On bilevel fractional programming

Abstract

The bilevel fractional programming problem (BFPP), in which the follower's objective function is a linear fractional functional, is introduced and studied in this paper. The leader's and the follower's decision variables are related by linear constraints. A solution strategy for (BFPP) when the leader's objective is a bottleneck function is presented. In this case the optimal solution is found to exist at an entreme point of the underlying region. However in the case when the leader's objective function is a linear function or a linear fractional function, the corresponding (BFPP) is found to be hard as its optimal solution may occur at a non-extreme point of the underlying region. This problem is posed as a potential area for further research.

Keywords:

• Bilevel Programming
• Bottleneck Programming
• Non-linear Programming
• Non-convex Programming