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On Solving Linear Fractional Programming Problems

Author

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  • Pandian Ponnaiah
  • Jayalakshmi Mohan

Abstract

A new method namely, denominator objective restriction method based on simplex method is proposed for solving linear fractional programming problems. Further, another method namely, decomposition-restriction method based on decomposition principle and the denominator objective restriction method is proposed for obtaining an optimal fuzzy solution to the fully fuzzy linear fractional programming problem. The procedures for the proposed methods are illustrated with the numerical examples.

Suggested Citation

  • Pandian Ponnaiah & Jayalakshmi Mohan, 2013. "On Solving Linear Fractional Programming Problems," Modern Applied Science, Canadian Center of Science and Education, vol. 7(6), pages 1-90, June.
    • Handle: RePEc:ibn:masjnl:v:7:y:2013:i:6:p:90
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    References listed on IDEAS

    as
    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Bela Martos & Andrew & Veronika Whinston, 1964. "Hyperbolic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 11(2), pages 135-155, June.
    3. P. C. Gilmore & R. E. Gomory, 1963. "A Linear Programming Approach to the Cutting Stock Problem---Part II," Operations Research, INFORMS, vol. 11(6), pages 863-888, December.
    4. G. R. Bitran & A. G. Novaes, 1973. "Linear Programming with a Fractional Objective Function," Operations Research, INFORMS, vol. 21(1), pages 22-29, February.
    5. Pandey, Pooja & Punnen, Abraham P., 2007. "A simplex algorithm for piecewise-linear fractional programming problems," European Journal of Operational Research, Elsevier, vol. 178(2), pages 343-358, April.
    6. Schaible, Siegfried, 1981. "Fractional programming: Applications and algorithms," European Journal of Operational Research, Elsevier, vol. 7(2), pages 111-120, June.
    7. Kanti Swarup, 1965. "Letter to the Editor—Linear Fractional Functionals Programming," Operations Research, INFORMS, vol. 13(6), pages 1029-1036, December.
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    More about this item

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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