Robust Facility Location Under Disruptions

Facility networks can be disrupted by, for example, power outages, poor weather conditions, or natural disasters, and the probabilities of these events may be difficult to estimate. This could lead to costly recourse decisions because customers cannot be served by the planned facilities. In this paper, we study a fixed-charge location problem (FLP) that considers disruption risks. We adopt a two-stage robust optimization method, by which facility location decisions are made here and now and recourse decisions to reassign customers are made after the uncertainty information on the facility availability has been revealed. We implement a column-and-constraint generation (C&CG) algorithm to solve the robust models exactly. Instead of relying on dualization or reformulation techniques to deal with the subproblem, as is common in the literature, we use a linear programming–based enumeration method that allows us to take into account a discrete uncertainty set of facility failures. This also gives the flexibility to tackle cases when the dualization technique cannot be applied to the subproblem. We further develop an approximation scheme for instances of a realistic size. Numerical experiments show that the proposed C&CG algorithm outperforms existing methods for both the robust FLP and the robust p-median problem.