The theory of probabilistic programming  may be conceived in several different ways. As a method of programming it analyses the implications of probabilistic variations in the parameter space of linear or nonlinear programming model. The generating mechanism of such probabilistic variations in the economic models may be due to incomplete information about changes in demand, pro­duction and technology, specification errors about the econometric relations presumed for different economic agents, uncertainty of various sorts and the consequences of imperfect aggregation or disaggregating of economic variables. In this Research we discuss the probabilistic programming problem when the coefficient b_i is random variable

The parametric programming considered as type of sensitivity analysis. In this research concerning to study the effect of the variations on linear programming model (objective function coefficients and right hand side) on the optimal solution. To determine the parameter (θ) value (-5≤ θ ≤5).Whereas the result، the objective function equal  zero and the decision variables are non basic، when the parameter (θ = -5).The objective function value increases when the parameter (θ= 5) and the decision variables are basic، with the except of X_24, X₃₄.Whenever the parameter value increase, the objectiv

            In this paper the definition of fuzzy anti-normed linear spaces and its basic properties are used to prove some properties of a finite dimensional fuzzy anti-normed linear space.    

The problem of Bi-level programming is to reduce or maximize the function of the target by having another target function within the constraints. This problem has received a great deal of attention in the programming community due to the proliferation of applications and the use of evolutionary algorithms in addressing this kind of problem. Two non-linear bi-level programming methods are used in this paper. The goal is to achieve the optimal solution through the simulation method using the Monte Carlo method using different small and large sample sizes. The research reached the Branch Bound algorithm was preferred in solving the problem of non-linear two-level programming this is because the results were better.

يرغب المرء أن يعيش في منزل يعبر عن اصالة تصميمه ذا اهداف جمالية كحاجته الى تحقيق الأهداف العملية. وعليه فمن الأهمية بمكان ان يشارك أصحابه مع المعنيين[1] بشؤون التصميم... وهنا ارتأت الباحثة ان تقوم بدراسة علمية حديثة حول ورق الجدران ثلاثي الابعاد وتوظيفة في غرفة المعيشة, وباسلوب عصري حديث يجمع بين جمالية التصميم والحداثة , إضافة الى تناول الإضاءة لما لها من دور في ابراز معالم وتفاصيل الأثاث

In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler an

The aim of this research is to compare traditional and modern methods to obtain the optimal solution using dynamic programming and intelligent algorithms to solve the problems of project management.

It shows the possible ways in which these problems can be addressed, drawing on a schedule of interrelated and sequential activities And clarifies the relationships between the activities to determine the beginning and end of each activity and determine the duration and cost of the total project and estimate the times used by each activity and determine the objectives sought by the project through planning, implementation and monitoring to maintain the budget assessed 

        In this paper, double Sumudu and double Elzaki transforms methods are used to compute the numerical solutions for some types of fractional order partial differential equations with constant coefficients and explaining the efficiently of the method by illustrating some numerical examples that are computed by using  Mathcad 15.and graphic in Matlab R2015a.

This paper presents a linear fractional programming problem (LFPP) with rough interval coefficients (RICs) in the objective function. It shows that the LFPP with RICs in the objective function can be converted into a linear programming problem (LPP) with RICs by using the variable transformations. To solve this problem, we will make two LPP with interval coefficients (ICs). Next, those four LPPs can be constructed under these assumptions; the LPPs can be solved by the classical simplex method and used with MS Excel Solver. There is also argumentation about solving this type of linear fractional optimization programming problem. The derived theory can be applied to several numerical examples with its details, but we show only two examples

Original Research Paper Mathematics 1-Introduction : In the light of the progress and rapid development of the applications of research in applications fields, the need to rely on scientific tools and cleaner for data processing has become a prominent role in the resolution of decisions in industrial and service institutions according to the real need of these methods to make them scientific methods to solve the problem Making decisions for the purpose of making the departments succeed in performing their planning and executive tasks. Therefore, we found it necessary to know the transport model in general and to use statistical methods to reach the optimal solution with the lowest possible costs in particular. And you know The Transportatio