%0 Journal Article
%A Saraj, M.
%A Safaei, N.
%T Integrating Goal Programming, Taylor Series, Kuhn-Tucker Conditions, and Penalty Function Approaches to Solve Linear Fractional Bi-level Programming Problems
%J Iranian Journal of Mathematical Sciences and Informatics
%V 10
%N 1
%U http://ijmsi.ir/article-1-281-en.html
%R 10.7508/ijmsi.2015.01.001
%D 2015
%K Bi-level programming, Fractional programming, Taylor Series, Kuhn-Tucker conditions, Goal programming, Penalty function.,
%X In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent to fractional objective functions. Then on using the Kuhn-Tucker optimality condition of the lower level problem, we transform the linear bilevel programming problem into a corresponding single level programming. The complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty, that can be reduce to a single objective function. In the other words, suitable transformations can be applied to formulate FBLP problems. Finally a numerical example is given to illustrate the complexity of the procedure to the solution.
%> http://ijmsi.ir/article-1-281-en.pdf
%P 1-10
%& 1
%!
%9 Research paper
%L A-10-291-1
%+ Shahid Chamran University
%G eng
%@ 1735-4463
%[ 2015