Distributionally Robust Facility Location

This chapter discusses distributional robust optimization (DRO) models and techniques for facility location problems. The classical capacitated facility location problem is extended. Different possibilities are considered for capturing uncertainty. In particular, a data-driven DRO model based on a Wasserstein ambiguity set, a decision-dependent DRO model, and a DRO model using a state-wise ambiguity set are presented. A nested Benders decomposition algorithm for solving the model exactly is discussed, which leverages the subgradients of the worst-case expected second-stage cost at the location decisions formed insightfully by the associated worst-case distributions. The nested Benders decomposition procedure ensures a finite-step convergence, which can also be regarded as an extension of the classic L-shaped algorithm for two-stage stochastic programming to the state-wise robust stochastic facility location problem with a conic representable ambiguity set. Finally, some suggestions for further reading are presented.