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Modeling and Simulation of Logistics Flows 1: Theory and Fundamentals

ISBN: 978-1-78630-106-2
378 pages
March 2017, Wiley-ISTE
Modeling and Simulation of Logistics Flows 1: Theory and Fundamentals (1786301067) cover image

Description

Volume 1 presents successively an introduction followed by 10 chapters and a conclusion:
- A logistic approach
- an overview of operations research
- The basics of graph theory
- calculating optimal routes
- Dynamic programming
- planning and scheduling with PERT and MPM;
- the waves of calculations in a network;
-  spanning trees and touring;
- linear programming
- modeling of road traffic

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Table of Contents

Chapter 1: discrete computerized flow simulation
Chapter 2: Mixed Flow Simulation
Chapter 3: 3D Flux and evacuation simulation
Chapter 4: 3D Flux, conveying and storage
Foreword  xiii

About This Book xvii

Introduction  xxiii

Chapter 1. Operational Research 1

1.1. A history  1

1.2. Fields of application, principles and concepts  2

1.2.1. Identification 2

1.2.2. Modeling  3

1.2.3. Solution 5

1.2.4. Validation 6

1.2.5. Implementation  6

1.2.6. Improvement 6

1.3. Basic models  7

1.4. The future of OR  7

Chapter 2. Elements of Graph Theory  9

2.1. Graphs and representations 9

2.2. Undirected graph 10

2.2.1. Multigraph 10

2.2.2. Planar and non-planar graph  11

2.2.3. Connected and unconnected graph 11

2.2.4. Complete graph  11

2.2.5. Bipartite graph  12

2.2.6. Partial graph, subgraph, clique and stable  12

2.2.7. Degree of a vertex and a graph 13

2.2.8. Chain and cycle in a graph 13

2.2.9. Level of connectivity (or beta index) 15

2.2.10. Eulerian graph  15

2.2.11. Hamiltonian graph 16

2.2.12. Planar graph 17

2.2.13. Isthmus  18

2.2.14. Tree and forest  19

2.2.15. Arborescence 20

2.2.16. Ordered arborescence  21

2.3. Directed graph or digraph  22

2.3.1. Path and circuit in a digraph  22

2.3.2. Absence of circuit in a digraph 23

2.3.3. Adjacency matrix 24

2.3.4. Valued graph matrix 24

2.4. Graphs for logistics  25

Chapter 3. Optimal Paths 27

3.1. Basic concepts 27

3.2. Dijkstra’s algorithm  28

3.2.1. An example of calculating minimal paths  28

3.2.2. Interpreting the results of the calculations  30

3.3. Floyd–Warshall’s algorithm 30

3.3.1. Creating the starting matrices (initialization of the algorithm)  30

3.3.2. Filling the matrices for the following repetitions  31

3.3.3. An example of calculating minimal paths  32

3.3.4. Interpreting the results  34

3.4. Bellman–Ford’s algorithm  35

3.4.1. Initialization  36

3.4.2. The next repetitions with relaxation  36

3.4.3. An example of calculation  37

3.4.4. Interpreting the results  39

3.5. Bellman–Ford’s algorithm with a negative circuit  40

3.5.1. Example  40

3.6. Exercises  43

3.6.1. Exercise 1: Optimizing journey time 43

3.6.2. Exercise 2: A directed graph with negative cost side  44

3.6.3. Exercise 3: Routing data packets  45

3.6.4. Solutions to exercise 1  45

3.6.5. Solutions to exercise 2  46

3.6.6. Solutions to exercise 3  48

Chapter 4. Dynamic Programming  51

4.1. The principles of dynamic programming 51

4.2. Formulating the problem 52

4.2.1. Example 1: The pyramid of numbers 52

4.2.2. Example 2: The Fibonacci sequence  54

4.2.3. Example 3: The knapsack  56

4.3. Stochastic process 60

4.4. Markov chains 60

4.4.1. Property of Markov chains 61

4.4.2. Classes and states of a chain  62

4.4.3. Matrix and graph 63

4.4.4. Applying Markov chains  64

4.5. Exercises  66

4.5.1. Exercise 1: Levenshtein distance  66

4.5.2. Exercise 2 67

4.5.3. Exercise 3: Ehrenfest model  67

4.5.4. Solutions to exercise 1  68

4.5.5. Solutions to exercise 2  69

4.5.6. Solutions to exercise 3  70

Chapter 5. Scheduling with PERT and MPM  73

5.1. Fundamental concepts  73

5.2. Critical path method  74

5.3. Precedence diagram  74

5.4. Planning a project with PERT-CPM  77

5.4.1. A brief history 77

5.4.2. Methodology 78

5.5. Example of determining a critical path with PERT 86

5.5.1. Using the example to create a precedence table 87

5.5.2. Creating the graph  87

5.5.3. Numbering of vertices  89

5.5.4. Determining earliest dates of each of the tasks 89

5.5.5. Determining the latest dates for each of the tasks  90

5.5.6. Determining the critical paths 92

5.6. Slacks  93

5.6.1. Total slack 94

5.6.2. Free slack 94

5.6.3. Certain slack (or independent slack)  94

5.6.4. Properties 94

5.7. Example of calculating slacks  95

5.8. Determining the critical path with the help of a double-entry table  96

5.8.1. Creating a table using our example  96

5.8.2 Filling out the table  96

5.8.3. ES dates  97

5.8.4. LF dates  99

5.8.5. Critical path  100

5.9. Methodology of planning with MPM 101

5.9.1. A brief history 101

5.9.2. Formalizing the graph  102

5.9.3. Rules of construction 103

5.9.4. Earliest and latest dates 104

5.9.5. Determining the critical path  105

5.10. Example of determining a critical path with MPM 106

5.10.1. Creating the graph  106

5.10.2. Determining the earliest dates for each task  107

5.10.3. Determining the latest dates of each task  108

5.10.4. Determining the critical path(s)  109

5.10.5. Slacks 109

5.11. Probabilistic PERT/CPM/MPM  111

5.11.1. Probability of tasks 112

5.11.2. Implementation in an example  113

5.11.3. Calculating average durations and variance 114

5.11.4. Calculating the average duration of the project  114

5.11.5. Calculating the probability of finishing the project in a chosen duration  114

5.11.6. Calculating the duration of the project for a given probability  115

5.12. Gantt diagram 116

5.12.1. Creating the diagram  116

5.12.2. Example 117

5.13. PERT-MPM cost 119

5.13.1. Method  120

5.13.2. Example 121

5.14. Exercises  125

5.14.1. Exercise 1 125

5.14.2. Exercise 2 126

5.14.3. Exercise 3 126

5.14.4. Exercise 4 127

5.14.5. Solutions to exercise 1 129

5.14.6. Solutions to exercise 2 130

5.14.7. Solutions to exercise 3 132

5.14.8. Solutions to exercise 4 133

Chapter 6. Maximum Flow in a Network 137

6.1. Maximum flow 137

6.2. Ford–Fulkerson algorithm  138

6.2.1. Presentation of the algorithm  139

6.2.2. Application of an example 141

6.3. Minimum cut theorem  147

6.3.1. Example of cuts  148

6.4. Dinic algorithm  149

6.4.1. Presenting the algorithm 149

6.4.2. Application in an example  150

6.5. Exercises  154

6.5.1. Exercise 1: Drinking water supply 154

6.5.2. Exercise 2: Maximum flow according to Dinic 155

6.5.3. Solutions to exercise 1  155

6.5.4. Solutions to exercise 2  158

Chapter 7. Trees, Tours and Transport 163

7.1. The basic concepts 163

7.2. Kruskal’s algorithm  165

7.2.1. Application to an example  165

7.3. Prim’s algorithm  168

7.3.1. Application to an example  170

7.4. Sollin’s algorithm 175

7.4.1. Application to an example  176

7.5. Little’s algorithm for solving the TSP 182

7.5.1. Application to an example  184

7.6. Exercises  195

7.6.1. Exercise 1: Computer network 195

7.6.2. Exercise 2: Deliveries  196

7.6.3. Solutions to exercise 1  197

7.6.4. Solutions to exercise 2  200

Chapter 8. Linear Programming  205

8.1. Basic concepts 205

8.1.1. Formulation of a linear program  206

8.2. The graphic resolution method 206

8.2.1. Identification 207

8.2.2. Formalization 207

8.2.3. Resolution 212

8.3. Simplex method  215

8.3.1. Steps  215

8.3.2. An example to be addressed  215

8.3.3. Formalization 216

8.3.4. Change into standard form 217

8.3.5. Creation of the table 218

8.3.6. Determination of the pivot 218

8.3.7. Iterations  219

8.3.8. Interpretation 222

8.4. Duality  223

8.4.1. Dual formulation 224

8.4.2. Passage from primal to dual formalization  224

8.4.3. Determination of the pivot 226

8.4.4. Iterations  227

8.4.5. Interpretation 228

8.5. Exercises . 228

8.5.1. Exercise 1: Video and festival 228

8.5.2. Exercise 2: Simplex 228

8.5.3. Exercise 3: Primal and dual 229

8.5.4. Solutions to exercise 1  229

8.5.5. Solutions to exercise 2  232

8.5.6. Solutions to exercise 3  234

Chapter 9. Modeling Road Traffic 237

9.1. A short introduction to road traffic 237

9.2. Scale of models and networks  239

9.3. Models and types 239

9.4. Learning more information about the models 240

9.4.1. Microscopic models 240

9.4.2. Macroscopic models 245

9.4.3. The families of macroscopic models 250

9.4.4. The discretization of models  252

9.4.5. Mesoscopic models  253

9.4.6. Hybrid models 254

9.5. Urban modeling  255

9.6. Intelligent transportation systems  256

9.7. Conclusion 256

Chapter 10. Software Programs  259

10.1. Software programs for OR and logistics 259

10.2. Spreadsheets 260

10.2.1. Existing software programs  262

10.3. Project managers 266

10.3.1. The procedure for creating a project 268

10.3.2. The different software programs available on the market  268

10.4. Flow simulators 271

10.4.1. Generalist software programs 273

10.4.2. Pedestrian simulators  281

10.4.3. Traffic simulators  288

10.4.4. The creation of a simulation process 300

Appendices  303

Appendix 1: Standard Normal Distribution Table  305

Appendix 2: GeoGebra  309

Conclusion 319

Glossary  323

Bibliography  329

Index 337

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