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

¹ Rouen Business School, 1 rue du Maréchal Juin, BP 215 – 76825 Mont Saint Aignan Cedex, France; rkj@rouenbs.fr
² LAMSADE, Université Paris-Dauphine, Pl. du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France.

Received: 1 July 2008
Accepted: 2 October 2009

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.