On the bilevel integer linear fractional programming problem

The bilevel programming problem is a leader–follower game in which two players try to maximize their own objective function over a common feasible region. In this paper we consider the bilevel programming problem in which both the objective functions are linear fractional and the variables take non-negative integral values. An algorithm to find the optimal integer solution is developed. The search is made among bases of the coefficient submatrix corresponding to the variables controlled by the follower's problem. An example to demonstrate the algorithm is presented.