Convexity and decomposition of mean-risk stochastic programs

• 成果类型: Article
• 署名作者: Ahmed, S
• 署名单位: University System of Georgia; Georgia Institute of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-005-0638-8
• 发表日期: 2006
• 页码: 433-446
• 关键词: dominance

摘要

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.