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Integer Programming Formulation of the Bilevel KnapsackProblem

Published online by Cambridge University Press:  26 August 2010

A. Taik ,
R. Mansi ,
S. Hanafi  and
L. Brotcorne
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Abstract

The Bilevel Knapsack Problem (BKP) is a hierarchical optimization problem in which thefeasible set is determined by the set of optimal solutions of parametric Knapsack Problem.In this paper, we propose two stages exact method for solving the BKP. In the first stage,a dynamic programming algorithm is used to compute the set of reactions of the follower.The second stage consists in solving an integer program reformulation of BKP. We show thatthe integer program reformulation is equivalent to the BKP. Numerical results show theefficiency of our method compared with those obtained by the algorithm of Moore andBard

Keywords

Bilevel programmingKnapsack problemdynamic programmingbranch-and-bound

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References

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