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Introduction ix
Chapter 1. Forecasting and Maintenance under Subcontracting Constraint with Delay in Transportation 1
1.1. Introduction 2
1.2. Production without retuned products 5
1.2.1. Statement of the problem 5
1.2.2. Notation 7
1.2.3. Optimization of production policy 8
1.2.4. Total production and inventory cost 10
1.2.5. Analytical study 11
1.2.6. Numerical example 15
1.3. Production with retuned products 20
1.3.1. Statement of the problem 20
1.3.2. Optimization of the production policy 21
1.3.3. Analytical formulation 22
1.3.4. Numerical example 28
1.3.5. Optimization of returned products by a specified deadline 31
1.4. Joint maintenance policy 35
1.4.1. Description of the problem 36
1.4.2. Analytical study 37
1.4.3. Numerical example 39
1.5. Conclusion 44
Chapter 2. Sequentially Optimizing Production, Maintenance and Delivery Activities Taking into Account Product Returns 47
2.1. Introduction 47
2.2. Planning of production, delivery and maintenance 51
2.2.1. Notation 52
2.2.2. Context and assumptions 55
2.2.3. Setting the problem 57
2.2.4. Mathematical analysis 60
2.3. Transformation of the stochastic production, maintenance and delivery planning model to a deterministic equivalent 63
2.3.1. Motivation 64
2.3.2. Transforming the production, inventory and delivery cost (expression [2.11]) into a deterministic equivalent 64
2.3.3. Transforming the service level constraint (equation [2.5]) into a deterministic equivalent 65
2.3.4. Transforming the maintenance cost (expression [2.12]) into a deterministic equivalent 68
2.4. Numerical example and numerical optimization procedure 72
2.4.1. Numerical optimization procedure 72
2.4.2. Numerical example 74
2.4.3. Variability study of delivery time, returned products and service level 83
2.5. Conclusion 92
Chapter 3. A Decision Optimization Model for Leased Manufacturing Equipment with Warranty for a Production-Maintenance Forecasting Problem 95
3.1. Introduction 95
3.2. Description of the problem 100
3.2.1. Notation 100
3.2.2. Statement of the problem 101
3.3. Mathematical model 103
3.3.1. Forecast production plan 103
3.3.2. Maintenance policy 105
3.3.3. Maximum additional cost for an extended warranty 108
3.3.4. Minimum price at which to sell the extended warranty 113
3.3.5. Win-win interval for the extended warranty cost 115
3.4. Numerical example 117
3.4.1. Variation in preventive maintenance and corrective maintenance costs 121
3.4.2. Effects of variation in production period length Î?t 122
3.5. Conclusion 123
Chapter 4. Global Control Policy Taking into Account Maintenance and Product Non-conformity 125
4.1. Introduction 125
4.2. Control strategy for stochastic multi-machine multi-product systems: analytical approach 128
4.2.1. Notations 129
4.2.2. Formulation of the cost optimization problem 129
4.2.3. Complexity of the optimal control problem 131
4.3. Description of the production system and the control strategy 131
4.4. Simulation model 133
4.4.1. Simulation principle 133
4.4.2. Simulation algorithm 134
4.5. Experimental analysis 137
4.5.1. Principle of the analysis 137
4.5.2. Determination and validation of the cost function 138
4.5.3. Determination and validation of the availability function 142
4.6. Finding the best compromise between cost, availability and quality: multi-criteria analysis 145
4.7. Conclusion 150 Appendices 153 Appendix 1 155 Appendix 2 159 Appendix 3 169 Bibliography 173 Index 183