On Tropical Fractional Linear Programming

Abstract Very recently, tropical counterparts of fractional linear programs have been studied. Some algorithms were proposed for solving them, with techniques ranging from bisection methods to homeomorphisms to formal power series. In this paper, some algorithms are also proposed. They mainly rely in the ability of finding the greatest and smallest solutions of tropical equations, a subject that was discussed in a previous work of the author

Formulation and Solving Fractional linear programming Models Using Development of Lagrange s’ Method

In this paper Lagrange’s method was used to solve Fractional linear programming problems and then developing this method by using mathematical forms by which it can be possible to find the solution without using complex derivations. Thus we can avoid a lot of derivations and summarize the number of probabilities of eradicating some of the changeable items which had rapidly got to the optimal solution . The research also includes programs written with Visual Basic language (Microsoft Visual Basic 6.0), represented the Lagrange’s method and development Lagrange’s method to get a good forms and solution of Fractional linear programming problems to help decision maker to find optimal solution of this problems by development manner with advanced language and important present programming languages.

Formulation and Solving Fractional linear programming Models Using Development of Lagrange s’ Method

In this paper Lagrange’s method was used to solve Fractional linear programming problems and then developing this method by using mathematical forms by which it can be possible to find the solution without using complex derivations. Thus we can avoid a lot of derivations and summarize the number of probabilities of eradicating some of the changeable items which had rapidly got to the optimal solution . The research also includes programs written with Visual Basic language (Microsoft Visual Basic 6.0), represented the Lagrange’s method and development Lagrange’s method to get a good forms and solution of Fractional linear programming problems to help decision maker to find optimal solution of this problems by development manner with advanced language and important present programming languages.

The method of Weighted Multi objective Fractional Linear Programming Problem (MOFLPP)

More theories and algorithms in non-linear programming with titles convexity (Convex). When the objective function is fractional function, will not have to have any swelling, but can get other good properties have a role in the development of algorithms decision problem.In this work we focus on the weights method- (one of the classical methods to solve Multi objective convex case problem). Since we have no convex or no concave objective functions, and this condition is essential part on this method implementation, we these valid conditions under method as generator sets efficient and weakly efficient this problem. This raises the need to a detailed study of pseudoconvex idea, cause convex idea, Invex, pseudoinvex idea,…, etc. concepts. Offer a numerical example to show the valid by the conditions previously set generate all weakly efficient set our problem

FINANCIAL STRUCTURE OPTIMIZATION BY USING A GOAL PROGRAMMING APPROACH

This paper proposes a new methodology for solving the multiple objective fractional linear programming problems using Taylor’s formula and goal programming techniques. The proposed methodology is tested on the example of company\u27s financial structure optimization. The obtained results indicate the possibility of efficient application of the proposed methodology for company\u27s financial structure optimization as well as for solving other multi-criteria fractional programming problems

A goal programming procedure for solving fuzzy multiobjective fractional linear programming problems

This paper presents a modification of Pal, Moitra and Maulik\u27s goal programming procedure for fuzzy multiobjective linear fractional programming problem solving. The proposed modification of the method allows simpler solving of economic multiple objective fractional linear programming (MOFLP) problems, enabling the obtained solutions to express the preferences of the decision maker defined by the objective function weights. The proposed method is tested on the production planning example

Solving Fractional Geometric Programming Problems via Relaxation approach

In the optimization literature , Geometric Programming problems play a very important role rather than primary in engineering designs. The geometric programming problem is a nonconvex optimization problem that has received the attention of many researchers in the recent decades. Our main focus in this issue is to solve a Fractional Geometric Programming(FGP) problem via linearization technique[1]. Linearizing separately both the numerator and denominator of the fractional geometric programming problem in the objective function, causes the problem to be reduced to a Fractional Linear Programming problem (FLPP) and then the transformed linearized FGP is solved by Charnes and Cooper method which in fact gives a lower bound solution to the problem. To illustrate the accuracy of the final solution in this approach, we will compar our result with the LINGO software solution of the initial FGP problem and we shall see a close solution to the globally optimum. A numerical example is given in the end to illustrate the methodology and efficiency of the proposed approach