Integer Programming Formulation of the Bilevel Knapsack Problem

被引：2

作者：

Mansi, R. ^{[1
]}

Hanafi, S. ^{[1
]}

Brotcorne, L. ^{[1
]}

机构：

[1] Univ Valenciennes, LAMIH SIADE, Valenciennes, France

来源：

MATHEMATICAL MODELLING OF NATURAL PHENOMENA | 2010年 / 5卷 / 07期

关键词：

Bilevel programming; Knapsack problem; dynamic programming; branch-and-bound;

D O I：

10.1051/mmnp/20105719

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The Bilevel Knapsack Problem (BKP) is a hierarchical optimization problem in which the feasible 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 that the integer program reformulation is equivalent to the BKP. Numerical results show the efficiency of our method compared with those obtained by the algorithm of Moore and Bard.

引用

页码：116 / 121

页数：6

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