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|Title:||Models for minimax stochastic linear optimization problems with risk aversion|
|Keywords:||Minimax stochastic optimization|
|Citation:||Bertsimas, D., Doan, X.V., Natarajan, K., Teo, C.-P. (2010). Models for minimax stochastic linear optimization problems with risk aversion. Mathematics of Operations Research 35 (3) : 580-602. ScholarBank@NUS Repository. https://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 productiontransportation 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. Copyright © 2010 INFORMS.|
|Source Title:||Mathematics of Operations Research|
|Appears in Collections:||Staff Publications|
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