Distributionally robust optimization (DRO) is a mathematical framework to incorporate ambiguity over the actual data-generating probability distribution. Data-driven DRO problems based on the Wasserstein distance are of particular interest for their sound mathematical properties. For right-hand-sided uncertainty, however, existing methods rely on dual vertex enumeration rendering the problem intractable in practical applications. In this context, we study decomposition methods for two-stage data-driven Wasserstein-based DROs with right-hand-sided uncertainty and rectangular support. We propose a novel finite reformulation that explores the rectangular uncertainty support to develop and test three new different decomposition schemes: Column-Constraint Generation, Single-cut Benders and Multi-cut Benders. We compare the efficiency of the proposed methods with existing benchmarks for a unit commitment problem with 5, 14, and 54 thermal generators over a 24-hour uncertainty dimension. The numerical results show the superiority of the Column-Constraint Generation algorithm for this problem, in contrast to the Benders-like alternatives and existing methods.
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Pontifical Catholic University of Rio de Janeiro (PUC-Rio), R. Marquês de São Vicente, 225, Brazil, October 2020,
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View A Novel Solution Methodology for Wasserstein-based Data-Driven Distributionally Robust Problems