 
Summary: Shabbir Ahmed
Convexity and decomposition of
meanrisk 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 meanrisk objective, where some
dispersion statistic is used as a measure of risk. We investigate the computational suitability
of various meanrisk objective functions in addressing risk in stochastic programming models.
We prove that the classical meanvariance criterion leads to computational intractability even
in the simplest stochastic programs. On the other hand, a number of alternative meanrisk
functions are shown to be computationally tractable using slight variants of existing stochastic
programming decomposition algorithms. We propose decompositionbased parametric cutting
plane algorithms to generate meanrisk efficient frontiers for two particular classes of meanrisk
objectives.
Key words. Stochastic programming, meanrisk 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)
