The Tree of Hubs Location Problem

This paper presents the Tree of Hubs Location Problem. It is a network hub location problem with single assignment where a fixed number of hubs have to be located, with the particularity that it is required that the hubs are connected by means of a tree. The problem combines several aspects of location, network design and routing problems. Potential applications appear in telecommunications and transportation systems, when set-up costs for links between hubs are so high that full interconnection between hub nodes is prohibitive. We propose an integer programming formulation for the problem. Furthermore, we present some families of valid inequalities that reinforce the formulation and we give an exact separation procedure for them. Finally, we present computational results using the well-known AP and CAB data sets.