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

Published online by Cambridge University Press:  27 April 2010

R. Kalaï,
M. A. Aloulou,
Ph. Vallin and
D. Vanderpooten
R. Kalaï
Affiliation:
Rouen Business School, 1 rue du Maréchal Juin, BP 215 – 76825 Mont Saint Aignan Cedex, France; rkj@rouenbs.fr
M. A. Aloulou
Affiliation:
LAMSADE, Université Paris-Dauphine, Pl. du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France.
Ph. Vallin
Affiliation:
LAMSADE, Université Paris-Dauphine, Pl. du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France.
D. Vanderpooten
Affiliation:
LAMSADE, Université Paris-Dauphine, Pl. du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France.
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Abstract

In the last decade, several robustness approaches have beendeveloped to deal with uncertainty. In decision problems, andparticularly in location problems, the most used robustnessapproach rely either on maximal cost or on maximal regretcriteria. However, it is well known that these criteria are tooconservative. In this paper, we present a new robustness approach,called lexicographic α-robustness, which compensatesfor the drawbacks of criteria based on the worst case. We applythis approach to the 1-median location problem under uncertaintyon node weights and we give a specific algorithm to determinerobust solutions in the case of a tree. We also show that thisalgorithm can be extended to the case of a general network.

Keywords

Robustness1-median location problemminmax cost/regret

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Type
Research Article
Information
RAIRO - Operations Research , Volume 44 , Issue 2 , April 2010, pp. 119 - 138
Copyright
© EDP Sciences, ROADEF, SMAI, 2010

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