The tree-of-hubs location problem: A comparison of formulations

The Tree-of-Hubs Location Problem is studied. This problem, which combines several aspects of some location, network design and routing problems, is inspired by those transportation systems in which (i) several locations send and receive a product, and (ii) the performance can be improved by using transshipment points (hubs) where the product is collected and distributed. We want to locate a fixed number of hubs and, instead of assuming that the transshipment points are fully interconnected, we require them to be connected by means of a tree. Potential applications appear when the set-up costs for the links between hubs are very high, so full interconnection is prohibitive. Three Integer Programming formulations are proposed and computationally compared. All of them are carefully implemented, with the natural constraints tightened as much as possible. The problem turns out to be difficult since in this initial stage of the research, only instances of size 20 can be approached and, sometimes, optimally solved.