Star p-hub median problem with modular arc capacities

We consider the hub location problem, where p hubs are chosen from a given set of nodes, each nonhub node is connected to exactly one hub and each hub is connected to a central hub. Links are installed on the arcs of the resulting network to route the traffic. The aim is to find the hub locations and the connections to minimize the link installation cost. We propose two formulations and a heuristic algorithm to solve this problem. The heuristic is based on Lagrangian relaxation and local search. We present computational results where formulations are compared and the quality of the heuristic solutions are tested.