The capacitated hub covering location-routing problem for simultaneous pickup and delivery systems

In this study, a specific type of hub network topology, called hub location-routing, is presented in which the routes between the nodes assigned to a hub form a tour in this topology. The model minimizes the total cost of hub location and vehicle routing, subject to predefined travel time, hub capacity, vehicle capacity, and simultaneous pickups and deliveries. A polynomial-size mixed integer programming formulation is introduced for the single allocation type of the problems. In this paper, a set of valid inequalities is proposed for the formulation. In addition, a tabu-search based heuristic is suggested which determines the hub location and vehicle routes simultaneously. Series of computational tests are then executed to evaluate the performance of valid inequalities and tabu-search based heuristic. The results show that using all valid inequalities improves the solution time of the pure proposed model. Meanwhile, the proposed heuristic works efficiently in finding good-quality solutions for the proposed hub location-routing model.