Article ID Journal Published Year Pages File Type
1141633 Discrete Optimization 2013 10 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Control and Optimization
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