Data-Envelopment-Analysis

Dateneinhüllanalyse (DEA ) and data envelopment analysis are terms of a technique for efficiency analysis in the field of operations research, which has found widespread use in economics. It is used for comparative measurement of the efficiency of organizational units, or decision units.

General description of the DEA

The DEA is attributed to Charnes, Cooper and Rhodes, although there are earlier applications ( Brockhoff 1970). It provides a technique for measuring the relative efficiency of so-called decision-making units ( Decision Making Units ( DMUs ) ) represents a decision unit can be any object that by inputs ( eg costs, labor hours) and outputs (eg, sales, quality level ) are characterized can. Decision units can, for example, Be universities, hospitals, bank branches, branches of a trading group or works of an automobile manufacturer.

All decision-making units of a group of decision units have the same inputs and outputs. Thus, the application of DEA provides a meaningful result, only decision units should be considered in an application are similar. There should be no hospitals with universities are compared. With the help of the DEA, the relative efficiency of decision-making units is measured as the decision units are used within the group as a benchmark.

The DEA makes it possible to take into consideration multiple inputs and outputs to the user. These factors are often not comparable with one another (e.g., as measured in the turnover value and the quality level ). Therefore, the inputs and the outputs are multiplied by importance weights. A special feature of the DEA efficiency compared to other analysis techniques is that the importance weights of inputs and outputs are determined within the model. The user does not specify this.

To assess the efficiency of decision units an efficiency value is calculated for each decision unit. This efficiency or inefficiency value measures based on the observed inputs and outputs of a DMU the distance to the efficient frontier (Data Envelope). This efficient edge is formed from the group of the decision units, which is considered in the respective DEA application. From the efficiency value of a decision unit can be directly responsible for the management of improvement derived.

Mathematical classification

In the application of DEA to a group of decision units, an optimization problem must be solved for each decision unit. In its basic form, a DEA model is a problem of the quotient programming. Because of the efficiency value of a decision unit is a quotient, in which the numerator is the sum of the weighted outputs and in the denominator the sum of the weighted inputs is.

: Efficiency values: outputs: inputs: Output Weights: Input weights

The solution of a problem of the quotient programming is not easy since the objective function is not linear. Therefore, the problem is transformed into a problem of the linear programming using the so-called Charnes Cooper transformation.

Each DEA model can be represented in the envelopment form and in the multiplier form. A model in envelopment form can be converted and vice versa by means of a primal- dual transformation in the multiplier form.

Historical development

Charnes, Cooper and Rhodes in 1978, the basic DEA model developed. It was later referred to by the initials of its developers as CCR model. This model assumes constant returns to scale. Banker, Charnes and Cooper presented in 1984 before the variable returns to scale accepting BCC model.

A further development is the window analysis. With this, the efficiency of a decision unit is compared in different periods with each other. Thus statements about the efficiency of development of decision units can be made. In addition, DEA models are developed, which expect fuzzy numbers by fuzzy logic will make use of approaches.

Alternative techniques for efficiency analysis

  • Efficiency Analysis Technique With Output satisficing ( EATWOS )
  • Free Disposable Hull ( FDH )
  • Cross -effectiveness analysis ( CEA )
  • Operational Competitiveness rating ( OCRA )
  • Stochastic Frontier Analysis (SFA )
  • TOPSIS ( Technique for Order Preference by Similarity to Ideal Solution)
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