1. Introduction to Data Envelopment Analysis and Its Applications
Shinn Sun
Department of Management
Fo Guang University
6/10/2015
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2. Professor W. W. Cooper-Founder of DEA and Shinn photoed at EURO XIV Conference on July 6, 1995
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3. V. Krivonozhko, J. C. Paradi, C
V. Krivonozhko, J. C. Paradi, C. Chen, Rajiv Banker, Shinn, Hsihu Chang photoed at 5th International Symposium on DEA, January 6, 2007
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4. Lawrence M. Seiford
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5. Tsutsui, Tone, Fukuyama, Morita, Shinn, Hirotsu
DEA Symposium 2012, Feb 20-21
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6. Thanassoulis, Yu, Tone, DEA Symposium 2012, Feb 20-21
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7. 魏權齡（左三）與孫遜
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8. Joe Zhu
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9. Outline What is Data Envelopment Analysis (DEA) Efficiency Measures
The Use of DEA
DEA Linear Programming Model
Example: Car Manufacturing
DEA Models
DEA Research
DEA Model Development
Evolution of DEA
Application Areas
Future for DEA
DEA Software
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10. Outline-continued
DEA Books
Conclusions
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11. What is DEA
Evaluating the productivity of Decision Making Units (DMUs)
Initially designed for non-profits where operating ratios may not be appropriate
schools
public utilities
vehicle maintenance of the Tactical Air Command (TAC)
Has been adopted for evaluating for-profit branches
Airline, Banking, Health Care, Hotels, Service Industry, Transportation, etc.
Recently, Hi-Tech Industry
How can you compare various DMUs
Determine appropriate inputs
Determine appropriate outputs
Measure relationships between these inputs and outputs
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12. Efficiency Measures
However, with multiple inputs and outputs, it becomes more difficult to evaluate the efficiency of DMUs.
Output
Efficiency =
Input
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13. Clearly, process A is more efficient than process B, but...
A new assessment based on office space shows that process B is more efficient than process A, so…
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14. The Use of DEA Multiple inputs, multiple outputs.
Measure efficiency relative to other DMUs.
Linear Programming is used to determine which DMUs are 100% efficient relative to the other units.
Determine relatively inefficient units.
Provide ways of determining how to reduce inefficiencies.
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15. DEA Linear Programming Model
Let Ek with k=1, 2, ... , K be the efficiency ratios of DMU k, where there are K total branch units.
Let uj, with j=1, 2, ... , M be the weight given for output j, where M is the total number of output types.
Let vi, with i=1, 2, ... , N be the weight given for input i, where N is the total number of input types.
Let Ojk be the number of observed units of output j generated by DMU k during one time period.
Let Iik be the number of actual units of input i used by DMU k during one time period
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16. DEA Efficiency Measure
Consider a single DMU B whose efficiency we want to measure.
Want to maximize its efficiency by choosing uj's and vi's.
However, in choosing, no other unit can exceed 100% efficiency. So we have the constraints
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17. DEA Linear Program
subject to
Generally K ≥ 2(N+M)
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18. Example: Car Manufacturing
Make-to-stock only
Six units
3-door, 4-door, and 5-door cars only.
Assume output 100 cars at each
Inputs vary
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19. For each DMU (unit) we need to solve a linear program to determine its efficiency.
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20. Unit #1 We see from its solution that it is 100% efficient
Linear program
Max 100 u1
subject to
100u1 - 2 v v2 ≤ 0
100u1 - 4 v v2 ≤ 0
100u1 - 4 v v2 ≤ 0
100u1 – 6 v v2 ≤ 0
100u1 - 8 v1 -80 v2 ≤ 0
100u v1 -50 v2 ≤ 0
2v v2 = 1
We see from its solution
that it is 100% efficient
relative to the other units.
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21. Consider Unit #4 Here we find that unit 4 is relatively inefficient.
The shadow prices presented imply that the unit's efficiency reference set are units 3 and 6.
Compare with the graph
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22. Composite Reference Unit
One efficient outcome can be obtained by combining the units in the efficiency set using the relative weight assigned to each in calculating the relative efficiency of unit 4.
These weights turn out to be just the shadow prices on the efficiency constraints.
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23. Alternate Efficient Changes
The values for v1 and v2 measure the relative weight given to the inputs labor-hours and material costs, respectively, in determining the efficiency.
For unit 4, each unit decrease in labor-hours, results in an efficiency increase of 5.55%.
An efficient firm is found by reducing labor-hours by
Also, for each unit decrease in material costs we increase efficiency by 0.67 % so unit 4 can become efficient by reducing costs by .
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24. DEA Models Traditional models: Charnes, Cooper and Rhodes Model (CCR)
Banker, Charnes and Rhodes Model (BCC)
Alternative models:
Additive Model
Slack-based Model
Free Disposal Hull
Multiplicative Model
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25. Cross Efficiency Model Window Analysis
Models under weights restrictions
Assurance Region Model
Cone-Ratio Model
Variable Models
Non-controllable Model
Categorical Model
Bilateral Model
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26. Profit Objective Model
Allocation Models
Profit Objective Model
Cost efficiency Model
Revenue Efficiency Model
Profit Efficiency Model
Revenue/Cost Efficiency Model
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27. DEA Research
A total of 1,030 journal articles is selected. (Theoretical Articles: 382, Applications: 648)
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28. DEA Model Development
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29. Evolution of DEA
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30. 佛光大學

31. Application Areas
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32. 佛光大學

33. Future for DEA Theoretical limitation Research Extended DEA models
Information Science
Statistics
Stochastic DEA
Dynamic DEA
Network DEA
Comparison of various DEA models
Introduction to quality variables
New Application area
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34. DEA Software Commercial available software: DEA Solver
Frontier Analyst
DEA Excel Solver
OnFront
Warwick DEA
MaxDEA, DEAOS
Free Software: DEAP, EMS
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35. DEA Books
Charnes et al. (1994) Data Envelopment Analysis: Theory, Methodology and Applications.
Coelli et al. (1997) An Introduction to Efficiency and Productivity Analysis.
Cooper et al. (2000, 2007) Data Envelopment Analysis: A Comprehensive Text with Models, Application, References and DEA Solver.
孫遜 (民93) 資料包絡分析法—理論與應用，揚智文化公司。
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36. Conclusions
Can understate the inefficiency because it is calculated by trying to put the inefficient DMU in the best light.
May correct by forcing one DMU, known to be efficient in general, to be explicitly efficient.
Much care must be taken in determining the input and output variables.
Can fail to give significant information if too few points available.
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37. Conclusions-continued
Serves as a tool for
- productivity analysis;
- performance measurement;
- technology forecasting;
- capacity planning;
- process re-design;
- R&D project evaluation;
- strategy alliances selection; and
- resources allocation.
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