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A Linearization to the Multi-objective Linear Plus Linear Fractional Program

Author

Listed:
  • Mojtaba Borza

    (Faculty of Science & Technology, UKM)

  • Azmin Sham Rambely

    (Faculty of Science & Technology, UKM)

  • Seyed Ahmad Edalatpanah

    (Ayandegan Institute of Higher Education)

Abstract

The structure of the sum of linear plus linear ratio program is complex and š’©š’«-completeness. In management science, game theory, and industry, there are problems such that their mathematical models can be represented as a multi-objective linear plus linear fractional programming problem (MOLLFPP). The aim of this study is to introduce a method to address the MOLLFPP. The approach is designed in 2 phases. In phase 1, a method is created to reach the global optimal solution of the linear plus linear fractional programming problem (LLFPP) using suitable variable transformations. In fact, in this phase, the LLFPP is changed into a linear programming problem (LPP). In phase 2, taking into account the information of phase 1, the MOLLFPP is transformed into LPPs by applying the weighted sum and maxā€“min techniques. Two examples are solved to illustrate the method and comparisons are made to show the accuracy.

Suggested Citation

  • Mojtaba Borza & Azmin Sham Rambely & Seyed Ahmad Edalatpanah, 2023. "A Linearization to the Multi-objective Linear Plus Linear Fractional Program," SN Operations Research Forum, Springer, vol. 4(4), pages 1-22, December.
    • Handle: RePEc:spr:snopef:v:4:y:2023:i:4:d:10.1007_s43069-023-00256-x
    DOI: 10.1007/s43069-023-00256-x
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    References listed on IDEAS

    as
    1. Hirche, Joachim, 1996. "A note on programming problems with linear-plus-linear-fractional objective functions," European Journal of Operational Research, Elsevier, vol. 89(1), pages 212-214, February.
    2. B. Radhakrishnan & P. Anukokila, 2014. "Fractional Goal Programming for Fuzzy Solid Transportation Problem with Interval Cost," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 6(3), pages 359-377, September.
    3. Mojtaba Borza & Azmin Sham Rambely, 2021. "A Linearization to the Sum of Linear Ratios Programming Problem," Mathematics, MDPI, vol. 9(9), pages 1-10, April.
    4. Siegfried Schaible, 1977. "A note on the sum of a linear and linearā€fractional function," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 24(4), pages 691-693, December.
    5. Mojtaba Borza & Azmin Sham Rambely, 2021. "A New Method to Solve Multi-Objective Linear Fractional Problems," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 13(3), pages 323-334, July.
    6. Chadha, S. S., 1993. "Dual of the sum of a linear and linear fractional program," European Journal of Operational Research, Elsevier, vol. 67(1), pages 136-139, May.
    7. Singh, Sanjeet & Gupta, Pankaj & Bhatia, Davinder, 2005. "Multiparametric sensitivity analysis in programming problem with linear-plus-linear fractional objective function," European Journal of Operational Research, Elsevier, vol. 160(1), pages 232-241, January.
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