DEA (Data Envelopment Analysis)

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DEA (Data Envelopment Analysis)

• Toshiyuki Sueyoshi
• New Mexico Tech
• Dept. of Management

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Data Envelopment Analysis

• (1) Relative Comparison
• (2) Multiple Inputs and Outputs
• (3) Efficiency Measurement (0-100)
• (4) Avoid the Specification Error between
• Inputs and Outputs
• (5) Production/Cost Analysis

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Case 1 input 1 output
Table 1.1 1 input 1 output Case
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Efficiency Frontier
E
G
Output
F
C
A
H
B
D
0
Employees
Figure 1.1Comparison of efficiencies in 1
input1 output case
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Efficiency Frontier
E
G
Output
F
C
A
Regression Line
H
B
D
0
Employees
Figure 1.2 Regression Line and Efficiency
Frontier
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Table 1.2 Efficiency
1 C gt G gt Agt B gt E gt D F gt H 0.4
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Efficiency Frontier
Output
C
D2
D1
D
0
Employees
Figure 1.3 Improvement of Company D
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Case 2 inputs 1 output
Table 1.3 2 inputs 1 output Case
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Production Possibility Set
G
F
C
A
I
Offices/Sales
E
D
B
Efficiency Frontier
H
0
Employees/Sales
Figure 1.4 2 inputs 1 output Case
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C
A
Offices/Sales
A1
A2
B
0
Employees/Sales
Figure 1.5 Improvement of Company A
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Case 1 input 2 outputs
Table 1.4 1 input 2 outputs Case
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A1
B
C
A
Efficiency Frontier
D
F
Offices/Sales
Production Possibility Set
E1
G
E
0
Customers/Offices
Figure 1.6 1 input 2 outputs Case
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Case Multiple inputs Multiple outputs
Table 1.5 Example of Multiple inputsMultiple
outputs Case
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CCR model
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R A Reference Set
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Primal Problem
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Dual Problem
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Slack
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Reference Set
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Example Problem
Table 1.6 2 inputs 1 output Case
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Primal Problem
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Dual Problem
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Efficiency Frontier
E
A
D
A1
F
C
0
Figure 1.7 Efficiency of DMU A
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Table 1.7 Results of DEA
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BCC model

• Variable Returns to Scale

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CCR model
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BCC model
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Dual Problem
BCC model
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Efficiency Frontier of CCR model
Efficiency Frontier of BCC model
(B)
d
c
Output
b
(C)
a
(A)
0
Input
Figure 2.1 Efficiency Frontier and Production
Possibility Set
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Cost Analysis
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Efficiency Frontier of CCR model
Efficiency Frontier of BCC model
f
g
g
E
b
c
b
h
h
i
i
d
e
j
j
k
P
0
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Dual Problem