This book aims to help engineers, Masters students and young researchers to understand and gain a general knowledge of logistic systems optimization problems and techniques, such as system design, layout, stock management, quality management, lot-sizing or scheduling.

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. Chapman–Kolmogorov 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 3.1. Introduction 93 3.2. The different types of production system 94 3.3. Equipment selection 97 viii Optimization of Logistics 3.3.1. General overview 97 3.3.2. Equipment selection with considerations of reliability 99 3.3.2.1. Introduction to reliability optimization 99 3.3.2.2. Design of a parallel-series system 100 3.4. Line balancing 110 3.4.1. The classification of line balancing problems 111 3.4.1.1. The simple assembly line balancing model (SALB) 111 3.4.1.2. The general assembly line balancing model (GALB) 112 3.4.2. Solution methods 112 3.4.2.1. Exact methods 112 3.4.2.2. Approximate methods 113 3.4.3. Literature review 113 3.4.4. Example 113 3.5. The problem of buffer sizing 114 3.5.1. General overview 116 3.5.2. Example of a multi-objective buffer sizing problem 116 3.5.3. Example of the use of genetic algorithms 117 3.5.3.1. Representation of the solutions 117 3.5.3.2. Calculation of the objective function 118 3.5.3.3. Selection of solutions for the archive 119 3.5.3.4. New population and stopping criterion 119 3.5.4. Example of the use of ant colony algorithms 119 3.5.4.1. Encoding 120 3.5.4.2. Construction of the ant trails 121 3.5.4.3. Calculation of the visibility 121 3.5.4.4. Global and local updates of the pheromones 122 3.5.5. Example of the use of simulation-based optimization 123 3.5.5.1. Simulation model 125 3.5.5.2. Optimization algorithms 129 3.5.5.3. The pairing of simulation and optimization 130 3.5.5.4. Results and comparison 130 3.6. Layout 132 3.6.1. Types of facility layout 132 3.6.1.1. Logical layout 132 3.6.1.2. Physical layout 133 3.6.2. Approach for treating a layout problem 133 3.6.2.1. Linear layout 134 3.6.2.2. Functional layout 135 3.6.2.3. Cellular layout 135 3.6.2.4. Fixed layout 135 3.6.3. The best-known methods 135 3.6.4. Example of arranging a maintenance facility 136 3.6.5. Example of laying out an automotive workshop 140 Chapter 4. Tactical Optimization 143 4.1. Introduction 143 4.2. Demand forecasting 143 4.2.1. Introduction 143 4.2.2. Categories and methods 144 4.2.3. Time series 145 4.2.4. Models and series analysis 146 4.2.4.1. Additive models 147 4.2.4.2. Multiplicative model 149 4.2.4.3. Exponential smoothing 150 4.3. Stock management 155 4.3.1. The different types of stocked products 156 4.3.2. The different types of stocks 157 4.3.3. Storage costs 157 4.3.4. Stock management 159 4.3.4.1. Functioning of a stock 159 4.3.4.2. Stock monitoring 161 4.3.4.3. Stock valuation 162 4.3.5. ABC classification method 163 4.3.6. Economic quantities 165 4.3.6.1. Economic quantity: the Wilson formula 166 4.3.6.2. Economic quantity with a discount threshold 167 4.3.6.3. Economic quantity with a uniform discount 168 4.3.6.4. Economic quantity with a progressive discount 169 4.3.6.5. Economic quantity with a variable ordering cost 170 4.3.6.6. Economic quantity with order consolidation 171 4.3.6.7. Economic quantity with a non-zero delivery time 172 4.3.6.8. Economic quantity with progressive input 172 4.3.6.9. Economic quantity with tolerated shortage 173 4.3.7. Replenishment methods 174 4.3.7.1. The (r, Q) replenishment method 175 4.3.7.2. The (T , S) replenishment method 175 4.3.7.3. The (s, S) replenishment method 175 4.3.7.4. The (T , r, S) replenishment method 176 4.3.7.5. The (T , r, Q) replenishment method 177 4.3.7.6. Security stock 177 4.4. Cutting and packing problems 178 4.4.1. Classifying cutting and packing problems 179 4.4.2. Packing problems in industrial systems 183 4.4.2.1. Model 183 4.4.2.2. Solution 185 4.5. Production and replenishment planning, lot-sizing methods 186 4.5.1. Introduction 186 x Optimization of Logistics 4.5.2. MRP and lot-sizing 186 4.5.3. Lot-sizing methods 187 4.5.3.1. The characteristic elements of the models 188 4.5.3.2. Lot-sizing in the scientific literature 189 4.5.4. Examples 190 4.5.4.1. The Wagner–Whitin method 191 4.5.4.2. The Florian and Klein method 193 4.6. Quality management 198 4.6.1. Evaluation, monitoring and improvement tools 198 4.6.1.1. The objective of metrology 198 4.6.1.2. Concepts of error and uncertainty 198 4.6.1.3. Statistical quality control 199 4.6.1.4. Stages of control 199 4.6.1.5. Tests of normality 200 4.6.2. Types of control 205 4.6.2.1. Reception or final control 205 4.6.2.2. Reception control by measurement 206 4.6.2.3. Manufacturing control 209 4.6.2.4. Control charts 214 Chapter 5. Scheduling 233 5.1. Introduction 233 5.2. Scheduling problems 234 5.2.1. Basic notions 234 5.2.2. Notation 234 5.2.3. Definition of the criteria and objective functions 234 5.2.3.1. Flow time 235 5.2.3.2. Lateness 235 5.2.3.3. Tardiness 235 5.2.3.4. The earliness 236 5.2.3.5. Objective functions 236 5.2.3.6. Properties of schedules 238 5.2.4. Project scheduling 239 5.2.4.1. Definition of a project 239 5.2.4.2. Projects with unlimited resources 240 5.2.4.3. Projects with consumable resources 247 5.2.4.4. Minimal-cost scheduling 252 5.2.5. Single-machine problems 254 5.2.5.1. Minimization of the mean flow time 5.2.5.2. Minimization of the mean weighted flow time 5.2.5.3. Minimization of the mean flow time 5.2.5.4. Minimization of the maximum tardiness Tmax, 1/ri = 0/Tmax 259 5.2.5.5. Minimization of the maximum tardiness when the jobs have different arrival dates, with pre-emption 1/ri, pmtn/Tmax 261 5.2.5.6. Minimization of the mean tardiness 1//T 261 5.2.5.7. Minimization of the flow time 1/ri/F 265 5.2.6. Scheduling a flow shop workshop 267 5.2.6.1. The two-machine problem 267 5.2.6.2. A particular case of the three-machine problem 268 5.2.6.3. The m-machine problem 268 5.2.7. Parallel-machine problems 270 5.2.7.1. Identical machines, ri = 0, M in F 270 5.2.7.2. Identical machines, ri = 0, M in Cmax interruptible jobs 271 Bibliography 273 Index 285