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Efficient Solution Concepts and Their Relations in Stochastic Multiobjective Programming

Author

Listed:
  • R. Caballero

    (University of Málaga)

  • E. Cerdá

    (Universidad Complutense de Madrid)

  • M. M. Muñoz

    (University of Málaga)

  • L. Rey

    (University of Málaga)

  • I. M. Stancu-Minasian

    (Romanian Academy)

Abstract

In this work, different concepts of efficient solutions to problems of stochastic multiple-objective programming are analyzed. We center our interest on problems in which some of the objective functions depend on random parameters. The existence of different concepts of efficiency for one single stochastic problem, such as expected-value efficiency, minimum-risk efficiency, etc., raises the question of their quality. Starting from this idea, we establish some relationships between the different concepts. Our study enables us to determine what type of efficient solutions are obtained by each of these concepts.

Suggested Citation

  • R. Caballero & E. Cerdá & M. M. Muñoz & L. Rey & I. M. Stancu-Minasian, 2001. "Efficient Solution Concepts and Their Relations in Stochastic Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 53-74, July.
    • Handle: RePEc:spr:joptap:v:110:y:2001:i:1:d:10.1023_a:1017591412366
    DOI: 10.1023/A:1017591412366
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    References listed on IDEAS

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    1. Abdelaziz, F. Ben & Lang, P. & Nadeau, R., 1995. "Distributional efficiency in multiobjective stochastic linear programming," European Journal of Operational Research, Elsevier, vol. 85(2), pages 399-415, September.
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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. 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.
    3. Caballero, Rafael & Cerda, Emilio & del Mar Munoz, Maria & Rey, Lourdes, 2004. "Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems," European Journal of Operational Research, Elsevier, vol. 158(3), pages 633-648, November.
    4. Ralph Steuer & Yue Qi & Markus Hirschberger, 2007. "Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection," Annals of Operations Research, Springer, vol. 152(1), pages 297-317, July.
    5. 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.
    6. 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.
    7. Fatima Bellahcene, 2019. "Decision maker's preferences modeling for multiple objective stochastic linear programming problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(3), pages 5-16.
    8. Jörg Fliege & Huifu Xu, 2011. "Stochastic Multiobjective Optimization: Sample Average Approximation and Applications," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 135-162, October.
    9. Juan Ribes & Jacinto González-Pachón, 2021. "Risk Attitude in Multicriteria Decision Analysis: A Compromise Approach," IJERPH, MDPI, vol. 18(12), pages 1-14, June.
    10. Fouad Ben Abdelaziz & Cinzia Colapinto & Davide La Torre & Danilo Liuzzi, 2020. "A stochastic dynamic multiobjective model for sustainable decision making," Annals of Operations Research, Springer, vol. 293(2), pages 539-556, October.
    11. S. Rangavajhala & A. A. Mullur & A. Messac, 2009. "Equality Constraints in Multiobjective Robust Design Optimization: Decision Making Problem," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 315-337, February.

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