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Analysis and comparisons of some solution concepts for stochastic programming problems

Author

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  • R. Caballero
  • E. Cerda
  • M. Muñoz
  • L. Rey

Abstract

The aim of this study is to analyse the resolution of Stochastic Programming Problems in which the objective function depends on parameters which are continuous random variables with a known distribution probability. In the literature on these questions different solution concepts have been defined for problems of these characteristics. These concepts are obtained by applying a transformation criterion to the stochastic objective which contains a statistical feature of the objective, implying that for the same stochastic problem there are different optimal solutions available which, in principle, are not comparable. Our study analyses and establishes some relations between these solution concepts.
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Suggested Citation

  • R. Caballero & E. Cerda & M. Muñoz & L. Rey, 2002. "Analysis and comparisons of some solution concepts for stochastic programming problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 101-123, June.
    • Handle: RePEc:spr:topjnl:v:10:y:2002:i:1:p:101-123
    DOI: 10.1007/BF02578943
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    References listed on IDEAS

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    1. Leclercq, J. -P., 1982. "Stochastic programming: An interactive multicriteria approach," European Journal of Operational Research, Elsevier, vol. 10(1), pages 33-41, May.
    2. Zare M., Yahia & Daneshmand, Ahmad, 1995. "A linear approximation method for solving a special class of the chance constrained programming problem," European Journal of Operational Research, Elsevier, vol. 80(1), pages 213-225, January.
    3. Kall, P., 1982. "Stochastic programming," European Journal of Operational Research, Elsevier, vol. 10(2), pages 125-130, June.
    4. A. Charnes & W. W. Cooper, 1963. "Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints," Operations Research, INFORMS, vol. 11(1), pages 18-39, February.
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    Cited by:

    1. Fatima Bellahcene & Philippe Marthon, 2021. "A compromise solution method for the multiobjective minimum risk problem," Operational Research, Springer, vol. 21(3), pages 1913-1926, September.
    2. Emilio Cerdá & Julio Moreno Lorente, 2009. "Chance Constrained Programming with one Discrete Random Variable in Each Constraint," Working Papers 2009-05, FEDEA.
    3. Muñoz, Maria M. & Ruiz, Francisco, 2009. "ISTMO: An interval reference point-based method for stochastic multiobjective programming problems," European Journal of Operational Research, Elsevier, vol. 197(1), pages 25-35, August.

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