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Generation of some methods for solving interval multi-objective linear programming models

Author

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  • Mehdi Allahdadi

    (University of Sistan and Baluchestan)

  • Aida Batamiz

    (University of Sistan and Baluchestan)

Abstract

In this paper, we consider interval multi-objective linear programming (IMOLP) models which are very important due to deal with inaccurate data and uncertainties. The aim of this paper is to solve the IMOLP models and obtaining efficient solutions. We first extend Ecker-Kouada method in which the variables are interval, and we introduce interval version of the Ecker-Kouada method which is called I-Ecker-Kouada method. Also, we introduce interval version of Benson’s method (I-Benson) which is not a complicated method. Finally, numerical examples and comparison with other methods are employed to illustrate the advantages of our methods.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:opsear:v:58:y:2021:i:4:d:10.1007_s12597-021-00512-w
    DOI: 10.1007/s12597-021-00512-w
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    1. Dilbagh Panchal & Umesh Jamwal & Priyank Srivastava & Kushal Kamboj & Rohit Sharma, 2018. "Fuzzy methodology application for failure analysis of transmission system," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 12(2), pages 220-237.
    2. Huang, Guo H. & Baetz, Brian W. & Patry, Gilles G., 1995. "Grey integer programming: An application to waste management planning under uncertainty," European Journal of Operational Research, Elsevier, vol. 83(3), pages 594-620, June.
    3. J W Chinneck & K Ramadan, 2000. "Linear programming with interval coefficients," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(2), pages 209-220, February.
    4. Dilbagh PANCHAL & Prasenjit CHATTERJEE & Rajendra Kumar SHUKLA & Tanupriya CHOUDHURY & Jolanta TAMOSAITIENE, 2017. "Integrated Fuzzy AHP-Codas Framework for Maintenance Decision in Urea Fertilizer Industry," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(3), pages 179-196.
    5. Zhou, Feng & Huang, Gordon H. & Chen, Guo-Xian & Guo, Huai-Cheng, 2009. "Enhanced-interval linear programming," European Journal of Operational Research, Elsevier, vol. 199(2), pages 323-333, December.
    6. 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.
    7. 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.
    8. Dilbagh Panchal & Priyank Srivastava, 2019. "Qualitative analysis of CNG dispensing system using fuzzy FMEA–GRA integrated approach," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(1), pages 44-56, February.
    9. 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.
    10. Dilbagh Panchal & Dinesh Kumar, 2017. "Risk analysis of compressor house unit in thermal power plant using integrated fuzzy FMEA and GRA approach," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 25(2), pages 228-250.
    11. 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.
    12. H. Isermann, 1974. "Technical Note—Proper Efficiency and the Linear Vector Maximum Problem," Operations Research, INFORMS, vol. 22(1), pages 189-191, February.
    13. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, December.
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