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Shabbir Ahmed Convexity and decomposition of
 

Summary: Shabbir Ahmed
Convexity and decomposition of
mean-risk stochastic programs
April 20, 2004. Revised February 8, 2005.
Abstract. Traditional stochastic programming is risk neutral in the sense that it is con-
cerned with the optimization of an expectation criterion. A common approach to addressing
risk in decision making problems is to consider a weighted mean-risk objective, 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 criterion 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 decomposition-based parametric cutting
plane algorithms to generate mean-risk efficient frontiers for two particular classes of mean-risk
objectives.
Key words. Stochastic programming, mean-risk objectives, computational complexity, de-
composition, cutting plane algorithms.
1. Introduction
This paper is concerned with stochastic programming problems of the form
min{ E[f(x, )] : x X}, (1)

  

Source: Ahmed, Shabbir - School of Industrial and Systems Engineering, Georgia Institute of Technology

 

Collections: Engineering