Dynamic Control of Quality in Production-Inventory Systems

Acknowledgments......Page 6
Contents......Page 8
1 Introduction......Page 12
1.2 Relations to Other Approaches......Page 13
1.3 Organization and Overview......Page 15
2.1 Stochastic and Likelihood-Ratio Orderings......Page 16
2.2 Stochastic Convexity......Page 18
2.3 Stochastic Submodularity......Page 22
2.4 Markov Chain Applications......Page 25
2.5 Notes......Page 27
3 Quality Control for Products with Warranty......Page 30
3.1 Warranty Cost Functions......Page 31
3.2 K-Submodularity......Page 34
3.3 Conditional Distribution for Defectives......Page 37
3.4 Optimal Policy......Page 38
3.5 The Individual Warranty Model......Page 42
3.6 Examples and Extensions......Page 45
3.7 Notes......Page 46
4 Process Control in Batch Production......Page 48
4.1 Machine Revision......Page 49
4.2.1 MDP Essentials......Page 53
4.2.2 The MDP Problem......Page 55
4.3.1 Optimality Equations......Page 56
4.3.2 Structural Properties......Page 58
4.3.3 Optimal Policies......Page 62
4.4 Average-Cost Model......Page 67
4.5 A Special Case: No Inspection Cost......Page 68
4.6 Notes......Page 73
5 Coordinated Production-Inspection in a Tandem System......Page 76
5.1.1 Problem Statement......Page 77
5.1.2 The SMDP Formulation......Page 78
5.2 Stationary Optimal Policies......Page 83
5.3 Structure of the Optimal Policy......Page 90
5.4 Notes......Page 97
6 Sequential Inspection Under Capacity Constraints......Page 100
6.1 Capacity Constraints......Page 101
6.2 Optimality of the Threshold Policy......Page 104
6.3 Further Characterization of the Optimal Policy......Page 111
6.4 An Application in Semiconductor Manufacturing......Page 115
6.5 Notes......Page 117
7 Coordination of Interstage Inspections......Page 120
7.1 Two-Stage Quality Control......Page 121
7.2 Analysis of Stage 1......Page 123
7.3.1 Priority Structure......Page 127
7.3.2 Threshold Structure......Page 131
7.4 A Special Case: Constant Defective Rates......Page 136
7.5 Optimal Policy at Stage 1......Page 138
7.6 General Cost Functions......Page 143
7.7 Notes......Page 147
8 Optimal Inspection in an Assembly System......Page 150
8.1 A Two-Component Assembly Model......Page 151
8.2 Dynamic Programming Formulation......Page 154
8.3 One Component with a Constant Defective Rate......Page 156
8.4 A Heuristic Policy......Page 165
8.5 Notes......Page 167
9 Coordinated Replenishment and Rework with Unreliable Supply Sources......Page 170
9.1 The Inspection/Rework Model......Page 171
9.2 Properties of the Cost Function......Page 173
9.3 Optimal Solution to the Inspection Problem......Page 177
9.4 Optimal Replenishment Quantities......Page 182
9.5 Optimal Replenishment over an Infinite Horizon......Page 188
9.6 A Random Yield Model with Multiple Sources......Page 195
9.7 Notes......Page 198
10.1 Model Description......Page 200
10.2 The Optimal Substitution Policy......Page 202
10.3 Formulation of the Replenishment Decision......Page 205
10.4 Concavity and Submodularity......Page 208
10.5 The Optimal Order Quantities......Page 211
10.6 Upper and Lower Bounds......Page 213
10.7 Notes......Page 215
References......Page 218
G......Page 227
S......Page 228
W......Page 229