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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
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 | ||||
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| Subjects: | H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management Q Science > QA Mathematics |
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| Divisions: | Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences Faculty of Social Sciences > Warwick Business School |
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| Journal or Publication Title: | Mathematics of Operations Research | ||||
| Publisher: | Informs | ||||
| ISSN: | 0364-765X | ||||
| Official Date: | August 2010 | ||||
| Dates: |
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| 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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