Resilient facility location against the risk of disruptions

- We propose a class of stochastic optimization problems to incorporate risk preferences in reliable facility location.
- We formulate a non-convex mixed-integer programming as a general model for considering risk attitudes under independent disruptions.
- We develop a branch-and-cut procedure with an augmented Lagrangian decomposition scheme that leads to a novel and practical algorithm.
- We formulate a MILP and propose a Lagrangian decomposition algorithm for risk-averse RUFL under correlated disruptions.
- We compare the effect of incorporating risk measures against the traditional risk-neutral model.

In this paper, we consider an uncapacitated facility location problem (RUFL) with random facility disruptions. We develop risk-averse optimization formulations to compute resilient location and customer assignment solutions for two cases (i.e., under either independent or correlated disruptions), where the risks are expressed through a family of risk measures including conditional value-at-risk (CVaR) and absolute-semideviation (ASD). The risk-averse RUFL with independent facility disruptions is to control the risks at each individual customer and modeled as a mixed-integer nonlinear programming, which is challenging to be solved. In response, we develop a branch-and-cut algorithm combined with augmented Lagrangian decomposition for globally optimizing the problem. As for the risk-averse RUFL with correlated facility disruptions, we propose a scenario-based model to minimize the total fixed costs and risks across the entire customer set. The resulting formulation is a pure MILP and a Lagrangian decomposition scheme is proposed for computational aspects in large-scale cases. Our numerical results show that the risk-averse models outperform the classic risk-neutral models in improving the reliability. Experiments demonstrate that our proposed algorithms perform well. To conclude, we extract managerial insights that suggest important guidelines for controlling risk in the face of disruption.