vii
TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGUERS
xii
LIST OF SYMBOLS
xiv
LIST OF APPENDIXES
xvii
INTRODUCTION
1
1.1 Introduction
1
1.2 Research Background
1
1.3 Motivation for Research
4
1.4 Problem Statements
4
1.5 Research Objectives
5
1.6 Research Questions
5
1.7 Significant of the Study
5
1.8 Scope of the Study
6
1.9 Research Methodology
6
1.10 Thesis Organization
6
LITRATURE REVIEW
9
2.1 Introduction
9
2.2 Data Envelopment Analysis
9
viii
3
4
5
6
2.3 Common DEA Models
11
2.4 Super-efficiency DEA Models
15
2.5 Allocation DEA Models
17
2.6 Non-controllable Data
19
2.7 Integer-valued DEA Models
20
2.8 Software for Solving DEA Models
22
2.9 Conclusion
22
ARASH METHOD IN DEA
23
3.1 Introduction
23
3.2 The Shortcomings in DEA Definitions and Techniques
23
3.3 Arash Method (AM)
27
3.4 AM and CF
36
3.5 AM and Non-controllable Data
38
3.6 Non-linear AM
42
3.7 Conclusion
49
KOUROSH METHOD IN DEA
50
4.1 Introduction
50
4.2 Kourosh Model (KM)
50
4.3 KM and Revenue-efficiency
55
4.4 Combining Kourosh and Arash Methods
56
4.5 KAM and Profit-efficiency
60
4.6 Conclusion
64
INTEGER ARASH METHOD
65
5.1 Introduction
65
5.2 Integer DEA Axioms
65
5.3 Integer Arash Model
66
5.4 Examining Integer AM
74
5.5 Conclusion
78
IMPROVED KOUROSH AND ARASH MODEL
79
6.1 Introduction
79
6.2 The Efficient Tape
79
ix
7
6.3 The Targets Regions and Sensitivity Index
81
6.4 Numerical Example
87
6.5 Conclusion
93
SUMMARY AND CONCLUSION
95
7.1 Summary of the Research
95
7.2 Conclusion
96
7.3 Suggestions for Future Research
96
REFERENCES
Appendix A
97
102
x
LIST OF TABLES
TABLE NO.
TITLE
PAGE
2.1
4 DMUs with two inputs and one output
11
2.2
Some of the previous common CRS DEA Models
14
2.3
Some of the common super-efficiency CRS DEA Models
16
2.4
Some of the allocation CRS DEA Models
19
2.5
Two non-controllable DEA models
19
2.6
Some mixed integer DEA models
21
3.1
The example of 3 DMUs with NFD
24
3.2
The example of 3 DMUs with clearer NFD
25
3.3
The example of 5 DMUs with NFD
26
3.4
The AM scores for DMUs in Tables 3.1, 3.2 and 3.3
32
3.5
17 airports with four inputs and three outputs
33
3.6
The score of conventional DEA models and AM in CRS
34
3.7
The score of conventional DEA models and AM in VRS
35
3.8
Three DMUs with two inputs and two outputs
37
3.9
The differences between 0-AM and CF model scores
38
3.10
The -AM scores by changing
3.11
The example of 12 DMUs with one non-controllable input
39
3.12
The scores of CCR, NCN and -AM (Equation 3.4)
40
3.13
The outcome of 0.00001-AM (Equation 3.5) and
3.14
The slacks of 0.00001errors in input values by AM
3.15
12 DMUs with two inputs and two outputs
43
3.16
The example of 6 DMUs
45
3.17
The example of 18 DMUs
47
3.18
The linear AM scores
48
3.19
The SBM and Non-linear AM scores
48
>0
38
.
40
41
xi
4.1
5 DMUs with one input and two outputs
54
4.2
The differences between 0-KM and RF model scores
56
4.3
The -KM scores by changing
4.4
The example of four DMUs
4.5
The scores of linear and non-linear AM, KM and KAM
60
4.6
The example of 3 DMUs
62
4.7
The scores of PF models and -KAM in VRS
62
4.8
The scores of PF models and -KAM in CRS
63
4.9
The scores of -KAM in CRS
64
5.1
The example of 6 DMUs
67
5.2
The efficiency score and proposed target by integer 0-AM
75
5.3
The outcome of integer 0.02-AM
75
5.4
The outcome of integer 0.00001-AM
77
6.1
The example of five DMUs.
87
6.2
The 0.1-KAM outcomes.
88
6.3
The example of 19 DMUs.
89
6.4
The outcomes of 10 -KAM CRS
91
6.5
>0
The outcomes of 10 -KAM VRS
56
59
91
xii
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
2.1
Radial Approach
12
2.2
Non-Radial Approach
12
2.3
AP method to rank technically efficient DMUs
17
2.4
Cost-efficiency
18
3.1
Three technically efficient DMUs
24
3.2
AP method for evaluating B
24
3.3
Five technically efficient DMUs
26
3.4
AP method to evaluate A
26
3.5
An epsilon error in data of A
28
3.6
Non-radial approach in AM
28
5.1
The integer and real inputs space
68
5.2
2% errors by the scale of ’s inputs
68
5.3
3% errors by the scale of ’s inputs
69
5.4
5% errors by the scale of ’s inputs
69
5.5
6% errors by the scale of ’s inputs
69
5.6
8% errors by the scale of ’s inputs
69
5.7
8% errors by the scale of ’s inputs
70
5.8
10% errors by minimum input scales
70
5.9
The example of eight DMUs
71
5.10
Arash Method outcomes
71
6.1
Production function and VRS PPS
80
6.2
Production function and CRS/VRS PPS
80
6.3
Production frontier and efficient tape
81
6.4
A region of target in efficient tape
81
6.5
An -higher PPS
82
xiii
6.7
T
6.8
T
The regions of targets by 0.1-KAM
88
6.9
The regions of targets by 0.25-KAM
88
6.10
10 -KAM CRS/VRS sensitivity indexes
92
6.6
6.11
6.12
frontiers in inputs space
83
frontiers in outputs space
83
The outcomes of 0.1-KAM CRS
92
The outcomes of 0.1-KAM VRS
93
xiv
LIST OF SYMBOLS
DEA
-
Data envelopment analysis
DMU
-
Decision making unit
CCR
-
Charnes, Cooper and Rhodes model
ADD
-
Additive model
SBM
-
Slack-based measure model
BCC
-
Banker, Charnes and Cooper model
ERM
-
Enhanced Russell measure model
AP
-
Andersen and Petersen model
LP
-
Linear programming
CF
-
Cost-efficiency model
RF
-
Revenue-efficiency model
PF
-
Profit-efficiency model
NCN
-
Non-controllable model
PPS
-
Production possibility set
CRS
-
Constant returns to scale
VRS
-
Variable returns to scale
NFD
-
Near and far data
AM
-
Arash Method/model
KM
-
Kourosh Method/model
KAM
-
Kourosh and Arash Method/model
-
Number of DMUs
-
Number of DMU inputs
-
Number of DMU outputs
-
Index of DMUs
-
Index of DMU inputs
-
Index of DMU outputs
-
Index of specific DMU whose efficiency is being assessed
-
Observed value of input of DMU
xv
Observed value of output
-
Multiplier used to compute linear combination of DMUs’ inputs/outputs
-
Cf
Rf
Pf
of DMU
-
Non-negative slack or potential reduction of input of DMU
Non-negative slack or potential increase of output
of DMU
Positive specified weight or price for input of DMU
Positive specified weight or price for output
of DMU
Optimal multipliers to identify the reference sets for a DMU
Optimal slack to identify an excess utilization of input of DMU
Optimal slack to identify a shortage utilization of output
Target of input of DMU after evaluation
Target of output
of DMU after evaluation
of DMU
-
Optimal technical efficiency score in input-oriented approach of CCR
-
Optimal technical efficiency score in output-oriented approach of CCR
-
Optimal technical efficiency score of SBM
-
Optimal technical efficiency score of input-oriented SBM
-
Optimal technical efficiency score of ERM
-
Optimal super-efficiency score of SBM
-
Optimal super-efficiency score of -norm
-
Optimal cost-efficiency score
-
Optimal revenue-efficiency score
-
Optimal profit-efficiency score
-
A positive real number
-
A positive real number
-
The nonnegative integer numbers set
-
The nonnegative real numbers set
-
The positive real numbers set
-
The empty set
-
A set of corresponding indexes of integer inputs
-
A set of corresponding indexes of integer outputs
-
A set of corresponding indexes of controllable data
-
A set of corresponding indexes of non-controllable data
-
A nonnegative real number corresponding to input
-
A nonnegative real number corresponding to output
-
A very small positive real number
-
For all
xvi
-
There is at least
-
Very less than
-
A very small positive real number
-
A very small number in
-
A very small positive real number corresponding to input
-
A very small positive real number corresponding to output
-
Optimal efficiency score of AM with degree of freedom
-
Optimal efficiency score of KM with degree of freedom
-
Optimal efficiency score of KAM with degree of freedom
-
The CRS PPS
-
The CRS PPS with degree of freedom
-
{0}
The efficient tape with 2 diagonals
Optimistic efficient target of input of DMU after evaluation
Optimistic efficient target of output
of DMU after evaluation
Pessimistic efficient target of input of DMU after evaluation
of DMU after evaluation
-
Pessimistic efficient target of output
-AM
-
Arash model with
-KM
-
Kourosh model with
-KAM
-
Kourosh and Arash model with degree of freedom
degree of freedom
degree of freedom
xvii
LIST OF APPENDICES
APPENDIX
A
TITLE
The accepted, proceedings published, presented in
conferences and submitted papers
PAGE
102