Reliable Facility Location Under Event-Correlated Uncertainty

Abstract

Problem definition: We study a capacitated facility location problem where facility capacity and customer demand are subject to uncertainties simultaneously. The joint distribution of the two types of uncertain parameters is not perfectly known, and only partial statistical information can be estimated. Methodology/results: We (i) propose a scenario-wise ambiguity set to characterize randomness of parameters; (ii) develop a two-stage distributionally robust optimization (DRO) model; (iii) apply an adaptation policy to the DRO model and reformulate it to a mixed-integer linear programming model; (iv) extend the proposed framework to a location and inventory pre-positioning problem with uncertainty in disaster operations management. We find that the scenario-wise ambiguity set is highly suitable for dealing with event-correlated uncertainty. The DRO model achieves a better trade-off between cost and service level in out-of-sample tests than other modeling schemes. Managerial implications: Decision makers can use the scenario-wise ambiguity set to capture uncertainties caused by different random events, or different magnitudes of the same event type, and to explicitly describe the correlation between provider-side and receiver-side uncertainties. The developed DRO framework provides a practical tool for decision makers to enhance supply chain robustness via facility location decisions in a systematic fashion.