ارائه مدل ریاضی جدید MILP جهت بهینه‌سازی خطوط مونتاژ مختلط با رویکرد فراابتکاری روش ABC-PSO
محورهای موضوعی : مدیریت صنعتیneda mozaffari 1 , HASAN MEHRMANESH 2 , mahmoud mohammadi 3
1 - Industrial Management, Faculty of Management, Islamic Azad University Central Tehran Branch،Tehran, Iran.
2 - Faculty of Management, Islamic Azad University Central Tehran Branch, Tehran, Iran
3 - Faculty of Management, Islamic Azad University Central Tehran Branch, Tehran, Iran.
کلید واژه: "بالانس خطوط مونتاژ, "روش MILP, الگوریتم فراابتکاری زنبورعسل", "بهینه‌سازی",
چکیده مقاله :
مسئله متعادل‌سازی خطوط مونتاژ از جمله مسائل بهینه‌سازی است که توسط محققین مختلف بسیاری مورد مطالعه قرارگرفته است. با این‌وجود و پس از شش دهه تحقیق و توسعه، وجود شکافی عمیق بین مطالعات دانشگاهی انجام‌شده در این زمینه با کاربردهای عملی مسئله متعادل‌سازی خط مونتاژ در محیط واقعی صنعت محسوس می‌باشد. به‌همین دلیل این تحقیق با هدف ایجاد تعادل در خطوط مونتاژ مختلط در جهت کاهش هزینه نیروی‌انسانی و کاهش تعداد ایستگاه‌های کاری انجام شده است. برای حل مساله از مجموعه داده شامل 7 ایستگاه کاری و 70 وظیفه و زمان حل 500 ثانیه و زمان انجام هر فعالیت شامل 260 فعالیت مشخص، با روابط پیش نیازی تعیین شده دو رویکرد کلی به کار گرفته می شود، ابتدا مساله با روش دقیق از طریق نرم افزار گمز مدل حل شده است. سپس یک بار دیگر مساله با الگوریتم فراابتکاری زنبورعسل تغییر یافته در نرم افزار متلب حل شده است و در نهایت با استفاده از روش جدید و تلفیقی الگوریتم زنبورعسل هیبریدی با روش PSO نیز حل شده است و در آخر مقادیر بدست آمده تابع هدف هر دو روش باهم مقایسه شده است و نتایج نشان می دهد که الگوریتم زنبورعسل هیبریدی در همان مراحل اولیه بهینه سازی به جواب بهینه رسیده است و مقدار تابع هدف آن به مینیمم مقدار خود رسیده است و کمترین مقدار تخطی قیود را نیز بدست آورده است و نشان از کاهش هزینه و کاهش ایستگاه‌های کاری به 3 ایستگاه دارد.
The problem of balancing assembly lines is one of the optimization problems that have been studied by many researchers. However, after six decades of research and development, there is a profound gap between academic studies in this area and the practical applications of the assembly line balancing problem in the real industry environment. For this reason, this study aimed to balance the complex assembly lines in order to reduce the cost of manpower and reduce the number of workstations. To solve the problem from the dataset consisting of 7 workstations and 70 tasks and the time to solve 500 seconds and the time of performing each activity including 260 specific activities, two general approaches are used to determine the prerequisite relationships. Gams model software is resolved. Then the problem is solved once again with the modified honeycomb algorithm in MATLAB software and finally solved by the new hybrid honeycomb algorithm with PSO method and finally the obtained values of the objective function of both methods are combined. Have been compared and the results show that the hybrid honeycomb algorithm is optimized at the same early stages of optimization and its objective function value reaches its minimum value and also obtained the least amount of constraint violation and shows cost and cost reductions. Reduces workstations to 3.
1- Adithan, M. (2007). Process Plsnning and Cost Estimation. Publishing for one world new age.computers &industrial engineering.pp.165-173.
2- Agha jani, Hasan Ali; Samadi Miarkalani, Hamzeh; Samadi Miarkalani, Hamzeh, Hussein; Lotfi, Hussein. (2015). A Simulation Approach for Improving the Assembly Line of DESA, Industrial Management Magazine, Volume 6, No. 4, pp. 635-664.
3- Akpinar, S., Elmi, A., & Bektaş, T. (2017). Combinatorial Benders cuts for assembly line balancing problems with setups. European Journal of Operational Research, 259(2), 527-537.
4- Anthony, K. A. (2016). Effect of Capacity Planning On Performance in Nigeria Brewing Industry: Southeast Perspective. Imperial Journal of Interdisciplinary Research, 3(1).
5- Battaïa, O., & Dolgui, A. (2013). A taxonomy of line balancing problems and their solution approaches. International Journal of Production Economics, 142(2), 259-277.
6- Bukchin, Y., & Raviv, T. (2017). Constraint programming for solving various assembly line balancing problems. Omega.
7- Chen, J. C., Chen, T. L., & Harianto, H. (2018). Capacity planning for packaging industry. Journal of manufacturing systems, 42, 153-169.
8- Company, Mahmud Saeed; Parham, Azimi. (2015). The Development of a New Two-Dimensional Model and its Solution by Optimization through Simulation for the OptimalAllocation of Human Resources and Parallel Equipment to the Stations in a Production Line, Industrial Management Studies . 15th year.
9- Ding, H., Reißig, G., Groß, D., & Stursberg, O. (2011). Mixed-integer programming for optimal path planning of robotic manipulators. In Automation Science and Engineering (CASE), 2011 IEEE Conference (pp. 133-138).
10- Fleszar, K. (2017). A new MILP model for the accessibility windows assembly line balancing problem level 2 (AWALBP-L2). European Journal of Operational Research, 259(1), 169-174.
11- Hasani, Ali Akbar. (2018). Multi-objective Meta-Heuristic for the Distributed Scheduling of M-Machine Reentrant Permutation Flowshop Problem by Considering the Preventive Maintenance under Uncertainty Conditions,Journal of Production Management and Operations,Volume (9), Issue 17, No. 2, pp. 1-21.
12- Husseini Malekabadi, Rasool. (2016). An Overview of the Problems Related to Improper Math Optimization, Isfahan University, Mathematics and Society, Vol. 1
13- Hwang, R.K., Katayama, H. & Gen, M. (2008). U-shaped assembly line balancing problem with genetic algorithm. International Journal of Production Research, 46(16), 4637-4649.
14- Jafari Asl,Abolfazl,solimanipour,maghsoud.ShankarRavi.(2019).Multi‑objectivemulti‑model assembly line balancing problem: a quantitative study in engine manufacturing industry. Operational Research Society of India.
15- Keckl, S., Kern, W., Abou-Haydar, A., & Westkämper, E. (2016). An analytical framework for handling production time variety at workstations of mixed-model assembly lines. Procedia CIRP, 41, 201-206.
16- Li, Z., Kucukkoc, I., & Tang, Q. (2017). New MILP model and station-oriented ant colony optimization algorithm for balancing U-type assembly lines. Computers & Industrial Engineering, 112, 107-121.
17- Mahmudi Rad, Ali; Nirumand, Sadegh; Sanei, Masoud. (2016). Fuzzy Multi-Objective Assembly Line Balance Problem: Fuzzy Mathematical Programming Method, New Research in Mathematics.
18- Makssoud, F., Battaïa, O., Dolgui, A., Mpofu, K., & Olabanji, O. (2015). Re-balancing problem for assembly lines: new mathematical model and exact solution method. Assembly Automation, 35(1), 16-21..
19- Matti Koivisto.(2017).Modelling, Simulation and Optimization of the Materials Flow of a Multi-product AssemblingPlant.Procedia Manufacturing, Volume 8, Pages 59-66.
20- Mohammadi Zanjirani, Dariush; Jokar, Saeedeh; Ismailis, Majid. (2016). Integrated Scheduling and Programming of Process Based on the Combination of Fuzzy Knowledge Base and Meta-Heuristic Methods. Quarterly Journal of Industrial Management Studies – 14th year, No. 34.
21- Nouri Darian, Mahsa; Talei Zadeh, Ataullah. (2018). The Development of Economic Production Model in Three-Level Integrated and Non-Integrated Supply Chains Regarding the Integrated Management of Inventory Control, Journal of Industrial Engineering, Vol. 52, No. 1, pp. 125 -137.
22- Pearce Bryan W., Kavit Antani, Laine Mears, Kilian Funk, Maria E. Mayorga, Mary E. Kurz.(2019). An effective integer program for a general assembly line balancing problem with parallel workers and additional assignment restrictions. Journal of Manufacturing Systems.50 .2019.180-192.
23- Popović, Ž, Brbaklić, B., & Knežević, S. (2017). A mixed integer linear programming based approach for optimal placement of different types of automation devices in distribution networks. Electric Power Systems Research, 148, 136-146.
24- Rabbani, M., Moghaddam, M. & Manavizadeh, N. (2012). Balancing of mixed-model two-sided assembly lines with multiple U-shaped layout. International Journal of Advanced Manufacturing Technology 59(9-12), 1191-1210.
25- Samiaria A.S. Vialarinhop.M (2004).A Genetic algorithm based approach to the mixed model assembly line balancing problem of type .computers&industrial engineering .47:391-407.
26- Samoue،Parvaneh،Ashayeri Jalal (2019). Developing optimization & robust models for a mixed-model assembly line balancing problem with semi-automated operations. Applied Mathematical Modelling. 72. 259-275.
27- Sikora, C. G. S., Lopes, T. C., & Magatão, L. (2018). Traveling worker assembly line (re) balancing problem: Model, reduction techniques, and real case studies. European Journal of Operational Research, 259(3), 949-971.
28- Tapkan, P., Ozbakir, L., & Baykasoglu, A. (2012). Modeling and solving constrained two-sided assembly line balancing problem via bee algorithms. Applied Soft Computing, 12(11), 3343-3355.
29- Taghavi Fard, Muhammad Taghi. (2011). A New Mathematical Model to Solve the Problems of Multi-Product Assembly Line Balance”, Industrial Management Magazine, Volume (3), No.6, pp. 1-16.
30- Tsutsumia Daisuke ,b,*,Dávid Gyulaic, András Kovácsc,Bence Tiparyc,Yumiko Uenoa, Youichi Nonakaa,Kikuo Fujitab.(2020). Joint optimization of product tolerance design ,process plan ,and production plan in high-precision multi-product assembly. Journal of Manufacturing Systems.54 (2020)336-347.
31- Wang, Y.F; Zhang, Y.F; & Fuh, J.Y.H. (2010). A PSO-based multiobjective optimization approach to the integration of process planning and scheduling. IEEE International Conference on Control and Automation, Xiamen, China, June 9-11.
32- Wengxiang gu.minghao yin.chunying wang. (2012).Self Adaptive Artificial Bee Colony for Global Numerical Optimization.Journal: IERI Procedia, Volume 1, Pages 59–65.
33- Zhang, W., & Gen, M. (2011). An efficient multiobjective genetic algorithm for mixed-model assembly line balancing problem considering demand ratio-based cycle time. Journal of Intelligent Manufacturing, 22(3), 367-378.
_||_1- Adithan, M. (2007). Process Plsnning and Cost Estimation. Publishing for one world new age.computers &industrial engineering.pp.165-173.
2- Agha jani, Hasan Ali; Samadi Miarkalani, Hamzeh; Samadi Miarkalani, Hamzeh, Hussein; Lotfi, Hussein. (2015). A Simulation Approach for Improving the Assembly Line of DESA, Industrial Management Magazine, Volume 6, No. 4, pp. 635-664.
3- Akpinar, S., Elmi, A., & Bektaş, T. (2017). Combinatorial Benders cuts for assembly line balancing problems with setups. European Journal of Operational Research, 259(2), 527-537.
4- Anthony, K. A. (2016). Effect of Capacity Planning On Performance in Nigeria Brewing Industry: Southeast Perspective. Imperial Journal of Interdisciplinary Research, 3(1).
5- Battaïa, O., & Dolgui, A. (2013). A taxonomy of line balancing problems and their solution approaches. International Journal of Production Economics, 142(2), 259-277.
6- Bukchin, Y., & Raviv, T. (2017). Constraint programming for solving various assembly line balancing problems. Omega.
7- Chen, J. C., Chen, T. L., & Harianto, H. (2018). Capacity planning for packaging industry. Journal of manufacturing systems, 42, 153-169.
8- Company, Mahmud Saeed; Parham, Azimi. (2015). The Development of a New Two-Dimensional Model and its Solution by Optimization through Simulation for the OptimalAllocation of Human Resources and Parallel Equipment to the Stations in a Production Line, Industrial Management Studies . 15th year.
9- Ding, H., Reißig, G., Groß, D., & Stursberg, O. (2011). Mixed-integer programming for optimal path planning of robotic manipulators. In Automation Science and Engineering (CASE), 2011 IEEE Conference (pp. 133-138).
10- Fleszar, K. (2017). A new MILP model for the accessibility windows assembly line balancing problem level 2 (AWALBP-L2). European Journal of Operational Research, 259(1), 169-174.
11- Hasani, Ali Akbar. (2018). Multi-objective Meta-Heuristic for the Distributed Scheduling of M-Machine Reentrant Permutation Flowshop Problem by Considering the Preventive Maintenance under Uncertainty Conditions,Journal of Production Management and Operations,Volume (9), Issue 17, No. 2, pp. 1-21.
12- Husseini Malekabadi, Rasool. (2016). An Overview of the Problems Related to Improper Math Optimization, Isfahan University, Mathematics and Society, Vol. 1
13- Hwang, R.K., Katayama, H. & Gen, M. (2008). U-shaped assembly line balancing problem with genetic algorithm. International Journal of Production Research, 46(16), 4637-4649.
14- Jafari Asl,Abolfazl,solimanipour,maghsoud.ShankarRavi.(2019).Multi‑objectivemulti‑model assembly line balancing problem: a quantitative study in engine manufacturing industry. Operational Research Society of India.
15- Keckl, S., Kern, W., Abou-Haydar, A., & Westkämper, E. (2016). An analytical framework for handling production time variety at workstations of mixed-model assembly lines. Procedia CIRP, 41, 201-206.
16- Li, Z., Kucukkoc, I., & Tang, Q. (2017). New MILP model and station-oriented ant colony optimization algorithm for balancing U-type assembly lines. Computers & Industrial Engineering, 112, 107-121.
17- Mahmudi Rad, Ali; Nirumand, Sadegh; Sanei, Masoud. (2016). Fuzzy Multi-Objective Assembly Line Balance Problem: Fuzzy Mathematical Programming Method, New Research in Mathematics.
18- Makssoud, F., Battaïa, O., Dolgui, A., Mpofu, K., & Olabanji, O. (2015). Re-balancing problem for assembly lines: new mathematical model and exact solution method. Assembly Automation, 35(1), 16-21..
19- Matti Koivisto.(2017).Modelling, Simulation and Optimization of the Materials Flow of a Multi-product AssemblingPlant.Procedia Manufacturing, Volume 8, Pages 59-66.
20- Mohammadi Zanjirani, Dariush; Jokar, Saeedeh; Ismailis, Majid. (2016). Integrated Scheduling and Programming of Process Based on the Combination of Fuzzy Knowledge Base and Meta-Heuristic Methods. Quarterly Journal of Industrial Management Studies – 14th year, No. 34.
21- Nouri Darian, Mahsa; Talei Zadeh, Ataullah. (2018). The Development of Economic Production Model in Three-Level Integrated and Non-Integrated Supply Chains Regarding the Integrated Management of Inventory Control, Journal of Industrial Engineering, Vol. 52, No. 1, pp. 125 -137.
22- Pearce Bryan W., Kavit Antani, Laine Mears, Kilian Funk, Maria E. Mayorga, Mary E. Kurz.(2019). An effective integer program for a general assembly line balancing problem with parallel workers and additional assignment restrictions. Journal of Manufacturing Systems.50 .2019.180-192.
23- Popović, Ž, Brbaklić, B., & Knežević, S. (2017). A mixed integer linear programming based approach for optimal placement of different types of automation devices in distribution networks. Electric Power Systems Research, 148, 136-146.
24- Rabbani, M., Moghaddam, M. & Manavizadeh, N. (2012). Balancing of mixed-model two-sided assembly lines with multiple U-shaped layout. International Journal of Advanced Manufacturing Technology 59(9-12), 1191-1210.
25- Samiaria A.S. Vialarinhop.M (2004).A Genetic algorithm based approach to the mixed model assembly line balancing problem of type .computers&industrial engineering .47:391-407.
26- Samoue،Parvaneh،Ashayeri Jalal (2019). Developing optimization & robust models for a mixed-model assembly line balancing problem with semi-automated operations. Applied Mathematical Modelling. 72. 259-275.
27- Sikora, C. G. S., Lopes, T. C., & Magatão, L. (2018). Traveling worker assembly line (re) balancing problem: Model, reduction techniques, and real case studies. European Journal of Operational Research, 259(3), 949-971.
28- Tapkan, P., Ozbakir, L., & Baykasoglu, A. (2012). Modeling and solving constrained two-sided assembly line balancing problem via bee algorithms. Applied Soft Computing, 12(11), 3343-3355.
29- Taghavi Fard, Muhammad Taghi. (2011). A New Mathematical Model to Solve the Problems of Multi-Product Assembly Line Balance”, Industrial Management Magazine, Volume (3), No.6, pp. 1-16.
30- Tsutsumia Daisuke ,b,*,Dávid Gyulaic, András Kovácsc,Bence Tiparyc,Yumiko Uenoa, Youichi Nonakaa,Kikuo Fujitab.(2020). Joint optimization of product tolerance design ,process plan ,and production plan in high-precision multi-product assembly. Journal of Manufacturing Systems.54 (2020)336-347.
31- Wang, Y.F; Zhang, Y.F; & Fuh, J.Y.H. (2010). A PSO-based multiobjective optimization approach to the integration of process planning and scheduling. IEEE International Conference on Control and Automation, Xiamen, China, June 9-11.
32- Wengxiang gu.minghao yin.chunying wang. (2012).Self Adaptive Artificial Bee Colony for Global Numerical Optimization.Journal: IERI Procedia, Volume 1, Pages 59–65.
33- Zhang, W., & Gen, M. (2011). An efficient multiobjective genetic algorithm for mixed-model assembly line balancing problem considering demand ratio-based cycle time. Journal of Intelligent Manufacturing, 22(3), 367-378.