Reliable Facility Location Design Under Uncertain Correlated Disruptions

Most previous studies on reliable facility location design assume that disruptions at different locations are independent. In this paper, we present a model that allows disruptions to be correlated with an uncertain joint distribution, and we apply distributionally robust optimization to minimize the expected cost under the worst-case distribution with given marginal disruption probabilities. The worst-case distribution has a practical interpretation with disruption propagation, and its sparse structure allows solving the problem efficiently. Our numerical results show that ignoring disruption correlation could lead to significant loss that increases dramatically in key factors such as source disaster probability, disruption propagation effect, and service interruption penalty. On the other hand, the robust model results in very low regret, even when disruptions are independent, and starts to outperform the model assuming independence when disruptions are mildly correlated. Most of the benefit of the robust model can be captured with a very low additional cost, which makes it easy to implement. Given these advantages, we believe that the robust model can serve as a promising alternative approach for solving reliable facility location problems.