HubLocator: an exact solution method for the multiple allocation hub location problem

Abstract

HubLocator is a new branch-and-bound procedure for the uncapacitated multiple allocation hub location problem. An existing optimal method developed by Klincewicz (Location Sci. 4 (1996) 173) is based on dual ascent and dual adjustment techniques applied to a disaggregated model formulation. These techniques have already successfully been used to solve the closely related simple plant location problem. However, due to the specific structure of the problem at hand, the success of these techniques in reducing the computational effort is rather restricted. Therefore, HubLocator additionally considers an aggregated model formulation enabling us to significantly tighten the lower bounds. Upper bounds which satisfy complementary slackness conditions for some constraints are constructed and improved by means of a simple heuristic procedure. Computational experiments demonstrate that optimal solutions for problems with up to 40 nodes can be found in a reasonable amount of time. Scope and purpose Ground and air transportation networks, postal delivery networks, and computer networks are often configured as hub-and-spoke systems. Traffic between two locations is not transported directly between these locations, but routed via particular switching or consolidation points called hubs. Due to increased traffic on linkages between hubs, larger vehicles can be used or the capacity of existing vehicles can be utilized more efficiently, resulting in smaller per unit transportation costs. The exploitation of scale economies as a result of the reduced number of linkages, which have to be operated in a hub-and-spoke system, compared to a fully interconnected network is an important advantage of this type of system. Designing hub-and-spoke networks deals with the selection of hubs from a given set of potential locations and the routing of traffic. We consider a special type of such a hub location problem and adapt a successful technique developed to find an optimal solution for the well-known simple plant location problem.