Reliable Facility Location Design Under Uncertain Correlated Disruptions

Abstract

Most of the 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 apply distributionally-robust optimization to minimize the expected cost under the worst-case distribution with the prespecified marginal disruption probabilities. We find this robust model to be advantageous in several aspects. First, the worst-case disruption distribution reflects a practical situation, known as the “ripple effect”, where a disastrous event at one source affects facilities within an impact region. Second, the structure of the worst-case distribution allows reformulating this seemingly much more complicated problem as a much easier stochastic program. Third, in a numerical study for the uncapacitated fixed-charge location problem, we find that failing to consider correlation could lead to excessive loss, which is also increasing in important factors such as disruption probability, propagation effect, and service interruption penalty. On the other hand, the robust model results in much lower regret even when disruptions are actually independent. Thus, we believe the robust optimization model could serve as an alternative approach for solving reliable facility location problems. Compared to the traditional approach, it better captures disruption propagation, requires much less computational effort, and delivers more favorable designs.