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A bilevel programming problem with maximization of a supermodular function in the lower level

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  • Diana Fanghänel

    (Universität Kassel)

Abstract

In bilevel programming there are two decision makers, the leader and the follower, who act in a hierarchy. In this paper we deal with a bilevel problem where the follower maximizes a supermodular function. The payoff for the leader is given by the weighted set that is chosen by the follower. To increase his payoff the leader can increase the supermodular function of the follower by a modular one, thus influencing the follower’s decision, but he has to pay a penalty for this. We want to find an optimum strategy for the leader. This is a bilevel programming problem with continuous variables in the upper level and a parametric supermodular maximization problem in the lower level. We analyze the structure of the bilevel problem. This we use to provide an equivalent one-level combinatorial problem. Finally, we investigate the properties of the new problem.

Suggested Citation

  • Diana Fanghänel, 2013. "A bilevel programming problem with maximization of a supermodular function in the lower level," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 568-584, October.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:3:d:10.1007_s10878-012-9478-7
    DOI: 10.1007/s10878-012-9478-7
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    References listed on IDEAS

    as
    1. Diana Fanghänel & Frauke Liers, 2010. "A fast exact algorithm for the problem of optimum cooperation and the structure of its solutions," Journal of Combinatorial Optimization, Springer, vol. 19(3), pages 369-393, April.
    2. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
    3. Clemens Heuberger, 2004. "Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 329-361, September.
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