Hub location under all-units discount policy

Hub location problem (HLP) is one of the strategic planning problems mostly encountered in logistics and telecommunications. The classical models in the literature of HLP assume a fixed discount factor on transportation costs of the flows being routed over the inter-hub connections. This assumption may results in solutions with large discounts for transporting small flows on inter-hub links. Nevertheless, in many situations in practice, the discount on the transportation cost depends on the magnitude of the flow to be transported. To address this issue, we consider a multiple allocation HLP with flow-dependent economies of scale for transportation costs on the inter-hub connections using an all-units discount policy. The problem is formulated as an MIP model and then is tightened by redefining decision variables. The proposed models are solved using a standard optimization software and their computational performances are compared. Finally, some managerial insights are derived based on the results obtained by the numerical experiments.