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Multi-objective enhanced interval optimization problem

Author

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  • P. Kumar

    (SRM Institute of Science and Technology)

  • A. K. Bhurjee

    (VIT Bhopal University)

Abstract

In this paper, we consider a multiple objective optimization problem whose decision variables and parameters are intervals. Existence of solution of this problem is studied by parameterizing the intervals. A methodology is developed to find the $$t\omega $$ t ω -efficient solution of the problem. The original problem is transformed to an equivalent deterministic problem and the relation between solutions of both is established. Finally, the methodology is verified in numerical examples.

Suggested Citation

  • P. Kumar & A. K. Bhurjee, 2022. "Multi-objective enhanced interval optimization problem," Annals of Operations Research, Springer, vol. 311(2), pages 1035-1050, April.
    • Handle: RePEc:spr:annopr:v:311:y:2022:i:2:d:10.1007_s10479-020-03870-8
    DOI: 10.1007/s10479-020-03870-8
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    References listed on IDEAS

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    1. 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.
    2. Gabriel R. Bitran, 1980. "Linear Multiple Objective Problems with Interval Coefficients," Management Science, INFORMS, vol. 26(7), pages 694-706, July.
    3. 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.
    4. P. Kumar & G. Panda & U.C. Gupta, 2016. "An interval linear programming approach for portfolio selection model," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 27(1/2), pages 149-164.
    5. 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.
    6. Ajay Kumar Bhurjee & Geetanjali Panda, 2019. "Parametric multi-objective fractional programming problem with interval uncertainty," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 35(1), pages 132-145.
    7. 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.
    8. Sankar Kumar Roy & Gurupada Maity & Gerhard Wilhelm Weber & Sirma Zeynep Alparslan Gök, 2017. "Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal," Annals of Operations Research, Springer, vol. 253(1), pages 599-620, June.
    9. Dorota Kuchta, 2011. "A concept of a robust solution of a multicriterial linear programming problem," 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. 19(4), pages 605-613, December.
    10. 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.
    11. A. K. Bhurjee & G. Panda, 2016. "Sufficient optimality conditions and duality theory for interval optimization problem," Annals of Operations Research, Springer, vol. 243(1), pages 335-348, August.
    12. Chanas, Stefan & Kuchta, Dorota, 1996. "Multiobjective programming in optimization of interval objective functions -- A generalized approach," European Journal of Operational Research, Elsevier, vol. 94(3), pages 594-598, November.
    13. A. Bhurjee & G. Panda, 2012. "Efficient solution of interval optimization problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 273-288, December.
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