 
Summary: Shabbir Ahmed
Meanrisk objectives in stochastic programming
April 20, 2004
Abstract. Traditional stochastic programming is risk neutral in the sense that it is concerned
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 program
ming decomposition algorithms. We propose a parametric cutting plane algorithm to generate
the entire meanrisk efficient frontier for a particular meanrisk objective.
Key words. Stochastic programming, meanrisk objectives, computational complexity, cut
ting plane algorithms.
1. Introduction
This paper is concerned with stochastic programming problems of the form
min{ E[f(x, )] : x X}, (1)
where x Rn
is a vector of decision variables; X Rn
