Data-Driven Reliable Facility Location Design

We study the reliable (uncapacitated) facility location (RFL) problem in a data-driven environment where historical observations of random demands and disruptions are available. Owing to the combinatorial optimization nature of the RFL problem and the mixed-binary randomness of parameters therein, the state-of-the-art RFL models applied to the data-driven setting either suggest overly conservative solutions or become computationally prohibitive for large- or even moderate-size problems. In this paper, we address the RFL problem by presenting an innovative prescriptive model aiming to balance solution conservatism with computational efficiency. In particular, our model selects facility locations to minimize the fixed costs plus the expected operating costs approximated by a tractable data-driven estimator, which equals to a probabilistic upper bound on the intractable Kolmogorov distributionally robust optimization estimator. The solution of our model is obtained by solving a mixed-integer linear program that does not scale in the training data size. Our approach is proved to be asymptotically optimal, and offers a theoretical guarantee for its out-of-sample performance in situations with limited data. In addition, we discuss the adaptation of our approach when facing data with covariate information. Numerical results demonstrate that our model significantly outperforms several important RFL models with respect to both in-sample and out-of-sample performances as well as computational efficiency.