Abstract
We develop a fuzzy multi-objective linear programming (FMOLP) model for solving multi-objective mixed-model assembly line problem. In practice, vagueness and imprecision of the goals in this problem make the fuzzy decision-making complicated. The proposed model considers minimizing total utility work, total production rate variation, and total setup cost, using a two-phase linear programming approach. In the first phase, the problem is solved using a max–min approach. The max–min solution not being efficient, in general, we propose a new model in the second phase to maximize a composite satisfaction degree at least as good as the degrees obtained by phase one. To show the effectiveness of the proposed approach, a numerical example is solved and the results are compared with the ones obtained by the fuzzy mixed integer goal programming and weighted additive methods. The computational results show that the proposed FMOLP model achieves lower objective functions as well as higher satisfaction degrees.
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Monden Y (1983) Toyota production system. Institute of Industrial Engineers Press, Atlanta
Miltenburg J (1989) Level schedules for mixed-model assembly lines in just-in-time production systems. Manage Sci 35(2):192–207 doi:10.1287/mnsc.35.2.192
Miltenburg J, Steiner G, Yeomans S (1990) A dynamic programming algorithm for scheduling mixed-model just-in-time production systems. Math Comput Model 13:57–66 doi:10.1016/0895-7177(90)90370-3
Inman PR, Bulfin RL (1991) Note on sequencing JIT mixed model assembly lines. Manage Sci 37(7):904–910 doi:10.1287/mnsc.37.7.901
Yano CA, Rachamadugu R (1991) Sequencing to minimize work overload in assembly lines with product options. Manage Sci 37:572–586 doi:10.1287/mnsc.37.5.572
Bard JF, Dar-El EM, Shtub A (1992) An analytic framework for sequencing mixed-model assembly lines. Int J Prod Res 30:35–48 doi:10.1080/00207549208942876
Okamura K, Yamshina H (1979) A heuristic algorithm for the assembly line model-mix sequencing problem to minimize the risk of stopping the conveyor. Int J Prod Res 17:233–247 doi:10.1080/00207547908919611
Kim S, Jeong B (2007) Product sequencing problem in mixed model assembly line to minimize unfinished works. Comput Ind Eng 53(2): 206–214 doi:10.1016/j.cie.2007.06.011
Bautista J, Cano J (2008) Minimizing work overload in mixed model assembly lines. Int J Prod Econ 112(1):177–191 doi:10.1016/j.ijpe.2006.08.019
Toksari MD, Isleyen SK, Guner E, Baykoc OF (2008) Simple and U-type assembly line balancing problems with a learning effect. Appl Math Model 32(12):2954–2961 doi:10.1016/j.apm.2007.10.007
Hyun CJ, Kim Y, Kim YK (1998) A genetic algorithm for multiple objective sequencing problems in mixed model assembly lines. Comput Oper Res 25(7–8):675–690 doi:10.1016/S0305-0548(98)00026-4
McMullen PR (1998) JIT sequencing for mixed-model assembly lines with setups using tabu search. Prod Plann Contr 9(5):504–510 doi:10.1080/095372898233984
Korkmazel T, Meral S (2001) Bicriteria sequencing methods for the mixed-model assembly line in just-in-time production systems. Eur J Oper Res 131:188–207 doi:10.1016/S0377-2217(00)00061-8
McMullen PR, Frazier GV (2000) A simulated annealing approach to mixed-model sequencing with multiple objectives on a JIT line. IIE Trans 32(8):679–686
McMullen PR (2001a) An efficient frontier approach to addressing JIT sequencing problems with setups via search heuristics. Comput Ind Eng 41:335–353 doi:10.1016/S0360-8352(01)00059-6
McMullen PR (2001b) A Kohonen self-organizing map approach to addressing a multiple objective, mixed-model JIT sequencing problem. Int J Prod Econ 72:59–71 doi:10.1016/S0925-5273(00)00091-8
McMullen PR (2001c) An ant colony optimization approaches to addressing a JIT sequencing problem with multiple objectives. Artif Intell Eng 15:309–317 doi:10.1016/S0954-1810(01)00004-8
Mansouri SA (2005) A multi-objective genetic algorithm for mixed-model sequencing on JIT assembly lines. Eur J Oper Res 167(3):696–716
Tavakkoli-Moghaddam R, Rahimi-Vahed AR (2006) Multi-criteria sequencing problem for a mixed-model assembly line in a JIT production system. Appl Math Comput 181(2):1471–1481
Rahimi-Vahed AR, Rabbani M, Tavakkoli-Moghaddam R, Torabi SA, Jolai F (2007) A multi-objective scatter search for a mixed model assembly line sequencing problem. Adv Eng Inform 21:85–99 doi:10.1016/j.aei.2006.09.007
Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1:45–56 doi:10.1016/0165-0114(78)90031-3
Lee S, Li RJ (1993) Fuzzy multiple objective programming and compromise programming with Pareto optimum. Fuzzy Sets Syst 53:275–288 doi:10.1016/0165-0114(93)90399-3
Li X, Li B (2006) Computing efficient solutions to fuzzy multiple objective linear programming problems. Fuzzy Sets Syst 157:1328–1332 doi:10.1016/j.fss.2005.12.003
Guu M, Wu Y (1999) Two-phase approach for solving the fuzzy linear programming problems. Fuzzy Sets Syst 107:191–195 doi:10.1016/S0165-0114(97)00304-7
Bellman RE, Zadeh LA (1970) Decision making in a fuzzy environment. Manage Sci 17:141–164 doi:10.1287/mnsc.17.4.B141
Javadi B, Rahimi-Vahed A, Rabbani M, Dangchi M (2007) Solving a multi-objective mixed-model assembly line sequencing problem by a fuzzy goal programming approach. Int J Adv Manuf Technol 39(9–10):975–982
Tiwari RN, Dharmahr S, Rao JR (1987) Fuzzy goal programming—an additive model. Fuzzy Sets Syst 24:27–34 doi:10.1016/0165-0114(87)90111-4
Lai YJ, Hwang CL (1994) Fuzzy multiple objective decision making, methods and applications. Springer, Berlin
Sakawa M (1993) Fuzzy sets and interactive multiobjective optimization. Plenum, New York
Hwang CL, Yoon K (1987) Multiple attribute decision making: methods and applications. Springer, Heidelberg
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Mahdavi, I., Javadi, B., Sahebjamnia, N. et al. A two-phase linear programming methodology for fuzzy multi-objective mixed-model assembly line problem. Int J Adv Manuf Technol 44, 1010–1023 (2009). https://doi.org/10.1007/s00170-008-1914-6
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DOI: https://doi.org/10.1007/s00170-008-1914-6