New results on minimax regret single facility ordered median location problems on networks

Authors:
Justo Puerto;Antonio M. Rodriguez-Chia;Arie Tamir
Affiliations:
Facultad de Matemáticas, Universidad de Sevilla;Facultad de Ciencias, Universidad de Cádiz;School of Mathematical Sciences, Tel Aviv University
Venue:
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Year:
2007

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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 also 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.