Journal
OPERATIONS RESEARCH
Volume 62, Issue 6, Pages 1358-1376Publisher
INFORMS
DOI: 10.1287/opre.2014.1314
Keywords
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Funding
- Engineering and Physical Sciences Research Council [EP/I014640/1]
- NUS Global Asia Institute
- National Research Foundation Singapore through the Singapore MIT Alliance for Research and Technology's Future Urban Mobility research programme
- EPSRC [EP/I014640/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/I014640/1] Funding Source: researchfish
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Distributionally robust optimization is a paradigm for decision making under uncertainty where the uncertain problem data are governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker's prior information. In this paper, we propose a unifying framework for modeling and solving distributionally robust optimization problems. We introduce standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold. These ambiguity sets are highly expressive and encompass many ambiguity sets from the recent literature as special cases. They also allow us to characterize distributional families in terms of several classical and/or robust statistical indicators that have not yet been studied in the context of robust optimization. We determine conditions under which distributionally robust optimization problems based on our standardized ambiguity sets are computationally tractable. We also provide tractable conservative approximations for problems that violate these conditions.
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