Modeling and Simulation of Logistics Flows : Theory and Fundamentals

Cover -- Title Page -- Copyright -- Contents -- Foreword -- About This Book -- Intended public -- Organization and contents of the book -- Conventions -- Vocabulary and definition -- Acknowledgments -- Introduction -- I.1. What is logistics? -- I.2. History -- I.3. New tools and new technologies -- 1. Operational Research -- 1.1. A history -- 1.2. Fields of application, principles and concepts -- 1.2.1. Identification -- 1.2.2. Modeling -- 1.2.3. Solution -- 1.2.4. Validation -- 1.2.5. Implementation -- 1.2.6. Improvement -- 1.3. Basic models -- 1.4. The future of OR -- 2. Elements of Graph Theory -- 2.1. Graphs and representations -- 2.2. Undirected graph -- 2.2.1. Multigraph -- 2.2.2. Planar and non-planar graph -- 2.2.3. Connected and unconnected graph -- 2.2.4. Complete graph -- 2.2.5. Bipartite graph -- 2.2.6. Partial graph, subgraph, clique and stable -- 2.2.7. Degree of a vertex and a graph -- 2.2.8. Chain and cycle in a graph -- 2.2.9. Level of connectivity (or beta index) -- 2.2.10. Eulerian graph -- 2.2.11. Hamiltonian graph -- 2.2.12. Planar graph -- 2.2.13. Isthmus -- 2.2.14. Tree and forest -- 2.2.15. Arborescence -- 2.2.16. Ordered arborescence -- 2.3. Directed graph or digraph -- 2.3.1. Path and circuit in a digraph -- 2.3.2. Absence of circuit in a digraph -- 2.3.3. Adjacency matrix -- 2.3.4. Valued graph matrix -- 2.4. Graphs for logistics -- 3. Optimal Paths -- 3.1. Basic concepts -- 3.2. Dijkstra's algorithm -- 3.2.1. An example of calculating minimal paths -- 3.2.2. Interpreting the results of the calculations -- 3.3. Floyd-Warshall's algorithm -- 3.3.1. Creating the starting matrices (initialization of the algorithm) -- 3.3.2. Filling the matrices for the following repetitions -- 3.3.3. An example of calculating minimal paths -- 3.3.4. Interpreting the results -- 3.4. Bellman-Ford's algorithm -- 3.4.1. Initialization.