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On linear bilevel problems with multiple objectives at the lower level

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  • Calvete, Herminia I.
  • Galé, Carmen
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    Abstract

    Bilevel programming problems provide a framework to deal with decision processes involving two decision makers with a hierarchical structure. They are characterized by the existence of two optimization problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimization problem. This paper focuses on bilevel problems for which the lower level problem is a linear multiobjective program and constraints at both levels define polyhedra. This bilevel problem is reformulated as an optimization problem over a nonconvex region given by a union of faces of the polyhedron defined by all constraints. This reformulation is obtained when dealing with efficient solutions as well as weakly efficient solutions for the lower level problem. Assuming that the upper level objective function is quasiconcave, then an extreme point exists which solves the problem. An exact and a metaheuristic algorithm are developed and their performance is analyzed and compared.

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    Bibliographic Info

    Article provided by Elsevier in its journal Omega.

    Volume (Year): 39 (2011)
    Issue (Month): 1 (January)
    Pages: 33-40

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    Handle: RePEc:eee:jomega:v:39:y:2011:i:1:p:33-40

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    Related research

    Keywords: Bilevel optimization Multiobjective optimization Efficient solution Weakly efficient solution Genetic algorithm;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Kunsch, P.L. & Kavathatzopoulos, I. & Rauschmayer, F., 2009. "Modelling complex ethical decision problems with operations research," Omega, Elsevier, vol. 37(6), pages 1100-1108, December.
    2. Bard, Jonathan F, 1983. "Coordination of a multidivisional organization through two levels of management," Omega, Elsevier, vol. 11(5), pages 457-468.
    3. Wayne F. Bialas & Mark H. Karwan, 1984. "Two-Level Linear Programming," Management Science, INFORMS, vol. 30(8), pages 1004-1020, August.
    4. Walker, Warren E., 2009. "Does the best practice of rational-style model-based policy analysis already include ethical considerations?," Omega, Elsevier, vol. 37(6), pages 1051-1062, December.
    5. Calvete, Herminia I. & Gale, Carmen & Mateo, Pedro M., 2008. "A new approach for solving linear bilevel problems using genetic algorithms," European Journal of Operational Research, Elsevier, vol. 188(1), pages 14-28, July.
    6. Ankhili, Z. & Mansouri, A., 2009. "An exact penalty on bilevel programs with linear vector optimization lower level," European Journal of Operational Research, Elsevier, vol. 197(1), pages 36-41, August.
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    Cited by:
    1. Lin, Rung-Chuan & Sir, Mustafa Y. & Pasupathy, Kalyan S., 2013. "Multi-objective simulation optimization using data envelopment analysis and genetic algorithm: Specific application to determining optimal resource levels in surgical services," Omega, Elsevier, vol. 41(5), pages 881-892.
    2. Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.
    3. Dempe, S., 2011. "Comment to "interactive fuzzy goal programming approach for bilevel programming problem" by S.R. Arora and R. Gupta," European Journal of Operational Research, Elsevier, vol. 212(2), pages 429-431, July.

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