A two-stage robust model for a reliable p-center facility location problem

We propose a two-stage robust model for reliable facility location when some facilities can be disrupted, for instance by a natural disaster. A reliable network is designed in a \proactive" planning phase, and when a facility is disrupted, its original clients can be reallocated to another available facility in a \reactive" phase. When demand and cost are uncertain, the initial design is also robust against the realizations (scenarios) of these data that will only be revealed post-disruption. Based on the p-center location model, which attempts to optimize the worst-case performance of the network, our model is concerned with the reliability for every client. Three solution methods have been implemented and tested to solve the model; we present an extensive numerical study to compare the performance of these methods. We find that, depending on the size of the instance (as given by the number of client sites and scenarios), either a Benders dual cutting plane method or a column-and-constraint generation method performs best. The effectiveness of our model is also examined in comparison with alternative facility location models.