Optimal Inventory Modeling of Systems: Multi-Echelon Techniques

Cover\r......Page 1
Recent titles in the INTERNATIONAL SERIES......Page 3
OPTIMAL INVENTORY MODELING OF SYSTEMS: Multi-Echelon Techniques Second Edition......Page 4
©......Page 5
Dedication......Page 6
Contents......Page 7
List of Figures......Page 14
List of Tables......Page 16
List of Variables......Page 18
Preface......Page 21
Acknowledgements......Page 26
1.1 Chapter Overview......Page 28
1.2 The System Approach......Page 29
1.3 The Item Approach......Page 30
1.4 Repairable vs. Consumable Items......Page 31
1.5 “Physics” of the Problem......Page 33
1.6 Multi-Item Optimization......Page 34
1.7 Multi-Echelon Optimization......Page 35
1.8 Multi-Indenture Optimization......Page 36
1.9 Field Test Experience......Page 37
1.10 The Item Approach Revisited......Page 40
1.11 The System Approach Revisited......Page 41
1.12 Summary......Page 44
1.13 Problems......Page 45
2.1 Chapter Overview......Page 46
2.2 Mean and Variance......Page 47
2.3 Poisson Distribution and Notation......Page 48
2.5 Justification of Independent Repair Times and Constant Demand......Page 49
2.6 Stock Level......Page 51
2.7 Item Performance Measures......Page 52
2.9 Single-Site Model......Page 56
2.10 Marginal Analysis......Page 57
2.11 Convexity......Page 60
2.12 Mathematical Solution of Marginal Analysis......Page 61
2.14 Availability......Page 64
2.15 Summary......Page 68
2.16 Problems......Page 69
3.1 Chapter Overview......Page 72
3.2 METRIC Model Assumptions......Page 73
3.3 METRIC Theory......Page 75
3.4 Numerical Example......Page 76
3.5 Convexification......Page 80
3.6 Summary of the METRIC Optimization Procedure......Page 81
3.7 Availability......Page 82
3.9 Problems......Page 83
4.1 Chapter Overview......Page 85
4.2 Poisson Process......Page 87
4.3 Negative Binomial Distribution......Page 88
4.4 Multi-Indenture Problem......Page 91
4.6 Variance of the Number of Units in the Pipeline......Page 93
4.7 Multi-Indenture Example Revisited......Page 97
4.8 Demand Rates that Vary with Time......Page 98
4.9 Bayesian Analysis......Page 99
4.10 Objective Bayes......Page 101
4.11 Bayesian Analysis in the Case of Initial Estimate Data......Page 106
4.12 James-Stein Estimation......Page 107
4.13 James-Stein Estimation Experiment......Page 109
4.15 Demand Prediction Experiment Design......Page 111
4.16 Demand Prediction Experiment Results......Page 113
4.17 Random Failure versus Wear-out Processes......Page 115
4.18 Goodness-of-Fit Tests......Page 118
4.19 Summary......Page 121
4.20 Problems......Page 122
5.1 Chapter Overview......Page 127
5.2 Mathematical Preliminary: Multi-Echelon Theory......Page 129
5.3 Definitions......Page 132
5.4 Demand Rates......Page 133
5.5 Mean and Variance for the Number of LRUs in Depot Repair......Page 134
5.6 Mean and Variance for the Number of SRUs in Base Repair or Resupply......Page 135
5.7 Mean and Variance for the Number of LRUs in Base Repair or Resupply......Page 136
5.8 Availability......Page 137
5.10 Generalization of the Resupply Time Assumptions......Page 138
5.11 Generalization of the Poisson Demand Assumption......Page 139
5.13 Consumable and Partially Repairable Items......Page 140
5.14 Numerical Example......Page 146
5.15 Item Criticality Differences......Page 148
5.16 Availability Degradation due to Maintenance......Page 149
5.17 Availability Formula Underestimates for Aircraft......Page 150
5.19 Problems......Page 151
6.1 Space Station Description......Page 154
6.2 Chapter Overview......Page 155
6.3 Maintenance Concept......Page 156
6.4 Availability as a Function of Time during the Cycle......Page 157
6.5 Probability Distribution of Backorders for an ORU......Page 158
6.6 Probability Distribution for Number of Systems Down for an ORU......Page 161
6.7 Probability Distribution for Number of Systems Down......Page 164
6.8 Availability......Page 165
6.9 Numerical Example for one ORU......Page 166
6.10 Optimization......Page 167
6.11 Multiple Resource Constraints......Page 168
6.12 REDUNDANCY BLOCK DIAGRAMS......Page 170
6.13 Numerical Examples......Page 172
6.14 Other Redundancy Configurations with 50% ORUs Operating......Page 178
6.15 Summary of the Theory......Page 181
6.16 Application of the Theory......Page 183
6.17 Problems......Page 184
7.1 Chapter Overview......Page 187
7.2 Availability over Different Cycle Lengths......Page 188
7.3 Availability Degradation due to Remove/Replace in Orbit......Page 189
7.4 Failures due to Wear Out......Page 191
7.5 Numerical Example......Page 194
7.6 Multiple Wear Out Failures at one Location during a Cycle......Page 196
7.7 Common Items......Page 201
7.8 Condemnations......Page 202
7.10 Summary......Page 203
7.11 Problems......Page 204
8.1 Chapter Overview......Page 205
8.2 Single Site Model......Page 207
8.3 Multi-Indenture Model......Page 210
8.4 Optimization of Availability......Page 212
8.5 Comparison of Objective Functions for Cannibalization......Page 214
8.6 Generalizations......Page 217
8.7 Dyna-METRIC and the Aircraft Sustainability Model......Page 218
8.9 Purpose of DRIVE......Page 219
8.10 Model Assumptions with DRIVE......Page 221
8.11 Implementation Problems with DRIVE......Page 223
8.12 Distribution Algorithm for DRIVE......Page 224
8.13 Field Test Results for DRIVE......Page 225
8.14 OVERDRIVE Separate Distribution and Repair Models......Page 226
8.15 Current Status of DRIVE......Page 230
8.16 Summary......Page 231
8.17 Problems......Page 232
9.1 Chapter Overview......Page 234
9.2 Airline Applications......Page 235
9.4 Periodic Resupply......Page 236
9.5 No Resupply: Flyaway Kits......Page 237
9.6 Items that are Sometimes Repaired-in-Place......Page 238
9.8 Probability Distribution of Delay Time......Page 239
9.10 Large Systems where Indenture Information may be Lacking......Page 241
9.11 Systems Composed of Multiple Sub-Systems......Page 242
9.13 Redundancy......Page 243
9.15 Summary......Page 244
10.1 Chapter Overview......Page 245
10.3 Use of Standards versus Measured Quantities......Page 247
10.4 Robust Estimation......Page 248
10.5 Assessment of Alternative Support Policies......Page 249
10.6 Model Implementation – Air Force......Page 250
10.7 Model Implementation Army......Page 252
10.9 Model Implementation – Coast Guard......Page 253
10.11 Model Hierarchies......Page 254
10.12 System Approach Revisited One More Time......Page 256
10.13 Problems......Page 257
A.1 Appendix Overview......Page 259
A.2 Preliminary Mathematics......Page 260
A.3 Proof of Palm’s Theorem......Page 261
A.5 Dynamic Form of Palm’s Theorem......Page 263
A.6 Problems......Page 264
B.1 Appendix Overview......Page 266
B.2 Background......Page 267
B.3 Simulation Description......Page 268
B.4 Parameter Values......Page 270
B.5 Depot-Repairable-Only Items......Page 271
B.6 Base-Repairable Items......Page 278
B.8 Summary......Page 279
C.1 Background......Page 281
C.2 Appendix Overview......Page 283
C.3 Description of the Demand Prediction Experiment......Page 284
C.4 Results of the Demand Prediction Experiment for C-5 Airframe......Page 289
C.5 Results of the Demand Prediction Experiment for A-10 Airframe......Page 294
C.6 Results of the F-16 Demand Prediction Experiment......Page 295
C.7 Demand Prediction for F-16 using Flying Hour Data......Page 296
C.8 Correlations......Page 301
C.9 Smaller Smoothing Constant for Low-Demand Items......Page 305
C.10 Summary......Page 306
D.1 Appendix Overview......Page 310
D.3 Literature Review......Page 311
D.4 Proposal for a Controlled Experiment......Page 312
D.5 Data Analysis – F-15 C/D Aircraft......Page 313
D.6 Analysis of Other Data Sets......Page 315
D.7 Summary......Page 317
E.1 Chapter Overview......Page 319
E.2 VMetric Screens......Page 320
Appendix F DEMAND ANALYSIS SYSTEM......Page 333
REFERENCES......Page 339
Index......Page 344