Models for minimax stochastic linear optimization problems with risk aversion
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. ISSN 0364-765XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1287/moor.1100.0445
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|
|Official Date:||August 2010|
|Page Range:||pp. 580-602|
|Access rights to Published version:||Restricted or Subscription Access|
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