One-level reformulation of the bi-level Knapsack problem using dynamic programming

Abstract : In this paper, we consider the Bilevel Knapsack Problem (BKP), which is a hierarchical optimization problem in which the feasible set is determined by the set of optimal solutions for a parametric Knapsack Problem. We introduce a new reformulation of the BKP into a one-level integer programming problem using dynamic programming. We propose an algorithm that allows the BKP to be solved exactly in two steps. In the first step, a dynamic programming algorithm is used to compute the set of follower reactions to leader decisions. In the second step, an integer problem that is equivalent to the BKP is solved using a branch-and-bound algorithm. Numerical results are presented to show the performance of our method.
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https://hal.inria.fr/hal-00759250
Contributor : Luce Brotcorne <>
Submitted on : Friday, November 30, 2012 - 12:26:50 PM
Last modification on : Thursday, February 21, 2019 - 10:52:49 AM

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Luce Brotcorne, Saïd Hanafi, Raïd Mansi. One-level reformulation of the bi-level Knapsack problem using dynamic programming. Discrete Optimization, Elsevier, 2013, 10 (1), pp.1-10. ⟨10.1016/j.disopt.2012.09.001⟩. ⟨hal-00759250⟩

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