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Deviation Measures in Linear Two-Stage Stochastic Programming

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  • Trine Kristoffersen

Abstract

We consider a linear two-stage stochastic program. Whereas optimization in the traditional setting is based solely on expectation, we include risk measures reflecting dispersions of the random objective. Presenting the mean-risk models, we aim to extend existing results for the expectation-based model. In particular, we discuss structural properties such as continuity, differentiability and convexity and address stability issues. Furthermore, we propose algorithmic treatment with a slight variation of the L-shaped method Copyright Springer-Verlag 2005

Suggested Citation

  • Trine Kristoffersen, 2005. "Deviation Measures in Linear Two-Stage Stochastic Programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 255-274, November.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:2:p:255-274
    DOI: 10.1007/s00186-005-0006-8
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    References listed on IDEAS

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    1. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    2. Rüdiger Schultz, 2000. "Some Aspects of Stability in Stochastic Programming," Annals of Operations Research, Springer, vol. 100(1), pages 55-84, December.
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    2. Prasad Parab & Lewis Ntaimo & Bernardo Pagnoncelli, 2025. "Stochastic decomposition for risk-averse two-stage stochastic linear programs," Journal of Global Optimization, Springer, vol. 91(1), pages 59-93, January.
    3. Michelle Alvarado & Lewis Ntaimo, 2018. "Chemotherapy appointment scheduling under uncertainty using mean-risk stochastic integer programming," Health Care Management Science, Springer, vol. 21(1), pages 87-104, March.
    4. João Claro & Jorge Sousa, 2010. "A multiobjective metaheuristic for a mean-risk static stochastic knapsack problem," Computational Optimization and Applications, Springer, vol. 46(3), pages 427-450, July.
    5. Zhiping Chen & Feng Zhang & Li Yang, 2011. "Postoptimality for mean-risk stochastic mixed-integer programs and its application," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 445-465, December.

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