Integrating goal programming, Taylor series, Kuhn-Tucker conditions, and penalty function approaches to solve linear fractional bi-level programming problems.

*(English)*Zbl 1332.90260Summary: 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.

##### MSC:

90C29 | Multi-objective and goal programming |

90C32 | Fractional programming |

41A58 | Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) |