Journal
INFORMS JOURNAL ON COMPUTING
Volume 28, Issue 2, Pages 319-333Publisher
INFORMS
DOI: 10.1287/ijoc.2015.0676
Keywords
knapsack problem; bilevel programming; min-max problem
Categories
Funding
- COST Action [TD1207]
- Portuguese Foundation for Science and Technology [SFRH/BD/79201/2011]
- MIUR, Italy [PRIN2009]
- Fundação para a Ciência e a Tecnologia [SFRH/BD/79201/2011] Funding Source: FCT
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We consider a bilevel integer programming model that extends the classic 0-1 knapsack problem in a very natural way. The model describes a Stackelberg game where the leader's decision interdicts a subset of the knapsack items for the follower. As this interdiction of items substantially increases the difficulty of the problem, it prevents the application of the classical methods for bilevel programming and of the specialized approaches that are tailored to other bilevel knapsack variants. Motivated by the simple description of the model, by its complexity, by its economic applications, and by the lack of algorithms to solve it, we design a novel viable way for computing optimal solutions. Finally, we present extensive computational results that show the effectiveness of the new algorithm on instances from the literature and on randomly generated instances.
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