A state of the art and a general formulation model of Hub Location-Routing Problems for LTL shipments

In many logistic systems for less than truckload (LTL) shipments, transportation of goods from one origin to its destination is made through collection tours to a hub and delivery tours from the same or another hub, while the goods are shipped between two hubs using Full Truckload (FTL) shipments. Therefore, managers need to determine the location of the hubs, the allocation of non-hub nodes, and the optimal collection and delivery routes within the network. This problem, known as the hub location-routing problem (HLRP), is related to both the hub location problem (HLP) and the locationrouting problem (LRP). The HLP involves the location of hub facilities concentrating flows in order to take advantage of economies of scale and through which flows are to be routed from origins to destinations. For an extensive review on the HLP, ones can refer to Alumur and Kara [1] or Campbell and O’Kelly [2]. The goals of the LRP are to determine the locations of the depots, the allocation of customers to depots, and to design the distribution (or collection) routes. Nagy and Salhi [7] presented a survey on issues, models and methods for the LRPs. In their classification, they pointed out a particular case of the LRP where inter-facilities routes are considered and both pick-up and delivery routes must be determined: the many-to-many location routing problem (MMLRP) that is similar to the HLRP. Different from the LRP which only considers one type of routes, the HLRP considers both collection and distribution routes. Hence, the objective of the HLRP is to minimize the total costs including hub costs, inter-hub transportation costs, and collection/distribution routing costs. Based on the literatures review, the aims of this paper are to analyze the state of the art, propose some generic mathematical models for the HLRP and implement some tests using a MIP solver.