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.

“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)

• Introduction xiiiChapter 1. Modeling and Performance Evaluation 11.1. Introduction 11.2. Markovian processes 21.2.1. Overview of stochastic processes 21.2.2. Markov processes 31.2.2.1. Basics 31.2.2.2. Chapman–Kolmogorov equations 41.2.2.3. Steady-state probabilities 51.2.2.4. Graph associated with a Markov process 61.2.2.5. Application to production systems 61.2.3. Markov chains 81.2.3.1. Basics 81.2.3.2. State probability vectors 91.2.3.3. Fundamental equation of a Markov chain 91.2.3.4. Graph associated with a Markov chain 101.2.3.5. Steady states of ergodic Markov chains 111.2.3.6. Application to production systems 121.3. Petri nets 141.3.1. Introduction to Petri nets 141.3.1.1. Basic definitions 141.3.1.2. Dynamics of Petri nets 151.3.1.3. Specific structures 161.3.1.4. Tools for Petri net analysis 181.3.1.5. Properties of Petri nets 191.3.2. Non-autonomous Petri nets 201.3.3. Timed Petri nets 20vi Optimization of Logistics1.3.4. Continuous Petri nets 231.3.4.1. Fundamental equation and performance analysis 241.3.4.2. Example 251.3.5. Colored Petri nets 271.3.6. Stochastic Petri nets 281.3.6.1. Firing time 291.3.6.2. Firing selection policy 291.3.6.3. Service policy 301.3.6.4. Memory policy 301.3.6.5. Petri net analysis 301.3.6.6. Marking graph 311.3.6.7. Generator of Markovian processes 311.3.6.8. Fundamental equation 321.3.6.9. Steady-state probabilities 321.3.6.10. Performance indices (steady state) 351.4. Discrete-event simulation 361.4.1. The role of simulation in logistics systems analysis 361.4.2. Components and dynamic evolution of systems 371.4.3. Representing chance and the Monte Carlo method 381.4.3.1. Uniform distribution U [0, 1] 381.4.3.2. The Monte Carlo method 391.4.4. Simulating probability distributions 411.4.4.1. Simulating random events 411.4.4.2. Simulating discrete random variables 441.4.4.3. Simulating continuous random variables 471.4.5. Discrete-event systems 521.4.5.1. Key aspects of simulation 521.5. Decomposition method 571.5.1. Presentation 571.5.2. Details of the method 58  Chapter 2. Optimization 612.1. Introduction 612.2. Polynomial problems and NP-hard problems 622.2.1. The complexity of an algorithm 622.2.2. Example of calculating the complexity of an algorithm 632.2.3. Some definitions 642.2.3.1. Polynomial-time algorithms 642.2.3.2. Pseudo-polynomial-time algorithms 642.2.3.3. Exponential-time algorithms 642.2.4. Complexity of a problem 642.2.4.1. Polynomial-time problems 642.2.4.2. NP-hard problems 642.3. Exact methods 642.3.1. Mathematical programming 642.3.2. Dynamic programming 652.3.3. Branch and bound algorithm 652.4. Approximate methods 662.4.1. Genetic algorithms 672.4.1.1. General principles 672.4.1.2. Encoding the solutions 672.4.1.3. Crossover operators 682.4.1.4. Mutation operators 702.4.1.5. Constructing the population in the next generation 702.4.1.6. Stopping condition 702.4.2. Ant colonies 702.4.2.1. General principle 702.4.2.2. Management of pheromones: example of the traveling salesman problem 712.4.3. Tabu search 722.4.3.1. Initial solution 732.4.3.2. Representing the solution 732.4.3.3. Creating the neighborhood 742.4.3.4. The tabu list 752.4.3.5. An illustrative example 762.4.4. Particle swarm algorithm 762.4.4.1. Description 762.4.4.2. An illustrative example 772.5. Multi-objective optimization 792.5.1. Definition 792.5.2. Resolution methods 802.5.3. Comparison criteria 812.5.3.1. The Riise distance 812.5.3.2. The Zitzler measure 822.5.4. Multi-objective optimization methods 822.5.4.1. Exact methods 822.5.4.2. Approximate methods 842.6. Simulation-based optimization 892.6.1. Dedicated tools 902.6.2. Specific methods 90Chapter 3. Design and Layout 933.1. Introduction 933.2. The different types of production system 943.3. Equipment selection 97viii Optimization of Logistics3.3.1. General overview 973.3.2. Equipment selection with considerations of reliability 993.3.2.1. Introduction to reliability optimization 993.3.2.2. Design of a parallel-series system 1003.4. Line balancing 1103.4.1. The classification of line balancing problems 1113.4.1.1. The simple assembly line balancing model (SALB) 1113.4.1.2. The general assembly line balancing model (GALB) 1123.4.2. Solution methods 1123.4.2.1. Exact methods 1123.4.2.2. Approximate methods 1133.4.3. Literature review 1133.4.4. Example 1133.5. The problem of buffer sizing 1143.5.1. General overview 1163.5.2. Example of a multi-objective buffer sizing problem 1163.5.3. Example of the use of genetic algorithms 1173.5.3.1. Representation of the solutions 1173.5.3.2. Calculation of the objective function 1183.5.3.3. Selection of solutions for the archive 1193.5.3.4. New population and stopping criterion 1193.5.4. Example of the use of ant colony algorithms 1193.5.4.1. Encoding 1203.5.4.2. Construction of the ant trails 1213.5.4.3. Calculation of the visibility 1213.5.4.4. Global and local updates of the pheromones 1223.5.5. Example of the use of simulation-based optimization 1233.5.5.1. Simulation model 1253.5.5.2. Optimization algorithms 1293.5.5.3. The pairing of simulation and optimization 1303.5.5.4. Results and comparison 1303.6. Layout 1323.6.1. Types of facility layout 1323.6.1.1. Logical layout 1323.6.1.2. Physical layout 1333.6.2. Approach for treating a layout problem 1333.6.2.1. Linear layout 1343.6.2.2. Functional layout 1353.6.2.3. Cellular layout 1353.6.2.4. Fixed layout 1353.6.3. The best-known methods 1353.6.4. Example of arranging a maintenance facility 1363.6.5. Example of laying out an automotive workshop 140Chapter 4. Tactical Optimization 1434.1. Introduction 1434.2. Demand forecasting 1434.2.1. Introduction 1434.2.2. Categories and methods 1444.2.3. Time series 1454.2.4. Models and series analysis 1464.2.4.1. Additive models 1474.2.4.2. Multiplicative model 1494.2.4.3. Exponential smoothing 1504.3. Stock management 1554.3.1. The different types of stocked products 1564.3.2. The different types of stocks 1574.3.3. Storage costs 1574.3.4. Stock management 1594.3.4.1. Functioning of a stock 1594.3.4.2. Stock monitoring 1614.3.4.3. Stock valuation 1624.3.5. ABC classification method 1634.3.6. Economic quantities 1654.3.6.1. Economic quantity: the Wilson formula 1664.3.6.2. Economic quantity with a discount threshold 1674.3.6.3. Economic quantity with a uniform discount 1684.3.6.4. Economic quantity with a progressive discount 1694.3.6.5. Economic quantity with a variable ordering cost 1704.3.6.6. Economic quantity with order consolidation 1714.3.6.7. Economic quantity with a non-zero delivery time 1724.3.6.8. Economic quantity with progressive input 1724.3.6.9. Economic quantity with tolerated shortage 1734.3.7. Replenishment methods 1744.3.7.1. The (r, Q) replenishment method 1754.3.7.2. The (T , S) replenishment method 1754.3.7.3. The (s, S) replenishment method 1754.3.7.4. The (T , r, S) replenishment method 1764.3.7.5. The (T , r, Q) replenishment method 1774.3.7.6. Security stock 1774.4. Cutting and packing problems 1784.4.1. Classifying cutting and packing problems 1794.4.2. Packing problems in industrial systems 1834.4.2.1. Model 1834.4.2.2. Solution 1854.5. Production and replenishment planning, lot-sizing methods 1864.5.1. Introduction 186x Optimization of Logistics4.5.2. MRP and lot-sizing 1864.5.3. Lot-sizing methods 1874.5.3.1. The characteristic elements of the models 1884.5.3.2. Lot-sizing in the scientific literature 1894.5.4. Examples 1904.5.4.1. The Wagner–Whitin method 1914.5.4.2. The Florian and Klein method 1934.6. Quality management 1984.6.1. Evaluation, monitoring and improvement tools 1984.6.1.1. The objective of metrology 1984.6.1.2. Concepts of error and uncertainty 1984.6.1.3. Statistical quality control 1994.6.1.4. Stages of control 1994.6.1.5. Tests of normality 2004.6.2. Types of control 2054.6.2.1. Reception or final control 2054.6.2.2. Reception control by measurement 2064.6.2.3. Manufacturing control 2094.6.2.4. Control charts 214Chapter 5. Scheduling 2335.1. Introduction 2335.2. Scheduling problems 2345.2.1. Basic notions 2345.2.2. Notation 2345.2.3. Definition of the criteria and objective functions 2345.2.3.1. Flow time 2355.2.3.2. Lateness 2355.2.3.3. Tardiness 2355.2.3.4. The earliness 2365.2.3.5. Objective functions 2365.2.3.6. Properties of schedules 2385.2.4. Project scheduling 2395.2.4.1. Definition of a project 2395.2.4.2. Projects with unlimited resources 2405.2.4.3. Projects with consumable resources 2475.2.4.4. Minimal-cost scheduling 2525.2.5. Single-machine problems 2545.2.5.1. Minimization of the mean flow time5.2.5.2. Minimization of the mean weighted flow time5.2.5.3. Minimization of the mean flow time5.2.5.4. Minimization of the maximum tardinessTmax, 1/ri = 0/Tmax 2595.2.5.5. Minimization of the maximum tardiness when the jobs have different arrival dates, with pre-emption 1/ri, pmtn/Tmax 2615.2.5.6. Minimization of the mean tardiness 1//T 2615.2.5.7. Minimization of the flow time 1/ri/F 2655.2.6. Scheduling a flow shop workshop 2675.2.6.1. The two-machine problem 2675.2.6.2. A particular case of the three-machine problem 2685.2.6.3. The m-machine problem 2685.2.7. Parallel-machine problems 2705.2.7.1. Identical machines, ri = 0, M in F 2705.2.7.2. Identical machines, ri = 0, M in Cmax interruptible jobs 271Bibliography 273Index 285

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.

“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)

• Introduction xiiiChapter 1. Modeling and Performance Evaluation 11.1. Introduction 11.2. Markovian processes 21.2.1. Overview of stochastic processes 21.2.2. Markov processes 31.2.2.1. Basics 31.2.2.2. Chapman–Kolmogorov equations 41.2.2.3. Steady-state probabilities 51.2.2.4. Graph associated with a Markov process 61.2.2.5. Application to production systems 61.2.3. Markov chains 81.2.3.1. Basics 81.2.3.2. State probability vectors 91.2.3.3. Fundamental equation of a Markov chain 91.2.3.4. Graph associated with a Markov chain 101.2.3.5. Steady states of ergodic Markov chains 111.2.3.6. Application to production systems 121.3. Petri nets 141.3.1. Introduction to Petri nets 141.3.1.1. Basic definitions 141.3.1.2. Dynamics of Petri nets 151.3.1.3. Specific structures 161.3.1.4. Tools for Petri net analysis 181.3.1.5. Properties of Petri nets 191.3.2. Non-autonomous Petri nets 201.3.3. Timed Petri nets 20vi Optimization of Logistics1.3.4. Continuous Petri nets 231.3.4.1. Fundamental equation and performance analysis 241.3.4.2. Example 251.3.5. Colored Petri nets 271.3.6. Stochastic Petri nets 281.3.6.1. Firing time 291.3.6.2. Firing selection policy 291.3.6.3. Service policy 301.3.6.4. Memory policy 301.3.6.5. Petri net analysis 301.3.6.6. Marking graph 311.3.6.7. Generator of Markovian processes 311.3.6.8. Fundamental equation 321.3.6.9. Steady-state probabilities 321.3.6.10. Performance indices (steady state) 351.4. Discrete-event simulation 361.4.1. The role of simulation in logistics systems analysis 361.4.2. Components and dynamic evolution of systems 371.4.3. Representing chance and the Monte Carlo method 381.4.3.1. Uniform distribution U [0, 1] 381.4.3.2. The Monte Carlo method 391.4.4. Simulating probability distributions 411.4.4.1. Simulating random events 411.4.4.2. Simulating discrete random variables 441.4.4.3. Simulating continuous random variables 471.4.5. Discrete-event systems 521.4.5.1. Key aspects of simulation 521.5. Decomposition method 571.5.1. Presentation 571.5.2. Details of the method 58  Chapter 2. Optimization 612.1. Introduction 612.2. Polynomial problems and NP-hard problems 622.2.1. The complexity of an algorithm 622.2.2. Example of calculating the complexity of an algorithm 632.2.3. Some definitions 642.2.3.1. Polynomial-time algorithms 642.2.3.2. Pseudo-polynomial-time algorithms 642.2.3.3. Exponential-time algorithms 642.2.4. Complexity of a problem 642.2.4.1. Polynomial-time problems 642.2.4.2. NP-hard problems 642.3. Exact methods 642.3.1. Mathematical programming 642.3.2. Dynamic programming 652.3.3. Branch and bound algorithm 652.4. Approximate methods 662.4.1. Genetic algorithms 672.4.1.1. General principles 672.4.1.2. Encoding the solutions 672.4.1.3. Crossover operators 682.4.1.4. Mutation operators 702.4.1.5. Constructing the population in the next generation 702.4.1.6. Stopping condition 702.4.2. Ant colonies 702.4.2.1. General principle 702.4.2.2. Management of pheromones: example of the traveling salesman problem 712.4.3. Tabu search 722.4.3.1. Initial solution 732.4.3.2. Representing the solution 732.4.3.3. Creating the neighborhood 742.4.3.4. The tabu list 752.4.3.5. An illustrative example 762.4.4. Particle swarm algorithm 762.4.4.1. Description 762.4.4.2. An illustrative example 772.5. Multi-objective optimization 792.5.1. Definition 792.5.2. Resolution methods 802.5.3. Comparison criteria 812.5.3.1. The Riise distance 812.5.3.2. The Zitzler measure 822.5.4. Multi-objective optimization methods 822.5.4.1. Exact methods 822.5.4.2. Approximate methods 842.6. Simulation-based optimization 892.6.1. Dedicated tools 902.6.2. Specific methods 90Chapter 3. Design and Layout 933.1. Introduction 933.2. The different types of production system 943.3. Equipment selection 97viii Optimization of Logistics3.3.1. General overview 973.3.2. Equipment selection with considerations of reliability 993.3.2.1. Introduction to reliability optimization 993.3.2.2. Design of a parallel-series system 1003.4. Line balancing 1103.4.1. The classification of line balancing problems 1113.4.1.1. The simple assembly line balancing model (SALB) 1113.4.1.2. The general assembly line balancing model (GALB) 1123.4.2. Solution methods 1123.4.2.1. Exact methods 1123.4.2.2. Approximate methods 1133.4.3. Literature review 1133.4.4. Example 1133.5. The problem of buffer sizing 1143.5.1. General overview 1163.5.2. Example of a multi-objective buffer sizing problem 1163.5.3. Example of the use of genetic algorithms 1173.5.3.1. Representation of the solutions 1173.5.3.2. Calculation of the objective function 1183.5.3.3. Selection of solutions for the archive 1193.5.3.4. New population and stopping criterion 1193.5.4. Example of the use of ant colony algorithms 1193.5.4.1. Encoding 1203.5.4.2. Construction of the ant trails 1213.5.4.3. Calculation of the visibility 1213.5.4.4. Global and local updates of the pheromones 1223.5.5. Example of the use of simulation-based optimization 1233.5.5.1. Simulation model 1253.5.5.2. Optimization algorithms 1293.5.5.3. The pairing of simulation and optimization 1303.5.5.4. Results and comparison 1303.6. Layout 1323.6.1. Types of facility layout 1323.6.1.1. Logical layout 1323.6.1.2. Physical layout 1333.6.2. Approach for treating a layout problem 1333.6.2.1. Linear layout 1343.6.2.2. Functional layout 1353.6.2.3. Cellular layout 1353.6.2.4. Fixed layout 1353.6.3. The best-known methods 1353.6.4. Example of arranging a maintenance facility 1363.6.5. Example of laying out an automotive workshop 140Chapter 4. Tactical Optimization 1434.1. Introduction 1434.2. Demand forecasting 1434.2.1. Introduction 1434.2.2. Categories and methods 1444.2.3. Time series 1454.2.4. Models and series analysis 1464.2.4.1. Additive models 1474.2.4.2. Multiplicative model 1494.2.4.3. Exponential smoothing 1504.3. Stock management 1554.3.1. The different types of stocked products 1564.3.2. The different types of stocks 1574.3.3. Storage costs 1574.3.4. Stock management 1594.3.4.1. Functioning of a stock 1594.3.4.2. Stock monitoring 1614.3.4.3. Stock valuation 1624.3.5. ABC classification method 1634.3.6. Economic quantities 1654.3.6.1. Economic quantity: the Wilson formula 1664.3.6.2. Economic quantity with a discount threshold 1674.3.6.3. Economic quantity with a uniform discount 1684.3.6.4. Economic quantity with a progressive discount 1694.3.6.5. Economic quantity with a variable ordering cost 1704.3.6.6. Economic quantity with order consolidation 1714.3.6.7. Economic quantity with a non-zero delivery time 1724.3.6.8. Economic quantity with progressive input 1724.3.6.9. Economic quantity with tolerated shortage 1734.3.7. Replenishment methods 1744.3.7.1. The (r, Q) replenishment method 1754.3.7.2. The (T , S) replenishment method 1754.3.7.3. The (s, S) replenishment method 1754.3.7.4. The (T , r, S) replenishment method 1764.3.7.5. The (T , r, Q) replenishment method 1774.3.7.6. Security stock 1774.4. Cutting and packing problems 1784.4.1. Classifying cutting and packing problems 1794.4.2. Packing problems in industrial systems 1834.4.2.1. Model 1834.4.2.2. Solution 1854.5. Production and replenishment planning, lot-sizing methods 1864.5.1. Introduction 186x Optimization of Logistics4.5.2. MRP and lot-sizing 1864.5.3. Lot-sizing methods 1874.5.3.1. The characteristic elements of the models 1884.5.3.2. Lot-sizing in the scientific literature 1894.5.4. Examples 1904.5.4.1. The Wagner–Whitin method 1914.5.4.2. The Florian and Klein method 1934.6. Quality management 1984.6.1. Evaluation, monitoring and improvement tools 1984.6.1.1. The objective of metrology 1984.6.1.2. Concepts of error and uncertainty 1984.6.1.3. Statistical quality control 1994.6.1.4. Stages of control 1994.6.1.5. Tests of normality 2004.6.2. Types of control 2054.6.2.1. Reception or final control 2054.6.2.2. Reception control by measurement 2064.6.2.3. Manufacturing control 2094.6.2.4. Control charts 214Chapter 5. Scheduling 2335.1. Introduction 2335.2. Scheduling problems 2345.2.1. Basic notions 2345.2.2. Notation 2345.2.3. Definition of the criteria and objective functions 2345.2.3.1. Flow time 2355.2.3.2. Lateness 2355.2.3.3. Tardiness 2355.2.3.4. The earliness 2365.2.3.5. Objective functions 2365.2.3.6. Properties of schedules 2385.2.4. Project scheduling 2395.2.4.1. Definition of a project 2395.2.4.2. Projects with unlimited resources 2405.2.4.3. Projects with consumable resources 2475.2.4.4. Minimal-cost scheduling 2525.2.5. Single-machine problems 2545.2.5.1. Minimization of the mean flow time5.2.5.2. Minimization of the mean weighted flow time5.2.5.3. Minimization of the mean flow time5.2.5.4. Minimization of the maximum tardinessTmax, 1/ri = 0/Tmax 2595.2.5.5. Minimization of the maximum tardiness when the jobs have different arrival dates, with pre-emption 1/ri, pmtn/Tmax 2615.2.5.6. Minimization of the mean tardiness 1//T 2615.2.5.7. Minimization of the flow time 1/ri/F 2655.2.6. Scheduling a flow shop workshop 2675.2.6.1. The two-machine problem 2675.2.6.2. A particular case of the three-machine problem 2685.2.6.3. The m-machine problem 2685.2.7. Parallel-machine problems 2705.2.7.1. Identical machines, ri = 0, M in F 2705.2.7.2. Identical machines, ri = 0, M in Cmax interruptible jobs 271Bibliography 273Index 285

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.

“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)

• Introduction xiiiChapter 1. Modeling and Performance Evaluation 11.1. Introduction 11.2. Markovian processes 21.2.1. Overview of stochastic processes 21.2.2. Markov processes 31.2.2.1. Basics 31.2.2.2. Chapman–Kolmogorov equations 41.2.2.3. Steady-state probabilities 51.2.2.4. Graph associated with a Markov process 61.2.2.5. Application to production systems 61.2.3. Markov chains 81.2.3.1. Basics 81.2.3.2. State probability vectors 91.2.3.3. Fundamental equation of a Markov chain 91.2.3.4. Graph associated with a Markov chain 101.2.3.5. Steady states of ergodic Markov chains 111.2.3.6. Application to production systems 121.3. Petri nets 141.3.1. Introduction to Petri nets 141.3.1.1. Basic definitions 141.3.1.2. Dynamics of Petri nets 151.3.1.3. Specific structures 161.3.1.4. Tools for Petri net analysis 181.3.1.5. Properties of Petri nets 191.3.2. Non-autonomous Petri nets 201.3.3. Timed Petri nets 20vi Optimization of Logistics1.3.4. Continuous Petri nets 231.3.4.1. Fundamental equation and performance analysis 241.3.4.2. Example 251.3.5. Colored Petri nets 271.3.6. Stochastic Petri nets 281.3.6.1. Firing time 291.3.6.2. Firing selection policy 291.3.6.3. Service policy 301.3.6.4. Memory policy 301.3.6.5. Petri net analysis 301.3.6.6. Marking graph 311.3.6.7. Generator of Markovian processes 311.3.6.8. Fundamental equation 321.3.6.9. Steady-state probabilities 321.3.6.10. Performance indices (steady state) 351.4. Discrete-event simulation 361.4.1. The role of simulation in logistics systems analysis 361.4.2. Components and dynamic evolution of systems 371.4.3. Representing chance and the Monte Carlo method 381.4.3.1. Uniform distribution U [0, 1] 381.4.3.2. The Monte Carlo method 391.4.4. Simulating probability distributions 411.4.4.1. Simulating random events 411.4.4.2. Simulating discrete random variables 441.4.4.3. Simulating continuous random variables 471.4.5. Discrete-event systems 521.4.5.1. Key aspects of simulation 521.5. Decomposition method 571.5.1. Presentation 571.5.2. Details of the method 58  Chapter 2. Optimization 612.1. Introduction 612.2. Polynomial problems and NP-hard problems 622.2.1. The complexity of an algorithm 622.2.2. Example of calculating the complexity of an algorithm 632.2.3. Some definitions 642.2.3.1. Polynomial-time algorithms 642.2.3.2. Pseudo-polynomial-time algorithms 642.2.3.3. Exponential-time algorithms 642.2.4. Complexity of a problem 642.2.4.1. Polynomial-time problems 642.2.4.2. NP-hard problems 642.3. Exact methods 642.3.1. Mathematical programming 642.3.2. Dynamic programming 652.3.3. Branch and bound algorithm 652.4. Approximate methods 662.4.1. Genetic algorithms 672.4.1.1. General principles 672.4.1.2. Encoding the solutions 672.4.1.3. Crossover operators 682.4.1.4. Mutation operators 702.4.1.5. Constructing the population in the next generation 702.4.1.6. Stopping condition 702.4.2. Ant colonies 702.4.2.1. General principle 702.4.2.2. Management of pheromones: example of the traveling salesman problem 712.4.3. Tabu search 722.4.3.1. Initial solution 732.4.3.2. Representing the solution 732.4.3.3. Creating the neighborhood 742.4.3.4. The tabu list 752.4.3.5. An illustrative example 762.4.4. Particle swarm algorithm 762.4.4.1. Description 762.4.4.2. An illustrative example 772.5. Multi-objective optimization 792.5.1. Definition 792.5.2. Resolution methods 802.5.3. Comparison criteria 812.5.3.1. The Riise distance 812.5.3.2. The Zitzler measure 822.5.4. Multi-objective optimization methods 822.5.4.1. Exact methods 822.5.4.2. Approximate methods 842.6. Simulation-based optimization 892.6.1. Dedicated tools 902.6.2. Specific methods 90Chapter 3. Design and Layout 933.1. Introduction 933.2. The different types of production system 943.3. Equipment selection 97viii Optimization of Logistics3.3.1. General overview 973.3.2. Equipment selection with considerations of reliability 993.3.2.1. Introduction to reliability optimization 993.3.2.2. Design of a parallel-series system 1003.4. Line balancing 1103.4.1. The classification of line balancing problems 1113.4.1.1. The simple assembly line balancing model (SALB) 1113.4.1.2. The general assembly line balancing model (GALB) 1123.4.2. Solution methods 1123.4.2.1. Exact methods 1123.4.2.2. Approximate methods 1133.4.3. Literature review 1133.4.4. Example 1133.5. The problem of buffer sizing 1143.5.1. General overview 1163.5.2. Example of a multi-objective buffer sizing problem 1163.5.3. Example of the use of genetic algorithms 1173.5.3.1. Representation of the solutions 1173.5.3.2. Calculation of the objective function 1183.5.3.3. Selection of solutions for the archive 1193.5.3.4. New population and stopping criterion 1193.5.4. Example of the use of ant colony algorithms 1193.5.4.1. Encoding 1203.5.4.2. Construction of the ant trails 1213.5.4.3. Calculation of the visibility 1213.5.4.4. Global and local updates of the pheromones 1223.5.5. Example of the use of simulation-based optimization 1233.5.5.1. Simulation model 1253.5.5.2. Optimization algorithms 1293.5.5.3. The pairing of simulation and optimization 1303.5.5.4. Results and comparison 1303.6. Layout 1323.6.1. Types of facility layout 1323.6.1.1. Logical layout 1323.6.1.2. Physical layout 1333.6.2. Approach for treating a layout problem 1333.6.2.1. Linear layout 1343.6.2.2. Functional layout 1353.6.2.3. Cellular layout 1353.6.2.4. Fixed layout 1353.6.3. The best-known methods 1353.6.4. Example of arranging a maintenance facility 1363.6.5. Example of laying out an automotive workshop 140Chapter 4. Tactical Optimization 1434.1. Introduction 1434.2. Demand forecasting 1434.2.1. Introduction 1434.2.2. Categories and methods 1444.2.3. Time series 1454.2.4. Models and series analysis 1464.2.4.1. Additive models 1474.2.4.2. Multiplicative model 1494.2.4.3. Exponential smoothing 1504.3. Stock management 1554.3.1. The different types of stocked products 1564.3.2. The different types of stocks 1574.3.3. Storage costs 1574.3.4. Stock management 1594.3.4.1. Functioning of a stock 1594.3.4.2. Stock monitoring 1614.3.4.3. Stock valuation 1624.3.5. ABC classification method 1634.3.6. Economic quantities 1654.3.6.1. Economic quantity: the Wilson formula 1664.3.6.2. Economic quantity with a discount threshold 1674.3.6.3. Economic quantity with a uniform discount 1684.3.6.4. Economic quantity with a progressive discount 1694.3.6.5. Economic quantity with a variable ordering cost 1704.3.6.6. Economic quantity with order consolidation 1714.3.6.7. Economic quantity with a non-zero delivery time 1724.3.6.8. Economic quantity with progressive input 1724.3.6.9. Economic quantity with tolerated shortage 1734.3.7. Replenishment methods 1744.3.7.1. The (r, Q) replenishment method 1754.3.7.2. The (T , S) replenishment method 1754.3.7.3. The (s, S) replenishment method 1754.3.7.4. The (T , r, S) replenishment method 1764.3.7.5. The (T , r, Q) replenishment method 1774.3.7.6. Security stock 1774.4. Cutting and packing problems 1784.4.1. Classifying cutting and packing problems 1794.4.2. Packing problems in industrial systems 1834.4.2.1. Model 1834.4.2.2. Solution 1854.5. Production and replenishment planning, lot-sizing methods 1864.5.1. Introduction 186x Optimization of Logistics4.5.2. MRP and lot-sizing 1864.5.3. Lot-sizing methods 1874.5.3.1. The characteristic elements of the models 1884.5.3.2. Lot-sizing in the scientific literature 1894.5.4. Examples 1904.5.4.1. The Wagner–Whitin method 1914.5.4.2. The Florian and Klein method 1934.6. Quality management 1984.6.1. Evaluation, monitoring and improvement tools 1984.6.1.1. The objective of metrology 1984.6.1.2. Concepts of error and uncertainty 1984.6.1.3. Statistical quality control 1994.6.1.4. Stages of control 1994.6.1.5. Tests of normality 2004.6.2. Types of control 2054.6.2.1. Reception or final control 2054.6.2.2. Reception control by measurement 2064.6.2.3. Manufacturing control 2094.6.2.4. Control charts 214Chapter 5. Scheduling 2335.1. Introduction 2335.2. Scheduling problems 2345.2.1. Basic notions 2345.2.2. Notation 2345.2.3. Definition of the criteria and objective functions 2345.2.3.1. Flow time 2355.2.3.2. Lateness 2355.2.3.3. Tardiness 2355.2.3.4. The earliness 2365.2.3.5. Objective functions 2365.2.3.6. Properties of schedules 2385.2.4. Project scheduling 2395.2.4.1. Definition of a project 2395.2.4.2. Projects with unlimited resources 2405.2.4.3. Projects with consumable resources 2475.2.4.4. Minimal-cost scheduling 2525.2.5. Single-machine problems 2545.2.5.1. Minimization of the mean flow time5.2.5.2. Minimization of the mean weighted flow time5.2.5.3. Minimization of the mean flow time5.2.5.4. Minimization of the maximum tardinessTmax, 1/ri = 0/Tmax 2595.2.5.5. Minimization of the maximum tardiness when the jobs have different arrival dates, with pre-emption 1/ri, pmtn/Tmax 2615.2.5.6. Minimization of the mean tardiness 1//T 2615.2.5.7. Minimization of the flow time 1/ri/F 2655.2.6. Scheduling a flow shop workshop 2675.2.6.1. The two-machine problem 2675.2.6.2. A particular case of the three-machine problem 2685.2.6.3. The m-machine problem 2685.2.7. Parallel-machine problems 2705.2.7.1. Identical machines, ri = 0, M in F 2705.2.7.2. Identical machines, ri = 0, M in Cmax interruptible jobs 271Bibliography 273Index 285