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Stochastic Approach versus Multiobjective Approach for Obtaining Efficient Solutions in Stochastic Multiobjective Programming Problems

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Abstract

In this work, we deal with obtaining efficient solutions for stochastic multiobjective programming problems. In general, these solutions are obtained in two stages: in one of them, the stochastic problem is transformed into its equivalent deterministic problem, and in the other one, some of the existing generating techniques in multiobjective programming are applied to obtain efficient solutions, which involves transforming the multiobjective problem into a problem with only one objective function. Our aim is to determine whether the order in which these two transformations are carried out influences, in any way, the efficient solution obtained. Our results show that depending on the type of stochastic criterion followed and the statistical characteristics of the initial problem, the order can have an influence on the final set of efficient solutions obtained for a given problem.

Suggested Citation

  • Rafael Caballero & Emilio Cerdá & Mª del Mar Muñoz & Lourdes Rey, 2002. "Stochastic Approach versus Multiobjective Approach for Obtaining Efficient Solutions in Stochastic Multiobjective Programming Problems," Documentos de Trabajo del ICAE 0217, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  • Handle: RePEc:ucm:doicae:0217
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    1. Liu, Baoding & Iwamura, Kakuzo, 1997. "Modelling stochastic decision systems using dependent-chance programming," European Journal of Operational Research, Elsevier, vol. 101(1), pages 193-203, August.
    2. Stein W. Wallace & Stein-Erik Fleten, 2002. "Stochastic programming in energy," GE, Growth, Math methods 0201001, EconWPA, revised 13 Nov 2003.
    3. F. Ben Abdelaziz & P. Lang & R. Nadeau, 1999. "Dominance and Efficiency in Multicriteria Decision under Uncertainty," Theory and Decision, Springer, pages 191-211.
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    Cited by:

    1. Abdelaziz, Fouad Ben, 2012. "Solution approaches for the multiobjective stochastic programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 1-16.
    2. repec:spr:fuzodm:v:16:y:2017:i:3:d:10.1007_s10700-016-9252-x is not listed on IDEAS
    3. repec:pal:jorsoc:v:60:y:2009:i:12:d:10.1057_jors.2008.106 is not listed on IDEAS
    4. Emilio Cerdá & Julio Moreno Lorente, 2009. "Chance Constrained Programming with one Discrete Random Variable in Each Constraint," Working Papers 2009-05, FEDEA.
    5. Zarghami, Mahdi & Szidarovszky, Ferenc, 2009. "Revising the OWA operator for multi criteria decision making problems under uncertainty," European Journal of Operational Research, Elsevier, vol. 198(1), pages 259-265, October.
    6. Chaabane Djamal & Mebrek Fatma, 2014. "Optimization of a linear function over the set of stochastic efficient solutions," Computational Management Science, Springer, vol. 11(1), pages 157-178, January.
    7. Mahdi Zarghami, 2010. "Urban Water Management Using Fuzzy-Probabilistic Multi-Objective Programming with Dynamic Efficiency," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(15), pages 4491-4504, December.
    8. Belaid AOUNI & Cinzia COLAPINTO & Davide LA TORRE, 2008. "Solving stochastic multi-objective programming through the GP model," Departmental Working Papers 2008-18, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

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    Keywords

    Stochastic Multiobjective Programming; Efficiency; Stochastic Approach; Multiobjective Approach.;

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