TY - JOUR
T1 - Integrating Goal Programming, Taylor Series, Kuhn-Tucker Conditions, and Penalty Function Approaches to Solve Linear Fractional Bi-level Programming Problems
TT -
JF - IJMSI
JO - IJMSI
VL - 10
IS - 1
UR - http://ijmsi.ir/article-1-281-en.html
Y1 - 2015
SP - 1
EP - 10
KW - Bi-level programming
KW - Fractional programming
KW - Taylor Series
KW - Kuhn-Tucker conditions
KW - Goal programming
KW - Penalty function.
N2 - 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.
M3 10.7508/ijmsi.2015.01.001
ER -