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 parameters, which 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, namely, a linear reformulation, a Benders dual cutting plane method, and a column-and-constraint generation method. 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 the Benders dual cutting plane method or column-and-constraint generation performs best. The effectiveness of our model is also examined in comparison with alternative facility location models.

In this study, we apply a robust optimization approach to a p-center facility location problem under uncertainty. Based on a symmetric interval and a multiple allocation strategy, we use three types of uncertainty sets to formulate the robust problem: box uncertainty, ellipsoidal uncertainty, and cardinality-constrained uncertainty. The equivalent robust counterpart models can be solved to optimality using Gurobi. Comprehensive numerical experiments have been conducted by comparing the performance of the different robust models, which illustrate the pattern of robust solutions, and allocating a demand node to multiple facilities can reduce the price of robustness, and reveal that alternative models of uncertainty can provide robust solutions with different conservativeness.