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by Hosseinzadeh Lotfi, Farhad (Author), Ali Ebrahimnejad (Author), Mohsen Vaez-Ghasemi (Author), Zohreh Moghaddas (Author)
About this book
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.
Brief contents
1 Introduction to Data Envelopment Analysis and Fuzzy Sets 1
1.1 A Brief Review on Data Envelopment Analysis 1
1.2 Basic Definitions 4
1.3 Different Models of DEA 6
1.4 Fuzzy Set Theory 10
1.5 Conclusion 15
References 15
2 Introductions and Definitions of R 19
2.1 Preliminaries of R. 19
2.2 Basic Definitions 20
2.3 Definition of Different Variables Types 23
2.4 Attributes 23
2.5 Data Storage. 24
2.5.1 Vectors 24
2.5.2 Matrixes 26
2.5.3 Arrays 30
2.5.4 Lists 31
2.5.5 Data Frames 32
2.6 Mathematical Operators. 33
2.7 Logical Operators 33
2.8 Use R in Calculation. 34
2.9 Basic Mathematical Functions 35
2.10 If Structure 36
2.11 If Conditional 37
2.11.1 Example: Consider the Following Example 37
2.12 If Else Conditional 37
2.13 For Function 38
2.14 While Command 39
2.15 Repeat Command 40
2.16 Import and Read Data in R 40
2.16.1 Data Command 40
2.16.2 Scan Command 41
2.16.3 Read.table Command 42
2.16.4 Read.delim Command 42
2.16.5 Fread Command. 43
2.16.6 Excel_sheets Command 44
2.16.7 Read_excel Command 44
2.17 Storage and Writing Data 44
2.17.1 Write.table Command 44
2.17.2 Sink Command 44
2.18 Write Functions in R 45
2.19 Convert Objects 45
2.20 Conclusion 50
References 51
3 Basic DEA Models with R Codes 53
3.1 Introduction 53
3.2 Input-Oriented DEA Models with R Codes 54
3.2.1 Input-Oriented CCR Envelopment Model with R Code 54
3.2.2 Input-Oriented CCR Multiplier Model with R Code 56
3.2.3 Input-Oriented BCC Multiplier Model with R Code 60
3.2.4 Input-Oriented BCC Envelopment Model with R Code 63
3.3 Output-Oriented DEA Models with R Codes 67
3.3.1 Output-Oriented CCR Envelopment Model with R Code 67
3.3.2 Output-Oriented CCR Multiplier Model with R Code 69
3.3.3 Output-Oriented BCC Multiplier Model with R Code 74
3.3.4 Output-Oriented BCC Envelopment Model with R Code 76
3.4 Additive DEA Models with R Codes 79
3.4.1 Additive CCR Model with R Code 79
3.4.2 Additive BCC Model with R Code 81
3.5 R Codes for Input-Oriented DEA Multiplier Model with e 86
3.5.1 R Code for Input-Oriented BCC Multiplier Model with e 86
3.5.2 R Code for Input-Oriented CCR Multiplier Model with e 89
3.6 Two-Phase Input-Oriented DEA Envelopment Model with R Code. 91
3.6.1 Two-Phase Input-Oriented BCC Envelopment Model with R Code 91
3.6.2 Two-Phase Input-Oriented CCR Envelopment Model with R Code 94
3.7 Conclusion 98
References 98
4 Advanced DEA Models with R Codes. 99
4.1 Introduction 99
4.2 AP Models with R Codes 99
4.2.1 Input-Oriented AP Envelopment Model with R Code 100
4.2.2 Output-Oriented AP Enveloping Model 102
4.2.3 Input-Oriented AP Multiplier Model 104
4.2.4 Output-Oriented AP Multiplier Model 106
4.3 MAJ Super-Efficiency Model with R Code 108
4.4 Norm L1 Super-Efficiency Model with R Code. 111
4.5 Returns to Scale—CCR Models with R Codes 114
4.5.1 Returns to Scale—CCR Envelopment Model with R Code 114
4.5.2 Returns to Scale—DEA Multiplier Model with R Code 118
4.6 Cost Efficiency Model with R Code. 122
4.7 Revenue Efficiency DEA Model with R Code 124
4.8 Malmquist Productivity Index—CCR Model with R Codes 127
4.8.1 Malmquist Productivity Index—CCR Multiplier Model with R Code 127
4.8.2 Malmquist Productivity Index—CCR Envelopment Model with R Code 131
4.9 SBM Models with R Codes 136
4.9.1 First Model of SBM with R Code 136
4.9.2 Second Model of SBM with R Code 139
4.10 Series Network DEA Model with R Code 141
4.11 Profit Efficiency DEA Model with R Code 143
4.12 Modified Slack Based DEA Models with R Codes 147
4.12.1 Input-Oriented Slack Based DEA Model with R Code 147
4.12.2 Output-Oriented Slack Based DEA Model with R Code 150
4.13 Congestion DEA Model with R Code 152
4.14 Common Set of Weights DEA Model with R Code 156
4.15 Directional Efficiency DEA Model with R Code. 158
4.16 Conclusion 162
References 162
5 Fuzzy Data Envelopment Analysis Models with R Codes 163
5.1 Introduction 163
5.2 The a–Level Approach 165
5.2.1 Kao and Liu’s Approach 166
5.2.2 Saati et al.’s Approach 173
5.3 The Fuzzy Ranking Approach 176
5.3.1 Guo and Tanaka’s Approach 176
5.3.2 Leon et al.’s Approach 180
5.3.3 Soleimani-damaneh et al.’s Approach 188
5.4 The Possibility Approach 190
5.5 The Fuzzy Arithmetic Approach 196
5.5.1 Wang et al.’s Approach 196
5.5.2 Bhardwaj et al.’s Approach. 207
5.5.3 Azar et al.’s Approach 214
5.5.4 The MOLP Approach 218
5.6 Conclusion 235
References 235
Series: Studies in Fuzziness and Soft Computing (Book 386)
Pages: 236 pages
Publisher: Springer; 1st ed. 2020 edition (September 28, 2019)
Language: English
ISBN-10: 3030242765
ISBN-13: 978-3030242763
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