Polyhedral analysis for the uncapacitated hub location problem with modular arc capacities

We consider the problem of installing a two-level telecommunication network. Terminal nodes communicate with each other through hubs. Hubs can be installed on terminal nodes and they are interconnected by a complete network. Each terminal is connected directly to a hub node. Integer amounts of capacity units are installed on the arcs between hub pairs and terminals and their hubs. The aim is to minimize the cost of installing hubs and capacity units on arcs. We present valid and facet defining inequalities for the polyhedron associated with this problem.