Data envelope analysis (DEA) is a nonparametric method in operations and economic research for estimating production limits. This is used to empirically measure the productive efficiency of a decision-making unit (or DMU). Although DEA ​​has a strong relationship with production theory in economics, it is also used for benchmarking in operations management, where a series of measures are selected to measure the performance of manufacturing and service operations. In a benchmark state, an efficient DMU, ​​as defined by the DEA, may not necessarily constitute a "production limit", but rather lead to "best practice boundaries" (Cook, Tone and Zhu, 2014). DEA is referred to as a "balanced comparison" by Sherman and Zhu (2013). The non-parametric approach has the benefit of not assuming a particular functional form for the border, but they do not provide a general relationship (equation) that links output and input. There is also a parametric approach used for estimating production limits (see Lovell & Schmidt 1988 for the initial survey). This requires that the form of a border be predictable by specifying a particular function that links the output to the input. One can also combine the relative strengths of each of these approaches in the hybrid method (Tofallis, 2001) where the border unit was first identified by the DEA and then a smooth surface was installed for this. This allows best practice relationships between multiple outputs and some inputs to estimate.
"This framework has been adapted from a multi-input, multi-output production function and is applied in many industries DEA develops a function that is shaped by the most efficient producers This method is different from Ordinary Least Square (OLS) statistical techniques that comparison relative to Average producers Like Frontier Stochastic Analysis (SFA), DEA identifies a "boundary" characterized as an extreme point method that assumes that if a firm can produce a certain level of output using a given level of input, another firm of the same scale must be able to do so The most efficient producer can form a 'joint manufacturer', enabling efficient calculation of solutions for each level of input or output.Where no actual matching firm, 'virtual producers' are identified to make comparisons "(Berg 2010).
Attempts to synthesize DEA and SFA, correcting the deficiencies, are also made in the literature, through the filing of various non-parametric SFA and Stochastic DEA versions.
Video Data envelopment analysis
Histori
In microeconomic production theory the combination of company input and output is described using the production function. Using such a function one can show the maximum output that can be achieved with a combination of possible inputs, that is, one can build a production technology frontier (Sieford & Thrall 1990). About 30 years ago DEA (and frontier engineering in general) was set to answer the question of how to use this principle in empirical applications while addressing the problem that for actual companies (or other DMUs) one can never observe all possible input-output combinations.
Building Farrell's ideas (1957), the seminal work "Measuring the efficiency of decision-making units" by Charnes, Cooper & amp; Rhodes (1978) used linear programming to estimate the frontier of empirical production technology for the first time. In Germany, this procedure was used earlier to estimate the marginal productivity of R & D and other production factors (Brockhoff 1970). Since then, there have been a large number of journal books and articles written in DEA or applying DEA in various sets of problems. In addition to comparing efficiency across DMUs within an organization, DEA has also been used to compare efficiency across companies. There are several types of DEA with the most basic CCR based on Charnes, Cooper & amp; Rhodes, but there is also a DEA that discusses various return scales, either CRS (constant yield scale, VRS (variable), unaltered yield scale or non-decreasing yield scale by Ylvinger (2000).DEC major developments in the 1970s and The 1980s are documented by Seiford & Thrall (1990).
Maps Data envelopment analysis
Technique
Data envelope analysis (DEA) is a linear programming methodology to measure the efficiency of some decision-making units (DMUs) when the production process presents the structure of various inputs and outputs.
"DEAs have been used for production and cost data.Using the selected variables, such as unit cost and output, DEA software looks for points with the lowest unit cost for the given output, connects those points to form efficiency limits. borders are considered inefficient, numerical coefficients are given to each firm, defining their relative efficiency, different variables that can be used to set efficiency limits are: number of employees, service quality, environmental safety, and fuel consumption An initial survey of studies on power distribution companies identifies over thirty DEA analyzes - demonstrating the widespread adoption of this technique in the networking industry (Jamasb, TJ, Pollitt, MG 2001). A number of studies using this technique have been published for water utility. The main advantage of this method is its ability to accommodate a wide range of input and out put, is also useful because it considers returning to scale in calculating efficiency, enabling the concept of increasing or decreasing efficiency based on size and output level. The drawback of this technique is that model specifications and inclusion/exceptional variables can affect results. "(Berg 2010)
Under common DEA benchmarks, for example, "if one benchmarks the performance of a computer, it's natural to consider different features (screen size and resolution, memory size, process speed, hard disk size, etc.).Then one should classify these features become "input" and "output" to implement proper DEA analysis, but these features may not really represent input and output at all, in the idea of ​​production standards.In fact, if we examine the benchmarking literature, Other terms, such as "indicators", "results", and "metrics", are used.The problem is now one way of classifying these performance measures into inputs and outputs, for use in DEA. "(Cook, Tone, and Zhu, 2014)
Some of the advantages of DEA are:
- need not explicitly specify a mathematical form for the production function
- proved useful in uncovering a relationship that remains hidden for other methodologies
- able to handle many input and output
- can be used with any input-output measurement
- the source of inefficiency can be analyzed and quantified for each unit evaluated
Some of the DEA's weaknesses are:
- the results are sensitive to input and output selection (Berg 2010).
- You can not test the best specs (Berg 2010).
- the number of efficient firms across the border tends to increase with the number of input and output variables (Berg 2010).
The desire to Increase DEA, by reducing losses or strengthening its superiority has been the main cause of many discoveries in recent literature. The most frequently used DEA method currently in place to obtain a unique efficiency rating is called cross-efficiency. Originally developed by Sexton et al. in 1986, he found extensive applications since Doyle and the 1994 Green publication. Cross-efficiency is based on the original DEA results, but implies a secondary goal in which each DMU assesses the counterpart of all other DMUs with their own factor weight. The average peer ratings score is then used to calculate the DMU cross-efficiency score. This approach avoids DEA losses because it has some efficient DMUs and un-unique weights. Another approach to fix some of the weaknesses of DEA is Stochastic DEA, which makes the synthesis of DEA and SFA.
Application examples
DEA is generally applied in the electric utility sector. For example, government authorities may choose a data envelope analysis as their measurement tool to design the level of individual regulation for each company based on its comparative efficiency. The input components will include man-hours, losses, capital (lines and transformers only), and goods and services. The output variables will include the number of subscribers, the energy delivered, the length of the line, and the level of coastal exposure. (Berg 2010)
DEA is also regularly used to assess the efficiency of public and nonprofit organizations, e.g. hospitals (Kuntz, Scholtes & Vera 2007; Kuntz & Vera 2007; Vera & Kuntz 2007) or police forces (Thanassoulis 1995; Sun 2002; Aristovnik et al., 2013, 2014).
Example
In the DEA methodology, formally developed by Charnes, Cooper and Rhodes (1978), efficiency is defined as the ratio of the weighted sum of outputs to the sum of the weighted inputs, where the structure of weights is calculated by using mathematical programming and constant returns to scale (CRS) assumed. In 1984, Banker, Charnes, and Cooper developed a model with a return to scale (VRS) variable.
Assume that we have the following data:
- Unit 1 generates 100 items per day, and the input per item is 10 dollars for materials and 2 hours of work
- Unit 2 produces 80 items per day, and its inputs are 8 dollars for materials and 4 working hours
- Unit 3 produces 120 items per day, and its input is 12 dollars for materials and 1.5 hours of work
To calculate the efficiency of unit 1, we define the objective function as
- maximize the efficiency = ( u 1 Ã, Â · 100)/( v 1 Ã, Â · 10 v 2 Ã, Â · 2)
which is subject to all other unit efficiency (efficiency can not be greater than 1):
- is subject to the efficiency of unit 1: ( u 1 Ã, Â · 100)/( v 1 Ã, Â · 10 v 2 Ã, Â · 2) <= 1
- is subject to unit efficiency 2: ( u 1 Ã, Â · 80)/( v 1 Ã, Â · 8 v 2 Ã, Â · 4) <= 1
- is subject to the efficiency of unit 3: ( u 1 Ã, Â · 120)/( v 1 Ã, Â · 12 v 2 Ã, Â · 1,5) <= 1
day non-negatif: u day v = 0.
But since linear programming can not handle fractions, we need to change the formulation, so we limit the denominator of the objective function and only allow linear programming to maximize the numerator.
Jadi formulasi baru adalah: 1 Ã, Â · 100 v 1 2 Ã, Â · 2) <= 0 v 1 v 2 Ã, Â · 4) <= 0 v 1 2 Ã, Â · 1.5) <= 0
Penguuran tidak efisien
Source of the article : Wikipedia
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