Journal
OPERATIONS RESEARCH LETTERS
Volume 38, Issue 4, Pages 328-333Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.orl.2010.04.005
Keywords
Bilevel programming; Stochastic integer programming; Value functions
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Funding
- National Science Foundation [CMMI-0826141, DMI-0620780]
- AFOSR [FA9550-08-1-0268]
- University of Pittsburgh
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [0826141] Funding Source: National Science Foundation
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We introduce the bilevel knapsack problem with stochastic right-hand sides, and provide necessary and sufficient conditions for the existence of an optimal solution. When the leader's decisions can take only integer values, we present an equivalent two-stage stochastic programming reformulation with binary recourse. We develop a branch-and-cut algorithm for solving this reformulation, and a branch-and-backtrack algorithm for solving the scenario subproblems. Computational experiments indicate that our approach can solve large instances in a reasonable amount of time. (C) 2010 Elsevier B.V. All rights reserved.
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