Euclidean Hub-and-Spoke Networks

The hub-and-spoke distribution paradigm has been a fundamental principle in geographic network design for more than 40 years. One of the primary advantages that such networks possess is their ability to exploit economies of scale in transportation by aggregating network flows through common sources. In this paper, we consider the problem of designing an optimal hub-and-spoke network in continuous Euclidean space: the "spokes" of the network are distributed uniformly over a service region, and our objective is to determine the optimal number of hub nodes and their locations. We consider seven different backbone network topologies for connecting the hub nodes, namely, the Steiner and minimum spanning trees, a travelling salesman tour, a star network, a capacitated vehicle routing tour, a complete bipartite graph, and a complete graph. We also perform an additional analysis on a multilevel network in which network flows move through multiple levels of transshipment before reaching the service region. We describe the asymptotically optimal (or near-optimal) configurations that minimize the total network costs as the demand in the region becomes large and give an approximation algorithm that solves our problem on a convex planar region for any values of the relevant input parameters.