Bounds on risk-averse mixed-integer multi-stage stochastic programming problems with mean-CVaR

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buir.contributor.authorMahmutoğulları, Ali İrfan
buir.contributor.authorÇavuş, Özlem
buir.contributor.authorAktürk, M. Selim
dc.citation.epage608en_US
dc.citation.issueNumber2en_US
dc.citation.spage595en_US
dc.citation.volumeNumber266en_US
dc.contributor.authorMahmutoğulları, Ali İrfanen_US
dc.contributor.authorÇavuş, Özlemen_US
dc.contributor.authorAktürk, M. Selimen_US
dc.date.accessioned2019-02-21T16:01:32Z
dc.date.available2019-02-21T16:01:32Z
dc.date.issued2018en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractRisk-averse mixed-integer multi-stage stochastic programming forms a class of extremely challenging problems since the problem size grows exponentially with the number of stages, the problem is non-convex due to integrality restrictions, and the objective function is nonlinear in general. We propose a scenario tree decomposition approach, namely group subproblem approach, to obtain bounds for such problems with an objective of dynamic mean conditional value-at-risk (mean-CVaR). Our approach does not require any special problem structure such as convexity and linearity, therefore it can be applied to a wide range of problems. We obtain lower bounds by using different convolution of mean-CVaR risk measures and different scenario partition strategies. The upper bounds are obtained through the use of optimal solutions of group subproblems. Using these lower and upper bounds, we propose a solution algorithm for risk-averse mixed-integer multi-stage stochastic problems with mean-CVaR risk measures. We test the performance of the proposed algorithm on a multi-stage stochastic lot sizing problem and compare different choices of lower bounds and partition strategies. Comparison of the proposed algorithm to a commercial solver revealed that, on the average, the proposed algorithm yields 1.13% stronger bounds. The commercial solver requires additional running time more than a factor of five, on the average, to reach the same optimality gap obtained by the proposed algorithm.
dc.description.provenanceMade available in DSpace on 2019-02-21T16:01:32Z (GMT). No. of bitstreams: 1 Bilkent-research-paper.pdf: 222869 bytes, checksum: 842af2b9bd649e7f548593affdbafbb3 (MD5) Previous issue date: 2018en
dc.embargo.release2020-04-16en_US
dc.identifier.doi10.1016/j.ejor.2017.10.038
dc.identifier.issn0377-2217
dc.identifier.urihttp://hdl.handle.net/11693/49868
dc.language.isoEnglish
dc.publisherElsevier B.V.
dc.relation.isversionofhttps://doi.org/10.1016/j.ejor.2017.10.038
dc.source.titleEuropean Journal of Operational Researchen_US
dc.subjectBoundingen_US
dc.subjectCVaRen_US
dc.subjectDynamic measures of risken_US
dc.subjectMixed-integer multi-stage stochastic programmingen_US
dc.subjectStochastic programmingen_US
dc.titleBounds on risk-averse mixed-integer multi-stage stochastic programming problems with mean-CVaRen_US
dc.typeArticleen_US

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