solving linear fractional transportation problem with interval cost‎, ‎source and destination parameters

In this paper, we focus on the fractional transportation problem where the cost coefficient of the objective functions, and the source and destination parameters have been expressed as interval values. the variable transformation solves the linear fractional transportation problem with interval coefficients in the objective function. in this method, instead of intervals in the function, using a convex combination of the left limit and right limit of the interval, linear fractional transportation problems with interval coefficients are reduced to a nonlinear programming problem. finally, the nonlinear problem is transformed into a linear programming problem with two more constraints and one more variable compared to the initial problem. the constraints with interval source and destination parameters have been converted into deterministic ones. numerical examples are presented to clarify the idea of the proposed approach for three possible cases of the original problem.