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Solving Linear Fractional Programming Problems in Uncertain Environments‎: ‎A Novel Approach with Grey Parameters

Document Type : Research Article

Authors

Department of Mathematics‎, ‎Payame Noor University (PNU)‎, P.O‎. ‎BOX 19395-4697‎, ‎Tehran‎, ‎Iran‎.

10.30473/coam.2023.67881.1235

Abstract

Fractional programming is a significant nonlinear planning tool within operation research‎. ‎It finds applications in diverse domains such as resource allocation‎, ‎transportation‎, ‎production programming‎, ‎performance evaluation‎, ‎and finance‎. ‎In practical scenarios‎, ‎uncertainties often make it challenging to determine precise coefficients for mathematical models‎. ‎Consequently‎, ‎utilizing indefinite coefficients instead of definite ones is recommended in such cases‎. ‎Grey systems theory‎, ‎along with probability theory‎, ‎randomness‎, ‎fuzzy logic‎, ‎and rough sets‎, ‎is an approach that addresses uncertainty‎. ‎In this study‎, ‎we address the problem of linear fractional programming with grey coefficients in the objective function‎. ‎To tackle this problem‎, ‎a novel approach based on the variable change technique proposed by Charnes and Cooper‎, ‎along with the convex combination of intervals‎, ‎is employed‎. ‎The article presents an algorithm that determines the solution to the grey fractional programming problem using grey numbers‎, ‎thus capturing the uncertainty inherent in the objective function‎. ‎To demonstrate the effectiveness of the proposed method‎, ‎an example is solved using the suggested approach‎. ‎The result is compared with solutions obtained using the whitening method‎, ‎employing Hu and Wong's technique and the Center and Greyness Degree Ranking method‎. ‎The comparison confirms the superiority of the proposed method over the whitening method‎, ‎thus suggesting adopting the grey system approach in such situations‎.

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References
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Control and Optimization in Applied Mathematics

Articles in Press, Accepted Manuscript
Available Online from 11 February 2024
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