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Models for minimax stochastic linear optimization problems with risk aversion

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Bertsimas, Dimitris, Doan, Xuan Vinh, Natarajan, K. and Teo, C. -P. (2010) Models for minimax stochastic linear optimization problems with risk aversion. Mathematics of Operations Research, 35 (3). pp. 580-602. doi:10.1287/moor.1100.0445

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Official URL: http://dx.doi.org/10.1287/moor.1100.0445

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Abstract

We propose a semidefinite optimization (SDP) model for the class of minimax two-stage stochastic linear optimization problems with risk aversion. The distribution of second-stage random variables belongs to a set of multivariate distributions with known first and second moments. For the minimax stochastic problem with random objective, we provide a tight SDP formulation. The problem with random right-hand side is NP-hard in general. In a special case, the problem can be solved in polynomial time. Explicit constructions of the worst-case distributions are provided. Applications in a production-transportation problem and a single facility minimax distance problem are provided to demonstrate our approach. In our experiments, the performance of minimax solutions is close to that of data-driven solutions under the multivariate normal distribution and better under extremal distributions. The minimax solutions thus guarantee to hedge against these worst possible distributions and provide a natural distribution to stress test stochastic optimization problems under distributional ambiguity.

Item Type: Journal Article
Subjects: H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management
Q Science > QA Mathematics
Divisions: Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences
Faculty of Social Sciences > Warwick Business School
Journal or Publication Title: Mathematics of Operations Research
Publisher: Informs
ISSN: 0364-765X
Official Date: August 2010
Dates:
DateEvent
August 2010Published
Volume: 35
Number: 3
Page Range: pp. 580-602
DOI: 10.1287/moor.1100.0445
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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