  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
set-up costs depend, not only on the 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.
