Mean-risk objectives in stochastic programming

Shabbir Ahmed (sahmedisye.gatech.edu)

Abstract: Traditional stochastic programming is risk neutral in the sense that it is concerned with the optimization of an expectation criteria. A common approach to addressing risk in decision making problems is to consider a weighted mean-risk criterion, where some dispersion statistic is used as a measure of risk. We investigate the computational suitability of various mean-risk objective functions in addressing risk in stochastic programming models. We prove that the classical mean-variance criteria leads to computational intractability even in the simplest stochastic programs. On the other hand, a number of alternative mean-risk functions are shown to be computationally tractable using slight variants of existing stochastic programming decomposition algorithms. We propose a parametric cutting plane algorithm to generate the entire mean-risk efficient frontier for a particular mean-risk objective.

Keywords: Stochastic programming, mean-risk objectives, computational complexity, cutting plane algorithms.

Category 1: Stochastic Programming

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Technical Report. School of Industrial & Systems Engineering, Georgia Institute of Technology.

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Entry Submitted: 04/12/2004
Entry Accepted: 04/16/2004
Entry Last Modified: 04/20/2004

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