DEA (Data Envelopment Analysis)

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 0 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 0 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 0 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 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

10. C A Offices/Sales A1 A2 B 0 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 0 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 A D A1 F C 0 Figure 1.7 : Efficiency of DMU A

26. Table 1.7 : Results of DEA

27. 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) 0 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 d e j j k P 0

34. Dual Problem