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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Veröffentlicht in:Annals of operations research Jg. 280; H. 1-2; S. 151 - 187
Hauptverfasser: Aldasoro, Unai, Merino, María, Pérez, Gloria
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.09.2019
Springer
Springer Nature B.V
Schlagworte:
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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Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-018-3032-7