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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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    1. Dong, C. & Huang, G.H. & Cai, Y.P. & Xu, Y., 2011. "An interval-parameter minimax regret programming approach for power management systems planning under uncertainty," Applied Energy, Elsevier, vol. 88(8), pages 2835-2845, August.
    2. Ishibuchi, Hisao & Tanaka, Hideo, 1990. "Multiobjective programming in optimization of the interval objective function," European Journal of Operational Research, Elsevier, vol. 48(2), pages 219-225, September.
    3. Gabriel R. Bitran, 1980. "Linear Multiple Objective Problems with Interval Coefficients," Management Science, INFORMS, vol. 26(7), pages 694-706, July.
    4. Wu, Hsien-Chung, 2009. "The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 49-60, July.
    5. M. Ehrgott & J. Puerto & A. M. Rodríguez-Chía, 2007. "Primal-Dual Simplex Method for Multiobjective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 483-497, September.
    6. S. Rivaz & M. Yaghoobi, 2013. "Minimax regret solution to multiobjective linear programming problems with interval objective functions coefficients," 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. 21(3), pages 625-649, September.
    7. Inuiguchi, Masahiro & Sakawa, Masatoshi, 1995. "Minimax regret solution to linear programming problems with an interval objective function," European Journal of Operational Research, Elsevier, vol. 86(3), pages 526-536, November.
    8. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    9. Inuiguchi, Masahiro & Kume, Yasufumi, 1991. "Goal programming problems with interval coefficients and target intervals," European Journal of Operational Research, Elsevier, vol. 52(3), pages 345-360, June.
    10. Oliveira, Carla & Antunes, Carlos Henggeler, 2007. "Multiple objective linear programming models with interval coefficients - an illustrated overview," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1434-1463, September.
    11. Goberna, M. A. & Lopez, M. A., 2002. "Linear semi-infinite programming theory: An updated survey," European Journal of Operational Research, Elsevier, vol. 143(2), pages 390-405, December.
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    Cited by:

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    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.
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    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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