Minimax Regret Single-Facility Ordered Median Location Problems on Networks

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.