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The Stochastic Bilevel Selection Problem

In: Operations Research Proceedings 2022

Author

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  • Jannik Irmai

    (TU Dresden)

Abstract

We consider a bilevel continuous knapsack problem where the leader controls the capacity of the knapsack, while the follower chooses a feasible packing maximizing his own profit. The leader’s aim is to optimize a linear objective function in the follower’s solution, but with respect to item values that can be different from the follower’s item values. We address a stochastic version of this problem where the follower’s profits are uncertain and only a probability distribution is known. This problem is #P-hard for the case of independently and uniformly distributed follower profits. In this paper, efficient algorithms are developed for the special case where all items have unit weight, as is the case in the bilevel selection problem. Generalizing these results to the case of arbitrary weights leads to pseudo-polynomial time algorithms for the bilevel continuous knapsack problem.

Suggested Citation

  • Jannik Irmai, 2023. "The Stochastic Bilevel Selection Problem," Lecture Notes in Operations Research, in: Oliver Grothe & Stefan Nickel & Steffen Rebennack & Oliver Stein (ed.), Operations Research Proceedings 2022, chapter 0, pages 51-57, Springer.
    • Handle: RePEc:spr:lnopch:978-3-031-24907-5_7
    DOI: 10.1007/978-3-031-24907-5_7
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