An efficient method for solving linear interval fractional transportation problems

Linear fractional programming (LFP) is a powerful mathematical tool for solving optimization problems with a ratio of linear functions as the objective function. In real-world applications, the coefficients of the objective function may be uncertain or imprecise, leading to the need for interval coefficients. This paper presents a comprehensive study on solving linear interval fractional transportation problems with interval objective function (ILFTP) which means that the coefficients of the variables in the objective function are uncertain and lie within a given interval. We propose a novel approach that combines interval analysis and optimization techniques to handle the uncertainty in the coefficients, ensuring robust and reliable solutions. The variable transformation method used in this study is a novel approach to solving this kind of problems. By reducing the problem to a nonlinear programming problem and then transforming it into a linear programming problem, the proposed method simplifies the solution process and improves the accuracy of the results. The effectiveness of the proposed method is demonstrated through various numerical examples and comparisons with existing methods. The outcomes demonstrate that the suggested approach is capable of precisely resolving ILFTPs. Overall, the proposed method provides a valuable contribution to the field of linear fractional transportation problems. It offers a practical and efficient solution to a challenging problem and has the potential to be applied in various real-world scenarios.

کلیدواژه ها:

Interval Coefficients ، Convex combination ، Linear fractional programming problems ، Linear fractional transportation problems