On hub location problems in geographically flexible networks

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