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On distributionally robust chance constrained programs with Wasserstein distance

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Abstract

This paper studies a distributionally robust chance constrained program (DRCCP) with Wasserstein ambiguity set, where the uncertain constraints should be satisfied with a probability at least a given threshold for all the probability distributions of the uncertain parameters within a chosen Wasserstein distance from an empirical distribution. In this work, we investigate equivalent reformulations and approximations of such problems. We first show that a DRCCP can be reformulated as a conditional value-at-risk constrained optimization problem, and thus admits tight inner and outer approximations. We also show that a DRCCP of bounded feasible region is mixed integer representable by introducing big-M coefficients and additional binary variables. For a DRCCP with pure binary decision variables, by exploring the submodular structure, we show that it admits a big-M free formulation, which can be solved by a branch and cut algorithm. Finally, we present a numerical study to illustrate the effectiveness of the proposed formulations.

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Acknowledgements

The author would like to thank Professor Shabbir Ahmed (Georgia Tech) for his helpful comments on an earlier version of the paper. Valuable comments from the editors and three anonymous reviewers are gratefully acknowledged.

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  1. Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA, 24061, USA

    Weijun Xie

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Xie, W. On distributionally robust chance constrained programs with Wasserstein distance. Math. Program. 186, 115–155 (2021). https://doi.org/10.1007/s10107-019-01445-5

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