Capacitated multiple allocation incomplete hub location problem allowing direct links between non-hub nodes

This paper addresses a flexible hub location problem in which the inter-hub network is incomplete, the allocation of non-hub nodes to hub nodes is multiple, direct links between non-hub nodes are allowed, with a limited capacity of both hubs and links. This problem has several real-world applications, in particular in air, urban and maritime transportation as well as in telecommunication networks. We propose an extension of a model previously developed in the literature by integrating the capacity constraints of located hubs and activated links in the network. In order to evaluate the behavior and performance of the proposed model, numerical experiments on reference instances from the hub location literature have been performed. Finally, an analysis of some optimal topologies leads to better understand the behavior of the model in the presence of capacity constraints.