Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion

Event Sponsor: 
Mathematics and Computer Science Division Seminar
Start Date: 
May 20 2009 - 1:30pm to 2:30pm
Building/Room: 
Building 221 Conference Room A216
Location: 
Argonne National Laboratory
Speaker(s): 
Xuan Vinh Doan
Speaker(s) Title: 
Host: 
Mihai Anitescu

In many stochastic optimization applications, there is some uncertainty about the probability distribution P of random parameters. In this talk, we study the minimax decision model for two-stage stochastic linear optimization problems
with the assumption that P belongs to a class of probability distributions specified by the first and second moments. We also incorporate risk considerations into the model with piecewise linear disutility functions. We show that the model is tractable for problems with random objective and some special instances of problems with random right-hand side, which are in general NP-hard. We are able to provide explicit constructions of the worst-case
extremal distributions for the minimax problems in these cases. We then demonstrate and compare the performance of minimax solutions with that of data-driven solutions under contaminated distributions using numerical examples. Applications include a production-transportation problem and a single facility minimax distance problem.

Computational results show that the minimax solutions clearly hedge against the worst-case distributions and provide lower variability in objective value than data-driven solutions under most of the contaminated distributions. Finally, we present an additional application of the proposed minimax model in providing moment bounds for an option pricing problem.

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