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Parametric approach to quadratically constrained multi-level multi-objective quadratic fractional programming

Author

Listed:
  • Vandana Goyal

    (Maharishi Markandeshwar (DU))

  • Namrata Rani

    (Maharishi Markandeshwar (DU))

  • Deepak Gupta

    (Maharishi Markandeshwar (DU))

Abstract

The paper proposed a method to study and obtain a set of Pareto optimal solutions or a set of representative solutions to a quadratically constrained multi-level multiobjective quadratic fractional programming problem. This problem involves several objectives to be fulfilled at multi levels under a common set of quadratic constraints. Initially, we used parametric approach to convert the fractional programming model to an equivalent non-fractional programming model by allocating a parametric vector to each fractional objective. Then, $$\varepsilon$$ ε -constraint method is used to convert this multiobjective programming model into an equivalent model with single objective. The solution of every previous level is followed by the next level in succession to find a solution which is suitable to each level decision maker. An algorithm and numerical example are also presented at the end of the paper to validate the proposed methodology for the Model.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:opsear:v:58:y:2021:i:3:d:10.1007_s12597-020-00497-y
    DOI: 10.1007/s12597-020-00497-y
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    References listed on IDEAS

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    1. Stein, Oliver & Still, Georg, 2002. "On generalized semi-infinite optimization and bilevel optimization," European Journal of Operational Research, Elsevier, vol. 142(3), pages 444-462, November.
    2. 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.
    3. Y. Almogy & O. Levin, 1971. "A Class of Fractional Programming Problems," Operations Research, INFORMS, vol. 19(1), pages 57-67, February.
    4. Wolf, Hartmut, 1986. "Solving special nonlinear fractional programming problems via parametric linear programming," European Journal of Operational Research, Elsevier, vol. 23(3), pages 396-400, March.
    5. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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    Cited by:

    1. Namrata Rani & Vandana Goyal & Deepak Gupta, 2021. "A solution procedure for multi-objective fully quadratic fractional optimization model," 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. 12(6), pages 1447-1458, December.
    2. 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.
    3. 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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