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DEA (Data Envelopment Analysis)

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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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