Nowadays our society pays more and more attention to the performance measurement and the evaluation activities of the organizations, such as hospitals, institutions, agencies, companies and so on, because the performance measurement can efficiently support the public and private decisions, the performance measurement has a spectrum of customary analyses. There are many varieties of methods and techniques for the performance measurement, such as Multi- Criteria Decision Analyse (MCDA), Balanced scorecard and so on. However, once multiple inputs and outputs need to be taken into account, problems and limitations from traditional methods in measuring productivity or efficiency may arise. Organizations urgent call for a more holistic evaluation solution to avoid flawed assessment.
DEA (Data Envelopment Analysis) has been widely used in assessing performance of many different kinds of companies or organizations engaged in different countries, in different contexts and different activities.  It is a nonparametric method and mathematical programming technique used in economics and operations research for the estimation of production frontiers.  It has also been demonstrated practically in some organizational units - hospitals, banks, business companies, even in universities. Nevertheless, DEA is named to be the most effective method in performance measurement, when the organization uses different inputs to generate multiple outputs. 
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The intent of this seminar thesis is to explore a full perspective and framework of organizational performance evaluation. Together with the theoretical foundations and historical development of performance methods, the basic mathematical models as well as the idea and useful software from DEA will be at the first blush introduced in Chapter 2 In Chapter 3, a deeper insights of practical applications in public sector will be given. After that strengths and limitations from DEA method will be discussed in Chapter 4. The last chapter will then be the conclusion.
Introduction of performance measurement
In recent years has the so-called performance measurement experienced a growing importance in research and practice of the business management. However, it is not in the literature clearly clarified what it means really to just under performance measurement, the present chapter is a conceptual Praezisierung and content specific.  However it is clear is that, the performance will be basically as more or less affectivity and efficiency understood. 
The performance measurement and ist assessment is not harmonized between Anglo-Saxon and Germany. For this reason, the following table collected some different concept clarification and its development instead of a conceptual framework that will contain the essential characteristics of the concept. The performance and the company used for their assessment performance measurement is not the Anglo-Saxon or German speaking harmonized. For this reason, authors make do without even completely a conceptual clarification and development instead a conceptual framework (Framework) that will contain the essential characteristics of the performance concept. 
Table 1 provides some selected interpretations of the concept of performance measurement and conveys an impression of the range of different performance-understandings in the literature.
Table 1: Selected Interpretations of Performance Measurement 
As Table 1 showed, the aspects and opinion of the performance are different. From the above different performance objects and the concept, the most approaches are the quantification of "effectiveness" and / or "efficiency", which contains monetary and non-monetary objective. As discussed earlier Leong, et al.  have suggested that the manufacturing task, the important dimensions of performance can be defined in terms of quality, time, price, and flexibility. Other authors take a different stance. Following their study of performance measurement in the service sector, Fitzgerald et al.  suggest that there are two basic types of performance measure (financial performance, competitiveness) in any organization - those that relate to results, which focus on the determinants of the results (innovation, flexibility, quality, and resource utilization). This suggests that it should be possible to build a performance measurement framework around the concepts of results and determinants. In theory and practice, there are a variety of performance measurement systems. The best known are: Balanced Scorecard, EFQM-Modell, Tableau de Bord, Data Envelopment Analysis, Skandia Navigator, Performance Pyramid, Performance Prism, Quantum Performance Measurement System, value-based management, Operative Index performance measurement, Performance Risikomanagement. 
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This section deals with the derivation of rudimentary requirements, which should meet a method for meaningful use in the performance measurement. Some of the requirement is already mentioned explicitly or implicitly in above; in addition, the requirements groups, individual requirements and pragmatic requirements are systematic cataloged in the Table 2. Principle, it can be categorized as the number of potential requirements based on the following issues: (a) Can this method in principle solves the problem? (b) To what extent by using the related method can the performance measurement work complete? (c) The method is feasible, i.e. there is an appropriate balance between their use-"expenses" and the resulting knowledge-"income"? 
Problem-related requirements are derived from the characteristics by the character from the task of measuring performance. They differ from the other requirements, which they must necessarily be met, at the same time allowing the performance measurement-related and pragmatic requirement a greater design freedom. The first main requirement is the comparison a set of alternative courses of action.
Since by a number of possible alternatives is to be achieved (eg, increased customer satisfaction and a low energy consumption), the methods have the ability to review the case of multiple targets. Regarding the fairness in measurement a priori weight of the objectives are not asked for. 
The table 2 shows the requirements category, groups and individual requirements of performance measurement Methods.
Table 2: Requirements for Performance Measurement Methods 
The performance is as (relative) effectiveness and efficiency comparable units understand in this paper, so it leads to the question: with which method can the effectiveness and efficiency are evaluated.  So, to determine the degree of the effectiveness and efficiency of the target are very necessary. For this reason, one of the performance measurement method- Data envelopment Analysis (DEA) will be introduced in the next chapter, the strengths and weakness of the method will be showed in chapter 4. 
Theoretical foundations of DEA
Data Envelopment Analysis (DEA) is a mathematic and nonparametric method, it is data oriented, and used for assessment of a set of entities, which is a relatively new "data oriented" approach, which is used for measuring the performance of Decision Making Units (DMUs) , they are called a set of peer entities, which convert multiple inputs into multiple outputs. 
The basic theoretical foundations of the DEA will be firstly introduced in the following section. The history and development of DEA as well as relevant context are discussed in 2.1. Then in the following parts the more detailed explanation about DEA-Method will be introduced.
History and development
The combinations of the Input and output of a firm are normally calculated with a production function (Output/Input) in microeconomic production theory. The Production technology frontier can be constructed, because using such a function the max. output can be showed, which can be obtained with any possible combination of inputs.  ( Seiford & Thrall 1990). DEA are 30 years ago used to solve the filmproblem,which was never solved all the possible input-output combinations with the principle in empirical applications. 
The linear programming are in 1978 by Charnes, Cooper & Rhodes (1978) with the work "Measuring the efficiency of decision making units" applied to estimate an empirical production technology frontier. However, in Germany this method was earlier used to estimate the marginal productivity and other factors of production ( Brockhoff 1970). A lot of books and journal articles since then have been written on DEA and the application of DEA. DEA has not only been used in comparing efficiency across organizations, but also used to compare the efficiency across firms.  The DEA-Model was formalized by Banker, Charnes and Cooper (BCC) (1984), and was extended by Färe, Grosskopf and Lovell (1985) with including the decomposition of overall efficiency into measures of technical and scale efficiency. The DEA-Method is deterministic and nonparametric. Thus, since the seminal work by Farrel (1957) on "measuring the efficiency of decision making units"', there are several types models of the DEA have emerged, which are mostly based on the CCR-Modell, at the same time a further development on the DEA is the BCC model, which point at the varying returns to scale-either constant returns to scale (CRS) or variable returns to scale (VRS). A good description of DEA can be found in Seiford and Thrall (1990) and Seiford (1996), the main development of DEA are also in this time. 
The basic models
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This part deals with one of the most basic and important DEA-Models, the CCR model (Charnes, Cooper and Rhodes in 1978.). In DEA, the organization under study is called a DMU (Decision Making Unit). DMU are used to evaluate in terms of the abilities to convert inputs into outputs, furthermore, to allow to use to a wide variety of activities.  The definition of DMU is rather loose and flexible to use. Generically a DMU is the entity, which is responsible for converting inputs into outputs and whose performances are to be evaluated, which such as supermarkets, department stores and banks, and extend to car makers, hospitals, schools, public libraries and so on. To make sure a relative comparison a set of DMUs is used to evaluate each other with each DMU having a certain degree of managerial freedom in decision making.  For each DMU, the virtual input and output will be formed by weights () and ():
Then using linear programming to determine the weight and so as to maximize the ratio:
Because the optimal weights of different DMUs may also different from each other. Thus, a best set of weights will be set to each DMU, instead of being fixed they are in advance derived from the data 
Suppose there are n DMUs: , , â€¦, . and Some common input and output items for each of these j= 1, â€¦, n DMUs are selected. Suppose m input items and s output items are selected. Let the input and output data for be () and (), respectively. The input data matrix X and the output data matrix Y can be arranged as follows,
The output data matrix Y
where X is an (m Ã- n )matrix and Y an (s Ã- n )matrix. 
The efficiency of each DMUs will be measured with the given data, once and hence need n optimizations, one for each to be evaluated. Let the to be evaluated on any trial to designated as (o ranges over 1, 2, â€¦ n.) We solve the following fractional programming problem to obtain values for the input "weights" () (i = 1, â€¦, m) and the output "weights" () (r = 1, â€¦, s) as variables.
The constraint means that the ratio of "virtual output" vs. "virtual input" for each DMU should not exceed 1. 
Now the above fractional program will be replaced by the following linear program:
Table 3 : the CCR model in input- and output-oriented versions 
With the 2 important theorems:
"Theorem 1 The fractional program (FP) is equivalent to linear program (LP)" 
"Theorem 2 (Units Invariance Theorem) The optimal values of max in are independent of the units in which the inputs and outputs are measured provided these units are the same for every DMU." 
shows that the efficiency of DMUs can be solved by the simplex method of linear programming, which will be more easily to calculated.  " is CCR-efficient if and there exists at least one optimal (), with and . Otherwise, CCR is not efficient." 
The input-oriented CCR-Modell is only one of the important DEA-Modell, behind the definition of DEA there are a model family.  In the literature the many different DEA-Modells will be often called "Basic DEA-Models".  Because there is no uniform definition of it, below the view of Allen, is the following DEA-based models mainly with four characteristics: firstly, they represent milestones in the development of the DEA; Secondly, they are applied in the empirical studies;
Thirdly, they can be relatively easy to calculate; and last but not least, they are not some specific ways of DEA, but only different in the technique adopted and used by the efficiency measurement. . 
These features limit the number of possible variants of DEA.  Table 5 contains a classification of popular DEA models based on the criteria "efficiency measure" and "technology".  The base models of the DEA are summarized bellowing.
Tabelle 4: classifikation common DEA-based models 
Table 5: Interpretations of selected software from DEA 
As table 3, there is much different software in the aim to calculate the DEA, and they are very helpful to evaluate the DMU efficiency.
Application steps of DEA
The evaluation process of the applications of DEA-methods can be summarized as the following steps.
Fig. 1 Application steps for DEA 
The above figure shows the application steps for DEA-Method. For instance, the measurement purpose is to compare a set of banks, and firstly the banks have multiple-input and multiple-output characteristics, so the DEA-method can be used in this evaluation. And then the evaluation process can be summarized as: chose the right DMUs, and establish the input- and output system, next step make a DEA-Model and do the evaluation and analysis, when the result is all right, then comes the conclusions-the efficiency of the banks; when not, go back and do some adjusting in the input- and output system then analyze again.
Strengths of DEA
Compared to most forms of such as stochastic frontier analysis (SFA), the DEA has many advantages, but its main attraction, is that it does not matter if the producers are different because no functional forms are imposed. 
DEA can at the same time handle multiple inputs and multiple outputs. DEA doesn't require relating inputs to outputs, because as quantitative and qualitative criteria can be processed. What's more, the comparisons are directly against peers and Inputs and outputs can have very different units. Acceptance of the DEA results in practice is high. No DMU with another different weighting can be better calculated by DEA. Efficiency comparison is multidimensional. 
Limitation of DEA
According to the characteristics of DEA-Method, then we shed light on some of their relative weaknesses.
DEA uses info on input and output quantities, and as such it DEA does not measure "absolute" efficiency, can only address the issue of technical efficiency.  DEA is nonparametric but deterministic.  The compared DMUs are virtual. At the same time, with this method there is only suggestive function but no analysis of causes. Statistical tests are not applicable and large problems can be computationally intensive. And what's more, the mathematic is very complex in DEA, not easily to use; Measurement error can cause significant problems. The measurement result is strongly dependent of the selection of the DMUs and the input and output sizes. Last but not least there is also no quality identification. 
For the good and wide application in performance measurement, Data Envelopment Analysis (DEA) has been acknowledged as a useful a practical decision support instrument and analytical research tool. Compared to most forms of performance measurement instruments, the DEA has many advantages. And there is much practical software to help calculate the math problem. A complete specification for the functional form of the production frontier nor the distribution of inefficient deviations from the frontier is not required, but only the distribution assumptions and general production. However, inefficiency levels may be in small samples systematically underestimated, if these assumptions are too weak. In addition, a bias over the frontier may cause erroneous assumptions. Therefore, the ability to transform, test and select the production assumptions is essential in conducting DEA-based research.  However, there is none of the performance measurement methods dominates on all dimensions; the conclusion is that, the choice of appropriate measurement method should be suited to the question addressed in each given particular study.