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An exact approach for the Stackelberg knapsack problem with weight selection

Author

Listed:
  • Yeonghun Lee

    (Korea Advanced Institute of Science and Technology)

  • Kiho Seo

    (Samsung Electronics)

  • Seulgi Joung

    (Ajou University)

  • Sungsoo Park

    (Korea Advanced Institute of Science and Technology)

Abstract

The Stackelberg knapsack game with weight selection (SKPW) is a variation of the bilevel knapsack problem in which the leader must determine the weights of a given subset of items, and then, the follower solves the knapsack problem to maximize the profit sum. The leader’s objective is to maximize the sum of the weights of the leader’s items included in the follower’s knapsack solution. In this paper, we present an exact algorithm to solve SKPW for the first time in the literature. We establish a strict linear inequality system with an exponential number of constraints, whose feasibility can be utilized to find an optimal solution for SKPW. To address the challenge posed by the strict inequalities more effectively, we propose a linear program with exponentially many constraints. We report computational results on several randomly generated instances and compare the solutions derived from the proposed exact algorithm with those obtained using heuristic algorithms.

Suggested Citation

  • Yeonghun Lee & Kiho Seo & Seulgi Joung & Sungsoo Park, 2025. "An exact approach for the Stackelberg knapsack problem with weight selection," Journal of Global Optimization, Springer, vol. 92(4), pages 973-991, August.
    • Handle: RePEc:spr:jglopt:v:92:y:2025:i:4:d:10.1007_s10898-025-01488-3
    DOI: 10.1007/s10898-025-01488-3
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    References listed on IDEAS

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    1. Pferschy, Ulrich & Nicosia, Gaia & Pacifici, Andrea & Schauer, Joachim, 2021. "On the Stackelberg knapsack game," European Journal of Operational Research, Elsevier, vol. 291(1), pages 18-31.
    2. Alberto Caprara & Margarida Carvalho & Andrea Lodi & Gerhard J. Woeginger, 2016. "Bilevel Knapsack with Interdiction Constraints," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 319-333, May.
    3. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2019. "Interdiction Games and Monotonicity, with Application to Knapsack Problems," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 390-410, April.
    4. David Pisinger, 1999. "Core Problems in Knapsack Algorithms," Operations Research, INFORMS, vol. 47(4), pages 570-575, August.
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