Ali Payan - Department of Mathematics, Zahedan Branch, Islamic Azad University, Zahedan, Iran
Sakine Keykha - Department of Mathematics, Zahedan Branch, Islamic Azad University, Zahedan, Iran

In this paper, we are going to solve bi-level linear fractional programming problem (BLFPP). Many approaches have been offered to solve the mentioned problem; however most of the suggested methods are just some techniques to solve the problem and they do not have a reliable theoretical background. In this paper, through expanding the variable transformation of Charnes and Cooper (1962), BLFPP will change to bi-level linear programming problem (BLPP). Considering that there are some efficient and theory-based algorithms to solve the BLPP, BLFPP is solvable, as well. In this paper, the k-th best method, which is one of the most applicable and popular methods to solve BLPP, is used as a technique to solve the obtained BLPP. A numerical example will be given, at the end, to explain the method.

Bi-level linear fractional programming problem (BLFPP), Bi-level linear programming problem (BLPP), Variable transformation, K-th best method