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Robust two-stage stochastic linear optimization with risk aversion
Ling, Aifan1; Sun, Jie2; Xiu, Naihua3; Yang, Xiaoguang4
AbstractWe study a two-stage stochastic linear optimization problem where the recourse function is risk-averse rather than risk neutral. In particular, we consider the mean-conditional value-at-risk objective function in the second stage. The model is robust in the sense that the distribution of the underlying random variable is assumed to belong to a certain family of distributions rather than to be exactly known. We start from analyzing a simple case where uncertainty arises only in the objective function, and then explore the general case where uncertainty also arises in the constraints. We show that the former problem is equivalent to a semidefinite program and the latter problem is generally NP-hard. Applications to two stage portfolio optimization, material order problems, stochastic production-transportation problem and single facility minimax distance problem are considered. Numerical results show that the proposed robust risk-averse two-stage stochastic programming model can effectively control the risk with solutions of acceptable good quality. (C) 2016 Elsevier B.V. All rights reserved.
KeywordUncertainty modeling Stochastic programming Robust optimization Conditional value-at-risk Semidefinite programming
Funding ProjectNational Natural Science Foundation of China[71371090] ; Science Foundation of Ministry of Education of China[13YJCZH160] ; Candidate Foundations of Distinguished Young Scientists in Jiangxi Province[20153BCB23006] ; key program of Jiangxi Province Education Department[GJJ150440]
WOS Research AreaBusiness & Economics ; Operations Research & Management Science
WOS SubjectManagement ; Operations Research & Management Science
WOS IDWOS:000384854500021
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Document Type期刊论文
Corresponding AuthorLing, Aifan
Affiliation1.Jiangxi Univ Finance & Econ, Sch Finance, Nanchang 330013, Peoples R China
2.Curtin Univ, Dept Math & Stat, Perth, WA, Australia
3.Beijing Jiaotong Univ, Sch Sci, Beijing 100044, Peoples R China
4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Ling, Aifan,Sun, Jie,Xiu, Naihua,et al. Robust two-stage stochastic linear optimization with risk aversion[J]. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH,2017,256(1):215-229.
APA Ling, Aifan,Sun, Jie,Xiu, Naihua,&Yang, Xiaoguang.(2017).Robust two-stage stochastic linear optimization with risk aversion.EUROPEAN JOURNAL OF OPERATIONAL RESEARCH,256(1),215-229.
MLA Ling, Aifan,et al."Robust two-stage stochastic linear optimization with risk aversion".EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 256.1(2017):215-229.
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