Introduction to Data Envelopment Analysis and Its Applications Shinn Sun Department of Management Fo Guang University 6/10/2015 佛光大學

Professor W. W. Cooper-Founder of DEA and Shinn photoed at EURO XIV Conference on July 6, 1995 佛光大學

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 佛光大學

Lawrence M. Seiford 佛光大學

Tsutsui, Tone, Fukuyama, Morita, Shinn, Hirotsu DEA Symposium 2012, Feb 20-21 佛光大學

Thanassoulis, Yu, Tone, DEA Symposium 2012, Feb 20-21 佛光大學

魏權齡（左三）與孫遜 佛光大學

Joe Zhu 佛光大學

Outline What is Data Envelopment Analysis (DEA) Efficiency Measures The Use of DEA DEA Linear Programming Model Example: Car Manufacturing DEA Models DEA Research 1996-2006 DEA Model Development Evolution of DEA Application Areas Future for DEA DEA Software 佛光大學

Outline-continued DEA Books Conclusions 佛光大學

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 佛光大學

Efficiency Measures However, with multiple inputs and outputs, it becomes more difficult to evaluate the efficiency of DMUs. Output Efficiency = Input 佛光大學

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… 佛光大學

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. 佛光大學

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 佛光大學

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 佛光大學

DEA Linear Program subject to Generally K ≥ 2(N+M) 佛光大學

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 佛光大學

For each DMU (unit) we need to solve a linear program to determine its efficiency. 佛光大學

Unit #1 We see from its solution that it is 100% efficient Linear program Max 100 u1 subject to 100u1 - 2 v1 -200 v2 ≤ 0 100u1 - 4 v1 -150 v2 ≤ 0 100u1 - 4 v1 -100 v2 ≤ 0 100u1 – 6 v1 -100 v2 ≤ 0 100u1 - 8 v1 -80 v2 ≤ 0 100u1 - 10 v1 -50 v2 ≤ 0 2v1 + 200 v2 = 1 We see from its solution that it is 100% efficient relative to the other units. 佛光大學

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 佛光大學

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. 佛光大學

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 . 佛光大學

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 佛光大學

Cross Efficiency Model Window Analysis Models under weights restrictions Assurance Region Model Cone-Ratio Model Variable Models Non-controllable Model Categorical Model Bilateral Model 佛光大學

Profit Objective Model Allocation Models Profit Objective Model Cost efficiency Model Revenue Efficiency Model Profit Efficiency Model Revenue/Cost Efficiency Model 佛光大學

DEA Research 1996-2006 A total of 1,030 journal articles is selected. (Theoretical Articles: 382, Applications: 648) 佛光大學

DEA Model Development 佛光大學

Evolution of DEA 佛光大學

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Application Areas 佛光大學

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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 佛光大學

DEA Software Commercial available software: DEA Solver Frontier Analyst DEA Excel Solver OnFront Warwick DEA MaxDEA, DEAOS Free Software: DEAP, EMS 佛光大學

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。 佛光大學

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. 佛光大學

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. 佛光大學