A key feature of hub-and-spoke networks is the consolidation of flows at hub facilities. This bundling of flows leads to reduced transportation costs, which are frequently modeled with a constant discount factor that is applied to all costs associated with the flows that are routed between pairs of hubs. It has been shown that the assumption of flow-independent costs can be an oversimplification in several applications, and may not only miscalculate the total transportation cost but may also erroneously select the optimal set of hubs and the allocation pattern of nodes to hubs. In this talk we present the Modular Hub Location Problem that explicitly models the flow dependency of the transportation cost on all arcs of the hub network. We present a branch-and-bound algorithm, which uses a Lagrangean relaxation algorithm to obtain lower bounds at every node of the enumeration tree. Computational results are reported.
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