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E-grāmata: Data Envelopment Analysis with R

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This book introduces readers to the use of R codes for optimization problems. First, it provides the necessary background to understand data envelopment analysis (DEA), with a special emphasis on fuzzy DEA. It then describes DEA models, including fuzzy DEA models, and shows how to use them to solve optimization problems with R. Further, it discusses the main advantages of R in optimization problems, and provides R codes based on real-world data sets throughout. Offering a comprehensive review of DEA and fuzzy DEA models and the corresponding R codes, this practice-oriented reference guide is intended for masters and Ph.D. students in various disciplines, as well as practitioners and researchers.

1 Introduction to Data Envelopment Analysis and Fuzzy Sets
1(18)
1.1 A Brief Review on Data Envelopment Analysis
1(3)
1.2 Basic Definitions
4(2)
1.3 Different Models of DEA
6(4)
1.4 Fuzzy Set Theory
10(5)
1.5 Conclusion
15(1)
References
15(4)
2 Introductions and Definitions of R
19(34)
2.1 Preliminaries of R
19(1)
2.2 Basic Definitions
20(3)
2.3 Definition of Different Variables Types
23(1)
2.4 Attributes
23(1)
2.5 Datastorage
24(9)
2.5.1 Vectors
24(2)
2.5.2 Matrixes
26(4)
2.5.3 Arrays
30(1)
2.5.4 Lists
31(1)
2.5.5 Data Frames
32(1)
2.6 Mathematical Operators
33(1)
2.7 Logical Operators
33(1)
2.8 Use R in Calculation
34(1)
2.9 Basic Mathematical Functions
35(1)
2.10 If Structure
36(1)
2.11 If Conditional
37(1)
2.11.1 Example: Consider the Following Example
37(1)
2.12 If Else Conditional
37(1)
2.13 For Function
38(1)
2.14 While Command
39(1)
2.15 Repeat Command
40(1)
2.16 Import and Read Data in R
40(4)
2.16.1 Data Command
40(1)
2.16.2 Scan Command
41(1)
2.16.3 Read.table Command
42(1)
2.16.4 Read.delim Command
42(1)
2.16.5 Fread Command
43(1)
2.16.6 Excel_sheets Command
44(1)
2.16.7 Read_excel Command
44(1)
2.17 Storage and Writing Data
44(1)
2.17.1 Write.table Command
44(1)
2.17.2 Sink Command
44(1)
2.18 Write Functions in R
45(1)
2.19 Convert Objects
45(5)
2.20 Conclusion
50(1)
References
51(2)
3 Basic DEA Models with R Codes
53(46)
3.1 Introduction
53(1)
3.2 Input-Oriented DEA Models with R Codes
54(13)
3.2.1 Input-Oriented CCR Envelopment Model with R Code
54(2)
3.2.2 Input-Oriented CCR Multiplier Model with R Code
56(4)
3.2.3 Input-Oriented BCC Multiplier Model with R Code
60(3)
3.2.4 Input-Oriented BCC Envelopment Model with R Code
63(4)
3.3 Output-Oriented DEA Models with R Codes
67(12)
3.3.1 Output-Oriented CCR Envelopment Model with R Code
67(2)
3.3.2 Output-Oriented CCR Multiplier Model with R Code
69(5)
3.3.3 Output-Oriented BCC Multiplier Model with R Code
74(2)
3.3.4 Output-Oriented BCC Envelopment Model with R Code
76(3)
3.4 Additive DEA Models with R Codes
79(7)
3.4.1 Additive CCR Model with R Code
79(2)
3.4.2 Additive BCC Model with R Code
81(5)
3.5 R Codes for Input-Oriented DEA Multiplier Model with e
86(5)
3.5.1 R Code for Input-Oriented BCC Multiplier Model with e
86(3)
3.5.2 R Code for Input-Oriented CCR Multiplier Model with e
89(2)
3.6 Two-Phase Input-Oriented DEA Envelopment Model with R Code
91(7)
3.6.1 Two-Phase Input-Oriented BCC Envelopment Model with R Code
91(3)
3.6.2 Two-Phase Input-Oriented CCR Envelopment Model with R Code
94(4)
3.7 Conclusion
98(1)
References
98(1)
4 Advanced DEA Models with R Codes
99(64)
4.1 Introduction `
99(1)
4.2 AP Models with R Codes
99(9)
4.2.1 Input-Oriented AP Envelopment Model with R Code
100(2)
4.2.2 Output-Oriented AP Enveloping Model
102(2)
4.2.3 Input-Oriented AP Multiplier Model
104(2)
4.2.4 Output-Oriented AP Multiplier Model
106(2)
4.3 MAJ Super-Efficiency Model with R Code
108(6)
4.4 Norm L1 Super-Efficiency Model with R Code Ill
4.5 Returns to Scale--CCR Models with R Codes
114(8)
4.5.1 Returns to Scale--CCR Envelopment Model with R Code
114(4)
4.5.2 Returns to Scale--DEA Multiplier Model with R Code
118(4)
4.6 Cost Efficiency Model with R Code
122(2)
4.7 Revenue Efficiency DEA Model with R Code
124(3)
4.8 Malmquist Productivity Index--CCR Model with R Codes
127(9)
4.8.1 Malmquist Productivity Index--CCR Multiplier Model with R Code
127(4)
4.8.2 Malmquist Productivity Index--CCR Envelopment Model with R Code
131(5)
4.9 SBM Models with R Codes
136(5)
4.9.1 First Model of SBM with R Code
136(3)
4.9.2 Second Model of SBM with R Code
139(2)
4.10 Series Network DEA Model with R Code
141(2)
4.11 Profit Efficiency DEA Model with R Code
143(4)
4.12 Modified Slack Based DEA Models with R Codes
147(5)
4.12.1 Input-Oriented Slack Based DEA Model with R Code
147(3)
4.12.2 Output-Oriented Slack Based DEA Model with R Code
150(2)
4.13 Congestion DEA Model with R Code
152(4)
4.14 Common Set of Weights DEA Model with R Code
156(2)
4.15 Directional Efficiency DEA Model with R Code
158(4)
4.16 Conclusion
162(1)
References
162(1)
5 Fuzzy Data Envelopment Analysis Models with R Codes
163
5.1 Introduction
163(2)
5.2 The a-Level Approach
165(11)
5.2.1 Kao and Liu's Approach
166(7)
5.2.2 Saati et al.'s Approach
173(3)
5.3 The Fuzzy Ranking Approach
176(14)
5.3.1 Guo and Tanaka's Approach
176(4)
5.3.2 Leon et al.'s Approach
180(8)
5.3.3 Soleimani-damaneh et al.'s Approach
188(2)
5.4 The Possibility Approach
190(6)
5.5 The Fuzzy Arithmetic Approach
196(39)
5.5.1 Wang et al.'s Approach
196(11)
5.5.2 Bhardwaj et al.'s Approach
207(7)
5.5.3 Azar et al.'s Approach
214(4)
5.5.4 The MOLP Approach
218(17)
5.6 Conclusion
235(1)
References
235