Title: Reformulation of bilevel linear fractional/linear programming problem into a mixed integer programming problem via complementarity problem

Authors: Anuradha Sharma

Addresses: Department of Mathematics, Maharaja Agrasen College, University of Delhi, New Delhi, 110096, India

Abstract: The bilevel programming problem is a static version of the Stackelberg's leader follower game in which Stackelberg strategy is used by the higher level decision maker called the leader given the rational reaction of the lower decision maker called the follower. The bilevel programming problem (BLPP) is a two-level hierarchical optimisation problem and is non-convex. This paper deals with finding links between the bilevel linear fractional/linear programming problem (BF/LP), the generalised linear fractional complementarity problem (GFCP) and mixed integer linear fractional programming problem (MIFP). The (BF/LP) is reformulated as a (GFCP) which in turn is reformulated as an (MIFP). The method is supported with the help of a numerical example.

Keywords: bilevel programming; generalised complementarity problem; mixed integer programming; fractional programming; reformulation; discrete solution.

DOI: 10.1504/IJCSM.2022.125903

International Journal of Computing Science and Mathematics, 2022 Vol.15 No.4, pp.359 - 370

Received: 18 Nov 2019
Accepted: 06 Feb 2020
Published online: 04 Oct 2022 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article