Optimization of Logistics

On the other hand, this book constitutes a valuable guide and convenient introduction to the fied of operations research applications for professionals, which deal with real production and logistic system design and management. It can be also recommended as a textbook for students of production management. (Zentralblatt Math, 1 May 2013)

Dr Alice Yalaoui is associate professor at the University of Technology of Troyes, France. Dr Hicham Chehade is an assistant professor at the University of Technology of Troyes (UTT), France. Professor Farouk Yalaou, is full professor at the University of Technology of Troyes, France (UTT), France. Professor Lionel Amodeo, is full professor at the University of Technology of Troyes, France (UTT), France.

Introduction xiii Chapter 1. Modeling and Performance Evaluation 1 1.1. Introduction 1 1.2. Markovian processes 2 1.2.1. Overview of stochastic processes 2 1.2.2. Markov processes 3 1.2.2.1. Basics 3 1.2.2.2. ChapmanKolmogorov equations 4 1.2.2.3. Steady-state probabilities 5 1.2.2.4. Graph associated with a Markov process 6 1.2.2.5. Application to production systems 6 1.2.3. Markov chains 8 1.2.3.1. Basics 8 1.2.3.2. State probability vectors 9 1.2.3.3. Fundamental equation of a Markov chain 9 1.2.3.4. Graph associated with a Markov chain 10 1.2.3.5. Steady states of ergodic Markov chains 11 1.2.3.6. Application to production systems 12 1.3. Petri nets 14 1.3.1. Introduction to Petri nets 14 1.3.1.1. Basic definitions 14 1.3.1.2. Dynamics of Petri nets 15 1.3.1.3. Specific structures 16 1.3.1.4. Tools for Petri net analysis 18 1.3.1.5. Properties of Petri nets 19 1.3.2. Non-autonomous Petri nets 20 1.3.3. Timed Petri nets 20 vi Optimization of Logistics 1.3.4. Continuous Petri nets 23 1.3.4.1. Fundamental equation and performance analysis 24 1.3.4.2. Example 25 1.3.5. Colored Petri nets 27 1.3.6. Stochastic Petri nets 28 1.3.6.1. Firing time 29 1.3.6.2. Firing selection policy 29 1.3.6.3. Service policy 30 1.3.6.4. Memory policy 30 1.3.6.5. Petri net analysis 30 1.3.6.6. Marking graph 31 1.3.6.7. Generator of Markovian processes 31 1.3.6.8. Fundamental equation 32 1.3.6.9. Steady-state probabilities 32 1.3.6.10. Performance indices (steady state) 35 1.4. Discrete-event simulation 36 1.4.1. The role of simulation in logistics systems analysis 36 1.4.2. Components and dynamic evolution of systems 37 1.4.3. Representing chance and the Monte Carlo method 38 1.4.3.1. Uniform distribution U [0, 1] 38 1.4.3.2. The Monte Carlo method 39 1.4.4. Simulating probability distributions 41 1.4.4.1. Simulating random events 41 1.4.4.2. Simulating discrete random variables 44 1.4.4.3. Simulating continuous random variables 47 1.4.5. Discrete-event systems 52 1.4.5.1. Key aspects of simulation 52 1.5. Decomposition method 57 1.5.1. Presentation 57 1.5.2. Details of the method 58 Chapter 2. Optimization 61 2.1. Introduction 61 2.2. Polynomial problems and NP-hard problems 62 2.2.1. The complexity of an algorithm 62 2.2.2. Example of calculating the complexity of an algorithm 63 2.2.3. Some definitions 64 2.2.3.1. Polynomial-time algorithms 64 2.2.3.2. Pseudo-polynomial-time algorithms 64 2.2.3.3. Exponential-time algorithms 64 2.2.4. Complexity of a problem 64 2.2.4.1. Polynomial-time problems 64 2.2.4.2. NP-hard problems 64 2.3. Exact methods 64 2.3.1. Mathematical programming 64 2.3.2. Dynamic programming 65 2.3.3. Branch and bound algorithm 65 2.4. Approximate methods 66 2.4.1. Genetic algorithms 67 2.4.1.1. General principles 67 2.4.1.2. Encoding the solutions 67 2.4.1.3. Crossover operators 68 2.4.1.4. Mutation operators 70 2.4.1.5. Constructing the population in the next generation 70 2.4.1.6. Stopping condition 70 2.4.2. Ant colonies 70 2.4.2.1. General principle 70 2.4.2.2. Management of pheromones: example of the traveling salesman problem 71 2.4.3. Tabu search 72 2.4.3.1. Initial solution 73 2.4.3.2. Representing the solution 73 2.4.3.3. Creating the neighborhood 74 2.4.3.4. The tabu list 75 2.4.3.5. An illustrative example 76 2.4.4. Particle swarm algorithm 76 2.4.4.1. Description 76 2.4.4.2. An illustrative example 77 2.5. Multi-objective optimization 79 2.5.1. Definition 79 2.5.2. Resolution methods 80 2.5.3. Comparison criteria 81 2.5.3.1. The Riise distance 81 2.5.3.2. The Zitzler measure 82 2.5.4. Multi-objective optimization methods 82 2.5.4.1. Exact methods 82 2.5.4.2. Approximate methods 84 2.6. Simulation-based optimization 89 2.6.1. Dedicated tools 90 2.6.2. Specific methods 90 Chapter 3. Design and Layout 93