نوع مقاله : مقاله پژوهشی

نویسندگان

گروه مهندسی صنایع و سیستم‏ها، دانشگاه تربیت مدرس، تهران، ایران.

چکیده

هدف: در این مطالعه با توجه به اهمیت مساله بالانس خطوط مونتاژ U شکل و از سوی دیگر اهمیت فاکتورهای انسانی و زمان‌های آماده‌سازی، یک مدل ریاضی دو‌هدفه با اهداف کاهش زمان چرخه و کاهش مجموع هزینه‌های کارگران تخصیص داده‌شده به ایستگاه‌های ‌کاری توسعه داده شده ‏است.
روش‌شناسی پژوهش: ازآن‌جا‌که مساله مورد‌نظر ازلحاظ پیچیدگی جزو مسایل Np-hard می‌باشد لذا از الگوریتم‌های فرا ابتکاری ژنتیک مرتب‌سازی نامغلوب II که الگوریتمی مبتنی‌بر جمعیت می‌باشد و هم‌چنین از نسخه دوم الگوریتم تکاملی مبتنی‌بر قوت پارتو برای حل مدل استفاده کرده‌ایم.
یافته‌ها: یک مدل ریاضی برای مساله تحت‌بررسی توسعه داده شده است. مساله مورد‌نظر با استفاده از الگوریتم‌‏های NSGA-II و SPEA-II حل شده است. در انتها نیز به‌منظور تحلیل نتایج مدل دو‌هدفه و ارزیابی عملکرد الگوریتم‌های تکاملی چندهدفه از چهار معیار تعداد جواب‌های پارتو، میانگین فاصله از نقطه ایده‌آل، شاخص گوناگونی و شاخص کیفیت استفاده نمودیم. نتایج محاسباتی نشان از برتری الگوریتم NSGA-II بر SPEA-II دارد.
اصالت/ارزش‌افزوده علمی: یک مدل ریاضی دو‌هدفه برای مساله بالانس خط مونتاژ U شکل با در‌نظر‌گرفتن زمان‌های آماده‌سازی و مهارت کارگران توسعه داده شده و مساله مورد‌‌بررسی با دو الگوریتم حل شده است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Multi-objective optimization of the U-shaped assembly line ‎balancing and worker assignment considering setup-times ‎and workers' skill

نویسندگان [English]

  • Ali Husseinzadeh Kashan
  • Saeed Afkhami
  • Parisa Maroofkhani

Department of Industrial and Systems Engineering, Tarbiat Modares University, Tehran, Iran.

چکیده [English]

Purpose: In this research due to the importance of the U-shaped assembly line balancing and, on the other hand, the importance of human factors and setup times, we want to develop a bi-objective mathematical model minimize the cycle time and the total cost.
Methodology: Since the research problem is shown to be NP-hard, NSGA-II, which is a population-based algorithm, and also SPEA-II are used to solve the problem.
Findings: A mathematical model for the problem on hand is developed. We solve the problem using NSGA-II and SPEA-II. We use four criteria for analyzing the results of the mathematical model and evaluating the performance of the multi-objective evolutionary algorithms. The experimental results demonstrate that NSGA-II is superior to SPEA-II.
Originality/Value: A bi-objective mathematical model for the U-shaped assembly line balancing problem considering setup-times and workers' skill is developed, and the problem is solved using two algorithms.

کلیدواژه‌ها [English]

  • U-shaped assembly line balancing
  • Setup time
  • Workers' skill
  • NSGA-II
  • SPEA-II
[1]     Sparling, D., & Miltenburg, J. (1998). The mixed-model U-line balancing problem. International journal of production research, 36(2), 485–501.
[2]     Faqih, N., & Montazeri, M. M. (2009). Genetic algorithms for assembly line balancing problem. Journal of industrial management, 1(1), 107–124.
[3]     Boysen, N., Fliedner, M., & Scholl, A. (2007). A classification of assembly line balancing problems. European journal of operational research, 183(2), 674–693.
[4]     Lusa, A. (2008). A survey of the literature on the multiple or parallel assembly line balancing problem. European journal of industrial engineering, 2(1), 50–72.
[5]     Emde, S., Boysen, N., & Scholl, A. (2009). Balancing mixed-model assembly lines: a computational evaluation of objectives to smoothen workload. International journal of production research, 48(11), 3173–3191. DOI: 10.1080/00207540902810577
[6]     Rekiek, B., & Delchambre, A. (2006). Assembly line design: the balancing of mixed-model hybrid assembly lines with genetic algorithms. Springer Science & Business Media.
[7]     Gökçen, H., Ağpak, K., & Benzer, R. (2006). Balancing of parallel assembly lines. International journal of production economics, 103(2), 600–609.
[8]     Chutima, P., & Naruemitwong, W. (2014). A Pareto biogeography-based optimisation for multi-objective two-sided assembly line sequencing problems with a learning effect. Computers & industrial engineering, 69, 89–104.
[9]     Miltenburg, G. J., & Wijngaard, J. (1994). The U-line line balancing problem. Management science, 40(10), 1378–1388.
[10]   Scholl, A., & Klein, R. (1999). ULINO: optimally balancing U-shaped JIT assembly lines. International journal of production research, 37(4), 721–736.
[11]   Fattahi, A., Elaoud, S., Sadeqi Azer, E., & Turkay, M. (2014). A novel integer programming formulation with logic cuts for the U-shaped assembly line balancing problem. International journal of production research, 52(5), 1318–1333.
[12]   Andres, C., Miralles, C., & Pastor, R. (2008). Balancing and scheduling tasks in assembly lines with sequence-dependent setup times. European journal of operational research, 187(3), 1212–1223.
[13]   Rabbania, M., Siadatiana, R., & Manavizadeh, N. (2017). Balancing and sequencing U-shaped mixed model assembly line problem considering setup times between tasks and demand ratio-base in dynamic environments. 13th international conference on industrial engineering (IIEC 2017). Mazandaran University of Science Technology. (In Persian). https://www.sid.ir/FileServer/SE/502e201713234.pdf
[14]   Delice, Y., Aydougan, E. K., Özcan, U., & Ilkay, M. S. (2017). Balancing two-sided U-type assembly lines using modified particle swarm optimization algorithm. 4or, 15(1), 37–66. DOI: 10.1007%2Fs10288-016-0320-4
[15]   Sahin, M., & Kellegöz, T. (2017). Increasing production rate in U-type assembly lines with sequence-dependent set-up times. Engineering optimization, 49(8), 1401–1419. DOI: 10.1080/0305215X.2016.1256394
[16]   Mozafari, N., Mehrmanesh, H., & Mohammadi, M. (2020). Presenting a new MILP mathematical model for the optimization of mixed assembly lines with the meta-heuristic approach of the ABC-PSO method. Quarterly magazine of strategic management in industrial systems (former industrial management), 14(50), 88–100.
[17]   Li, Z., Janardhanan, M. N., & Rahman, H. F. (2021). Enhanced beam search heuristic for U-shaped assembly line balancing problems. Engineering optimization, 53(4), 594–608. DOI: 10.1080/0305215X.2020.1741569
[18]   Hazır, Ö., & Dolgui, A. (2015). A decomposition based solution algorithm for U-type assembly line balancing with interval data. Computers & operations research, 59(1), 126–131. DOI: https://doi.org/10.1016/j.cor.2015.01.010
[19]   Li, Y., Hu, X., Tang, X., & Kucukkoc, I. (2019). Type-1 U-shaped assembly line balancing under uncertain task time. IFAC-papers online, 52(13), 992–997.
[20]   Ghandi Bidgoli, S., & Karimi, F. (2020). A simulation-based optimization approach for mixed model two-sided assembly line balancing with stochastic task times (case study: Beh Afarinan Datis Tiva company). Journal of industrial engineering research in production systems, 8(16), 199–213.
[21]   Nakade, K., & Ohno, K. (1999). An optimal worker allocation problem for a U-shaped production line. International journal of production economics, 60, 353–358.
[22]   Nakade, K., & Ohno, K. (2003). Separate and carousel type allocations of workers in a U-shaped production line. European journal of operational research, 145(2), 403–424.
[23]   Corominas, A., Pastor, R., & Plans, J. (2008). Balancing assembly line with skilled and unskilled workers. Omega, 36(6), 1126–1132.
[24]   Öksüz, M. K., & Satouglu, C. (2014). Balancing u-shaped assembly lines by considering human factors [presentation]. Proceedings of the global conference on engineering and technology management (pp. 23–26). https://www.academia.edu/download/45192526/Balancing_U-Shaped_Assembly_Lines_by_Considering_Human_Factors.pdf
[25]   Toksari, M. D., Icsleyen, S. K., Güner, E., & Baykoç, Ö. F. (2008). Simple and U-type assembly line balancing problems with a learning effect. Applied mathematical modelling, 32(12), 2954–2961.
[26]   Otto, C., & Otto, A. (2014). Extending assembly line balancing problem by incorporating learning effects. International journal of production research, 52(24), 7193–7208.
[27]   Asadi-Zonouz, M., Khalili, M., & Tayebi, H. (2020). A hybrid unconscious search algorithm for mixed-model assembly line balancing problem with SDST, parallel workstation and learning effect. Journal of optimization in industrial engineering, 13(2), 123–140.
[28]   Miralles, C., Garcia-Sabater, J. P., Andres, C., & Cardos, M. (2007). Advantages of assembly lines in sheltered work centres for disabled. A case study. International journal of production economics, 110(1–2), 187–197.
[29]   Miralles, C., Garcia-Sabater, J. P., Andrés, C., & Cardós, M. (2008). Branch and bound procedures for solving the assembly line worker assignment and balancing problem: application to sheltered work centres for disabled. Discrete applied mathematics, 156(3), 352–367.
[30]   Vila, M., & Pereira, J. (2014). A branch-and-bound algorithm for assembly line worker assignment and balancing problems. Computers & operations research, 44, 105–114.
[31]   Borba, L., & Ritt, M. (2014). A heuristic and a branch-and-bound algorithm for the assembly line worker assignment and balancing problem. Computers & operations research, 45, 87–96.
[32]   Polat, O., Kalayci, C. B., Mutlu, Ö., & Gupta, S. M. (2016). A two-phase variable neighbourhood search algorithm for assembly line worker assignment and balancing problem type-II: an industrial case study. International journal of production research, 54(3), 722–741.
[33]   Oksuz, M. K., Buyukozkan, K., & Satoglu, S. I. (2017). U-shaped assembly line worker assignment and balancing problem: a mathematical model and two meta-heuristics. Computers & industrial engineering, 112, 246–263.
[34]   Janardhanan, M. N., Li, Z., & Nielsen, P. (2019). Model and migrating birds optimization algorithm for two-sided assembly line worker assignment and balancing problem. Soft computing, 23, 11263–11276.
[35]   Moreira, M. C. O., Cordeau, J. F., Costa, A. M., & Laporte, G. (2015). Robust assembly line balancing with heterogeneous workers. Computers & industrial engineering, 88, 254–263.
[36]   Moreira, M. C. O., Miralles, C., & Costa, A. M. (2015). Model and heuristics for the assembly line worker integration and balancing problem. Computers & operations research, 54, 64–73.
[37]   Nakade, K., Ito, A., & Ali, S. M. (2015). U-shaped assembly line balancing with temporary workers. International journal of industrial engineering: theory, applications and practice, 22(1). DOI: 10.23055/ijietap.2015.22.1.1211
[38]   Xin, B., Li, Y., Yu, J., & Zhang, J. (2015). An adaptive BPSO algorithm for multi-skilled workers assignment problem in aircraft assembly lines. Assembly automation, 35(4), 317–328.
[39]   Nakade, K. (2017). Effect of worker sequence on cycle time in a U-shaped line with chase mode. International journal of production research, 55(10), 2752–2763.
[40]   Salehi, M., Maleki, H. R., & Niroomand, S. (2018). A multi-objective assembly line balancing problem with worker’s skill and qualification considerations in fuzzy environment. Applied intelligence, 48, 2137–2156.
[41]   Mirabedini, S. N., Mina, H., Iranmanesh, S. H., & Saleckpay, B. (2013). Optimization of a single model u-slab with stochastic duration with integration of genetic algorithm and computer simulation. Research journal of applied sciences, engineering and technology, 6(15), 2846–2858.
[42]   Delice, Y., Aydougan, E. K., Söylemez, I., & Özcan, U. (2018). An ant colony optimisation algorithm for balancing two-sided U-type assembly lines with sequence-dependent set-up times. Sādhanā, 43, 1–15. DOI: doi.org/10.1007/s12046-018-0969-9
[43]   Yolmeh, A., & Salehi, N. (2017). A branch, price and remember algorithm for the U shaped assembly line balancing problem. DOI: 10.48550/arXiv.1708.04127
[44]   Özcan, U., & Toklu, B. (2010). Balancing two-sided assembly lines with sequence-dependent setup times. International journal of production research, 48(18), 5363–5383.
[45]   Ayazi, S., Hajizadeh, A., Nooshabadi, M., & Jalaie, H. (2011). Multi-objective assembly line balancing using genetic algorithm. International journal of industrial engineering computations, 2(4), 863–872.
[46]   Deb, K., Agrawal, S., Pratap, A., & Meyarivan, T. (2000). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics), 1917, 849–858. DOI: 10.1007/3-540-45356-3_83/COVER
[47]   DE, G. (1989). Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Longman Publishing Co., Inc.
[48]   Zitzler, E., Laumanns, M., & Thiele, L. (2001). SPEA2: improving the strength pareto evolutionary algorithm (No. 103). https://doi.org/10.3929/ethz-a-004284029
[49]   Taguchi, G. (1986). Introduction to quality engineering: designing quality into products and processes. Quality Resources.
[50]   Montgomery, D. C. (2017). Design and analysis of experiments. John Wiley & Sons.