The design of single allocation incomplete hub networks

The hub location problem deals with finding the location of hub facilities and allocating the demand nodes to these hub facilities so as to effectively route the demand between any origin-destination pair. In the extensive literature on this challenging network design problem, it has widely been assumed that the subgraph induced by the hub nodes is complete. Relaxation of this basic assumption constitutes the starting point of the present work. In this study, we provide a uniform modeling treatment to all the single allocation variants of the existing hub location problems, under the incomplete hub network design. No network structure other than connectivity is imposed on the induced hub network. Within this context, the single allocation incomplete p-hub median, the incomplete hub location with fixed costs, the incomplete hub covering, and the incomplete p-hub center network design problems are defined, and efficient mathematical formulations for these problems with O (n3) variables are introduced. Computational analyses with these formulations are presented on the various instances of the CAB data set and on the Turkish network.