EXTENSIONS TO THE HUB LOCATION PROBLEM - FORMULATIONS AND NUMERICAL EXAMPLES

Although a tremendous amount of analytical research is being conducted on the hub location problem, few models exist that extend the number of characteristics found in actual hub-and-spoke networks. Four extens ions are presented in this paper: (1) a capacitated network model; (2) a minimum threshold model; (3) a model that endogenously determines t he number of open hubs for the network; and (4) a model that incorpora tes a flow-dependent cost function for the spokes as well as the inter hub links. Both the capacitated and the minimum threshold models drop the assumption of a completely interconnected network commonly found i n hub location models. Numerical results show that total network costs are often minimized by closing a few interhub links. The third extens ion is the first known hub location model to determine the optimal num ber of hubs based on the needs of the network. In this model, the numb er of open hubs depends on the distribution of flows in the network an d how cost effectively the flows can be moved across the network. Prev ious models that endogenously determined the number of open hubs utili zed a fixed cost for establishing each hub in order to limit the numbe r of hubs in the network. The final extension recognizes the potential of all links to amalgamate flows and includes a separate flow-depende nt cost function for the spokes in addition to the one for the interhu b links. Numerical results are shown for all four models.