Multiple Allocation Hub Location Model with Fixed Arc Costs

This article formulates a model to analyze the role of fixed costs in the design of optimal transportation hub networks. The primary purpose of this article is to better model costs in hub networks, an issue that has attracted considerable attention. This article allows particular versions of hub networks to emerge from the cost structure, rather than by imposing a rigid predefined connectivity protocol. The article integrates modeling approaches from an environmental hub location model with the three-index formulation of Ernst and Krishnamoorthy to produce a hub location model with fixed and variable costs for all arcs. Our goal is to demonstrate how the inclusion of a richer cost model in transportation hub location can generate a wide range of different network types, depending on the relative magnitudes of the cost elements. While the existence of special case network solutions is well known and has been exploited in optimization, the current research provides added insight to the cost of flow in a more, or less, connected hub network. Eight fundamental prototype networks are derived as special cases, and some additional unanticipated network types also emerge. The results are illustrated with a standard CAB25 data set.