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Data Envelopment Analysis
Data Envelopment Analysis (DEA) is an increasingly popular management tool. This write-up is an introduction to Data Envelopment Analysis (DEA) for people unfamiliar with the technique.
For a more in-depth discussion of DEA, the interested reader is referred to Seiford and Thrall [1990]or the seminal work by Charnes, Cooper, and 代写留学生论文Rhodes [1978].DEA is commonly used to evaluate the eciency of a number of producers. A typical statisticalapproach is characterized as a central tendency approach and it evaluates producers relative to an
average producer In contrast, DEA compares each producer with only the "best" producers. Bythe way, in the DEA literature, a producer is usually referred to as a decision making unit or DMU.
DEA is not always the right tool for a problem but is appropriate in certain cases. (See Strengthsand Limitations of DEA.)
In DEA, there are a number of producers. The production process for each producer is to takea set of inputs and produce a set of outputs. Each producer has a varying level of inputs and givesa varying level of outputs. For instance, consider a set of banks. Each bank has a certain numberof tellers, a certain square footage of space, and a certain number of managers (the inputs). Thereare a number of measures of the output of a bank, including number of checks cashed, number of
loan applications processed, and so on (the outputs). DEA attempts to determine which of thebanks are most ecient, and to point out speci c ineciencies of the other banks.A fundamental assumption behind this method is that if a given producer, A, is capable ofproducing Y(A) units of output with X(A) inputs, then other producers should also be able to
do the same if they were to operate eciently. Similarly, if producer B is capable of producingY(B) units of output with X(B) inputs, then other producers should also be capable of the sameproduction schedule. Producers A, B, and others can then be combined to form a composite
producer with composite inputs and composite outputs. Since this composite producer does notnecessarily exist, it is typically called a virtual producer.The heart of the analysis lies in nding the "best" virtual producer for each real producer. Ifthe virtual producer is better than the original producer by either making more output with the
same input or making the same output with less input then the original producer is inecient. Thesubtleties of DEA are introduced in the various ways that producers A and B can be scaled up or
down and combined.
12.1 Numerical Example
To illustrate how DEA works, let's take an example of three banks. Each bank has exactly 10tellers (the only input), and we measure a bank based on two outputs: Checks cashed and Loan
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applications. The data for these banks is as follows:
Bank A: 10 tellers, 1000 checks, 20 loan applications
Bank B: 10 tellers, 400 checks, 50 loan applications
Bank C: 10 tellers, 200 checks, 150 loan applications
Now, the key to DEA is to determine whether we can create a virtual bank that is better than
one or more of the real banks. Any such dominated bank will be an inecient bank.Consider trying to create a virtual bank that is better than Bank A. Such a bank would use nomore inputs than A (10 tellers), and produce at least as much output (1000 checks and 20 loans).
Clearly, no combination of banks B and C can p