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The purpose of this research is to estimate the reliability of the mixture of two exponential distributions for two subpopulations we use the Bayesian estimate method for the failure times in two kinds of population, one of them each unit of sample is belong to some population while in the second population there in formation is not available, when the unit belong for the first population we estimate reliability by Bayes method , while for the second population we apply maximum likelihood method to estimate reliability .The experimental comparison was done by simulation procedure. Several experiments using the important statistical measure which is the mean square error (MSE). The method of direct search method, are used for finding MLE. Then these two important methods are used to estimate the reliability function for mixed exponential model. All the results of simulation are explained by tables

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The evaluation process of transportation problem required finding basic feasible solution (bfs). Represent the base of decision making process. To purpose start anther batter solution to able from decisions taking process, consider the decision making process, find (bfs) represent the standard form in linear programming (LP). Most important stage of update (bsf) stages that achieved minimum cost (the optimal solution). the goal of paper to improving & evaluation (bfs) by new procedure (proposed method) comparison with Vogel method.2- المقدمة

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The statistical distributions study aimed to obtain on best descriptions of variable sets phenomena, which each of them got one behavior of that distributions . The estimation operations study for that distributions considered of important things which could n't canceled in variable behavior study, as result this research came as trial for reaching to best method for information distribution estimation which is generalized linear failure rate distribution, throughout studying the theoretical sides by depending on statistical posteriori methods like greatest ability, minimum squares method and Mixing method (suggested method). The research has contained such a comparing between sixth estimations methods for generalized linear information of failure rates distribution (GLFRD), by depending on two important statistical measurements which are: error squares medial (MSE), absolute relative error medial (MAPE), for obtaining on the best estimation method .

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The researcher studied transportation problem because it's great importance in the country's economy. This paper which ware studied several ways to find a solution closely to the optimization, has applied these methods to the practical reality by taking one oil derivatives which is benzene product, where the first purpose of this study is, how we can reduce the total costs of transportation for product of petrol from warehouses in the province of Baghdad, to some stations in the Karsh district and Rusafa in the same province. Secondly, how can we address the Domandes of each station by required quantity which is depending on absorptive capacity of the warehouses (quantities supply), And through results reached by the researcher find the best method came after linear programming was the exponential method because it gave a solution closely to the optimization as were the result linear programming (4,357,575), either the of result exponential method was (4,365,061) followed by method Ones Method amounting the total cost (4,371,841 ) and after the result approach (A.S.M) was the total cost (4,372,585) and there were other methods reported in the research gave a high cost compared with the methods mentioned above .

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The object of this study is to establish a global model to use of DeNovo programming the strategies of multi-Decision making process in the city of Baghdad.Thus, we have chosen an important and an effective subject in the life of the citizen due to the importance of this subject in the Iraqi citizen of luck of water and for many reasons.In this thesis, we have tackled the establishment of a global model to be able to reach solution or an alternative model a money the available alternative. The alternative proposed here utilizes the application of the (DeNovo) programming approach suggested by (1982) in solving the capacity allocation problem. Unlike the usual optimization using mathematical models where level of resource, the right hand side of the assumed to be fixed or known, the (DeNovo) approach considers the level of resources as being decision variables that affect the value of the objective function.

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The exploitation of all available resources and benefiting from them is one of the most important problems facing the decision makers at the present time. In order to exploit these resources, it is necessary to organize the conflicting objectives, which is the main work in the project management, which enables the development of a plan that decision makers can use to shorten the total completion time and reduce the total cost of the project. Through the use of modern scientific techniques, and therefore the researcher using the critical path method using the technology of programming goals to find more efficient ways to make appropriate decisions where the researcher worked to solve the problems in the construction of the Department of sewage streams The results were within the level of ambition for the decision maker where the conflict between the objectives was resolved from reducing the total cost to the total time and the cost of evasion through Use linear programming objectives and the results were within the level of ambition of the decision-maker.

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In general Gradation transportation problem within operation research problems, the transportation model considered from sub-application important to linear programming. There is a great important for the transportation and effective role as an important pillar of the economic development of countries. to solve the problem of the transportation initial basic fesiable solution (I.B.F.S) is needed, and then to continue in the developing solution until reaching the better solution (less cost). there is no ending in theorems of finding best solutions until geating the optimal solution in order to take the convenient decision. the aim of this paper is to suggest a new method from by the researcher to find initial basic fesiable solution and then compare it with vogel's approaximation method and a nother methods to show the importance and the accuracy of the proposed method. through the findings of the researcher it turned out to be innovative method to give high-efficient results based on the total cost least and they approaching to the optimal solution.ء

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