A bi-level bi-objective mathematical model for cellular manufacturing system applying evolutionary algorithms

Document Type : Article


1 Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, P.O. Box 4716685635, Iran.

2 Department of Industrial Engineering, Babol Noshirvani University of Technology, Babol, P.O. Box 4714871167, Iran


The present study aimed to design a bi-objective bi-level mathematical model for multi-dimensional cellular manufacturing system. Minimizing the total number of voids and balancing the assigned workloads to cells are regarded as two objectives of the upper level of the model. However, the lower level attempts to maximize the workers' interest to work together in a special cell. To this aim, two nested bi-level metaheuristics including particle swarm optimization (NBL-PSO) and a population-based simulated annealing algorithm (NBL-PBSA) were implemented to solve the model. In addition, the goal programming approach was utilized in the upper level procedure of these algorithms. Further, nine numerical examples were applied to verify the suggested framework and the TOPSIS method was used to find the better algorithm. Furthermore, the best weights for upper level objectives were tuned by using a weight sensitivity analysis. Based on computational results, all three objectives were different from their ideal goals when decisions about inter and intra-cell layouts, and cell formation to balance the assigned workloads by considering voids and workers' interest were simultaneously madeby considering a wide assumption-made problem closer to the real world. Finally, NBL-PBSA could perform better than NBL-PSO, which confirmed the efficiency of the proposed framework.


Main Subjects

1. Tompkins, J.A., White, J.A., Bozer, Y.A., and Tanchoco, J.M.A. "Facilities planning - 4th edition", Int. J. Prod. Res., 49(24), pp. 7519-7520 (2011).
2. Behnia, B., Mahdavi, I., Shirazi, B., and Paydar, M.M. "A bi-level mathematical programming for cell formation problem considering workers' interest", Int. J. Ind. Eng. Prod. Res., 28(3), pp. 267-277 (2017).
3. Dale, B.G., Burbidge, J.L., and Cottam, M.J. "Planning the Introduction of Group Technology", Int. J. Oper. Prod. Manag., 4(1), pp. 34-47 (1984).
4. Wemmerlov, U. and Hyer, N.L. "Research issues in cellular manufacturing", Int. J. Prod. Res., 25(3), pp. 413-431 (1987).
5. Bajestani, M.A., Rabbani, M., Rahimi-Vahed, A.R., and Baharian Khoshkhou, G. "A multi-objective scatter search for a dynamic cell formation problem", Comput. Oper. Res., 36(3), pp. 777-794 (2009).
6. Sudhakara Pandian, R. and Mahapatra, S.S. "Manufacturing cell formation with production data usingneural networks", Comput. Ind. Eng., 56(4), pp. 1340-1347 (2009).
7. Yin, Y. and Yasuda, K. "Similarity coefficient methods applied to the cell formation problem: a comparative investigation", Comput. Ind. Eng., 48(3), pp. 471-489 (2005).
8. Forghani, K. and Mohammadi, M. "A genetic algorithm for solving integrated cell formation and layout problem considering alternative routings and machine capacities", Sci. Iran. Trans. E, 21(6), pp. 2326-2346 (2014).
9. Shafer, S.M. and Rogers, D.F. "A goal programming approach to the cell formation problem", J. Oper. Manag., 10(1), pp. 28-43 (1991).
10. Mahdavi, I., Aalaei, A., Paydar, M.M., and Solimanpur, M. "Designing a mathematical model for dynamic cellular manufacturing systems considering production planning and worker assignment", Comput. Math. with Appl., 60(4), pp. 1014-1025 (2010).
11. Mahdavi, I., Javadi, B., Fallah-Alipour, K., and Slomp, J. "Designing a new mathematical model for cellular manufacturing system based on cell utilization", Appl. Math. Comput., 190(1), pp. 662-670 (2007).
12. Liao, T.W. "Classification and coding approaches to part family formation under a fuzzy environment", Fuzzy Sets Syst., 122(3), pp. 425-441 (2001).
13. Renzi, C., Leali, F., Cavazzuti, M., and Andrisano, A.O. "A review on artificial intelligence applications to the optimal design of dedicated and reconfigurable manufacturing systems", Int. J. Adv. Manuf. Technol., 72(1-4), pp. 403-418 (2014).
14. Mahdavi, I., Aalaei, A., Paydar, M.M., and Solimanpur, M. "A new mathematical model for integrating all incidence matrices in multi-dimensional cellular manufacturing system", J. Manuf. Syst., 31(2), pp. 214-223 (2012).
15. Hosseini, A., Paydar, M.M., Mahdavi, I., and Jouzdani, J. "Cell forming and cell balancing of virtual cellular manufacturing systems with alternative processing routes using genetic algorithm", J. Optim. Ind. Eng., 9(20), pp. 41-51 (2016).
16. Offodile, O.F., Mehrez, A., and Grznar, J. "Cellular manufacturing: A taxonomic review framework", J. Manuf. Syst., 13(3), pp. 196-220 (1994).
17. Singh, N. "Design of cellular manufacturing systems: An invited review", Eur. J. Oper. Res., 69(3), pp. 284- 291 (1993).
18. Joines, J.A., Culbreth, C.T., and King, R.E. "Manufacturing cell design: an integer programming model employing genetic algorithms", IIE Trans., 28(1), pp. 69-85 (1996).
19. Mohammadi, M. and Forghani, K. "Designing cellular manufacturing systems considering S-shaped layout", Comput. Ind. Eng., 98, pp. 221-236 (2016).
20. Bootaki, B., Mahdavi, I., and Paydar, M.M. "New criteria for configuration of cellular manufacturing considering product mix variation", Comput. Ind. Eng., 98, pp. 413-426 (2016).
21. Aalaei, A. and Davoudpour, H. "A robust optimization model for cellular manufacturing system into supply chain management", Int. J. Prod. Econ., 183, pp. 667- 679 (2017).
22. Imran, M., Kang, C., Lee, Y.H., Jahanzaib, M., and Aziz, H. "Cell formation in a cellular manufacturing system using simulation integrated hybrid genetic algorithm", Comput. Ind. Eng., 105, pp. 123-135 (2017).
23. Delgoshaei, A. and Gomes, C. "A multi-layer perceptron for scheduling cellular manufacturing systems in the presence of unreliable machines and uncertain cost", Appl. Soft Comput., 49, pp. 27-55 (2016).
24. Aljuneidi, T. and Bulgak, A.A. "Designing a cellular manufacturing system featuring remanufacturing, recycling, and disposal options: A mathematical modeling approach", CIRP J. Manuf. Sci. Technol., 19, pp. 25-35 (2017).
25. Jawahar, N. and Subhaa, R. "An adjustable grouping genetic algorithm for the design of cellular manufacturing system integrating structural and operational parameters", J. Manuf. Syst., 44, pp. 115-142 (2017).
26. Kuo, Y. and Liu, C.-C. "Operator assignment in a labor-intensive manufacturing cell considering intercell manpower transfer", Comput. Ind. Eng., 110, pp. 83-91 (2017).
27. Rabbani, M., Habibnejad-Ledari, H., Rafiei, H., and Farshbaf-Geranmayeh, A. "A bi-objective mathematical model for dynamic cell formation problem considering learning effect, human issues, and worker assignment", Sci. Iran., 23(5), pp. 2341-2354 (2016).
28. Rabbani, M., Keyhanian, S., Manavizadeh, N., and Farrokhi-Asl, H. "Integrated dynamic cell formationproduction planning: A new mathematical model", Sci. Iran., 24(5), pp. 2550-2566 (2017).
29. Mahootchi, M., Forghani, K., and Abdollahi Kamran, M. "A two-stage stochastic model for designing cellular manufacturing systems with simultaneous multiple processing routes and subcontracting", Sci. Iran., 25(5), pp. 2824-2837 (2018).
30. Saranwong, S. and Likasiri, C. "Product distribution via a bi-level programming approach: Algorithms and a case study in municipal waste system", Expert Syst. Appl., 44, pp. 78-91 (2016).
31. Calvete, H.I., Gale, C., and Iranzo, J.A. "Planning of a decentralized distribution network using bilevel optimization", Omega, 49, pp. 30-41 (2014).
32. Ma, Y., Yan, F., Kang, K., and Wei, X. "A novel integrated production-distribution planning model with conflict and coordination in a supply chain network", Knowledge-Based Syst., 105, pp. 119-133 (2016).
33. Safaei, A.S., Farsad, S., and Paydar, M.M. "Robust bilevel optimization of relief logistics operations", Appl. Math. Model., 56, pp. 359-380 (2018).
4. Safaei, A.S., Farsad, S., and Paydar, M.M. "Emergency logistics planning under supply risk and demand uncertainty", Oper. Res., pp. 1-24 (2018) (In Press).
35. Mokhlesian, M. and Zegordi, S.H. "Pricing and advertising decisions in a dominant-retailer supply chain: A multi-follower bi-level programming approach", Sci. Iran., 25(4), pp. 2254-2266 (2018).
36. Talbi, E.G., Metaheuristics for Bi-level Optimization, Springer Berlin Heidelberg, Berlin, Heidelberg (2013).
37. Leung, S.C.H. and Chan, S.S.W. "A goal programming model for aggregate production planning with resource utilization constraint", Comput. Ind. Eng., 56(3), pp. 1053-1064 (2009).
38. Gen, M., Altiparmak, F., and Lin, L. "A genetic algorithm for two-stage transportation problem using priority-based encoding", OR Spectr., 28(3), pp. 337- 354 (2006).
39. Michalewicz, Z., Vignaux, G., and Hobbs, M. "A nonstandard genetic algorithm for the non-linear transportation problem.", ORSA J. Comput., 3, pp. 307- 316 (1991).
40. Prufer, H. "Neuer Beweis eines Satzes uber Permutationen.", Arch. Der Math. Und Phys., 27, pp. 142-144 (1918).
41. Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P.  Optimization by simulated annealing", Science, New Series, 220(4598), pp. 671-680 (1983).
42. Mafarja, M.M. and Mirjalili, S. "Hybrid whale optimization algorithm with simulated annealing for feature selection", Neurocomputing, 260, pp. 302-312 (2017).
43. Assadi, M.T. and Bagheri, M. "Differential evolution and population-based simulated annealing for truck scheduling problem in multiple door cross-docking systems", Comput. Ind. Eng., 96, pp. 149-161 (2016).
44. Maghsoudlou, H., Kahag, M.R., Niaki, S.T.A., and Pourvaziri, H. "Bi-objective optimization of a threeechelon multi-server supply-chain problem in congested systems: Modeling and solution", Comput. Ind. Eng., 99, pp. 41-62 (2016).
45. Eberhart, R. and Kennedy, J. "A new optimizer using particle swarm theory", MHS'95. Proc. Sixth Int. Symp. Micro Mach. Hum. Sci., pp. 39-43 (1995).
46. Taguchi, G. Introduction to Quality Engineering: Designing Quality into Products and Processes, Illustrated The Organization, White Plains (1986).
47. Kuo, R.J., Lee, Y.H., Zulvia, F.E., and Tien, F.C. "Solving bi-level linear programming problem through hybrid of immune genetic algorithm and particle swarm optimization algorithm", Appl. Math. Comput., 266(43), pp. 1013-1026 (2015).
48. Sarrafha, K., Rahmati, S.H.A., Niaki, S.T.A., and Zaretalab, A. "A bi-objective integrated procurement, production, and distribution problem of a multiechelon supply chain network design: A new tuned MOEA", Comput. Oper. Res., 54, pp. 35-51 (2015).
49. Hwang, C.L. and Yoon, K., Multiple Attributes Decision Making Methods & Applications, Springer, Berlin (1981).
50. Hwang, C.-L., Lai, Y.-J., and Liu, T.-Y. "A new approach for multiple objective decision making", Comput. Oper. Res., 20(8), pp. 889-899 (1993).