Hub Location Problems with Allocation Constraints

Hub location problems, with the hub-and-spoke network structure, involve locating hub facilities, allocating the non-hubs (spokes) to the hubs, and determining the path for each origin-destination pair. In a pure hub-and-spoke network, all hubs, which act as intermediate switching or transshipment points for internodal flows, are fully interconnected and none of the non-hubs are directly connected (i.e., all flows must be routed through the hubs). Two types of allocations are commonly found in the literature. In the multiple allocation, each non-hub is allowed to be allocated to all the hubs (Figure 1). The single allocation restricts each non-hub to be allocated to a single hub (Figure 2). In real world situations, however, the allocation of the non-hubs to the hubs does not always fall under multiple allocation or single allocation. In many practical situations, each non-hub is restricted to be connected with a few hubs, perhaps two or three. In this chapter, we discuss hub location problems with such allocation constraints. Models for hub location problems with allocation constraints are presented. Data sets for these types of hub location problems are also described.