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Ambiguous joint chance constraints under mean and dispersion information

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Title: Ambiguous joint chance constraints under mean and dispersion information
Authors: Hanasusanto, G
Roitch, V
Kuhn, D
Wiesemann, W
Item Type: Journal Article
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. The online appendix is available at https://doi.org/10.1287/opre.2016.1583.
Issue Date: May-2017
Date of Acceptance: 2-Aug-2016
URI: http://hdl.handle.net/10044/1/44226
DOI: 10.1287/opre.2016.1583
ISSN: 1526-5463
Publisher: INFORMS (Institute for Operations Research and Management Sciences)
Start Page: 751
End Page: 767
Journal / Book Title: Operations Research
Volume: 65
Issue: 3
Copyright Statement: © 2017, INFORMS
Sponsor/Funder: Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/M028240/1
Keywords: Social Sciences
Science & Technology
Operations Research & Management Science
Business & Economics
robust optimization
distributionally robust optimization
joint chance constraints
Operations Research
0102 Applied Mathematics
0802 Computation Theory and Mathematics
1503 Business and Management
Publication Status: Published
Online Publication Date: 2017-03-30
Appears in Collections:Imperial College Business School