The hub location problem with comparisons of compact formulations: A note

Abstract

Hub location is a planning problem that involves choosing, from a set of nodes, a subset to designate as hub facilities, linking the hubs to the remaining nodes using a hub-and-spoke structure, and routing of flows on the resulting network. This paper presents theoretical and computational comparisons of the fundamental compact formulations of the p-hub location problem (p-HLP) for three allocation strategies, namely single, multiple and r-allocation. Our theoretical results show that path-based formulations offer the strongest linear programming relaxation. The computational experiments, run on three prominent datasets using a state-of-the-art commercial solver indicate that, flow-based formulations generally solve the largest number of instances to optimality and require the shortest solution time, especially for large-scale instances.