Said Tantawy

In this paper a feasible direction method is presented to find all efficient extreme points for a special class of multiple objective linear fractional programming problems, when all denominators are equal. This method is based on the conjugate gradient projection method, so that we start with a feasible point and then a sequence of feasible direct...

In this paper a feasible direction method is presented to find all efficient extreme points for a special class of multiple objective linear fractional programming problems, when all denominators are equal. This method is based on the conjugate gradient projection method, so that we start with a feasible point and then a sequence of feasible direct...

This paper presents a new procedure for solving the integer linear programming problem when the objective function is a linear function and the set of constraints is in the form of linear inequality constraints. The proposed procedure is based on the conjugate gradient projection method together with the use of the spirit of Gomory cut. The main id...

This paper investigates the advantages of using a simple linear programming problem with one unknown to show that whether the given multiple objectives linear programming (MOLP) problems is solvable or not. This kind of investigation is based mainly on both of feasibility and efficiency characterization of the (MOLP) problem. Our goal of this inves...

Under the linear mapping efficient extreme points in decision space of multiple objectives linear programming (MOLP) may not map to non dominated extreme points in objective space, condition that two or even more multiple objective linear programming (MOLP) problems to have the same objective space is given, the important of this study is that the...

We give the construction of the objective space of multiple objectives linear fractional programming with equal denominators under the linear fractional mapping. In this case the decision space maps to an objective space of less dimension which happens in most of real problems when the number of objectives is small compared to the number of the dec...

An iterative method based on conjugate gradient projection method (and not on any variant of Karmarkars algorithm) for solving linear programming problems is given. Our method consists of a sequence of moves: Starting with an initial interior point x0 our procedure finds a second feasible point x1 then a third point and so on until the optimal poin...

In this paper an iterative method for solving linear fraction programming (LFP) problem is proposed, it will be shown that this method can be used for sensitivity analysis when a scalar parameter is introduced in the objective function coefficients and our task of this sensitivity investigation is to maintain the optimality of the problem under con...

An iterative method based on the conjugate gradient projection method for solving linear fractional programming problems is given. Our proposed method consists of a sequence of moves; starting with an initial interior point x0x0 our method finds a second feasible point x1x1, then a third feasible point x2x2, and so on, until the optimal point is re...

In this study, an iterative method is suggested for solving the problem in which the objective function is a sum of linear and linear fractional functions, where the constraint functions are in the form of inequalities. The proposed method is based mainly upon the conjugate gradient projection method which is applicable to solve nonlinear programmi...

Efficient extreme points in decision space of multiple objective linear programming (MOLP) may not map to non dominated extreme points in objective space under the linear mapping, condition that efficient extreme points have a non dominated extreme is given, the important of this study is that the decision-Maker may depends on extreme points of the...

We presented a feasible direction method to find all optimal extreme points for the linear programming problem. Our method depends on the conjugate gradient projection method starting with an initial point we generate a sequence of feasible directions towards all alternative extremes.

In this paper a new method is suggested for solving the problem in which the objective function is a linear fractional function, and where the constraint functions are in the form of linear inequalities. The proposed method is based mainly upon solving this problem algebraically using the concept of duality. Since the earlier methods based on the v...

Anew method to find all alternative ext reme o ptimal points for l inear programming problems is given in t his paper, this feasible direction m ethod depends on t he co njugate gradient projection m ethod, starting wi th an initial feasible po int we generate a sequence of feasible d irections towards all alternative extremes. Asimple example is g...

Choosing the best r individuals from m independent groups by the regular way, doesn’t consider the competition “between” these groups, but it only considers the competition “within” the groups. In this study we discuss the selection by considering the competition with both between and within the groups, by using a Linear Programming (LP) approach a...

Most of the current methods for solving multiple objective linear programs (MOLP) depend on the simplex tableau in multi objective form to find the set of efficient solutions of this problem. In this paper we present a feasible direction method to find all efficient extreme points for (MOLP). Our method based on the conjugate gradient projection me...