Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion
Name
Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion.pdf
Description
to appear in Mathematics of Operations Research
Size
383.87 KB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Doan, Xuan Vinh
Natarajan, Karthik
Teo, Chung-Piaw
Bertsimas, Dimitris J
Date Issued
August 2010
Journal
Mathematics of Operations Research
Publisher
Institute for Operations Research and the Management Sciences
Citation
Bertsimas, D. et al. “Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion.” Mathematics of Operations Research 35.3 (2010): 580–602.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1287/moor.1100.0445
