Minimax Regret Single-Facility Ordered Median Location Problems on Networks

Authors:
J. Puerto;A. M. Rodríguez-Chía;A. Tamir
Affiliations:
Facultad de Matemáticas, Universidad de Sevilla, 41012 Seville, Spain;Facultad de Ciencias, Universidad de Cádiz, 11510 Cádiz, Spain;School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Venue:
INFORMS Journal on Computing
Year:
2009

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Abstract

We consider the single-facility ordered median location problem with uncertainty in the parameters (weights) defining the objective function. We study two cases. In the first case, the uncertain weights belong to a region with a finite number of extreme points, and in the second case, they must satisfy some order constraints and belong to some box (convex case). To deal with the uncertainty, we apply the minimax regret approach, providing strongly polynomial time algorithms to solve these problems. Finally, we also extend the proposed methodology to other problems with order constraints, which are not necessarily convex.