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Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem

Author

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  • S. Rivaz

    (Yasouj University
    Shahid Bahonar University of Kerman)

  • M. A. Yaghoobi

    (Shahid Bahonar University of Kerman)

  • M. Hladík

    (Charles University)

Abstract

The current research concerns multiobjective linear programming problems with interval objective functions coefficients. It is known that the most credible solutions to these problems are necessarily efficient ones. To solve the problems, this paper attempts to propose a new model with interesting properties by considering the minimax regret criterion. The most important property of the new model is attaining a necessarily efficient solution as an optimal one whenever the set of necessarily efficient solutions is nonempty. In order to obtain an optimal solution of the new model, an algorithm is suggested. To show the performance of the proposed algorithm, numerical examples are given. Finally, some special cases are considered and their characteristic features are highlighted.

Suggested Citation

  • S. Rivaz & M. A. Yaghoobi & M. Hladík, 2016. "Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 237-253, September.
    • Handle: RePEc:spr:fuzodm:v:15:y:2016:i:3:d:10.1007_s10700-015-9226-4
    DOI: 10.1007/s10700-015-9226-4
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    References listed on IDEAS

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    Cited by:

    1. Dranichak, Garrett M. & Wiecek, Margaret M., 2019. "On highly robust efficient solutions to uncertain multiobjective linear programs," European Journal of Operational Research, Elsevier, vol. 273(1), pages 20-30.
    2. Milan Hladík, 2023. "Various approaches to multiobjective linear programming problems with interval costs and interval weights," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(3), pages 713-731, September.
    3. P. Kumar & A. K. Bhurjee, 2022. "Multi-objective enhanced interval optimization problem," Annals of Operations Research, Springer, vol. 311(2), pages 1035-1050, April.
    4. Schöbel, Anita & Zhou-Kangas, Yue, 2021. "The price of multiobjective robustness: Analyzing solution sets to uncertain multiobjective problems," European Journal of Operational Research, Elsevier, vol. 291(2), pages 782-793.
    5. Henriques, C.O. & Inuiguchi, M. & Luque, M. & Figueira, J.R., 2020. "New conditions for testing necessarily/possibly efficiency of non-degenerate basic solutions based on the tolerance approach," European Journal of Operational Research, Elsevier, vol. 283(1), pages 341-355.
    6. Groetzner, Patrick & Werner, Ralf, 2022. "Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach," European Journal of Operational Research, Elsevier, vol. 296(1), pages 101-115.
    7. Henriques, C.O. & Luque, M. & Marcenaro-Gutierrez, O.D. & Lopez-Agudo, L.A., 2019. "A multiobjective interval programming model to explore the trade-offs among different aspects of job satisfaction under different scenarios," Socio-Economic Planning Sciences, Elsevier, vol. 66(C), pages 35-46.
    8. Mehdi Allahdadi & Aida Batamiz, 2021. "Generation of some methods for solving interval multi-objective linear programming models," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 1077-1115, December.

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