Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Calvete H I and Gale C “On the quasi-concave bilevel programming problem”, Journal of optimization Theory and Applications, vol. 98, No. 3, (1998), 613–622.
Calvete H I and Gale C “The bilevel linear/linear fractional programming problem”, European Journal of operational Reserch, 114, (1999), 188–197.
Mathur K and Puri M C “On belive fractional programming”, optimization, Vol. 35, (1995), 215–226.
Thriwani D Arora S R “An algorithm for the integer linear fractional bilevel programming problem”, optimization, Vol. 39, (1997), 56–67.
Verma V Bakshi H C and Puri M C “Ranking in integer linear fractional programming problem”, Zor-Methods and Models of Operations Reserch, 34, (1990), 325–334.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Alemayehu, G., Arora, S.R. On the Bilevel Integer Linear Fractional Programming Problem. OPSEARCH 38, 508–519 (2001). https://doi.org/10.1007/BF03398654
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03398654