Production and Maintenance Optimization Problems

This book focuses on industrial constraints such as subcontracting, warranty, and quality in manufacturing and logistic fields and gives new integrated maintenance strategies. It presents new production and maintenance Control Policies compared to the Hedging Point theory Strategy and different integrated strategies of maintenance are developed under industrial constraints in order to propose a robustness production and maintenance plan.

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 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