Table of Contents

Cover

Title

Foreword

About This Book

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
1.3. Basic models
1.4. The future of OR

2 Elements of Graph Theory

2.1. Graphs and representations
2.2. Undirected graph
2.3. Directed graph or digraph
2.4. Graphs for logistics

3 Optimal Paths

3.1. Basic concepts
3.2. Dijkstra’s algorithm
3.3. Floyd–Warshall’s algorithm
3.4. Bellman–Ford’s algorithm
3.5. Bellman–Ford’s algorithm with a negative circuit
3.6. Exercises

4 Dynamic Programming

4.1. The principles of dynamic programming
4.2. Formulating the problem
4.3. Stochastic process
4.4. Markov chains
4.5. Exercises

5 Scheduling with PERT and MPM

5.1. Fundamental concepts
5.2. Critical path method
5.3. Precedence diagram
5.4. Planning a project with PERT-CPM
5.5. Example of determining a critical path with PERT
5.6. Slacks
5.7. Example of calculating slacks
5.8. Determining the critical path with the help of a double-entry table
5.9. Methodology of planning with MPM
5.10. Example of determining a critical path with MPM
5.11. Probabilistic PERT/CPM/MPM
5.12. Gantt diagram
5.13. PERT-MPM cost
5.14. Exercises

6 Maximum Flow in a Network

6.1. Maximum flow
6.2. Ford–Fulkerson algorithm
6.3. Minimum cut theorem
6.4. Dinic3 algorithm
6.5. Exercises

7 Trees, Tours and Transport

7.1. The basic concepts
7.2. Kruskal’s algorithm
7.3. Prim’s algorithm
7.4. Sollin’s algorithm
7.5. Little’s algorithm for solving the TSP
7.6. Exercises

8 Linear Programming

8.1. Basic concepts
8.2. The graphic resolution method
8.3. Simplex method
8.4. Duality
8.5. Exercises

9 Modeling Road Traffic

9.1. A short introduction to road traffic
9.2. Scale of models and networks
9.3. Models and types
9.4. Learning more information about the models
9.5. Urban modeling
9.6. Intelligent transportation systems
9.7. Conclusion

10 Software Programs

10.1. Software programs for OR and logistics
10.2. Spreadsheets
10.3. Project managers
10.4. Flow simulators

Appendices

Appendix 1: Standard Normal Distribution Table
1. A1.1. Use
Appendix 2: GeoGebra
1. A2.1. Presentation of the software
2. A2.2. Using GeoGebra

Conclusion

Glossary

Bibliography

Index

End User License Agreement

List of Tables

3 Optimal Paths

Table 3.1. Repetitions of the algorithm
Table 3.2. Initialization
Table 3.3. Repetition no. 1
Table 3.4. Repetition no. 2
Table 3.5. Repetition no. 3
Table 3.6. Repetition no. 4
Table 3.7. Repetition no. 5
Table 3.8. Initialization of the vertices
Table 3.9. Initialization of the vertices in the example
Table 3.10. Table of relaxation for repetition no. 1
Table 3.11. Table of the vertices for repetition no. 1
Table 3.12. Table of relaxation for repetition no. 2
Table 3.13. Table of the vertices for repetition no. 2
Table 3.14. Table of relaxation for repetition no. 3
Table 3.15. Table of the vertices for repetition no. 3
Table 3.16. Table of vertices at initialization
Table 3.17. Table of relaxation for repetition no. 1
Table 3.18. Table of the vertices for repetition no. 1
Table 3.19. Table of relaxation for repetition no. 2
Table 3.20. Table of the vertices for repetition no. 2
Table 3.21. Table of relaxation for repetition no. 3
Table 3.22. Table of vertices for repetition no. 3
Table 3.23. Table of relaxation for repetition no. 4
Table 3.24. Table of vertices for repetition no. 4
Table 3.25. The repetitions of the algorithm
Table 3.26. Initialization
Table 3.27. Repetition no. 1
Table 3.28. Repetition no. 2
Table 3.29. Repetition no. 3
Table 3.30. Repetition no. 4
Table 3.31. Initialization
Table 3.32. Table of relaxation for repetition no. 1
Table 3.33. Table of the vertices for repetition no. 1
Table 3.34. Table of relaxation for repetition no. 2
Table 3.35. Table of the vertices for repetition no. 2

4 Dynamic Programming

Table 4.1. Objects, values and weight
Table 4.2. The table obtained from phase 1 of the algorithm
Table 4.3. Phase 2b
Table 4.4. Phase 2b, objects and the knapsack
Table 4.5. Monthly figures for the hire company

5 Scheduling with PERT and MPM

Table 5.1. Predecessors
Table 5.2. Predecessors–successors
Table 5.3. Tasks and predecessors for a sound system
Table 5.4. Earliest starts and latest finishes
Table 5.5. Calculating slacks
Table 5.6. Double-entry matrix, empty, for our example
Table 5.7. Double-entry matrix, filled with the duration of tasks
Table 5.8. Double-entry matrix. The earliest dates are present
Table 5.9. Double-entry matrix. The earliest and latest dates are present
Table 5.10. The double-entry matrix and determining the critical path
Table 5.11. Example of section 5.5.1 with new durations
Table 5.12. Average durations and variances
Table 5.13. All of the data necessary for a Gantt diagram
Table 5.14. Durations, costs and accelerated costs
Table 5.15. Marginal costs
Table 5.16. Summary of costs
Table 5.17. Table of predecessors
Table 5.18. Durations and predecessors
Table 5.19. The precedences for exercise 4
Table 5.20. Costs and durations for exercise 4
Table 5.21. Total slacks and free slacks
Table 5.22. Precedence table
Table 5.23. Double-entry matrix with the earliest and latest dates
Table 5.24. Total slacks and free slacks
Table 5.25. Calculating average durations and variances for critical tasks
Table 5.26. Calculation of normal cost
Table 5.27. Calculation of accelerated and marginal costs
Table 5.28. Calculation of optimized cost

7 Trees, Tours and Transport

Table 7.1. The symmetric matrix
Table 7.2. Search for the minimums in each row
Table 7.3. Reduction of the matrix according to the minimums in each row and search for the minimums in each column
Table 7.4. Reduction of the matrix according to the minimums in each column
Table 7.5. Calculation of regret
Table 7.6. The new matrix
Table 7.7. Removal of loop BN (subtours)
Table 7.8. Search for the minimums in each row
Table 7.9. Reduction of the matrix according to the minimums in each row and search for the minimums in each column
Table 7.10. Calculation of regret
Table 7.11. New matrix with removal of subtour BP and reduction
Table 7.12. Calculation of regret
Table 7.13. New matrix with removal of the subtours LM and reduction
Table 7.14. Calculation of regret
Table 7.15. New matrix and reduction
Table 7.16. Calculation of regret
Table 7.17. Distances between the shops given in meters
Table 7.18. Reduction no. 1
Table 7.19. Calculation of regrets no. 1
Table 7.20. Reduction no. 2
Table 7.21. Calculation of regrets no. 2
Table 7.22. Reduction no. 3
Table 7.23. Calculation of regrets no. 3
Table 7.24. Reduction no. 4 of the matrix for calculating branches B3B1 excluded and B3B1 included
Table 7.25. Calculation of regrets no. 4
Table 7.26. Reduction no. 5
Table 7.27. Calculation of regrets no. 5
Table 7.28. The final matrix: we can add B5B4 and B6B2 without increasing cost

8 Linear Programming

Table 8.1. All of the data in the example
Table 8.2. All of the data of the example being addressed
Table 8.3. The simplex table
Table 8.4. Determination of the pivot
Table 8.5. Entering and leaving base
Table 8.6. Calculation of row e1
Table 8.7. Calculation of row e2
Table 8.8. Calculation of row e3
Table 8.9. Calculation of row z
Table 8.10. The new table at iteration no. 1
Table 8.11. Determination of the new pivot
Table 8.12. The new table at iteration no. 2
Table 8.13. From the primal to the dual
Table 8.14. Cost coefficients of the primal
Table 8.15. Dual simplex table
Table 8.16. Determination of the pivot
Table 8.17. The simplex at iteration no. 1
Table 8.18. The simplex at iteration no. 2
Table 8.19. The solution using the simplex
Table 8.20. The succession of iterations for calculating the simplex of the PL primal
Table 8.21. The succession of iterations for calculating the simplex of the PL dual

9 Modeling Road Traffic

Table 9.1. Transportation models and goals to be met (source: [COS 13])

Appendix 1: Standard Normal Distribution Table

Table A1.1. Standard normal distribution

List of Illustrations

Introduction

Figure I.1. Antoine de Jomini (source: Wikipedia)

2 Elements of Graph Theory

Figure 2.1. A graph
Figure 2.2. A multigraph – the vertex b has a loop and a and e are connected by two edges
Figure 2.3. A planar graph (left) and a non-planar graph (right)
Figure 2.4. A connected graph (left) and an unconnected graph with two connected components {a, e} and {b, c, d, f} (right)
Figure 2.5. A complete graph
Figure 2.6. A bipartite graph
Figure 2.7. Graph G and its subgraph G′
Figure 2.8. A 4-degree graph (on a, c and f)
Figure 2.9. A graph with eight vertices and 12 edges
Figure 2.10. A Eulerian graph
Figure 2.11. A planar graph
Figure 2.12. A clique K₅ and a bipartite graph K_3,3
Figure 2.13. A graph where the edge (G, H) is an isthmus
Figure 2.14. A tree (left) and a forest (right)
Figure 2.15. A graph and one of its roots, G
Figure 2.16. An arborescence
Figure 2.17. An arborescence divided into levels and the rows of its vertices
Figure 2.18. The ordered arborescence of the algebraic expression (3x + 2)/4x(x – 4)
Figure 2.19. An arborescence and its two searches
Figure 2.20. Un digraph
Figure 2.21. A digraph without circuit
Figure 2.22. A digraph without circuit with its rows and levels
Figure 2.23. An example of a graph and its adjacency matrix
Figure 2.24. A valued digraph

3 Optimal Paths

Figure 3.1. An example of a road network
Figure 3.2. The road network used for the example
Figure 3.3. The graph of our example with five towns A–F
Figure 3.4. An example of a graph with a negative circuit
Figure 3.5. A graph representing a metro network
Figure 3.6. A graph with a negative cost side
Figure 3.7. The network connecting the two servers

4 Dynamic Programming

Figure 4.1. The methods: dynamic programming (left) and divide and conquer (right)
Figure 4.2. The initial pyramid of numbers to cross
Figure 4.3. The tree of possibilities with the possible calculations (above) and their results (below). The highest totals are indicated in bold. For a color version of this figure, see www.iste.co.uk/reveillac/modeling1.zip
Figure 4.4. The pyramid obtained by retaining only the maximum totals in each line. The numbers in bold are the maximal values in each line. For a color version of this figure, see www.iste.co.uk/reveillac/modeling1.zip
Figure 4.5. Multiplicity of calculations when carrying out the algorithm
Figure 4.6. The transition graph G
Figure 4.7. The digraph corresponding to our example
Figure 4.8. The maze for exercise 2
Figure 4.9. The graph for exercise 2: question 1
Figure 4.10. The graph of the Erhenfest model

5 Scheduling with PERT and MPM

Figure 5.1. A matrix
Figure 5.2. A codified task or activity A, of duration 5, framed by vertices 1 and 2
Figure 5.3. Different assembly of possible tasks in a PERT graph. At the top A is previous to B and B comes after A
Figure 5.4. Two examples of complex dependencies of several tasks
Figure 5.5. The different logistical sequences of overlapping
Figure 5.6. A fictive task X within a graph
Figure 5.7. Rules to respect when constructing a PERT graph
Figure 5.8. Several examples of possible numbering. In the top graph, task E, with a duration of 7 min, can be marked by the pair (2, 6)
Figure 5.9. The different types of calculations from the earliest date in a PERT graph
Figure 5.10. The different types of calculations of the latest date in a PERT graph
Figure 5.11. The graph of our example corresponding to the precedence table. One may note the presence of the fictive task X with duration of 0 min
Figure 5.12. Another possibility of tracing fictive task X
Figure 5.13. The graph with its vertices (steps)
Figure 5.14. PERT graph with the earliest dates calculated and displayed above each vertex
Figure 5.15. PERT graph with the latest dates calculated and displayed below each peak
Figure 5.16. The critical path of our example
Figure 5.17. Earliest start, latest start, earliest finish and latest finish available for a task on the PERT graph
Figure 5.18. Some possible representations of a task and an associated constraint (arch) in an MPM graph
Figure 5.19. Different assembly of possible tasks in an MPM graph
Figure 5.20. The two types of calculation of an earliest date on an MPM graph
Figure 5.21. Two types of calculation of a latest date on an MPM graph
Figure 5.22. MPM graph with its tasks and their durations placed at each step
Figure 5.23. MPM graph of our example with the earliest dates calculated
Figure 5.24. MPM graph for our example with the earliest dates and latest dates calculated
Figure 5.25. Critical tasks (A, D, F, G and I) in the MPM graph of our example
Figure 5.26. Determining the earliest start of the following task on an MPM graph. We can see the specific case of task B that goes toward C and F
Figure 5.27. Determining the latest finishing date on an MPM graph. We can see the specific case of task B that goes toward C, D and E
Figure 5.28. The system of axes of the Gantt diagram for our example
Figure 5.29. Gantt diagram and its tasks
Figure 5.30. The diagram with its margins
Figure 5.31. Arrows showing successive constraints.
Figure 5.32. The project after reducing the duration of task A to 58 min
Figure 5.33. The project after reducing the duration of task G to 20 min
Figure 5.34. The project after reducing the duration of task F to 12 min
Figure 5.35. The project after reducing the duration of task D to 18 min
Figure 5.36. PERT graph
Figure 5.37. PERT diagram
Figure 5.38. The Gantt diagram with its legend, all of the tasks and slacks, as well as the anteriority constraints
Figure 5.39. MPM diagram with its critical tasks (in yellow)
Figure 5.40. PERT graph

6 Maximum Flow in a Network

Figure 6.1. The principle of marking
Figure 6.2. The graph of our example
Figure 6.3. Initialization
Figure 6.4. The graph after marking no. 1 (the dotted lines are the augmenting chain)
Figure 6.5. The graph once the edges of the augmenting chain sADt have been calculated
Figure 6.6. The graph after marking no. 2 (the dotted lines are the augmenting chain)
Figure 6.7. The graph once the edges of the augmenting chain sACt have been calculated
Figure 6.8. The graph after marking no. 3 (the dotted lines are the augmenting chain)
Figure 6.9. The graph once the edges of the augmenting chain sBDt have been calculated
Figure 6.10. The graph after marking no. 4 (the dotted lines are the augmenting chain)
Figure 6.11. The graph once the edges of the augmenting chain sBCt have been calculated
Figure 6.12. The graph after marking no. 5 (the dotted lines are the augmenting chain)
Figure 6.13. The graph once the edges of the augmenting chain sBDACt have been calculated
Figure 6.14. Four cuts defined in the previous example
Figure 6.15. A network for our algorithm
Figure 6.16. Initialization step
Figure 6.17. The graph G_L with its four levels
Figure 6.18. Graphs G and G_f at the first passage in loops 1 and 2
Figure 6.19. Graphs G and G_f at the first passage in loop 1 and at the second passage in loop 2
Figure 6.20. Graphs G and Gf at the first passage in loop 1 and at the third passage in loop 2
Figure 6.21. The level graph G_L at the second passage in loop 1
Figure 6.22. Graphs G and G_f at the second passage in loop 1 and at the first passage in loop 2
Figure 6.23. The level graph G_L. We can see that the sink can no longer be reached
Figure 6.24. The water distribution and supply network for the municipality of Monchâteau
Figure 6.25. The network for exercise 2
Figure 6.26. The completed network
Figure 6.27. The first three steps of the solution
Figure 6.28. The last four steps of the solution
Figure 6.29. The final step of the Ford–Fulkerson algorithm for question 5.4
Figure 6.30. The level graph G_L of exercise 2 once the vertices have been reordered
Figure 6.31. Graphs G and the associated residual graphs G_f
Figure 6.32. Graph G_L
Figure 6.33. Graphs G and the associated residual graphs G_f
Figure 6.34. Graph G_L
Figure 6.35. Graphs G and the associated residual graphs G_f
Figure 6.36. The final graph G_L: passage is no longer possible between level 1 and 4

7 Trees, Tours and Transport

Figure 7.1. The graph of our example
Figure 7.2. The graph of step 6. The arcs with dotted lines have already been chosen
Figure 7.3. The graph of step 8
Figure 7.4. Step 1
Figure 7.5. Step 2
Figure 7.6. Step 3
Figure 7.7. Step 4
Figure 7.8. Step 5
Figure 7.9. Step 6
Figure 7.10. Step 7
Figure 7.11. Initialization
Figure 7.12. Step 1
Figure 7.13. Step 2
Figure 7.14. Step 3
Figure 7.15. Step 4
Figure 7.16. Step 5
Figure 7.17. Step 6
Figure 7.18. Step 7
Figure 7.19. Step 8
Figure 7.20. The map used in our example
Figure 7.21. The parent vertex (node) of our search tree
Figure 7.22. Creation of branches and nodes 2 and 3 from parent node 1
Figure 7.23. Child node 3 of the included branch with its cost
Figure 7.24. Child nodes 4 and 5 with their costs
Figure 7.25. Child nodes 6 and 7 with their costs
Figure 7.26. Child nodes 8 and 9 with their costs
Figure 7.27. Child nodes 10 and 11 with their costs
Figure 7.28. The solution to our example: the shortest tour for visiting all of the cities
Figure 7.29. The possible layout of the network with the overall costs of the work (burying and positioning of the fiber, linking, materials, labor, etc.), related, for each of the connections, in thousands of dollars
Figure 7.30. The graph obtained after reorganization
Figure 7.31. The minimum spanning tree providing a solution to exercise 1
Figure 7.32. The global search tree: solution to our exercise
Figure 7.33. Tour B2B5B4B1B3B6B2

8 Linear Programming

Figure 8.1. Plot of the first half-plane defined by the constraint 3q₁ + 6q₂ ≤ 24. The straight line passes through the pairs of coordinates (0, 4) and (2, 3)
Figure 8.2. Plot of the second half-plane defined by the constraint 3q1 + 3q2 ≤ 15. The straight line passes through the pairs of coordinates (1, 4) and (3, 2)
Figure 8.3. Plot of the third half-plane defined by the constraint 3q1 ≤ 12. The straight line passes through q1 = 4 whatever q2 is
Figure 8.4. Plot of the fourth half-plane defined by the constraint q1 ≥ 0. The straight line passes through q1 = 0 whatever q2 is
Figure 8.5. Plot of the fifth half-plane defined by the constraint q2 ≥ 0. The straight line passes through q2 = 0 whatever q1 is
Figure 8.6. The area of the solutions
Figure 8.7. Straight line 3q1 + 2q2 = 0. The straight line passes through the pairs of coordinates (–2, 2) and (2, –3)
Figure 8.8. The solution showing the optimum obtained for b = 28. The straight line passes through the pairs of coordinates (2, 4) and (4, 1)
Figure 8.9. Symmetry also exists between the two tables of the simplex (primal on the lower left, dual on the upper right)
Figure 8.10. The constraints and the cost function which define all of the solutions represented by the light area of the plot. For a color version of this figure, see www.iste.co.uk/reveillac/modeling1.zip
Figure 8.11. The pairs to be kept as solutions to our exercise. For a color version of this figure, see www.iste.co.uk/reveillac/modeling1.zip
Figure 8.12. The graphic solution. For a color version of this figure, see www.iste.co.uk/reveillac/modeling1.zip

9 Modeling Road Traffic

Figure 9.1. Total change in the sale of cars between 2010 and 2014: 43.3% for China, 33% for Russia, 6.4% for India and 5.6% for Brazil (source: INOVEV – 2015). For a color version of this figure, see www.iste.co.uk/reveillac/modeling1.zip
Figure 9.2. Example of a diagram modeling the trajectory of two vehicles A and B
Figure 9.3. The four possibilities for characterizing of the spatial and temporal parameters of the two vehicles A and B that are following each other
Figure 9.4. Formalization of the variables on a single axis. (xn(t): position of the vehicle n in time t; Ln – 2: length of vehicle n – 2; Δv: interdistance between vehicles n and n – 1
Figure 9.5. A lane change by vehicle n made in order to pass leader n – 1
Figure 9.6. A necessary lane change made by taking a ramp
Figure 9.7. A merger within an intersection with a stop sign
Figure 9.8. An example of a fundamental diagram
Figure 9.9. Diagram showing the concept of flow
Figure 9.10. Diagram showing the concept of concentration
Figure 9.11. Diagram showing the relationships between flow, concentration and speed
Figure 9.12. An example of the shape of a curve for a fundamental diagram with its two zones: fluid traffic and congested traffic, with C_critical: critical concentration (it separates fluid traffic fluid from congested traffic); Qmax: maximum of the section eing studied; Sl: free speed; Sc: critical speed
Figure 9.13. A platoon on a major road. In this case, the truck, leader of the platoon, is the origin of its creation
Figure 9.14. An example of discretization of the network
Figure 9.15. Hybrid modeling with macro–micro coupling

10 Software Programs

Figure 10.1. A calculation table in VisiCalc
Figure 10.2. The Microsoft MULTIPLAN spreadsheet
Figure 10.3. Microsoft Excel 2013 and its macro instruction development window with Visual Basic Application (VBA)
Figure 10.4. LibreCalc spreadsheet from the LibreOffice suite
Figure 10.5. iWork Numbers 3.0, Apple's spreadsheet in OS X
Figure 10.6. Andropen Office spreadsheet on an Android tablet
Figure 10.7. Calc XLS on an iPad with iOS
Figure 10.8. Google Sheets from Mozilla Firefox on OS X
Figure 10.9. One of the first versions of Microsoft Project
Figure 10.10. Microsoft Project 2013
Figure 10.11. Sciforma IT Project, a project management software
Figure 10.12. The project manager Gantt Project version 2.7.2 for OS X
Figure 10.13. GanttMan on a tablet with Android
Figure 10.14. An example of flow simulation. We can see in the background the window that models the organization chart of the process and, in the foreground, the visualization window of the simulation in 3D
Figure 10.15. A simple model made with ExtendSim CP
Figure 10.16. A portion of a simulated model designed with ExtendSim OR
Figure 10.17. Screen capture made during a 3D simulation of a warehouse model
Figure 10.18. Simulation of an assembly line with FlexSim
Figure 10.19. Dashboard and graphics in FlexSim
Figure 10.20. A simulated model of a consulting room developed with FlexSim HC
Figure 10.21. Some examples of objects available within the HC version
Figure 10.22. An example of a tree diagram for patient monitoring
Figure 10.23. Dashboard for patient monitoring
Figure 10.24. Importation of a building in PathFinder
Figure 10.25. Triangulated network of a concert hall
Figure 10.26. Lines and access gates
Figure 10.27. The movement of agents. We can see the tracks linked to their respective movement
Figure 10.28. Pedestrian flow on different levels with the use of different staircases or passageways
Figure 10.29. Arborescence of agent profiles
Figure 10.30. 3D rendering during the simulation process
Figure 10.31. Graphic statistics and simulation modes crossing flow and time
Figure 10.32. Graph showing the transition rate for a chosen group of doors
Figure 10.33. A simulation where the contours of the agents have been implemented
Figure 10.34. Visualization of traffic in 2D with TransModeler
Figure 10.35. Simulation of traffic in 3D with TransModeler
Figure 10.36. Parameter table of management of a complex downtown intersection complex
Figure 10.37. Road and rail network
Figure 10.38. PTV Vissim in action with the visualization of an intersection at two levels of zoom (global on the left, detailed on the right)
Figure 10.39. Intersection in 2D mixing rail and road transportation
Figure 10.40. Freeway, signaling and multiple lanes
Figure 10.41. An intersection, with its different traffic lanes, simulated in Aimsun
Figure 10.42. Traffic simulation in 2D
Figure 10.43. The sequence and design environment of a model within Aimsun (source: TSS)
Figure 10.44. 3D representation in Aimsun
Figure 10.45. Results presented in Microsoft Word and Excel
Figure 10.46. Four screen captures from AnyLogic: system dynamics (top left), simulation of pedestrian traffic (top right), state diagram (lower left) and action diagrams (lower right) – (source: Anylogic)
Figure 10.47. AnyLogic traffic management and its “Road Traffic” library
Figure 10.48. Integration of Anylogic with other software programs (source: AnyLogic)

Appendix 2: GeoGebra

Figure A2.1. GeoGebra 5 when it is opened
Figure A2.2. The line of inequation 3x + 6y ≤ 24 in GeoGebra
Figure A2.3. Functions of the icons on the upper toolbar
Figure A2.4. The PREFERENCES window with its STYLE and BASIC tabs
Figure A2.5. Global modification of the properties of five inequations
Figure A2.6. The GRAPHICS toolbar opened up
Figure A2.7. The GRID tab of the PREFERENCES – GRAPHICS subset
Figure A2.8. GeoGebra with the group of curves linked to our five inequations (a–e). Their names and their definitions are displayed as well as the grid. The area in white (reverse filling) represents the solution space
Figure A2.9. The line 6x + 4y = 0 (3x + 2y = 0 after simplification by GeoGebra) charted in black within the frame
Figure A2.10. The line representing the solution of the problem: 6x + 4y = 28 (3x + 2y = 14 after simplification)

First published 2017 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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The rights of Jean-Michel Réveillac to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2016957972

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ISBN 978-1-78630-106-2

Foreword

In a society in which the fundamental role of transport only fully appears when it does not work or works badly, logistics does not tend to be seen negatively. This is not due to the fact that the average citizen possesses knowledge of the processes behind it, the requirements and the missions of such a phenomenon, but because very often logistics seem almost foreign, merely associated with transportation and the mobility of goods. A social representation of logistics would not only require one to envisage the geographical division of work but also consider the infinite consequences that come from a mass consumption system, an absolute social phenomenon described by E. Durkheim¹.

The term logistics covers three crucial dimensions regarding the flow of goods, which every business that produces such commodities will encounter: supply, flow within the business – one thus speaks of production management – and distribution. Every movement of people or goods, whether the destination be near or far, will demand space, time and energy. Logistics, perceived as a general discipline in the realm of flow management, is somewhat strange in that its effectiveness is inversely proportional to its visibility. The better the performance, the less visible it becomes and many economic powers, both local and global, will only realize their main concerns when, for many reasons, they are unable to find answers to the complex problems that they set out to solve.

“Thoughts arise from action in order to return to action”², H. Wallon once affirmed. If there is one world in which this quotation proves productive, it is in that of logistics. Logistics is to transportation and mobility what thoughts are to action. As demonstrated in the few historical pages of the work that you are currently reading, though for centuries soldiers have created flows that enable their armed forces to move systematically, it was not until the second half of the last century, during which the concept of mobility was made commonplace in Western societies along with the emergence of global labor division and a globalized society of mass consumption, that the rationalized organization of flow became a crucial discipline for the productivity of firms. Assimilated in chart of accounts as an expenditure account, despite everything logistics is still very often associated with loss for businesses that produce goods. It is about time that it is seen as an asset.

Logistics has established itself using empirical knowledge that is modeled so as to offer us tools that rationalize modes of mobility, and each concept or logistical model is immediately confronted with reality in terms of effectiveness: modify the packaging of your product and the characteristics of transportation are immediately modified. Change the providers and you change the chain of supply and the storage techniques. Create a new product and it is your chain of production that must then be remodeled.

We could, for example, be faced with the task of delivering four parcels in two different locations. Easy! But we could also be faced with the task of organizing the rounds of 140 drivers (some employed by our business, others temporarily contracted and even more subcontracted), each with a vehicle that contains over 10 tons of goods spread throughout more than 250 parcels to be delivered to 50 different locations. Some of these delivery locations can belong to the same client and be several dozens or hundreds of kilometers away. Here, we are faced with a jigsaw puzzle that consists of over a million possibilities. Rational types would opt to travel in a straight line, losing time, space and money. It is better to maintain to a Pascalien vision of modelized management of uncertainties. Yet the creation of a systemic and complex vision of flow reality and its crucial concrete effectiveness demands one to abandon one’s common sense.

Until the oil crisis of the 1970s, needs for the future always exceeded those of the past. Consequently, there was little concern about vehicle fill rate, the pollution caused or the global cost of stocks as long as the “trip” was profitable.

At the start of the 21st Century, conditions changed. In the international framework of sustainable mobility, for reasons regarding productivity, traceability, quality, etc., it is no longer possible to ignore the optimization of flux or to misunderstand logistics. The knowledge acquired by logistics coordinators must be shared, spread and popularized, such that mobility is perceived as one of the fundamental concepts in sustainable development and an inevitable dimension of profitability of productive actions. A product can only be regarded as complete insofar as it is available to anyone who needs it: logistics, which enables this access, is an integral and inescapable part of industry.

Every exchange of goods requires information to be transferred between those concerned. Today, manufacturers must find the best balance between geo-space, concerning land, and cyberspace, concerning the virtual land of exchanging data.

Logistics are everywhere, all the time. Of course, all is not logistic, but logistics can be perceived in everything. Yet today, knowledge of logistics is only shared between specialists. The aim of this book is to make sense of the issue to explain modelizations coming from knowledge accumulated by logistics coordinators in order to find realistic applications. This book, dotted with numerous graphs and images, is not only a collection of techniques that help produce decisions. The intentión is to spread this knowledge onto a public that is much greater in number than the experts. My friend J.-M. Reveillac has purposefully limited vast mathematical demonstrations in order to make the modelizations of flux management understandable while adding value to operational research.

Undertaking logistics involves finding the best balance between all the coercive systems, which circulate around mobility in order to transform it into something that is accessible. And this must no longer be made up, as in business it is humans themselves who will ultimately decide the actions of other humans.

Pascal MAUNY
Head of IUT at Chalon sur Saône
University of Bourgogne

Modeling and Simulation of Logistics Flows 1

Theory and Fundamentals

Foreword