Time consistent expected mean-variance in multistage stochastic quadratic optimization: a model and a matheuristic

In this paper, we present a multistage time consistent Expected Conditional Risk Measure for minimizing a linear combination of the expected mean and the expected variance, so-called Expected Mean-Variance. The model is formulated as a multistage stochastic mixed-integer quadratic programming proble...

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Vydané v:	Annals of operations research Ročník 280; číslo 1-2; s. 151 - 187
Hlavní autori:	Aldasoro, Unai, Merino, María, Pérez, Gloria
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.09.2019 Springer Springer Nature B.V
Predmet:	Business and Management Combinatorics Cost analysis Mathematical optimization Mathematical research Multistage Operations research Operations Research/Decision Theory Optimization Original Research Production planning Quadratic functions Quadratic programming Risk analysis Stochastic processes Studies Theory of Computation Variance Spain 90C20 Time consistent risk aversion McCormick relaxation Branch-and-Fix Coordination Multistage stochastic optimization Quadratic mixed 0–1 programming Matheuristic algorithms Production planning 90C15 90C59 Expected Conditional Risk Measures
ISSN:	0254-5330, 1572-9338
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Abstract	In this paper, we present a multistage time consistent Expected Conditional Risk Measure for minimizing a linear combination of the expected mean and the expected variance, so-called Expected Mean-Variance. The model is formulated as a multistage stochastic mixed-integer quadratic programming problem combining risk-sensitive cost and scenario analysis approaches. The proposed problem is solved by a matheuristic based on the Branch-and-Fix Coordination method. The multistage scenario cluster primal decomposition framework is extended to deal with large-scale quadratic optimization by means of stage-wise reformulation techniques. A specific case study in risk-sensitive production planning is used to illustrate that a remarkable decrease in the expected variance (risk cost) is obtained. A competitive behavior on the part of our methodology in terms of solution quality and computation time is shown when comparing with plain use of CPLEX in 150 benchmark instances, ranging up to 711,845 constraints and 193,000 binary variables.
AbstractList	In this paper, we present a multistage time consistent Expected Conditional Risk Measure for minimizing a linear combination of the expected mean and the expected variance, so-called Expected Mean-Variance. The model is formulated as a multistage stochastic mixed-integer quadratic programming problem combining risk-sensitive cost and scenario analysis approaches. The proposed problem is solved by a matheuristic based on the Branch-and-Fix Coordination method. The multistage scenario cluster primal decomposition framework is extended to deal with large-scale quadratic optimization by means of stage-wise reformulation techniques. A specific case study in risk-sensitive production planning is used to illustrate that a remarkable decrease in the expected variance (risk cost) is obtained. A competitive behavior on the part of our methodology in terms of solution quality and computation time is shown when comparing with plain use of CPLEX in 150 benchmark instances, ranging up to 711,845 constraints and 193,000 binary variables.
Audience	Academic
Author	Aldasoro, Unai Merino, María Pérez, Gloria
Author_xml	– sequence: 1 givenname: Unai orcidid: 0000-0002-9393-5766 surname: Aldasoro fullname: Aldasoro, Unai email: unai.aldasoro@ehu.eus organization: Department of Applied Mathematics, University of the Basque Country (UPV/EHU) – sequence: 2 givenname: María orcidid: 0000-0002-4947-2784 surname: Merino fullname: Merino, María organization: Department of Applied Mathematics and Statistics and Operations Research, University of the Basque Country (UPV/EHU) – sequence: 3 givenname: Gloria orcidid: 0000-0002-6182-296X surname: Pérez fullname: Pérez, Gloria organization: Department of Applied Mathematics and Statistics and Operations Research, University of the Basque Country (UPV/EHU)
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CitedBy_id	crossref_primary_10_1007_s10479_020_03726_1 crossref_primary_10_1108_TQM_10_2019_0243
Cites_doi	10.1007/s10479-015-1899-0 10.1057/jors.2014.41 10.1016/j.ejor.2006.09.105 10.1007/s10107-012-0621-0 10.1016/j.cor.2008.09.009 10.1007/s10479-007-0255-4 10.1007/BF03006558 10.1007/s10898-012-0022-1 10.1007/s10107-009-0321-6 10.1007/s10107-007-0165-x 10.1287/mnsc.22.4.455 10.1007/BF01580665 10.1007/s10107-005-0638-8 10.1287/opre.28.4.889 10.1142/6478 10.1016/j.cor.2013.06.015 10.1007/s10479-012-1165-7 10.1016/j.ejor.2015.05.048 10.1016/j.cor.2009.06.023 10.1016/j.ijpe.2005.09.001 10.1016/j.disopt.2004.03.006 10.1016/j.ejor.2016.08.072 10.1016/j.cor.2008.11.011 10.1109/TPWRS.2004.831652 10.1016/j.orl.2009.02.005 10.1007/s11750-009-0083-6 10.1016/j.cor.2011.06.021 10.1016/j.omega.2004.05.001 10.1007/978-3-642-46317-4_26 10.1007/0-387-33477-7 10.1007/s10107-017-1131-x 10.1007/978-1-4614-0237-4
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Keywords	90C20 Time consistent risk aversion McCormick relaxation Branch-and-Fix Coordination Multistage stochastic optimization Quadratic mixed 0–1 programming Matheuristic algorithms Production planning 90C15 90C59 Expected Conditional Risk Measures
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Snippet	In this paper, we present a multistage time consistent Expected Conditional Risk Measure for minimizing a linear combination of the expected mean and the...
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SubjectTerms	Business and Management Combinatorics Cost analysis Mathematical optimization Mathematical research Multistage Operations research Operations Research/Decision Theory Optimization Original Research Production planning Quadratic functions Quadratic programming Risk analysis Stochastic processes Studies Theory of Computation Variance
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Title	Time consistent expected mean-variance in multistage stochastic quadratic optimization: a model and a matheuristic
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