A class of integer linear fractional bilevel programming problems

Abstract

The bilevel programming (BLP) problem is a leader-follower game in which two players try to maximize their own objective functions over a common feasible region. This paper discusses an integer BLP with bounded variables in which the objective function of the first level is linear fractional, the objective function of the second level is linear and the common constraint region is a polyhedron. Various cuts have been discussed, which successively rank and scan the set of feasible solutions in decreasing order of leader’s objective function. By making use of these ranked solutions, we are able to solve the given BLP. An extension of BLP is also discussed in the form of constrained BLP, where in addition to the existing primary constraints, a set of secondary constraints is also introduced.

Keywords:

• fractional programming
• bilevel programming
• constrained programming
• integer programming
• extreme points

AMS Subject Classifications:

• 90C32
• 90C10
• 90C49

Acknowledgments

The authors are thankful to the University Grants Commission for the financial assistance provided for this work.