Capacitated plant selection in a decentralized manufacturing environment: a bilevel optimization approach. (English) Zbl 1077.90555

Summary: Most facility selection and production planning approaches assume centralized decision making using monolithic models. In this paper, we address a capacitated plant selection problem in a decentralized manufacturing environment where the principal firm and the auxiliary plants operate independently in an organizational hierarchy. A non-monolithic model is developed for plant selection in the decentralized decision making process. The developed model considers the independence relationship between the principal firm and the selected plants. It also takes into account the opportunity costs of over-setting production capacities in the opened plants. The developed mathematical programming model is a two-level nonlinear programming model with integer and continuous decision variables. It was transformed into an equivalent single level model, linearized and solved by available optimization software. Computational examples are presented.


90C29 Multi-objective and goal programming
90C11 Mixed integer programming
90B50 Management decision making, including multiple objectives


LINGO; Tabu search; LINDO
Full Text: DOI


[1] Audet, C.; Hansen, P.; Jaumard, B.; Savard, G., Links between linear bilevel and mixed 0-1 programming problems, Journal of optimization theory and applications, 93, 273-300, (1997) · Zbl 0901.90153
[2] Bard, J.F., Practical bilevel optimization, (1998), Kluwer Academic Publishers Dordrecht, The Netherlands · Zbl 0943.90078
[3] Bard, J.F.; Falk, J.E., An explicit solution to the multi-level programming problems, Computers & operations research, 9, 77-100, (1982)
[4] Bialas, W.F.; Karwan, M.H., Two-level linear programming, Management science, 30, 1004-1029, (1984) · Zbl 0559.90053
[5] Canel, C.; Khumawala, B., International facilities location: A heuristic procedure for the dynamic uncapacited problem, International journal of production research, 39, 3975-4000, (2001) · Zbl 1037.90512
[6] Cao, D.; Leung, L., A partial cooperation model for non-unique linear two-level decision problems, European journal of operational research, 140, 135-142, (2002)
[7] Chen, M., A model for integrated production planning in cellular manufacturing systems, Integrated manufacturing systems, 12, 275-284, (2001)
[8] Diaz, J.; Fernandez, E., A branch-and-price algorithm for single source capacitated plant location problem, Journal of the operational research society, 53, 728-739, (2002) · Zbl 1130.90354
[9] Ertogral, K.; Wu, S., Auction-theoretic coordination of production planning in the supply chain, IIE transactions, 32, 931-940, (2000)
[10] Fortuny, J.; McCarl, B., A representation and economic interpretation of a two-level programming problem, Journal of the operational research society, 32, 783-792, (1981) · Zbl 0459.90067
[11] Gen, M.; Cheng, R., Genetic algorithms and engineering design, (1996), Wiley New York, NY
[12] Ghiani, G.; Guerriero, F.; Musmanno, R., The capacitated plant location problem with multiple facilities in the same site, Computers & operations research, 29, 1903-1912, (2002) · Zbl 1259.90059
[13] Glover, F.; Laguna, M., Tabu search, (1997), Kluwer Academic Publishers Dordrecht, The Netherlands · Zbl 0930.90083
[14] Jaramillo, J.; Bhadury, J.; Batta, R., On the use of genetic algorithms to solve location problems, Computers & operations research, 29, 761-769, (2002) · Zbl 0995.90060
[15] LINDO Systems Inc., 1997. LINGO 6.0 User’s Guide. Chicago, Ill.
[16] Mallozzi, L.; Morgan, J., Hierarchical systems with weighted reaction set, (), 271-282 · Zbl 0985.91008
[17] Miller, T., Hierarchical operations and supply chain planning, (2001), Springer London
[18] Sakawa, M.; Nishizaki, I., Interactive fuzzy programming for cooperate two-level linear fractional programming problems with multiple decision makers, International journal of fuzzy systems, 1, 48-59, (1999)
[19] Sakawa, M.; Nishizaki, I.; Uemura, Y., Interactive fuzzy programming for two-level linear and linear fractional production and assignment problems: a case study, European journal of operational research, 135, 142-157, (2001) · Zbl 1077.90564
[20] Schrage, L., LINDO: an optimization modeling system, (1991), Boyd & Fraser Danvers, MA
[21] Soismaa, M., A note on efficient solution for the linear bilevel programming problem, European journal of operational research, 112, 427-431, (1999) · Zbl 0937.90064
[22] Steuer, R., Multiple criteria optimization-theory, algorithms and applications, (1987), Wiley New York
[23] Vicente, L.; Calamai, P., Bilevel and multilevel programming: A bibliography review, Journal of global optimization, 15, 291-306, (1994) · Zbl 0822.90127
[24] Wen, U.-P.; Hsu, S.T., Efficient solution for the linear bilevel programming problem, European journal of operational research, 62, 354-362, (1991)
[25] Wen, P.; Huang, D., A simple tabu search method to solve the mixed integer linear bilevel program, European journal of operational research, 88, 563-571, (1996) · Zbl 0908.90194
[26] White, D.J.; Anandalingam, G., A penalty function approach for solving bi-level linear programs, Journal of global optimization, 3, 397-419, (1993) · Zbl 0791.90047
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