Solving Continuous Hub Location Problems in Multiple Assignment Networks by the Hyperbolic Smoothing Approach

Hub-and-spoke (HS) network designs arise in transportation and telecommunications systems, where items must flow among spatially separate nodes and scale economies can be attained through the shared use of high capacity links between hubs. As an alternative for the discrete approach of selecting a subset of the existing nodes as hubs, this paper explores the possibility of their continuous location. Therefore, the problem is to find the least expensive HS network, continuously locating hubs and assigning traffic to them, given the demands between each origin-destination pair and the respective transportation costs. The problem leads to a strongly non-differentiable min − sum − min formulation. The proposed method overcomes this difficulty with a smoothing strategy that uses a special differentiable function. The approach is an application of the hyperbolic smoothing technique,