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.
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Ahmed, S. Convexity and decomposition of mean-risk stochastic programs. Math. Program. 106, 433–446 (2006). https://doi.org/10.1007/s10107-005-0638-8
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DOI: https://doi.org/10.1007/s10107-005-0638-8