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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 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.

Keywords

Robustness1-median location problemminmax cost/regret
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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