| edoc-Server der Humboldt-Universität zu Berlin |
| Author(s): | Shabbir Ahmed, Georgia Institute of Technology | Title: | Mean-risk objectives in stochastic programming |
| Date of Acceptance: | 16.04.2004 |
| Submission Date: | 12.04.2004 |
| Series Title: |
Stochastic Programming E-Print Series (SPEPS) |
| Editors: | Julie L. Higle; Werner Römisch; Surrajeet Sen |
| Complete Preprint: | pdf (urn:nbn:de:kobv:11-10059496) |
| Keywords (eng): | Stochastic programming, mean-risk objectives, computational complexity, cutting plane algorithms |
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| Abstract (eng): | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 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 a parametric cutting plane algorithm to generate the entire mean-risk efficient frontier for a particular mean-risk objective. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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