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The lexicographic α-robust knapsack problem

Author

Listed:
  • Rim Kalaï

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, Pôle Customer, Retail and Supply Chain - Rouen Business School - Rouen Business School)

  • Daniel Vanderpooten

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

The knapsack problem is a classical combinatorial optimization problem used to model many industrial situations. The robust version of this problem was studied in the literature using a max-min or min-max regret criterion. In this paper, we show the drawbacks of such criteria and propose a new robustness approach, called lexicographic α-robustness. We show that the complexity of the lexicographic α-robust problem does not increase compared with the max-min version and present a pseudo-polynomial algorithm in the case of a bounded number of scenarios.

Suggested Citation

  • Rim Kalaï & Daniel Vanderpooten, 2011. "The lexicographic α-robust knapsack problem," Post-Print hal-00820135, HAL.
    • Handle: RePEc:hal:journl:hal-00820135
    DOI: 10.1111/j.1475-3995.2010.00786.x
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    Cited by:

    1. Fabrice Talla Nobibon & Roel Leus, 2014. "Complexity Results and Exact Algorithms for Robust Knapsack Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 533-552, May.

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