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DEA (Data Envelopment Analysis)

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

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DEA (Data Envelopment Analysis)

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  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

  14. CCR model

  15. R : A Reference Set

  16. Primal Problem

  17. Dual Problem

  18. Slack

  19. Reference Set:

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

  21. Primal Problem

  22. Dual Problem

  23. Efficiency Frontier E A D A1 F C 0 Figure 1.7 : Efficiency of DMU A

  24. Table 1.7 : Results of DEA

  25. BCC model Variable Returns to Scale

  26. CCR model

  27. BCC model

  28. BCC model: Dual Problem

  29. 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

  30. Cost Analysis

  31. 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

  32. Dual Problem

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