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A compromise solution for the multiobjective stochastic linear programming under partial uncertainty

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  • Ben Abdelaziz, Fouad
  • Masri, Hatem

Abstract

This paper solves the multiobjective stochastic linear program with partially known probability. We address the case where the probability distribution is defined by crisp inequalities. We propose a chance constrained approach and a compromise programming approach to transform the multiobjective stochastic linear program with linear partial information on probability distribution into its equivalent uniobjective problem. The resulting program is then solved using the modified L-shaped method. We illustrate our results by an example.

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  • Ben Abdelaziz, Fouad & Masri, Hatem, 2010. "A compromise solution for the multiobjective stochastic linear programming under partial uncertainty," European Journal of Operational Research, Elsevier, vol. 202(1), pages 55-59, April.
    • Handle: RePEc:eee:ejores:v:202:y:2010:i:1:p:55-59
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    References listed on IDEAS

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    1. Peter Kall & János Mayer, 2005. "Stochastic Linear Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-24440-2, December.
    2. Liesiö, Juuso & Mild, Pekka & Salo, Ahti, 2008. "Robust portfolio modeling with incomplete cost information and project interdependencies," European Journal of Operational Research, Elsevier, vol. 190(3), pages 679-695, November.
    3. Ben Abdelaziz, F. & Masri, H., 2005. "Stochastic programming with fuzzy linear partial information on probability distribution," European Journal of Operational Research, Elsevier, vol. 162(3), pages 619-629, May.
    4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    5. Abdelaziz, Fouad Ben & Aouni, Belaid & Fayedh, Rimeh El, 2007. "Multi-objective stochastic programming for portfolio selection," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1811-1823, March.
    6. Urli, Bruno & Nadeau, Raymond, 2004. "PROMISE/scenarios: An interactive method for multiobjective stochastic linear programming under partial uncertainty," European Journal of Operational Research, Elsevier, vol. 155(2), pages 361-372, June.
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    Cited by:

    1. Junna Bi & Jun Cai & Yan Zeng, 2021. "Equilibrium reinsurance-investment strategies with partial information and common shock dependence," Annals of Operations Research, Springer, vol. 307(1), pages 1-24, December.
    2. Javier León & Justo Puerto & Begoña Vitoriano, 2020. "A Risk-Aversion Approach for the Multiobjective Stochastic Programming Problem," Mathematics, MDPI, vol. 8(11), pages 1-26, November.
    3. Abdelaziz, Fouad Ben, 2012. "Solution approaches for the multiobjective stochastic programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 1-16.
    4. Yilun Zhang & Jianghang Chen & Zhibin Jiang, 2023. "Optimal product service system configuration considering pairing utility and uncertain customer behavior," Flexible Services and Manufacturing Journal, Springer, vol. 35(2), pages 343-375, June.
    5. Mingfa Zheng & Yuan Yi & Zutong Wang & Tianjun Liao, 2017. "Relations among efficient solutions in uncertain multiobjective programming," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 329-357, September.
    6. D. La Torre & F. Mendivil, 2022. "Stochastic efficiency and inefficiency in portfolio optimization with incomplete information: a set-valued probability approach," Annals of Operations Research, Springer, vol. 311(2), pages 1085-1098, April.
    7. Engau, Alexander & Sigler, Devon, 2020. "Pareto solutions in multicriteria optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 357-368.
    8. M. S. Osman & A. M. Abd Elazeem & M. A. Elsisy & M. M. Rashwan, 2018. "Duality in the fuzzy-parametric space for fuzzy-parametric nonlinear programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 55(3), pages 662-676, November.
    9. Meryem Masmoudi & Fouad Ben Abdelaziz, 2018. "Portfolio selection problem: a review of deterministic and stochastic multiple objective programming models," Annals of Operations Research, Springer, vol. 267(1), pages 335-352, August.
    10. Zhe Liu & Shurong Li, 2022. "A numerical method for interval multi-objective mixed-integer optimal control problems based on quantum heuristic algorithm," Annals of Operations Research, Springer, vol. 311(2), pages 853-898, April.
    11. 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.
    12. D. La Torre & F. Mendivil, 2018. "Portfolio optimization under partial uncertainty and incomplete information: a probability multimeasure-based approach," Annals of Operations Research, Springer, vol. 267(1), pages 267-279, August.

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