An Algorithm for Solving Bi-Level Integer Linear Fractional Programming Problem based on Fuzzy Approach

This paper presents a fuzzy approach for solving the bi-level integer linear fractional programming problem (BILFPP). At the first phase of the solution algorithm and to avoid the complexity of non convexity of this problem, we begin by finding the convex hull of its original set of constraints using the cutting-plane algorithm, and then the Charnes & Cooper transformation is used to convert the BILFPP to an equivalent bilevel linear programming problem (BLPP). At the second phase, a membership function is constructed to develop a fuzzy model for obtaining the optimal solution of the BLPP. Finally, an illustrative numerical example is provided to clarify the proposed approach.