1. DEA (Data Envelopment Analysis)
Toshiyuki Sueyoshi
New Mexico Tech
Dept. of Management

2. 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

3. Case : 1 input – 1 output
Table 1.1 : 1 input – 1 output Case

4. Efficiency Frontier E G
Output F C A H B D
Employees
Figure 1.1:Comparison of efficiencies in 1 input–1 output case

5. Efficiency Frontier E G
Output F C A
Regression Line H B D
Employees
Figure 1.2 : Regression Line and Efficiency Frontier

6. Table 1.2 : Efficiency
1 = C > G > A> B > E > D = F > H = 0.4

7. Efficiency Frontier
Output C D2 D1 D
Employees
Figure 1.3 : Improvement of Company D

8. Case : 2 inputs – 1 output
Table 1.3 : 2 inputs – 1 output Case

9. Production Possibility SetG C F
Offices/Sales A I E D B
Efficiency Frontier H
Employees/Sales
Figure 1.4 : 2 inputs – 1 output Case

10. C A
Offices/Sales A1 A2 B
Employees/Sales
Figure 1.5 : Improvement of Company A

11. Case : 1 input – 2 outputs
Table 1.4 : 1 input – 2 outputs Case

12. A1 B C A
Efficiency Frontier D F
Offices/Sales
Production Possibility Set E1 G E
Customers/Offices
Figure 1.6 : 1 input – 2 outputs Case

13. Case : Multiple inputs – Multiple outputs
Table 1.5 : Example of Multiple inputs–Multiple outputs Case

15. CCR model

16. R : A Reference Set

17. Primal Problem

18. Dual Problem

19. Slack

20. Reference Set:

21. Example Problem
Table 1.6 : 2 inputs – 1 output Case

22. Primal Problem

23. Dual Problem

24. Efficiency Frontier E D A A1 F C
Figure 1.7 : Efficiency of DMU A

26. Table 1.7 : Results of DEA

27. Variable Returns to Scale
BCC model
Variable Returns to Scale

28. CCR model

29. BCC model

30. BCC model:
Dual Problem

31. Efficiency Frontier of CCR model
Efficiency Frontier of BCC model
(B) d c
Output b
(C) a
(A)
Input
Figure 2.1 : Efficiency Frontier and Production Possibility Set

32. Cost Analysis

33. Efficiency Frontier of CCR model
Efficiency Frontier of BCC model f g g E c b b h h i i e d j j k P

34. Dual Problem