Ambiguous Joint Chance Constraints Under Mean and Dispersion Information

Grani A. Hanasusanto (), Vladimir Roitch (), Daniel Kuhn () and Wolfram Wiesemann ()
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Grani A. Hanasusanto: Graduate Program in Operations Research and Industrial Engineering, The University of Texas at Austin, Austin, Texas 78712
Vladimir Roitch: Department of Computing, Imperial College London, Kensington, London SW7 SAZ, United Kingdom
Daniel Kuhn: Risk Analytics and Optimization Chair, École Polytechnique Fédérale de Lausanne, 1015 Lausanne Switzerland
Wolfram Wiesemann: Imperial College Business School, Imperial College London, Kensington, London SW7 2AZ, United Kingdom

Operations Research, 2017, vol. 65, issue 3, 751-767

Abstract: We study joint chance constraints where the distribution of the uncertain parameters is only known to belong to an ambiguity set characterized by the mean and support of the uncertainties and by an upper bound on their dispersion. This setting gives rise to pessimistic (optimistic) ambiguous chance constraints, which require the corresponding classical chance constraints to be satisfied for every (for at least one) distribution in the ambiguity set. We demonstrate that the pessimistic joint chance constraints are conic representable if (i) the constraint coefficients of the decisions are deterministic, (ii) the support set of the uncertain parameters is a cone, and (iii) the dispersion function is of first order, that is, it is positively homogeneous. We also show that pessimistic joint chance constrained programs become intractable as soon as any of the conditions (i), (ii) or (iii) is relaxed in the mildest possible way. We further prove that the optimistic joint chance constraints are conic representable if (i) holds, and that they become intractable if (i) is violated. We show in numerical experiments that our results allow us to solve large-scale project management and image reconstruction models to global optimality.

Keywords: robust optimization; distributionally robust optimization; joint chance constraints (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (32)

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