Wasserstein Distributionally Robust Optimization for Chance Constrained Facility Location Under Uncertain Demand

The purpose of this paper is to present a novel optimization framework that enhances Wasserstein Distributionally Robust Optimization (WDRO) for chance-constrained facility location problems under demand uncertainty. Traditional methods often rely on predefined probability distributions, limiting their flexibility in adapting to real-world demand fluctuations. To overcome this limitation, the proposed approach integrates two methodologies, specifically a Genetic Algorithm to search for the optimal decision about facility opening, inventory, and allocation, and a constrained Jordan–Kinderlehrer–Otto (cJKO) scheme for dealing with robustness in the objective function and chance-constraint with respect to possible unknown fluctuations in demand. Precisely, cJKO is used to construct Wasserstein ambiguity sets around empirical demand distributions (historical data) to achieve robustness. As a result, computational experiments demonstrate that the proposed hybrid approach achieves over 90% demand satisfaction with limited violations of probabilistic constraints across various demand scenarios. The method effectively balances operational cost efficiency with robustness, showing superior performance in handling demand uncertainty compared to traditional approaches.