scenario 1: Takes place if the cell go into the ‘out-of-control’ condition before attaining SS. Constraint 𝜏𝜏 𝑇𝑇 < 𝑆𝑆𝑆𝑆⁄(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑) imposes the occurrence of scenario 1. Scenario 2: Conditioned by the constraint 𝜏𝜏 𝑇𝑇 ≥ 𝑆𝑆𝑆𝑆⁄(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑), it takes place if the security inventory is at present filled. The probability to be into Scenario 1 (Scenario 2) can be expressed by Eq. 18 (Eq. 19). 𝑁𝑁𝑁𝑁𝑆𝑆 −1 𝑆𝑆𝑆𝑆 (18) PrII1 = � 𝑅𝑅(𝑇𝑇)𝑘𝑘 𝐹𝐹(𝑇𝑇) + 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝑆𝑆 𝐹𝐹 � mod 𝑇𝑇� 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑 𝑘𝑘=0 PrII2 = 1 − PrII1 (19) NMS denotes the highest preventive maintenance interventions performed prior to the attainment 𝑆𝑆𝑆𝑆 of the inventory level SS (𝑁𝑁𝑁𝑁𝑆𝑆 = div 𝑇𝑇). 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 −𝑑𝑑 According to sub-policy II, the occurrence probability of an inventory excess (scarcity) circumstance does not depend on manifestation of Scenario 1 (Scenario 2). Thus, these probabilities are provided by Eqs. 20 and 21, for i = II and j = 1, 2. Pr𝐻𝐻𝐻𝐻𝐻𝐻 = 𝐻𝐻(𝑆𝑆𝑆𝑆⁄𝑑𝑑) (20) 𝐶𝐶𝐶𝐶𝐻𝐻𝐻𝐻𝐻𝐻 = 𝐸𝐸𝑖𝑖𝑖𝑖 (𝜏𝜏 𝑇𝑇 ) + 𝐿𝐿𝐿𝐿𝐿𝐿 + 𝑆𝑆𝑆𝑆⁄𝑑𝑑 (22) Pr𝑆𝑆𝑆𝑆𝑆𝑆 = 1 − 𝐻𝐻(𝑆𝑆𝑆𝑆⁄𝑑𝑑) (21) The total expense CTII is given by Eq. 2, with cycle lengths and production/restoration phase costs are assessed in the following paragraphs. The average renewal cycle length in a surplus (shortage) situation is given by Eq. 22 (Eq. 23), for i = II and j = 1, 2. 𝐶𝐶𝐶𝐶𝑆𝑆𝑆𝑆𝑆𝑆 = 𝐸𝐸𝑖𝑖𝑖𝑖 (𝜏𝜏 𝑇𝑇 ) + 𝐿𝐿𝐿𝐿𝐿𝐿 + 𝐸𝐸𝑖𝑖𝑖𝑖 (𝑡𝑡𝑟𝑟 ) 𝐸𝐸𝑖𝑖𝑖𝑖 (𝜏𝜏 𝑇𝑇 ) and 𝐸𝐸𝑖𝑖𝑖𝑖 (𝑡𝑡𝑟𝑟 ) are given by Eqs. 24, 25, and 26, respectively (i = II, j = 1, 2). 𝐸𝐸II1 (𝜏𝜏 𝑇𝑇 ) = �� 𝑁𝑁𝑁𝑁𝑆𝑆 −1 𝑘𝑘=0 ∞ 𝐸𝐸II2 (𝜏𝜏 𝑇𝑇 ) = �� 𝑘𝑘=𝑁𝑁𝑁𝑁𝑆𝑆 𝑘𝑘 𝑅𝑅(𝑇𝑇) � 𝑘𝑘 (𝑘𝑘+1)𝑇𝑇 𝑘𝑘 𝑇𝑇 𝑅𝑅(𝑇𝑇) � 𝜏𝜏 𝑓𝑓(𝜏𝜏 − 𝑘𝑘 (𝑘𝑘+1)𝑇𝑇 𝑘𝑘 𝑇𝑇 𝑆𝑆𝑆𝑆 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 −𝑑𝑑 𝑇𝑇)𝑑𝑑𝑑𝑑 + 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝑆𝑆 � 𝜏𝜏 𝑁𝑁𝑁𝑁𝑆𝑆 𝑇𝑇 𝜏𝜏 𝑓𝑓(𝜏𝜏 − 𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑 ∞ 𝐸𝐸𝑖𝑖𝑖𝑖 (𝑡𝑡𝑟𝑟 ) = � 𝑆𝑆𝑆𝑆⁄𝑑𝑑 𝑆𝑆𝑆𝑆 𝑓𝑓(𝜏𝜏 − 𝑁𝑁𝑁𝑁𝑆𝑆 𝑇𝑇)𝑑𝑑𝑑𝑑��PrII1 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 −𝑑𝑑 − 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝑆𝑆 � 𝜏𝜏 𝑓𝑓(𝜏𝜏 𝑁𝑁𝑁𝑁𝑆𝑆 𝑇𝑇 𝑡𝑡𝑟𝑟 ℎ(𝑡𝑡𝑟𝑟 )𝑑𝑑𝑡𝑡𝑟𝑟 �Pr𝑆𝑆𝑆𝑆𝑆𝑆 Advances in Production Engineering & Management 19(4) 2024 − 𝑁𝑁𝑁𝑁𝑆𝑆 𝑇𝑇)𝑑𝑑𝑑𝑑 ��PrII2 (23) (24) (25) (26) 519 BouAbid, Dhouib, Gharbi Eq. 3 assesses the encountered charge throughout the production stage where the inventory expense is evaluated by Eq. 4 and the average amount seized into security stock for Scenario 1 (Scenario 2) is calculated by Eq. 27 (Eq. 28). 𝑆𝑆𝑆𝑆 2 ������ 𝐼𝐼𝐼𝐼II1 = (𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑) �𝐿𝐿𝐿𝐿𝐿𝐿 𝐸𝐸II1 (𝜏𝜏 𝑇𝑇 ) + ∫0𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚−𝑑𝑑 𝜏𝜏 2 𝑓𝑓(𝜏𝜏)𝑑𝑑𝑑𝑑�2 PrII1 � 2 + �𝑆𝑆𝑆𝑆 − 2𝑆𝑆𝑆𝑆 𝐸𝐸II1 (𝜏𝜏 𝑇𝑇 )(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑) + (𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑) � 𝑆𝑆𝑆𝑆 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 −𝑑𝑑 0 𝜏𝜏 2 𝑓𝑓(𝜏𝜏)𝑑𝑑𝑑𝑑� PrII1 ��2(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 (1 − 𝛼𝛼) − 𝑑𝑑) +�𝑆𝑆𝑆𝑆 − 𝐸𝐸II1 (𝜏𝜏 𝑇𝑇 ) (𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑)��𝐿𝐿𝐿𝐿𝐿𝐿 − �𝑆𝑆𝑆𝑆 − 𝐸𝐸II1 (𝜏𝜏 𝑇𝑇 ) (𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑)�⁄(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 (1 − 𝛼𝛼) − 𝑑𝑑)� ������ 𝐼𝐼𝐼𝐼II2 = 𝑆𝑆𝑆𝑆 (𝐸𝐸II2 (𝜏𝜏𝑇𝑇 ) + 𝐿𝐿𝐿𝐿𝐿𝐿) − 𝑆𝑆𝑆𝑆 2 ⁄2(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑) (27) (28) The NCCij are given by Eqs. 29 and 30 and the PMCij by Eq. 5, where NbPMij are given by Eqs. 31 and 32, for i = II and j = 1, 2. 𝑁𝑁𝑁𝑁𝑁𝑁II1 = (𝐶𝐶𝑅𝑅𝑅𝑅 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 + 𝐶𝐶𝑀𝑀𝑀𝑀𝑀𝑀 )𝛼𝛼�𝑆𝑆𝑆𝑆 − 𝐸𝐸II1 (𝜏𝜏𝑇𝑇 )(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑)�⁄(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 (1 − 𝛼𝛼) − 𝑑𝑑) + (𝐶𝐶𝑅𝑅𝑅𝑅 𝑑𝑑 + 𝐶𝐶𝑀𝑀𝑀𝑀𝑀𝑀 ⁄(1 + 𝛼𝛼))𝛼𝛼�𝐿𝐿𝐿𝐿𝐿𝐿 − �𝑆𝑆𝑆𝑆 − 𝐸𝐸II1 (𝜏𝜏𝑇𝑇 )(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑)�⁄(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 (1 − 𝛼𝛼) − 𝑑𝑑)� 𝑁𝑁𝑁𝑁𝑁𝑁II2 = 𝛼𝛼 (𝐶𝐶𝑅𝑅𝑅𝑅 𝑑𝑑 + 𝐶𝐶𝑀𝑀𝑀𝑀𝑀𝑀 ⁄(1 + 𝛼𝛼)) 𝐿𝐿𝐿𝐿𝐿𝐿 𝑁𝑁𝑁𝑁𝑆𝑆 −1 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁II1 = �� 𝑘𝑘=0 𝑘𝑘 𝑅𝑅(𝑇𝑇)𝑘𝑘 𝐹𝐹(𝑇𝑇) + 𝑁𝑁𝑁𝑁𝑆𝑆 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝑆𝑆 𝐹𝐹 � 𝑆𝑆𝑆𝑆 mod 𝑇𝑇���PrII1 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑 ∞ 𝑆𝑆𝑆𝑆 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁II2 = �𝑁𝑁𝑁𝑁𝑆𝑆 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝑆𝑆 �𝐹𝐹(𝑇𝑇) − 𝐹𝐹 � mod 𝑇𝑇�� + � 𝑘𝑘 𝑅𝑅(𝑇𝑇)𝑘𝑘 𝐹𝐹(𝑇𝑇)��PrII2 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑 𝑘𝑘=𝑁𝑁𝑁𝑁𝑆𝑆 +1 (29) (30) (31) (32) The incurred expense throughout the restoration stage can be expressed by Eq. 6 (Eq. 7) in a surplus (shortage) situation, and Eq. 8, with the mean amount detained in inventory and the sum of lost demands can be appraised by Eqs. 33 and 34, respectively, for i = II and j = 1, 2. ������� 𝐼𝐼𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅 = 𝑆𝑆𝑆𝑆 2⁄2𝑑𝑑 (33) 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖𝑖𝑖 = 𝑑𝑑 �𝐸𝐸𝑖𝑖𝑖𝑖 (𝑡𝑡𝑟𝑟 ) − 𝑆𝑆𝑆𝑆⁄𝑑𝑑� (34) 4.3 Sub-policy III: HPP and the stock policy SS ≥ SLDP When mandatory security stock quantity is superior to SLDP based on production parameters (high level), the production rate will also be governed by Eq. 17. Throughout the stage of production, the system may occur in either of three following scenarios (nIII = 3) dependent on the change instant to the ‘out-of-control’ condition (Fig. 4). Scenario 1: Takes place if the producing cell enters ‘out-of-control’ condition before attaining SLDP. This is the only scenario in which non-conforming items are manufactured for a period exceeding the LDP. The proposed sub-policy explicitly recommends continuing manufacturing until 𝑆𝑆𝑆𝑆−𝑆𝑆 imposes the ocreaching the SS to mitigate the possibility of deficiencies. Constraint 𝜏𝜏𝑇𝑇 < 𝑈𝑈 𝐿𝐿𝐿𝐿𝐿𝐿 −𝑑𝑑 currence of Scenario 1. Scenario 2: Trained by the constraint 𝑆𝑆𝑆𝑆−𝑆𝑆𝐿𝐿𝐿𝐿𝐿𝐿 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 −𝑑𝑑 ≤ 𝜏𝜏 𝑇𝑇 < 𝑆𝑆𝑆𝑆 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 −𝑑𝑑 𝑚𝑚𝑚𝑚𝑚𝑚 , it happens when the cell enters out-of-control state as its inventory is split between SLDP and SS. Scenario 3: Conditioned by the constraint 𝜏𝜏 𝑇𝑇 ≥ 𝑆𝑆𝑆𝑆⁄(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑), it occurs once the security stock SS level is by now reached. The probability of being in Scenarios 1, 2, and 3 are given by Eqs. 35, 36, and 37. 𝑁𝑁𝑁𝑁𝐿𝐿 −1 𝑆𝑆𝐿𝐿𝐿𝐿𝐿𝐿 (35) PrIII1 = � 𝑅𝑅(𝑇𝑇)𝑘𝑘 𝐹𝐹(𝑇𝑇) + 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝐿𝐿 𝐹𝐹 � mod 𝑇𝑇� 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑 𝑘𝑘=0 𝑁𝑁𝑁𝑁𝑆𝑆 −1 𝑆𝑆𝐿𝐿𝐿𝐿𝐿𝐿 𝑆𝑆𝑆𝑆 PrIII2 = � 𝑅𝑅(𝑇𝑇)𝑘𝑘 𝐹𝐹(𝑇𝑇) − 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝐿𝐿 𝐹𝐹 � mod 𝑇𝑇� + 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝑆𝑆 𝐹𝐹 � mod 𝑇𝑇� (36) 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑 𝑘𝑘=𝑁𝑁𝑁𝑁𝐿𝐿 520 Advances in Production Engineering & Management 19(4) 2024 Integrated production and maintenance policy for manufacturing systems prone to products' quality degradation PrIII3 = 1 − (PrIII1 + PrIII2 ) (37) NML expresses the highest preventive maintenance interventions executed prior to the comple𝑆𝑆 tion of the inventory level SLDP (𝑁𝑁𝑁𝑁𝐿𝐿 = 𝐿𝐿𝐿𝐿𝐿𝐿 div 𝑇𝑇). 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 −𝑑𝑑 The probability of being in excess (lack) circumstances is given by Eq. 20 (Eq. 21). The total charge CTIII is given by Eq. 2, with cycle lengths and production/restoration phase costs are assessed as follows. The average renewal cycle length for Scenario 1 in a holding (shortage) case is given by Eq. 38 (Eq. 39), and by Eq. 22 (Eq. 23) for Scenarios 2 and 3, where i = III and j = 2, 3. 𝐶𝐶𝐶𝐶𝐻𝐻III1 = (𝑆𝑆𝑆𝑆 − 𝛼𝛼 𝐸𝐸III1 (𝜏𝜏 𝑇𝑇 ) 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 )⁄(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 (1 − 𝛼𝛼) − 𝑑𝑑) + 𝑆𝑆𝑆𝑆⁄𝑑𝑑 (38) 𝐶𝐶𝐶𝐶𝑆𝑆III1 = (𝑆𝑆𝑆𝑆 − 𝛼𝛼 𝐸𝐸III1 (𝜏𝜏 𝑇𝑇 ) 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 )⁄(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 (1 − 𝛼𝛼) − 𝑑𝑑) + 𝐸𝐸III1 (𝑡𝑡𝑟𝑟 ) 𝐸𝐸𝑖𝑖𝑖𝑖 (𝜏𝜏 𝑇𝑇 ) is given by Eqs. 40, 41, and 42, and 𝐸𝐸𝑖𝑖𝑖𝑖 (𝑡𝑡𝑟𝑟 ) is given by Eq. 26, for i = III and j = 1, 2, 3. 𝐸𝐸III1 (𝜏𝜏 𝑇𝑇 ) = �� 𝑁𝑁𝑁𝑁𝐿𝐿 −1 𝑘𝑘=0 ⎛ 𝐸𝐸III2 (𝜏𝜏 𝑇𝑇 ) = ⎜ ⎜ ⎝ 𝑘𝑘 𝑅𝑅(𝑇𝑇) � (𝑘𝑘+1)𝑇𝑇 𝑘𝑘𝑘𝑘 𝑆𝑆𝑆𝑆 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 −𝑑𝑑 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝑆𝑆 � 𝜏𝜏 𝑁𝑁𝑁𝑁𝑆𝑆 𝑇𝑇 ∞ 𝐸𝐸III3 (𝜏𝜏 𝑇𝑇 ) = �� 𝑘𝑘=𝑁𝑁𝑁𝑁𝑆𝑆 𝑆𝑆𝐿𝐿𝐿𝐿𝐿𝐿 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 −𝑑𝑑 + 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝐿𝐿 � 𝜏𝜏 𝑓𝑓(𝜏𝜏 𝜏𝜏 𝑓𝑓(𝜏𝜏 − 𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑 𝑁𝑁𝑁𝑁𝐿𝐿 −1 𝑓𝑓(𝜏𝜏 − 𝑁𝑁𝑁𝑁𝑆𝑆 𝑇𝑇)𝑑𝑑𝑑𝑑 + � 𝑆𝑆𝐿𝐿𝐿𝐿𝐿𝐿 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 −𝑑𝑑 −𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝐿𝐿 � 𝜏𝜏 𝑘𝑘 𝑅𝑅(𝑇𝑇) � (𝑘𝑘+1)𝑇𝑇 𝑘𝑘 𝑇𝑇 𝑁𝑁𝑁𝑁𝐿𝐿 𝑇𝑇 𝜏𝜏 𝑓𝑓(𝜏𝜏 − 𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑 𝑘𝑘=𝑁𝑁𝑁𝑁𝐿𝐿 𝑁𝑁𝑁𝑁𝐿𝐿 𝑇𝑇 𝑅𝑅(𝑇𝑇)𝑘𝑘 � (𝑘𝑘+1)𝑇𝑇 𝑘𝑘𝑘𝑘 𝑓𝑓(𝜏𝜏 − 𝑁𝑁𝑁𝑁𝐿𝐿 𝑇𝑇)𝑑𝑑𝑑𝑑 𝑆𝑆𝑆𝑆 𝜏𝜏 𝑓𝑓(𝜏𝜏 − 𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 −𝑑𝑑 − 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝑆𝑆 � 𝜏𝜏 𝑓𝑓(𝜏𝜏 𝑁𝑁𝑁𝑁𝑆𝑆 𝑇𝑇 − 𝑁𝑁𝑁𝑁𝐿𝐿 𝑇𝑇)𝑑𝑑𝑑𝑑��PrIII1 (39) (40) ⎞ ⎟�PrIII2 (41) ⎟ ⎠ − 𝑁𝑁𝑁𝑁𝑆𝑆 𝑇𝑇)𝑑𝑑𝑑𝑑 ��PrIII3 (42) The recorded cost during the fabrication stage is evaluated by Eq. 3. The cost of inventory held can be assessed by Eq. 4 with the expected amount seized at occurrence of Scenarios 1, 2, and 3 can be evaluated by Eqs. 43, 44, and 45, respectively. ⁄𝑈𝑈 −𝑑𝑑 𝑆𝑆 ������� 𝐼𝐼𝐼𝐼III1 = (𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑) ∫0 𝐿𝐿𝐿𝐿𝐿𝐿 𝑚𝑚𝑚𝑚𝑚𝑚 𝜏𝜏2 𝑓𝑓(𝜏𝜏)𝑑𝑑𝑑𝑑�2 PrIII1 + 𝑆𝑆 �𝑆𝑆𝑆𝑆 2 − (𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑)2 ∫0 𝐿𝐿𝐿𝐿𝐿𝐿 ⁄𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 −𝑑𝑑 2 𝜏𝜏 𝑓𝑓(𝜏𝜏)𝑑𝑑𝑑𝑑�PrIII1 ��2(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 (1 − 𝛼𝛼) − 𝑑𝑑) 𝑆𝑆𝑆𝑆⁄𝑈𝑈 −𝑑𝑑 ������� 𝐼𝐼𝐼𝐼III2 = (𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑) ∫𝑆𝑆 ⁄𝑚𝑚𝑚𝑚𝑚𝑚 𝜏𝜏2 𝑓𝑓(𝜏𝜏)𝑑𝑑𝑑𝑑�2 PrIII2 + 𝑆𝑆𝑆𝑆 𝐿𝐿𝐿𝐿𝐿𝐿 − 𝑈𝑈 −𝑑𝑑 𝐿𝐿𝐿𝐿𝐿𝐿 𝑚𝑚𝑚𝑚𝑚𝑚 2 �𝑆𝑆𝑆𝑆 − 𝐸𝐸III2 (𝜏𝜏𝑇𝑇 )(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑)� �2(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 (1 − 𝛼𝛼) − 𝑑𝑑) ������� 𝐼𝐼𝐼𝐼III3 = 𝑆𝑆𝑆𝑆 (𝐸𝐸III3 (𝜏𝜏𝑇𝑇 ) + 𝐿𝐿𝐿𝐿𝐿𝐿 − 𝑆𝑆𝑆𝑆⁄(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑)) + 𝑆𝑆𝑆𝑆 2⁄2(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑) (43) (44) (45) The NCCij are given by Eqs. 46, 47, and 48 and the PMCij by Eq. 5, where NbPMij are given by Eqs. 49, 50, and 51, for i = III and j = 1, 2, 3. 𝑁𝑁𝑁𝑁𝑁𝑁III1 = (𝐶𝐶𝑅𝑅𝑅𝑅 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 + 𝐶𝐶𝑀𝑀𝑀𝑀𝑀𝑀 )𝛼𝛼�𝑆𝑆𝑆𝑆 − 𝐸𝐸III1 (𝜏𝜏𝑇𝑇 )(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑)�⁄(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 (1 − 𝛼𝛼) − 𝑑𝑑) (46) 𝑁𝑁𝑁𝑁𝑁𝑁III2 = (𝐶𝐶𝑅𝑅𝑅𝑅 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 + 𝐶𝐶𝑀𝑀𝑀𝑀𝑀𝑀 )𝛼𝛼�𝑆𝑆𝑆𝑆 − 𝐸𝐸III2 (𝜏𝜏𝑇𝑇 )(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑)�⁄(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 (1 − 𝛼𝛼) − 𝑑𝑑) + (𝐶𝐶𝑅𝑅𝑅𝑅 𝑑𝑑 + 𝐶𝐶𝑀𝑀𝑀𝑀𝑀𝑀 ⁄(1 + 𝛼𝛼))𝛼𝛼�𝐿𝐿𝐿𝐿𝐿𝐿 − �𝑆𝑆𝑆𝑆 − 𝐸𝐸III2 (𝜏𝜏𝑇𝑇 )(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑)�⁄(𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 (1 − 𝛼𝛼) − 𝑑𝑑)� 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁III1 = �� 𝑁𝑁𝑁𝑁𝑁𝑁III3 = 𝛼𝛼 (𝐶𝐶𝑅𝑅𝑅𝑅 𝑑𝑑 + 𝐶𝐶𝑀𝑀𝑀𝑀𝑀𝑀 ⁄(1 + 𝛼𝛼)) 𝐿𝐿𝐿𝐿𝐿𝐿 𝑁𝑁𝑁𝑁𝐿𝐿 −1 𝑘𝑘=0 ⎛ 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁III2 = ⎜ 𝑆𝑆𝐿𝐿𝐿𝐿𝐿𝐿 𝑘𝑘 𝑅𝑅(𝑇𝑇)𝑘𝑘 𝐹𝐹(𝑇𝑇) + 𝑁𝑁𝑁𝑁𝐿𝐿 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝐿𝐿 𝐹𝐹 � mod 𝑇𝑇���PrIII1 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑 𝑆𝑆𝐿𝐿𝐿𝐿𝐿𝐿 mod 𝑇𝑇�� + 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑 𝑁𝑁𝑁𝑁𝐿𝐿 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝐿𝐿 �𝐹𝐹(𝑇𝑇) − 𝐹𝐹 � ⎞ ⎟�PrIII2 𝑆𝑆𝑆𝑆 � 𝑘𝑘 𝑅𝑅(𝑇𝑇)𝑘𝑘 𝐹𝐹(𝑇𝑇) + 𝑁𝑁𝑁𝑁𝑆𝑆 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝑆𝑆 𝐹𝐹 � mod 𝑇𝑇� 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑 ⎝ 𝑘𝑘=𝑁𝑁𝑁𝑁𝐿𝐿+1 ⎠ 𝑁𝑁𝑁𝑁𝑆𝑆 −1 Advances in Production Engineering & Management 19(4) 2024 (47) (48) (49) (50) 521 BouAbid, Dhouib, Gharbi ∞ 𝑆𝑆𝑆𝑆 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁III3 = �𝑁𝑁𝑁𝑁𝑆𝑆 𝑅𝑅(𝑇𝑇)𝑁𝑁𝑁𝑁𝑆𝑆 �𝐹𝐹(𝑇𝑇) − 𝐹𝐹 � mod 𝑇𝑇�� + � 𝑘𝑘 𝑅𝑅(𝑇𝑇)𝑘𝑘 𝐹𝐹(𝑇𝑇)��PrIII3 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑑𝑑 𝑘𝑘=𝑁𝑁𝑁𝑁𝑆𝑆 +1 (51) In an excess (deficiency) condition, the accrued restoration phase charge is given by Eq. 6 (Eq. 7) and Eq. 8 with the expected amount detained in inventory and the amount of lost demands can be given by Eqs. 33 and 34, respectively, for i = III and j = 1, 2, 3. 5. Numerical resolution methodology, results and comparative analysis 5.1 Optimization numerical procedure Two decision variables specify the optimal solution: the security stock capacity SS, and the preventive maintenance age T. A numerical resolution procedure has been designed and coded based on the programming language ‘Fortran’, to determine the optimal solution (SS *, T *) minimizing the overall expected cost (CT*). This algorithm, which is illustrated in Fig. 5, combines a number of subroutines to calculate the probability of each scenario, predicted cycle durations, several KPIs, and expenses suffered during the production and restoration cycles for the three sub-policies. 5.2 Numerical results and analytical model validation Consider first a base case describing the production cell. All costs and operating, demand, quality, and maintenance parameters are provided in Table 1. The time in-control state (to restore) has a Weibull (Gamma) distribution. After executing the numerical program, we established that the minimum total cost (CT*), as determined by the optimal decision variables SS* = 1,314 items & T* = 0.14 months, is equal to 96,621.37 $/month. Fig. 6 presents the evolution of CT depending on decision variables SS and T. One can note the convex character of the surface confirming the presence of the optimum value. Table 1 Sample of 6 manufacturing cell configurations with randomly generated parameters Operating Parameters Cost Parameters C a s e Base CH CS CRM CMCO CSU 40 400 500 150,000 5,000 1 80 385 150 200,500 2 50 200 250 250,000 3 90 500 300 4 25 430 240 5 120 420 6 15 630 CPM d Umax MTIC α (%) LDP MTTR 10,000 2,000 20,160 32,400 0.9027 1 0.10 0.05 2,800 9,000 3,800 22,350 40,000 1.2638 19 0.11 0.022 3,000 15,000 2,800 18,000 35,000 1.8054 5 0.08 0.10 220,000 5,500 20,000 4,000 13,000 20,000 0.9027 20 0.10 0.02 160,000 6,200 7,000 4,200 21,540 38,500 1.1735 11 0.03 0.1 290 350,000 6,000 14,000 2,500 20,000 35,100 1.0832 12 0.12 0.067 140 90,000 3,000 4,000 2,700 28,000 44,000 0.6319 8 0.09 0.033 CR To validate the proposed approach, the analytical stochastic models and the numerical resolution procedure, a simulation model is constructed with ARENA simulation package. It imitates the production cell dynamic and stochastic behaviour. Table 2 presents first the validation of the base case. Hundreds of cell configurations were randomly generated, evaluated for optimal solutions, and then analytical results were validated through simulation. Each simulation is executed during 1,000,000 cycles (Production-Restoration) with warmup delay of 100,000 cycles to assure the steadiness of performance measures. Ten replications were carried out for every cell configuration. Table 2 also presents a sample of 6 cell configurations (cases 1 to 6) with randomly generated parameters validated through simulation model (Tab. 1); the results show that all analytically computed KPIs fell inside the simulation’s 95 % confidence interval. The key performance indicators analysed in this paper are the expected values of the following: cycle length (CL), work in process (WIP), number of lost demand (NbLD), number of non-conforming items (NbNC), number of preventive maintenance interventions (NbPM), and total incurred cost (TC*). 522 Advances in Production Engineering & Management 19(4) 2024 Integrated production and maintenance policy for manufacturing systems prone to products' quality degradation BEGIN Read : Operating settings & Cost Parameters Smax , ∆S , Tmax , ∆T Compute : SLDP (Eq. 1) T = ∆T SS = 0 Yes SS = 0 No No SS < SLDP Yes Policy II Policy III Compute : Scenorios probabilities Compute : Scenorios probabilities Compute : Cycle length Compute : Cycle lengths Compute : Cycle lengths Compute : Production Phase cost Compute : Production Phase cost Compute : Production Phase cost Compute : Restoration Phase cost Compute : Restoration Phase cost Compute : Restoration Phase cost Policy I (Eqs. 20-21, 35-37) (Eqs. 18-21) (Eqs. 22-23, 26, 38-42) (Eqs. 22-26) (Eq. 11) (Eqs. 3-5, 43-51) (Eqs. 3-5, 27-32) (Eqs. 3-5, 14-15) (Eqs. 7, 9, 16) (Eqs. 6-9, 33-34) (Eqs. 6-9, 33-34) Evaluate : Total Cost (Eqs. 2-9) SS = SS + ∆S T = T + ∆T Yes SS ≤ Smax Yes No T ≤ Tmax No Print : Optiml solution CT*, Z*, T*, and KPIs END TC(SS,T) x 104 Fig. 5 Optimal policy resolution algorithm 4 x 10 10.3 10.2 10.2 10.15 10.1 10.1 10.05 10 10 9.9 9.95 9.9 9.8 9.85 9.7 9.8 9.6 0.1 9.75 0.12 0.14 T 0.16 0.18 1000 1100 1200 1300 1400 SS 1500 1600 000 9.7 Fig. 6 Evolution of the total incurred cost CT(SS,T) Advances in Production Engineering & Management 19(4) 2024 523 BouAbid, Dhouib, Gharbi C a s e Base 1 2 3 4 5 6 Table 2 Analytical results validation by simulation for manufacturing cell configurations defined in Table 1 CL WIP 2.860 [2.853 - 2.863] 4.420 [4.416 - 4.427] 8.719 [8.707 - 8.728] 2.720 [2.718 - 2.721] 3.914 [3.903 - 3.918] 6.070 [6.061 - 6.079] 1.480 [1.478 - 1.483] Key Performance Indicators NbLD NbNC 1,270.52 [1,270.37 - 1,270.59] 120.36 [120.367 - 120.369] 0 [0 - 0] 225.351 [225.350 - 225.353] 2,998.14 [2,997.75 - 2,998.26] 0 [0 - 0] 2,275.11 [2,274.56 – 2,275.36] NbPM 171.24 20.35 18.59 [20.34 - 20.36] [18.55 - 18.62] [170.61 - 172.27] 379.44 476.12 28.01 [379.06 - 379.86] [467.12 - 467.12] [27.97 - 28.03] 1,800 72 77.02 [72 - 72] [76.92 - 77.11] [1,798.8 - 1,801.5] 84.47 260.25 16.71 [84.26 - 84.62] [260.24 - 260.26] [16.69 - 16.72] 286.38 89.55 22.66 [285.13 - 288.53] [89.49 - 89.70] [22.59 - 22.68] 1,333.33 288 117.07 [1332.35 - 1334.46] [288 - 288] [116.88 - 117.24] 16.77 215.93 5.60 [16.54 - 17.01] [215.83 - 216.07] [5.59 - 5.62] TC* Optimal Solution T* SS* 96,621.4 [96,540.1 - 96,761.8] 86008.1 [85,959.4 - 86,107.7] 70,263.73 [70,210.7 - 70,361.9] 99,821.7 [99,797.8 - 99,871.7] 139,729.7 [139,655.4 - 140,004.7] 158,260.3 [158,110.6 - 158,507.9] 77,041.9 [76,937.9 - 77,160.1] 0.14 1,314 0.15 121 0.11 0 0.15 228 0.16 3,142 0.05 0 0.21 2,481 5.3 Comparative analysis To highlight the contribution of the suggested approach, a comparative investigation was carried out with strategies considered in the literature and practice: Strat. 1: The Proposed policy, described by 3 sub-policies and 6 scenarios. Strat. 2: proposal of Chelbi et al. [29], described by 2 scenarios (no sub-policies), and can only handle the case SS > SLDP. Strat. 3: proposal of Dhouib et al. [31], described by 3 scenarios (no sub-policies), and can only handle the case SS > SLDP. Strat. 4: The proposed policy (Strat. 1) but limited to a range of safety stock level SS > SLDP as considered in Strat. 2 and Strat. 3. Strat. 5: The proposed policy (Strat. 1) without preventive maintenance. The comparative study is based on the sample of 7 manufacturing cell configurations with randomly generated parameters presented in Table 1 (Base case and cases 1 to 6). Table 3 displays first the optimal control solution for the proposed Strat. 1 (SS*,T*,TC*) and according to which optimal sub-policy (P*) it belongs (P* = I, II or III). It also presents optimal solutions for the other compared strategies. First, we must recall that all the results generated by the proposed approach (Strat. 1) are validated by comparing them with those made by simulation, confirming the exactness of the proposed analytic models. The results demonstrate that the recommended approach (Strat. 1) outperforms other ones and allowing cost savings of up to 96 % (60 %) compared to the proposal of Chelbi et al. (2008) (Strat. 2 – case 1) (Dhouib et al. (2012) (Strat. 3 – case 5)); The primary reason for this discrepancy is because these models do not account for any potential security stock value ranges. C a s e Table 3 Comparison of the proposed policy to ones from literature and practice Strat. 1 - Proposed - SS* Strat. 2 121 2 0 3 4 5 6 228 Strat. 5 Cost TC* Red. SS* T* (%) 1,314 0.14 96,621 0 SS* T* 2,087 - Cost Red. (%) 113,809 17.8 0.15 86,008 II 1,106 0.14 168,782 96.3 1,106 0.3 131,641 53.1 1,106 0.29 127,107 47.8 638 - 134,278 56.1 0.11 70,129 1,220 0.16 112,269 60.1 1,220 0.20 107,329 53.1 1,220 0.20 102,766 46.5 1,666 - 150,759 114.9 52.9 T* TC* P* I 0.15 99,821 II 3,142 0.16 139,729 III 0 Strat. 4 Cost SS* T* TC* Red. (%) 1,493 0.17 105,955 9.7 Base 1,314 0.14 96,621 III 1 Strat. 3 Cost SS* T* TC* Red. (%) 1,202 0.09 116,924 21.1 0.05 158,260 I 2,481 0.21 77,041 III 521 0.11 154,108 54.4 300 0.16 111,862 12.1 300 0.17 100,646 8.3 TC* 426 - 152,680 4,712 - 153,390 9.8 1,307 0.09 237,428 50.1 1,592 - 346,397 125.2 2,481 0.21 77,041 2,869 - 88,905 15.4 4,218 0.19 172,126 23.2 3,691 0.31 155,617 11.4 3,142 0.16 139,729 1,307 0.06 281,517 77.8 1,307 0.07 253,460 60.2 3,246 0.16 100,747 30.8 2,532 0.24 89,867 16.7 0 0 Strat. 4, which is a limited version of Strat. 1, surpasses Strat. 2 and Strat. 3 on all studied configurations, but it generates errors of up to 50 % compared to Strat. 1 (case 5). Finally, comparing Strat. 5 to the proposed Strat. 1 show that preventive maintenance allowed reducing the total incurred cost of up to 125 % (case 5). We note that the high-cost reductions are obtained when the zero-stock is the best sub-policy; in fact, this joint policy is based on high inventory holding 524 Advances in Production Engineering & Management 19(4) 2024 Integrated production and maintenance policy for manufacturing systems prone to products' quality degradation cost, and since no preventive maintenance is planned with Strat. 5, it reacts by increasing the security stock capacity (SS*), from 0 (Strat. 1 – case 5) to 1,592 (Strat. 5 – case 5) implying high and costly WIP. 6. Conclusion In this manuscript, we introduce a comprehensive strategy for production planning and preventive maintenance concerning manufacturing systems prone to quality degradation considering every potential range of values for the security stock. An age-based AMP plan is implemented to diminish the amount of non-compliant items. Three joint control sub-policies are developed based on a specific value of the security stock capacity determined by the production system characteristics and the amount added to the security stock during the logistic delay period (SLDP): Sub-policy I – HPP and the zero-inventory policy, Sub-policy II – HPP and the stock policy SS < SLDP, and Subpolicy III – HPP and the stock policy SS ≥ SLDP. The three inferred sub-policies and related scenarios are addressed using a broad stochastic multi-model method for industrial systems with general distributions of the restoration delay and the alteration period to the ‘out-of-control’ condition. We develop a numerical approach to address intricate stochastic models and assess the optimal integrated control policy by computing the expected overall cost. A simulation model has also been built and hundreds of system configurations with randomly generated parameters were tested to validate the recommended analytical models showing the quality and the effectiveness of the provided approach. Finally, we examined various control policies derived as of existing literature and applied in practical situations to underline the efficacy of the recommended integrated policy. The findings indicate that, for all randomly generated configurations, the proposed policy outperforms other ones and can achieve substantial economic gains. This work is intended to inspire additional research on integrated production control and preventive maintenance policies. Indeed, the suggested strategy can be extended to circumstances involving maintenance and restoration efforts which are imperfect. Control charts and sampling inspection programs are two more quality inspection procedures that may be taken into consideration in a future work. 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Introduction to stochastic processes, Dover Publications, New-York, USA. 526 Advances in Production Engineering & Management 19(4) 2024 [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] Advances in Production Engineering & Management ISSN 1854-6250 Volume 19 | Number 4 | December 2024 | pp 527–538 Journal home: apem-journal.org https://doi.org/10.14743/apem2024.4.522 Original scientific paper Integrating simulation modelling for sustainable, human-centred Industry 5.0: ESG-based evaluation in collaborative workplaces Ojstersek, R.a,*, Javernik, A.a, Buchmeister, B.a aUniversity of Maribor, Faculty of Mechanical Engineering, Maribor, Slovenia ABSTRACT ARTICLE INFO This research explores the role of simulation modelling in the development of human-centred, sustainable manufacturing processes in the context of Industry 5.0. We analyse collaborative workplaces where humans and collaborative robots (CR) work together, emphasizing the environmental, social, and governance (ESG) criteria. The research work focuses on how personalized CR parameters and optimized work environments contribute to improved productivity, well-being, and sustainability. Through simulations, the paper evaluates the operational efficiency of both manual assembly and human-robot collaborative (HRC) setups, providing insight into the economic, environmental, and social impacts of Industry 5.0 manufacturing systems. The results show significant improvements in sustainability, productivity, and worker well-being achieved through adaptive CR integration and ESG-driven engineering practices. Keywords: Human-Centred manufacturing; Simulation modelling; Sustainability – ESG; Industry 5.0; Collaborative workplace; Human-robot interaction; Assembly process *Corresponding author: robert.ojstersek@um.si (Ojstersek, R.) Article history: Received 23 August 2024 Revised 28 November 2024 Accepted 5 December 2024 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 rapidly evolving landscape of industrial manufacturing, the transition from Industry 4.0 to Industry 5.0 [1] marks a paradigm shift toward human-centred and sustainable production systems [2]. While Industry 4.0 focused on automation, digitization, and connectivity [3], Industry 5.0 emphasizes the integration of advanced technologies with human well-being as a main optimization goal [4]. This transformation addresses the multiple objectives of enhancing productivity and fostering a sustainable, ethical, and socially responsible global competitive manufacturing environments [5, 6]. A significant challenge in manufacturing today lies in achieving optimal synergy between humans and collaborative robots (CRs), while maintaining a balance among economic performance, worker well-being, and environmental sustainability [7, 8]. Current manufacturing systems are often either overly automated (lacking manufacturing flexibility) or heavily reliant on manual labour (with a lack of suitable labour force), leading to inefficiencies in resource utilization, high 527 Ojstersek, Javernik, Buchmeister operational costs, worker fatigue (physical and physical), and inconsistent quality [9]. Furthermore, while Environmental, Social, and Governance (ESG) criteria are increasingly emphasized in industrial settings, existing systems frequently fail to integrate these metrics effectively into the design and evaluation of collaborative workplaces [10, 11]. A lot of research works are trying to answer the question: Can growing field of Human-Robot Collaboration (HRC) offers a promising solution to obtain efficient competitive manufacturing systems [12]? HRC systems combine the precision, speed, and reliability of robots with the creativity, flexibility, and problem-solving capabilities of humans [13]. Various implementations of HRC have demonstrated improvements in production efficiency, reduced worker fatigue, and enhanced products quality [14]. Simulation modelling has also emerged as a powerful tool for analysing and optimizing these systems, enabling the evaluation of production processes under different scenarios without disrupting realworld operations [15]. Among existing solutions, simulation-based evaluations of HRC systems stand out as the most effective approach. These models provide a holistic view of production processes, incorporating economic, environmental, and social factors into performance assessments. By simulating dynamic interactions between humans and robots, these tools help identify bottlenecks, optimize task allocation, and evaluate ESG impacts [16]. Despite its potential, the current simulation-based methods face significant limitations [17]. Most models focus heavily on economic performance while neglecting the social aspects of manufacturing, such as worker wellbeing, safety, and engagement. Additionally, few studies effectively integrate environmental and governance criteria, such as energy efficiency and ethical labour practices, into the simulation frameworks [18]. This lack of comprehensive models hinders the ability of manufacturers to design truly sustainable and human-centred systems, particularly in the context of Industry 5.0 [19, 20]. This research aims to address these limitations by developing a simulation-based approach that evaluates collaborative workplaces through the lens of ESG criteria [21]. By incorporating real-world data, the paper seeks to: • Enhance economic performance by reducing operational costs, idle times, and energy consumption. • Improve worker well-being by redistributing repetitive and physically demanding tasks to robots, thereby reducing fatigue and enhancing safety. • Promote environmental sustainability by minimizing energy usage and waste generation. • Strengthen governance practices by aligning production processes with ethical and regulatory standards. Paper research goal is to provide a framework for designing human-centred and sustainable manufacturing systems, enabling the realization of Industry 5.0 principles in diverse industrial settings [22, 23]. This study contributes to the existing body of knowledge by demonstrating how simulation modelling can bridge the gap between productivity and sustainability, offering actionable insights for optimizing human-robot collaboration while meeting ESG goals. 2. Problem description In the context of Industry 5.0, where the integration of human-centred and sustainable practices is crucial, the need for effective simulation modelling to evaluate manufacturing systems from an ESG (Environmental, Social, Governance) perspective has become critical. While Industry 4.0 emphasized the integration of automation and data-driven systems, Industry 5.0 highlights the necessity of aligning technological advancements with human well-being and environmental sustainability. The ESG framework, presented in Fig. 1, provides comprehensive criteria’s for assessing the impact of manufacturing processes, but there remains a significant gap in evaluating collaborative workplaces especially those involving human-robot collaboration (HRC). The ESG framework shown in the Fig. 1 emphasizes the integration of sustainable, ethical, and socially responsible practices into production systems. By adopting this framework, production facilities can monitor and improve their impact on the environment, enhance worker conditions, and considering governance regulations. Simulation models, when integrated with these ESG criteria, can help optimize production systems while balancing productivity with sustainability, aligning closely with Industry 5.0 principles. 528 Advances in Production Engineering & Management 19(4) 2024 Integrating simulation modelling for sustainable, human-centred Industry 5.0: ESG-based evaluation in collaborative … Fig. 1 Proposed ESG framework for production systems Existing models are often limited with the social aspects of worker well-being, which are essential for long-term operational efficiency. This gap is particularly notable in production processes supported by the concepts of the Industry 5.0, where technology must not only optimize productivity but also support sustainable and socially responsible practices. To address this issue, this research work proposes a simulation-based approach to evaluate HRC based on ESG metrics, specifically focusing on the integration of environmental sustainability, social impacts, and governance in decision-making processes. Our research emphasizes the role of human-centred design in optimizing production systems, ensuring that both economic efficiency and worker well-being are balanced through simulation. Fig. 2 illustrates the evaluated production process in a typical dynamic job shop manufacturing environment, where machines and human workers share tasks. The figure provides a layout of the production line, showing how each machine (from M1 to M7 and manual assembly workplace WP1) interacts within the production process. The machines M1 to M7 include the following: M1 and M7 are KUKA KR 40 industrial robots. Machines M2 and M3 are Haas UMC 500 5-axis CNC centres, while machines M4 and M6 are Okuma MA 550-VB 3-axis CNC machine centres. Machine M5 is a Mazak QTS 200 model CNC machine. WP1 presents manual assembly operation, which will be replaced by HRC for the purpose of ESG simulation model evaluation. We will present how this change influence entire manufacturing system in corelation to Industry 5.0 aspects. Table 1 presents the real-world data collected from the evaluated production process, including costs associated with machines, worker involvement, and energy consumption across multiple machines from M1 to M7 and manual assembly workplace WP1. These parameters are critical in calculating the ESG Index, as they reflect the economic, environmental, and social impacts of the manufacturing process. The table highlights key metrics which was used for calculating Total machines and WP1 costs presented by the processing and idle costs. These parameters are then incorporated into data drive simulation model to assess the production system’s sustainability performance, focusing on reducing energy and scrap rate, electrical energy consumption and optimizing worker conditions while maintaining production efficiency. Fig. 2 Evaluated production process Advances in Production Engineering & Management 19(4) 2024 529 Ojstersek, Javernik, Buchmeister Table 1 Production process real-world data Cost calculation parameter Purchase value of the machine (1000 of €) Machine power (kW) Workplace area (m2) Depreciation period (year) Useful capacity (h/year) Machine write-off value (€/h) Interests (€/h) Maintenance costs (€/h) Workplace area costs (€/h) Energy consumption costs (€/h) Workplace tool costs (€/h) Total machine costs (€/h) Worker costs (€/h) Additional costs (€/h) Workplace total processing costs (€/h) Workplace total idle costs (€/h) M1 40 3.75 8.5 5 4649 1.72 0.26 0.26 1.828 0.3 0.17 4.54 6 0.07 10.61 5.30 M2 140 20 8.8 5 4649 6.02 0.90 0.90 1.893 1.6 0.60 11.92 6 0.18 18.10 12.13 M3 140 20 8.8 5 4649 6.02 0.90 0.90 1.893 1.6 0.60 11.92 6 0.18 18.10 12.13 WP1 (MA/HRC) 31.25 6.25 0.05 0.15 1.7 1.7 5 5 4649 4649 1.34 0.27 0.20 0.04 0.20 0.04 0.366 0.366 0.004 0.004 0.13 0.03 2.25 0.75 15 15 0.03 0.01 17.29 15.76 17.29 15.76 M4 150 20 17.5 5 4649 6.45 0.97 0.97 3.764 1.6 0.65 14.40 6 0.22 20.61 13.81 M5 50 7.5 4.2 5 4649 2.15 0.32 0.32 0.903 0.6 0.22 4.51 6 0.07 10.58 5.29 M6 150 20 17.5 5 4649 6.45 0.97 0.97 3.764 1.6 0.65 14.40 6 0.22 20.61 13.81 M7 40 3.75 8.5 5 4649 1.72 0.26 0.26 1.828 0.3 0.17 4.54 6 0.07 10.61 3.5 To evaluate the sustainability of collaborative workplaces, the simulation model integrates the following ESG-related metrics: • Energy consumption was modelled based on machine power (as shown in Table 1). Energyefficient processes are simulated to compare their impacts on overall production costs. • Worker costs and utilization rates from Table 1 are used to simulate worker efficiency. • Governance aspects such as worker effective capacity planning with regulations and ethical labour practices are integrated as constraints in the simulation, ensuring that the production process reflects high standards of corporate responsibility. By combining these factors, the simulation model provides a comprehensive ESG-based evaluation of the production system, identifying areas for improvement in production efficiency, sustainability and worker well-being, from a human-centred perspective. 3. Methodology This research work uses simulation modelling to evaluate the sustainable performance of collaborative and manual workstations, incorporating real-world data and simulation environment Simio to analyse both the economic, environmental, and social (ESG) metrics. The simulation scenarios are developed to assess how collaborative workplace and manual assembly workstation perform in terms of production efficiency, worker well-being, and environmental impact in an Industry 5.0 context. The production system, consists of machines from M1 to M7, operates under two distinct setups: • Manual assembly WP1, human worker performs assembly tasks, with no collaborative robot assistance. • HRC WP1, human worker is assisted by collaborative robot in assembly tasks, reducing human workload. Each machine and WP1 operate based on actual production data from the factory floor. The following assumptions and parameters were included in the simulation model: • Effective production system capacity is 4649 hours/year, where 252 working days/year is considered, with 3 shifts/day, 7.5 effective working hours/shift with the 82 % production process efficiency are assumed. • The hourly salary rate for workers operating machines M1 to M7 is 18 EUR/h, with three workers required to supervising all seven machines. For manual assembly workstation WP1, one additional worker is needed with salary of 15 EUR/h. 530 Advances in Production Engineering & Management 19(4) 2024 Integrating simulation modelling for sustainable, human-centred Industry 5.0: ESG-based evaluation in collaborative … • The electrical energy cost is 0.16 EUR/kWh, with machine-specific power consumption included in the analysis. In addition, electrical energy consumption for each machine is based on its power rating, where used value is presented by 50 % of individual machine maximum power consumption. • Operational and idle costs are included as calculated in Table 1, where maintenance costs are 3 %, tool costs are 2 % and additional machine costs are 1.5 % of the machine purchase value. • The conveyor belt in the system operates at a speed of 0.75 m/s, while the forklift moves at 2 m/s, with loading and unloading times of 10 s each. • Simulation time was 92 h with the warm-up period of 8 h. Table 2 outlines the parameters used for modelling the manual assembly workstation WP1 and the associated machines. Processing time of the machines ranges from 15 s (M1) to 85 s (WP1) at the manual assembly workplace. Processing time of the WP1 is modelled by random normal distribution, where 85 s present mean value and 12 s its standard deviation (85; 12). Electrical energy power is given such as M2, M3, M4, and M6 consume 20 kW, while others like M1 and M7 consume 3.75 kW. WP1, a manual workstation, uses only 0.05 kW. Calculated workplace total costs for each machine’s ranges from 10.61 EUR/h (M1, M7) to 20.61 EUR/h (M4, M6). For the manual assembly workplace scrap rate of 8 % is modelled. Data in Table 2 serves as a baseline for modelling manual assembly WP1 production process. Table 2 Manual assembly WP1 modelling parameters Machine/workplace Simulation model parameter M1 M2 M3 WP1 M4 Processing time (s) 15 35 40 85; 12 40 Machine power (kW) 3.75 20 20 0.05 20 Workplace total processing costs 10.61 18.10 18.10 15.76 20.61 (€/h) Workplace total idle costs (€/h) 5.30 12.13 12.13 15.76 20.61 Scrap rate (%) 8 - M5 60 7.5 10.58 10.58 - M6 35 20 20.61 20.61 - M7 25 3.75 10.61 10.61 - Fig. 3 Manual assembly production system model Fig. 3 presents the configuration of the production system with the manual assembly workplace WP1, showing how machines (M1-M7) and the manual assembly workstation (WP1) are laid out in the production process. It visualizes the interactions between machines and workers, providing a clear representation of how simulation model inside Simio software is modelled in correlation to the real-world data. Table 3 presents simulation modelling parameters for WP1 where manual assembly operation is replaced with the HRC workplace. In relation to the manual assembly operation, processing times for the machines from M1 to M7 remain the same, but for WP1 with HRC, the processing Advances in Production Engineering & Management 19(4) 2024 531 Ojstersek, Javernik, Buchmeister time is significantly reduced to 55 seconds with a standard deviation of 6 seconds, compared to 85 seconds in the manual assembly operation. From an environmental perspective, the scrap rate of the HRC WP1 shows an improvement in production quality, with a reduced scrap rate of 4.5 %, compared to 8 % modelled at the manual assembly WP1. Fig. 4 visualizes the layout of the production system with the HRC WP1, where collaborative robot performs assembly tasks with human worker. The model presents how human-robot collaboration can reduce task processing times and improve overall system efficiency by optimizing the task allocation for CR and workers. The simulation model compares two scenarios (manual assembly operation vs. collaborative workstations), using the ESG framework described in Fig 1. Key performance indicators of energy consumption, scrap rate, worker utilization, processing and idle costs rates are evaluated to identify areas for improvement the economic, environmental and social sustainability. By incorporating ESG metrics and scenario-based analysis, the study demonstrates the potential for HRC to optimize production systems while improving worker well-being. Table 3 HRC assembly WP1 modelling parameters Machine/workplace Simulation model parameter M1 M2 M3 WP1 M4 M5 Processing time (s) 15 35 40 42; 6 40 60 Machine power (kW) 3.75 20 20 0.05 20 7.5 Workplace total processing costs 10.61 18.10 18.10 17.29 20.61 10.58 (€/h) Workplace total idle costs (€/h) 5.30 12.13 12.13 17.29 13.81 5.29 Scrap rate (%) 4.5 - 4. Results M6 35 20 20.61 13.81 - M7 25 3.75 10.61 3.5 - Fig. 4 HRC assembly production system model The simulation model was run to compare the performance of manual assembly operations with HRC at the WP1 in terms of utilization, power consumption, processing and idle costs, output quantity and scrap rate. The results highlight the differences in production efficiency, energy use, and operational costs between the two setups, emphasizing the benefits of HRC in achieving Industry 5.0 objectives. In Table 4, the utilization of the manual workstation WP1 reached a high value of 98.9 %, reflecting the bottleneck of the production process. However, several machines such as M1 (35.7 %), M4 (43.7 %), and M7 (27.3 %), exhibited significantly lower utilization, indicating unequal machine balancing. Total power consumption in the manual assembly setup was 532 Advances in Production Engineering & Management 19(4) 2024 Integrating simulation modelling for sustainable, human-centred Industry 5.0: ESG-based evaluation in collaborative … relatively high for the major machines. M2 and M3 consumed 1532.7 kW and 1751.7 kW, respectively, while WP1, being largely manual, consumed just 4.5 kW. The processing costs for the manual setup remained high, particularly for machines like M3 (€1585.3) and WP1 (€1434.0). The manual operation incurred significant idle costs for machines such as M7 (€709.6), demonstrating inefficiency in resource utilization. The manual assembly system produced 3613 finished products, with 289 scrap products, representing an 8 % scrap rate, supported by the real-world modelled parameter. Table 4 Simulation model results of the manual assembly WP1 Machine/workplace Simulation model parameter M1 M2 M3 WP1 M4 Utilization (%) 35.7 83.3 95.2 98.9 43.7 Machine power consumption (kW) 123.2 1532.7 1751.7 4.5 804.1 Processing costs (EUR) 348.5 1387.1 1585.3 1434.0 828.6 Idle costs (EUR) 313.5 186.4 53.6 15.9 1067.5 Number of finished products (pcs) 3613 Scrap products (pcs) 289 M5 65.5 452.0 637.6 335.8 M6 38.2 702.9 724.3 1171.8 M7 27.3 94.2 266.5 709.6 In contrast, the HRC workstation WP1, presented in Table 5, utilization slightly decreased to 95.9 %, but this reduction was compensated by a significant increase in the utilization of other machines. For example, M4 utilization improved to 90.9 %, and M7 to 41.6 %, showing that HRC distributes the workload more evenly across the manufacturing system. In the HRC scenario, the power consumption for WP1 increased to 13.2 kW due to the CR integration. However, more efficient operation across the system led to better overall energy usage, with M4 consuming 1672.6 kW, much higher than the manual setup but justified by improved product workflow. Processing costs increased for WP1 (€1525.5) due to the CR integration investments costs but resulted in an overall improvement in resource use. The idle costs for machines like M7 decreased to €570.1, indicating better synchronization between human and CR activities. The HRC system produced 5515 finished products, a significant improvement while scrap products increased to 344 products, reducing the scrap rate to 4.5 %. This shows that HRC improves overall product quality and reduces waste. Simulation model parameter Utilization (%) Machine power consumption (kW) Processing costs (EUR) Idle costs (EUR] Number of finished products (pcs) Scrap products (pcs) Table 5 Simulation model results of the HRC WP1 Machine/workplace M1 M2 M3 WP1 M4 36.8 82.9 94.9 95.9 90.9 127.0 1525.4 1746.2 13.2 1672.6 359.2 308.2 1380.5 190.8 1580.3 56.9 1525.5 1723.6 65.2 172.5 5515 M5 99.1 683.8 964.6 8.8 M6 58.3 1072.7 1105.4 790.7 M7 41.6 143.5 406.1 570.1 344 Fig. 5 presents that HRC WP1 significantly improves machine utilization, reducing idle time and improving overall productivity. The higher utilization in HRC indicates that CR help manage tasks, reducing worker strain and improving throughput. The average utilization of the manual assembly WP1 was 69.7 %, reflecting a high workload on human workers but suboptimal distribution of tasks across other machines. In the HRC system, the average utilization increased to 85.8 %, showing a more balanced distribution of work between humans and robots, leading to better resource efficiency. Fig. 6 demonstrates that while the HRC system consumes more energy, this increase is accompanied by improved production efficiency. The trade-off between higher energy use and greater output efficiency is clear in the comparison, where total power consumption for the manual assembly WP1 was 5465.2 kW, with machines like M2 and M3 consuming a significant portion of energy. The HRC setup showed a higher total power consumption of 6984.2 kW, mainly due to the added power required for HRC WP1 (13.2 kW vs. 4.5 kW in the manual assembly WP1). Advances in Production Engineering & Management 19(4) 2024 533 Ojstersek, Javernik, Buchmeister Fig. 5 Workplaces utilization results comparison Fig. 6 Workplaces power consumption comparison The total processing costs at the manual assembly WP1 amounted to 7211.8 EUR, largely driven by the intensive human labour required. Processing costs in the HRC system were 9045.1 EUR, reflecting the higher costs associated with integrating CR, but also the benefits of increased productivity. As shown in Fig. 7, the higher costs of HRC are offset by the increase in finished products, making it a more cost-effective option in the long term due to the reduction in errors and improved utilization. Fig. 7 Processing costs results comparison In Fig. 8, idle costs for the manual assembly WP1 were high, totalling 3540.6 EUR, with machines such as M7 incurring significant idle time due to underutilization. The HRC WP1 dramatically reduced idle costs to 2163.2 EUR, as the CR helped minimize downtime by keeping machines and workers engaged in tasks. As shown in Fig. 9, the integration of HRC not only increased total production but also improved product quality by reducing the scrap rate, which is essential for sustainable production systems. 534 Advances in Production Engineering & Management 19(4) 2024 Integrating simulation modelling for sustainable, human-centred Industry 5.0: ESG-based evaluation in collaborative … Fig. 8 Idle costs results comparison 5. Discussion Fig. 9 Number of finished and scrap products comparison The results demonstrate the advantages of HRC workplaces in the context of Industry 5.0 manufacturing, particularly from the human-centred manufacturing perspective. By integrating HRC at the WP1, we observed improvements in both production efficiency and sustainability, aligned with proposed ESG criteria in Fig. 1. Regarding energy consumption per product, at the manual assembly WP1, the average energy consumption was 1.51 W per product, where at the HRC WP1 energy consumption decreased to 1.27 W per product, representing a 15.9 % electrical energy consumption reduction. This reduction in energy consumption is attributed to the optimized task distribution between worker and CR. The HRC help reduce idle times and ensure smoother production flows, thus lowering the energy footprint per product. In the context of ESG, this improvement supports environmental sustainability, as reduced energy use leads to lower carbon emissions and a more energy-efficient production. On the other hand, processing costs per product at the manual assembly WP1 were 2 EUR per product, where at the HRC WP1 processing costs dropped to 1.64 EUR per product, resulting in an 18 % processing cost reduction. The integration of CR in the HRC significantly lowers labour costs, as robots take over repetitive and high-strain physical tasks, enabling workers to focus on higher-value tasks. This reduction in processing costs underscores the economic benefits of HRC, making it a more cost-effective solution over the long term, particularly when considering reduced errors and improved output quality. More detailed costs evaluation was taking into concern with the idle costs per product parameter where idle cost for manual assembly WP1 were 0.98 EUR per product. At the HRC WP1 idle costs were reduced to 0.39 EUR per product, indicating a significant 60.2 % decrease. The reduction in idle costs demonstrates the enhanced efficiency of HRC, as CR can maintain consistent operations and reduce downtime between tasks. From a governance perspective, this improvement in resource utilization reflects better production capacity, which is critical in highly dynamic production Advances in Production Engineering & Management 19(4) 2024 535 Ojstersek, Javernik, Buchmeister environments. If summarizing total cost per product at the manual assembly WP1 were 2.98 EUR and at the HRC WP1 were reduced to 2.03 EUR, representing a 31.9 % total cost reduction. This significant reduction in total costs per product reinforces the economic advantages of HRC. Not only does HRC improve resource utilization, but it also reduces operational costs, leading to a more sustainable manufacturing process that aligns with ESG goals. Form the environmental view the production output and scrap rate were evaluated, where at the manual assembly WP1 3613 finished products with a scrap rate of 8 % were made. At the HRC WP1 output quantity increased to 5515 finished products with a reduced scrap rate of 4.5 %. HRC's higher production output and lower scrap rate reflect the improved product quality and efficiency of HRC. This improvement supports the social sustainability aspect of ESG, as it reduces waste, improves product reliability, and enhances the overall working environment. The HRC offers substantial benefits in terms of human-centred manufacturing, which is a core principle of Industry 5.0. By redistributing tasks between humans and CR, HRC ensures that workers are less exposed to physically demanding or monotonous tasks, which contributes to better worker well-being and reduces stress levels. This improvement in working conditions supports the social pillar of ESG, emphasizing safety, engagement, and health in the workplace. The increased production efficiency and reduced waste contribute to the environmental and governance aspects of ESG by minimizing resource use, enhancing productivity, and promoting more sustainable and responsible manufacturing practices. 6. Conclusion The implementation of the HRC workstations in manufacturing has been shown that can lead to significant improvements in both economic and production processes performance, while simultaneously supporting sustainability goals as defined by ESG criterion. By reducing energy consumption, processing costs, idle times, and scrap rates, HRC systems offer a way to optimize production efficiency while enhancing the working environment. The integration of HRC is not only beneficial from an economic standpoint, but it also directly impacts worker well-being, a central theme in Industry 5.0. By redistributing strenuous and repetitive tasks to CR, workers experience lower physical and cognitive stress, leading to improved job satisfaction. This reinforces the social sustainability aspect of the ESG framework, ensuring safer and healthier workplaces. Presented results emphasize the potential for HRC to drive the future of manufacturing, enabling a harmonious balance between productivity, worker well-being, and environmental responsibility. As industries continue to move toward sustainable manufacturing, HRC systems present a solution for maintaining competitiveness while addressing the increasing demand for ethical and sustainable production practices. The presented research has broad applicability across various industries. The findings from this research could be applied in the manufacturing processes optimization, where the distribution of labour and production capacities between manual and automated systems can enhance overall production system performance. Insights can support the integration of ESG criteria into operational decision-making, ensuring that manufacturing systems are not only economically viable but also socially and environmentally responsible. In the future research we will focus on evaluation the physical and mental stress experienced by workers in HRC environments. Wearable technologies such as heart rate monitors or stress sensors will be employed to measure the impact of HRC on worker health. With those we will be able to provide additional insights into the human-centred design of workstations. While HRC systems improve operational performance, the next step is to optimize these systems for worker well-being. This could involve adjusting CR parameters to reduce cognitive load and physical strain on workers, potentially using adaptive algorithms that adjust CR speeds and tasks in realtime based on worker feedback. In addition, our future research work involves integrating worker knowledge management into HRC systems. By leveraging worker experience and expertise, manufacturing systems could be dynamically adapted to improve both efficiency and quality. For example, artificial intelligence driven knowledge management systems could capture worker inputs and suggestions, enhancing manufacturing system performance and further reducing errors or downtime. Incorporating these research directions would help evolve the Industry 5.0 paradigm, 536 Advances in Production Engineering & Management 19(4) 2024 Integrating simulation modelling for sustainable, human-centred Industry 5.0: ESG-based evaluation in collaborative … where human creativity and knowledge are enhanced by CR and artificial intelligence, leading to a more sustainable, efficient, and worker-friendly production environment. Acknowledgement The authors gratefully acknowledge the support of the Slovenian Research and Innovation Agency (ARIS), Research Core Funding No. P2-0190. 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Human factors considerations and metrics in shared space human-robot collaboration: A systematic review, Frontiers, Vol. 9, Article No. 799522, doi: 10.3389/FROBT.2022.799522. 538 Advances in Production Engineering & Management 19(4) 2024 Calendar of events • 16th EAI International Conference on Simulation Tools and Techniques, December 9-10, 2024, Bratislava, Slovakia. • International Conference on Smart Materials & Structures, March 27-28, 2025, Berlin, Germany. • 14th Spring World Congress on Engineering and Technology (SCET 2025), April 19-21, 2025, Guilin, China. • International Connect & Expo on Material Science and Engineering, April 28-20, 2025, Rome, Italy. • 2025 Annual Modeling and Simulation Conference (ANNSIM’25), May 26-29, 2025, Madrid, Spain. • Fifth International Conference on Simulation for Additive Manufacturing (Sim-AM 2025), September 9-11, 2025, Pavia, Italy. 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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 19 | Number 4 | December 2024 | pp 411-542 Contents Scope and topics 414 A bi-objective Genetic Algorithm for flexible flow shop scheduling: A real-world application in the electrical industry Escobar, D.; Chivata, B.; Nino, K. 415 Reducing scrap in long rolled round steel bars using Genetic Programming after ultrasonic testing Kovacic, M.; Zupanc, A.; Zuperl, U.; Brezocnik, M. 435 Optimizing electric vehicle charging strategies using multi-layer perception-based spatio-temporal prediction of charging station load Wang, Y.N.; Zhang, Z.J.; Ping, A.; Wang, R.J.; Gong, D.Q. 443 Sustainable design of products: Balancing quality, life cycle impact, and social responsibility Siwiec, D.; Gawlik, R.; Pacana, A. 460 An algorithmic review of the technological progress and milestones in resource-constrained project planning Pourhejazy, P.; Ying, K.-C.; Cheng, C.-Y. 489 Integrated production and maintenance policy for manufacturing systems prone to products' quality degradation BouAbid, H.; Dhouib, K.; Gharbi, A. 512 Integrating simulation modelling for sustainable, human-centred Industry 5.0: ESG-based evaluation in collaborative workplaces Ojstersek, R.; Javernik, A.; Buchmeister, B. 527 Calendar of events 539 Notes for contributors 541 Published by CPE, University of Maribor ISSN 1854-6250 9 771854 625008 apem-journal.org