On hub location problems in geographically flexible networks

In this paper, we propose an extension of the uncapacitated hub location problem where the potential positions of the hubs are not fixed in advance. Instead, they are allowed to belong to a region around an initial discrete set of nodes. We give a general framework in which the collection, transportation, and distribution costs are based on norm-based distances and the hub-activation setup costs depend not only on the location of the hub that are opened but also on the size of the region where they are placed. Two alternative mathematical programming formulations are proposed. The first one is a compact formulation while the second one involves a family of constraints of exponential size that we separate efficiently giving rise to a branch-and-cut algorithm. The results of an extensive computational experience are reported showing the advantages of each of the approaches.