IDEAS home Printed from
   My bibliography  Save this article

On linear bilevel problems with multiple objectives at the lower level


  • Calvete, Herminia I.
  • Galé, Carmen


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.

Suggested Citation

  • Calvete, Herminia I. & Galé, Carmen, 2011. "On linear bilevel problems with multiple objectives at the lower level," Omega, Elsevier, vol. 39(1), pages 33-40, January.
  • Handle: RePEc:eee:jomega:v:39:y:2011:i:1:p:33-40

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Bard, Jonathan F, 1983. "Coordination of a multidivisional organization through two levels of management," Omega, Elsevier, vol. 11(5), pages 457-468.
    2. Wayne F. Bialas & Mark H. Karwan, 1984. "Two-Level Linear Programming," Management Science, INFORMS, vol. 30(8), pages 1004-1020, August.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. 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.
    2. repec:spr:joptap:v:167:y:2015:i:2:d:10.1007_s10957-015-0789-6 is not listed on IDEAS
    3. 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.
    4. Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jomega:v:39:y:2011:i:1:p:33-40. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.