An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

Authors

1 Department of Mathematics, Addis Ababa University, P.O. Box 1176, Addis Ababa, Ethiopia

2 Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology (BIUST), P/Bag Mail 16, Palapye, Botswana

3 Department of Mathematics, Wollo University, P.O. Box 1145, Dessie, Ethiopia

Abstract

Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.

Keywords