Single allocation p-hub median location and routing problem with simultaneous pick-up and delivery

We introduce the single allocation p-hub median location and routing problem with simultaneous pick-up and delivery based on observations from real life hub networks. The aim of our problem is to minimize the cost of transferring the flow between hubs and routing the flow in the network. We propose several mixed integer programming formulations and two heuristic approaches based on multi start simulated annealing and ant colony system to solve these problems. Extensive results demonstrate that using our methods good solutions can be found despite the computationally challenging nature of the problem.