The impact of hub failure in Hub-and-Spoke networks: Mathematical formulations and solution techniques

Hub facilities are subject to unpredictable disruptions caused by severe weather condition, natural disasters, labour dispute, and vandalism to cite a few. Disruptions at hubs result in excessive transportation costs and economic losses as customers (demand) initially served by these facilities must now be served by other hubs. In this study, we first present a novel mathematical model that builds hub-and-spoke systems under the risk of hub disruption. In developing the model, we assume that once a hub stops normal operations, the entire demand initially served by this hub is handled by a backup facility. The objective function of the model minimizes the weighted sum of transportation cost in regular situation and the expected transportation cost following hub failure. We adopted a linearization for the model and present an efficient evolutionary approach with specifically designed operators. We solved a number of small problem instances from the literature using CPLEX for our enhanced mathematical model. The obtained results are also used as a platform for assessing the performance of our proposed meta-heuristic which is then tested on large instances with promising results. We further study and provide results for the relaxed problem in which demand points affected by disruption are allowed to be reallocated to any of the operational hubs in the network.