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Lexicographic α-robustness : an application to the 1-median problem

Author

Listed:
  • Rim Kalai-Jemai

    (Pôle Customer, Retail and Supply Chain - Rouen Business School - Rouen Business School)

  • M.A Aloulou

    (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)

  • P.H Vallin

    (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)

  • D. 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

In the last decade, several robustness approaches have been developed to deal with uncertainty. In decision problems, and particularly in location problems, the most used robustness approach rely either on maximal cost or on maximal regret criteria. However, it is well known that these criteria are too conservative. In this paper, we present a new robustness approach, called lexicographic α-robustness, which compensates for the drawbacks of criteria based on the worst case. We apply this approach to the 1-median location problem under uncertainty on node weights and we give a specific algorithm to determine robust solutions in the case of a tree. We also show that this algorithm can be extended to the case of a general network.

Suggested Citation

  • Rim Kalai-Jemai & M.A Aloulou & P.H Vallin & D. Vanderpooten, 2010. "Lexicographic α-robustness : an application to the 1-median problem," Post-Print hal-00565530, HAL.
    • Handle: RePEc:hal:journl:hal-00565530
    DOI: 10.1051/ro/2010010
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    Cited by:

    1. Kalaı¨, Rim & Lamboray, Claude & Vanderpooten, Daniel, 2012. "Lexicographic α-robustness: An alternative to min–max criteria," European Journal of Operational Research, Elsevier, vol. 220(3), pages 722-728.

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