The bilevel linear/linear fractional programming problem

✍ Scribed by Herminia I. Calvete; Carmen Galé

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 140 KB
• Volume: 114
• Category: Article
• ISSN: 0377-2217
• DOI: 10.1016/s0377-2217(98)00078-2

✦ Synopsis

Bilevel programming involves two optimization problems where the constraint region of the ®rst level problem is implicitly determined by another optimization problem. In this paper we consider the bilevel linear/linear fractional programming problem in which the objective function of the ®rst level is linear, the objective function of the second level is linear fractional and the feasible region is a polyhedron. For this problem we prove that an optimal solution can be found which is an extreme point of the polyhedron. Moreover, taking into account the relationship between feasible solutions to the problem and bases of the technological coecient submatrix associated to variables of the second level, an enumerative algorithm is proposed that ®nds a global optimum to the problem.