The last decade has seen an explosion in the availability of data for operations research applications as part of the Big Data revolution. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are computationally tractable, both theoretically and practically. Furthermore, optimal solutions to these problems enjoy a strong, finite-sample probabilistic guarantee. We also propose concrete guidelines for practitioners and illustrate our approach with applications in portfolio management and queueing. Computational evidence confirms that our data-driven sets significantly outperform traditional robust optimization techniques whenever data is available.
Bertsimas et al. REF utilize statistical hypothesis tests to construct convex uncertainty sets from data.
Data-Driven Robust Optimization
arXiv: Optimization and Control
Mathematics Computer Science