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Shabbir Ahmed Mean-risk objectives in stochastic programming

Summary: Shabbir Ahmed
Mean-risk 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 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 program-
ming decomposition algorithms. We propose a parametric cutting plane algorithm to generate
the entire mean-risk efficient frontier for a particular mean-risk objective.
Key words. Stochastic programming, mean-risk 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


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


Collections: Engineering