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Solution approach to multi-objective linear fractional programming problem using parametric functions

Author

Listed:
  • Suvasis Nayak

    (Indian Institute of Technology Bhubaneswar)

  • Akshay Kumar Ojha

    (Indian Institute of Technology Bhubaneswar)

Abstract

In this paper, an iterative technique based on the use of parametric functions is proposed to obtain the best preferred optimal solution of a multi-objective linear fractional programming problem. The decision maker ascertains own desired tolerance values for the objectives as termination constants and imposes them on each iteratively computed objective functions in terms of termination conditions. Each fractional objective is transformed into non-fractional parametric function using certain initial values of parameters. The parametric values are iteratively computed and $$\epsilon $$ ϵ -constraint method is used to obtain the pareto (weakly) optimal solutions in each step. The computations get terminated when all the termination conditions are satisfied at a pareto optimal solution of an iterative step. A numerical example is discussed at the end to illustrate the proposed method and fuzzy max–min operator method is applied to validate the obtained results.

Suggested Citation

  • Suvasis Nayak & Akshay Kumar Ojha, 2019. "Solution approach to multi-objective linear fractional programming problem using parametric functions," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 174-190, March.
    • Handle: RePEc:spr:opsear:v:56:y:2019:i:1:d:10.1007_s12597-018-00351-2
    DOI: 10.1007/s12597-018-00351-2
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    References listed on IDEAS

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    6. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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    Citations

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    Cited by:

    1. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "An algorithm for quadratically constrained multi-objective quadratic fractional programming with pentagonal fuzzy numbers," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(1), pages 49-71.
    2. Vandana Goyal & Namrata Rani & Deepak Gupta, 2021. "Parametric approach to quadratically constrained multi-level multi-objective quadratic fractional programming," OPSEARCH, Springer;Operational Research Society of India, vol. 58(3), pages 557-574, September.
    3. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "FGP approach to quadratically constrained multi-objective quadratic fractional programming with parametric functions," OPSEARCH, Springer;Operational Research Society of India, vol. 59(2), pages 594-602, June.
    4. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "Rouben Ranking Function and parametric approach to quadratically constrained multiobjective quadratic fractional programming with trapezoidal fuzzy number coefficients," 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. 13(2), pages 923-932, April.

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