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dc.contributor.authorBertsimas, Dimitris J.
dc.contributor.authorGoyal, Vineet
dc.date.accessioned2012-03-22T15:29:46Z
dc.date.available2012-03-22T15:29:46Z
dc.date.issued2010-05
dc.date.submitted2009-12
dc.identifier.issn0364-765X
dc.identifier.issn1526-5471
dc.identifier.urihttp://hdl.handle.net/1721.1/69831
dc.description.abstractWe consider a two-stage mixed integer stochastic optimization problem and show that a static robust solution is a good approximation to the fully adaptable two-stage solution for the stochastic problem under fairly general assumptions on the uncertainty set and the probability distribution. In particular, we show that if the right-hand side of the constraints is uncertain and belongs to a symmetric uncertainty set (such as hypercube, ellipsoid or norm ball) and the probability measure is also symmetric, then the cost of the optimal fixed solution to the corresponding robust problem is at most twice the optimal expected cost of the two-stage stochastic problem. Furthermore, we show that the bound is tight for symmetric uncertainty sets and can be arbitrarily large if the uncertainty set is not symmetric. We refer to the ratio of the optimal cost of the robust problem and the optimal cost of the two-stage stochastic problem as the stochasticity gap. We also extend the bound on the stochasticity gap for another class of uncertainty sets referred to as positive. If both the objective coefficients and right-hand side are uncertain, we show that the stochasticity gap can be arbitrarily large even if the uncertainty set and the probability measure are both symmetric. However, we prove that the adaptability gap (ratio of optimal cost of the robust problem and the optimal cost of a two-stage fully adaptable problem) is at most four even if both the objective coefficients and the right-hand side of the constraints are uncertain and belong to a symmetric uncertainty set. The bound holds for the class of positive uncertainty sets as well. Moreover, if the uncertainty set is a hypercube (special case of a symmetric set), the adaptability gap is one under an even more general model of uncertainty where the constraint coefficients are also uncertain.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (NSF Grant DMI-0556106)en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (NSF Grant EFRI-0735905)en_US
dc.language.isoen_US
dc.publisherInstitute for Operations Research and the Management Sciencesen_US
dc.relation.isversionofhttp://dx.doi.org/10.1287/moor.1090.0440en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alike 3.0en_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/en_US
dc.sourceProf. Bertsimas via Alex Caracuzzoen_US
dc.titleOn the Power of Robust Solutions in Two-Stage Stochastic and Adaptive Optimization Problemsen_US
dc.typeArticleen_US
dc.identifier.citationBertsimas, D., and V. Goyal. “On the Power of Robust Solutions in Two-Stage Stochastic and Adaptive Optimization Problems.” Mathematics of Operations Research 35.2 (2010): 284–305.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Operations Research Centeren_US
dc.contributor.departmentSloan School of Managementen_US
dc.contributor.approverBertsimas, Dimitris J.
dc.contributor.mitauthorGoyal, Vineet
dc.contributor.mitauthorBertsimas, Dimitris J.
dc.relation.journalMathematics of Operations Researchen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsBertsimas, D.; Goyal, V.en
dc.identifier.orcidhttps://orcid.org/0000-0002-1985-1003
mit.licenseOPEN_ACCESS_POLICYen_US
mit.metadata.statusComplete


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