Distributionally robust facility location with uncertain facility capacity and customer demand

This study explores a capacitated facility location problem where facility capacity and customer demand are subject to uncertainties simultaneously. This problem decides the subset of facilities to open at the system design phase to serve customers during the operational phase. The objective is to minimize the total cost, including the first-stage location cost and the second-stage recourse cost, and guarantee the system's reliability, i.e., meeting demand as much as possible when uncertainties arise. A distributionally robust optimization (DRO) framework is utilized to model the problem. A scenario-wise ambiguity set with partial distributional information of random variables is constructed, which can capture uncertainties caused by different random events or different magnitudes of the same event type and explicitly represent the correlation between facilities' uncertain capacity and customers' uncertain demand. We apply an adaptation policy to the DRO model and reformulate it to a mixed-integer linear programming model, which is solvable by off-the-shelf solvers. Numerical results show that the scenario-wise DRO framework can provide a better trade-off between cost and service level than the stochastic programming model and the DRO model with a marginal moment-based ambiguity set, demonstrating that the proposed scenario-wise DRO model offers a practical decision-making tool for enhancing supply chain robustness via facility location.