Performance Evaluation: Network Data Envelopment Analysis

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Performance Evaluation Network Data Envelopment
Analysis

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• 100?11?5?

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

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1. Efficiency
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• 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. KoopmansA 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).
• gt Pareto optimality

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MeasurementParametric approachRegression
analysis (Aigner-Chu)Nonparametric
approachData envelopment analysis
(Charnes-Cooper-Rhodes)
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Parametric approach

• Production function

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Two-input single-output
Y0
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Input efficiency
Isoquant (Y0)
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Single-input two-output
(X0)
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• Example

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2. Data Envelopment Analysis
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Non-parametric approach
Single-input single-output output side Single-input single-output output side Single-input single-output output side
DMU X Y
A 10 5
B 20 20
C 30 30
D 40 35
E 36 22

Eff.
1
1
1
1
2/3
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Input side
DMU X1 X2 Y Y
A 20 5 100 100
B 30 3 100 100
C 50 2 100 100
D 40 4 100 100
E 48 3 100 100

Eff.
1
1
1
4/5
5/6
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Output side Output side Output side Output side
DMU X Y1 Y2 Y2
A 100 20 50 50
B 100 40 40 40
C 100 50 20 20
D 100 30 30 30
E 100 40 12 12

Eff.
1
1
1
3/4
4/5
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Emrouznejad et al. (2008) Socio-economic Planning
Science 42, 151-157
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3. Mathematical Models
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• Ratio form
• Input i and output r of DMU j (Xij , Yrj)

DMU k chooses most favorable multipliers ur ,vi
to calculate Ek
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• Linear transformation

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• Envelopment form
• (Dual of the ratio form)

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is the
target on the frontier.
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• Variable returns-to-scale

Technical Eff.A/A,
Scale Eff. A/A0,
Aggregate Eff.A/A0(A/A)