1 / 44

Performance Evaluation: Network Data Envelopment Analysis

Performance Evaluation: Network Data Envelopment Analysis. 高 強 國立成功大學工業與資訊管理學系 於 中山大學企業管理系 100 年 11 月 5 日. Contents 1. Efficiency 2. Data Envelopment Analysis 3. Mathematical Models 4. Network Models 5. Research Areas. 1. Efficiency. Definition Output point of view

athena-gibson
Download Presentation

Performance Evaluation: Network Data Envelopment Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Performance Evaluation: Network Data Envelopment Analysis 高 強國立成功大學工業與資訊管理學系 於 中山大學企業管理系 100年11月5日

  2. Contents 1. Efficiency 2. Data Envelopment Analysis 3. Mathematical Models 4. Network Models 5. Research Areas

  3. 1. Efficiency

  4. Definition Output point of view (Actual output produced)/(Maximal output can be produced) Input point of view (Minimal input required)/(Actual input used) Technically Efficient Production T. Koopmans：A feasible input/output vector where it is technologically impossible to increase any output (and/or reduce any input) without simultaneously reducing another output (and/or increasing any other input). => Pareto optimality

  5. MeasurementParametric approachRegression analysis (Aigner-Chu)Nonparametric approachData envelopment analysis (Charnes-Cooper-Rhodes)

  6. output Max. production Ave. production Output Eff.＝A/A* Input Eff.＝I*/I input Parametric approach Production function

  7. Two-input single-output Y0

  8. X 2 o Dominated region o ● o Input Eff.＝OA*/OA ● O X 1 Input efficiency Isoquant (Y0)

  9. Y 2 ● Output Eff.=OA/OA* * A * O ● 2 A o O o ● ● 2 o Product transformation curve Dominated region O * O O Y 1 1 1 Single-input two-output (X0)

  10. Production function: unrestricted in sign. Example:

  11. 2. Data Envelopment Analysis

  12. Y Production function E* D ● C ● E ● B ● X A ● O Non-parametric approach

  13. X2 Isoquant X1

  14. Production transformation curve

  15. Emrouznejad et al. (2008) Socio-economic Planning Science 42, 151-157

  16. 3. Mathematical Models

  17. Ratio form Input i and output r of DMU j: (Xij , Yrj) DMU k chooses most favorable multipliers ur ,vi to calculate Ek

  18. Linear transformation

  19. Envelopment form (Dual of the ratio form) ● is the target on the frontier.

  20. Constant RTS Variable RTS Variable returns-to-scale Technical Eff.＝A/A＊, Scale Eff.＝ A＊/A0, Aggregate Eff.=A/A0＝(A/A＊)×(A*/A0)

  21. 4. Network Models

  22. DMU k X1k Y1k X2k Y2k . . . . . . Xmk Ysk Conventional black box concept

  23. CCR Ratio model

  24. Envelopment model θ unrestricted in sign

  25. Zqk X1k X2k Xmk Z2k Z1k System DMU k Y2k Ysk Y1k Process 1 Process 2 . . . . . . . . . Two-stage series systemZpj:Intermediate product p of DMU j

  26. Ratio model

  27. Envelopment model

  28. Xi Yr Zp(l) Zp(t) h t l … r=1,…,s i=1,…,m p=1,…,q p=1,…,q … General case System efficiency is the product of the h process efficiencies.

  29. More general case

  30. Ratio model

  31. Envelopment model

  32. Parallel system

  33. Ratio model

  34. 1 X1, X2 Y1, Y2, Y3 3 2 A network system

  35. Model

  36. Efficiencies

  37. 5. Research Areas

  38. Models I: Increasing marginal product II: Decreasing marginal product III: Negative marginal product- Congestion

  39. Multipliers Strictly positive ：non-Archimedean number，10-5 Absolute range Relative range (Assurance region, cone ratio)

  40. Data type  Traditional data  Undesirable data  Ordinal data  Qualitative data  Interval data  Stochastic data  Fuzzy data

  41. Applications Novel application A new area A new journal Implications Special data type Derivation of multiplier restrictions

  42. References • Chiang Kao and Shiuh-Nan Hwang, 2008, Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan. European J. Operational Research 185, 418-429. • Chiang Kao, 2009, Efficiency decomposition in network data envelopment analysis: A relational model. European J. Operational Research 192, 949-962. • Chiang Kao, 2009, Efficiency measurement for parallel production systems. European J. Operational Research 196, 1107-1112. • Chiang Kao and Shiuh-Nan Hwang, 2010, Efficiency measurement for network systems: IT impact on firm performance. Decision Support Systems 48, 437-446. • Chiang Kao and Shiuh-Nan Hwang, 2011, Decomposition of technical and scale efficien-cies in two-stage production systems. European J. Operational Research 211, 515-519. • Chiang Kao, 2011, Efficiency decomposition for parallel production systems. J. Operational Research Society (accepted) (SCI) doi:10.1057/jors.2011.16. • Chiang Kao, 2008, A linear formulation of the two-level DEA model. Omega, Int. J. Management Science 36, 958-962. • Chiang Kao and Shiang-Tai Liu, 2004, Predicting bank performance with financial forecasts: A case of Taiwan commercial banks. J. Banking & Finance 28, 2353-2368.

  43. Thank You

More Related