Hub location and routing problem

Abstract

Hubs are special facilities that consolidate and disseminate ows in many-to-many distribution systems. The hub location problem aims to nd locations of hubs and allocate non-hub nodes directly to the hubs. However, this problem is necessary to extend when nodes do not have su cient demand to justify direct connections between the non-hub nodes to the hubs since such direct connections increase the number of vehicles required and decrease the utilization of vehicles. Hence, it is necessary to construct local tours among the nodes allocated to the same hubs to generate economies of scale and to decrease vehicle costs. Nevertheless, forcing each non-hub node to be visited by a local tour is not the best way to design a many-to-many distribution system. Therefore, in this study two options for each non-hub node are given: (i) either it could be visited by a local tour or (ii) it could be directly connected to a hub without an economy of scale. We develop a mixed integer programming formulation and strengthen it with valid inequalities. We also develop three di erent Benders formulations as exact solution methods. In addition, we develop a hierarchical heuristic with two phases in order to solve large-sized problem instances. We test the performances of our solution methodologies on CAB and TR data sets.