In this article,the authors discuss the optimal conditions of the linear fractionalprogramming problem and prove that a locally optional solution is a globally optional solution and the locally optimal solution can be...In this article,the authors discuss the optimal conditions of the linear fractionalprogramming problem and prove that a locally optional solution is a globally optional solution and the locally optimal solution can be attained at a basic feasible solution withconstraint condition.展开更多
A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equ...A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.展开更多
In this paper, we study a new approach for solving linear fractional programming problem (LFP) by converting it into a single Linear Programming (LP) Problem, which can be solved by using any type of linear fractional...In this paper, we study a new approach for solving linear fractional programming problem (LFP) by converting it into a single Linear Programming (LP) Problem, which can be solved by using any type of linear fractional programming technique. In the objective function of an LFP, if βis negative, the available methods are failed to solve, while our proposed method is capable of solving such problems. In the present paper, we propose a new method and develop FORTRAN programs to solve the problem. The optimal LFP solution procedure is illustrated with numerical examples and also by a computer program. We also compare our method with other available methods for solving LFP problems. Our proposed method of linear fractional programming (LFP) problem is very simple and easy to understand and apply.展开更多
This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for...This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.展开更多
基金Supported by the Natural Science Foundation of Henan Province（0511012000 0511013600） Supported by the Science Foundation for Pure Research of Natural Science of the Education Department of Henan Province（200512950001）
文摘In this article,the authors discuss the optimal conditions of the linear fractionalprogramming problem and prove that a locally optional solution is a globally optional solution and the locally optimal solution can be attained at a basic feasible solution withconstraint condition.
基金supported by the National Natural Science Foundation of China(70771080)the Special Fund for Basic Scientific Research of Central Colleges+2 种基金China University of Geosciences(Wuhan) (CUG090113)the Research Foundation for Outstanding Young TeachersChina University of Geosciences(Wuhan)(CUGQNW0801)
文摘A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.
文摘In this paper, we study a new approach for solving linear fractional programming problem (LFP) by converting it into a single Linear Programming (LP) Problem, which can be solved by using any type of linear fractional programming technique. In the objective function of an LFP, if βis negative, the available methods are failed to solve, while our proposed method is capable of solving such problems. In the present paper, we propose a new method and develop FORTRAN programs to solve the problem. The optimal LFP solution procedure is illustrated with numerical examples and also by a computer program. We also compare our method with other available methods for solving LFP problems. Our proposed method of linear fractional programming (LFP) problem is very simple and easy to understand and apply.
文摘This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.
