Routing and scheduling decisions in the hierarchical hub location problem

Hubs are facilities that consolidate and disseminate flow in many-to-many distribution systems. The hub location problem considers decisions that include the locations of hubs in a network and also the allocations of the demand (non-hub) nodes to these hubs. We propose a hierarchical multimodal hub network. Based on this network, we define a hub covering problem with a service time bound. The hierarchical network consists of three layers. We consider two different structures: ring-star-star (RSS) and ring-ring-star (RRS). The multimodal network has three different types of vehicles in each layer: airplanes, large trucks and small trucks. For the proposed problems (RSS and RRS), we present and strengthen two mathematical models with some variable fixing rules and valid inequalities. We conduct the computational analysis over the Turkish network and the CAB data sets