Convexity and decomposition of mean-risk stochastic programs

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 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, com...

• Type: Journal
• Year: 2006
• Where: MP
• Authors: Shabbir Ahmed
• Keywords: Mean-risk Objectives, MP 2006, Stochastic Programming, Traditional Stochastic Programming