Solving Linear Fractional Programming Problem with Fuzzy-Random Variables in Objective Function: A New Approach

In this paper we present an algorithm to solve a linear fractional programming problem with uncertain coefficients in the objective function. We have applied recent concepts of fuzzy solution based on α-cuts and Pareto optimal solutions of a bi-objective optimization problem. As far as solving methods are concerned, the linear fractional programming, as an extension of linear programming, is easy enough to be handled by means of linear programming but complicated enough to elude a simple analogy. We follow the construction of the fuzzy solution for the linear case introduced by Dempe and Ruziyeva (2012) and avoid the inconvenience of the classic weighted sum method for determining Pareto optimal solutions. Then, we generate the set of solutions for a linear fractional program with fuzzy- random coefficients in the objective function.