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

Kalaï, Rim; Aloulou, Mohamed Ali; Vallin, Philippe; Vanderpooten, Daniel

Kalaï, Rim; Aloulou, Mohamed Ali; Vallin, Philippe; Vanderpooten, Daniel (2010), Lexicographic α-robustness: an application to the 1-median problem, RAIRO, 44, 2, p. 119-138. http://dx.doi.org/10.1051/ro/2010010

Type

Article accepté pour publication ou publié

Date

2010

Journal name

RAIRO

Volume

Number

Publisher

Centrale des revues Dunod-Gauthier-Villars

Pages

119-138

Abstract (EN)

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.

Subjects / Keywords

regret; minmax cost; 1-median location problem; Robustness