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Programming with linear fractional functionals

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  • Stanley Zionts

Abstract

Charnes and Cooper [1] showed that a linear programming problem with a linear fractional objective function could be solved by solving at most two ordinary linear programming problems. In addition, they showed that where it is known a priori that the denominator of the objective function has a unique sign in the feasible region, only one problem need be solved. In the present note it is shown that if a finite solution to the problem exists, only one linear programming problem must be solved. This is because the denominator cannot have two different signs in the feasible region, except in ways which are not of practical importance.

Suggested Citation

  • Stanley Zionts, 1968. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 15(3), pages 449-451, September.
    • Handle: RePEc:wly:navlog:v:15:y:1968:i:3:p:449-451
    DOI: 10.1002/nav.3800150308
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    Cited by:

    1. Tunjo Perić & Josip Matejaš & Zoran Babić, 2023. "Advantages, sensitivity and application efficiency of the new iterative method to solve multi-objective linear fractional programming problem," 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. 31(3), pages 751-767, September.
    2. V. Charles & D. Dutta, 2006. "Extremization of multi-objective stochastic fractional programming problem," Annals of Operations Research, Springer, vol. 143(1), pages 297-304, March.
    3. Sehgal, Ruchika & Sharma, Amita & Mansini, Renata, 2023. "Worst-case analysis of Omega-VaR ratio optimization model," Omega, Elsevier, vol. 114(C).

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