## Optimal Inventory Modeling of Systems: Multi-Echelon TechniquesMost books on inventory theory use the item approach to determine stock levels, ignoring the impact of unit cost, echelon location, and hardware indenture. Optimal Inventory Modeling of Systems is the first book to take the system approach to inventory modeling. The result has been dramatic reductions in the resources to operate many systems - fleets of aircraft, ships, telecommunications networks, electric utilities, and the space station. Although only four chapters and appendices are totally new in this edition, extensive revisions have been made in all chapters, adding numerous worked-out examples. Many new applications have been added including commercial airlines, experience gained during Desert Storm, and adoption of the Windows interface as a standard for personal computer models. Book Reviews of the first edition "This book is a remarkable review and summary of nearly 30 years work on applied inventory theory. The book is a model of clarity and coherence. Even those concerned with other problem domains may benefit from the distilled wisdom it offers." Interfaces – Professor Steve New, University of Manchester "A large number of solved numerical examples help with the understanding of the models and mathematics used. Undoubtedly, a book of such integrity deserves a place on the shelf of any person, library or organization whose interests lie in the domain of inventory theory and its application to complex systems." Logistics Spectrum – Professor Mirce Knezevic, Exeter University Book Review of the second edition "In the second edition, the basics remain the same and should be considered essential knowledge for logisticians and system managers. Sherbrooke has spent his career solving real inventory problems. Practical examples help the reader understand critical concepts like marginal analysis, expected backorders, cost-availability curves, optimization, and analytical versus simulation based models. In Optimal Inventory Modeling of Systems, Sherbrooke tells us how we (public and private sector managers) can better understand and act on the critical trade-offs between cost and system availability. This reference text should be on your bookshelf." George T. Babbitt, General, USAF (Retired), Formerly Commander, Air Force Material Command; Director, Defense Logistics Agency. |

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### Contents

INTRODUCTION | 1 |

12 The System Approach | 2 |

13 The Item Approach | 3 |

14 Repairable vs Consumable Items | 4 |

15 Physics of the Problem | 6 |

16 MultiItem Optimization | 7 |

17 MultiEchelon Optimization | 8 |

18 MultiIndenture Optimization | 9 |

616 Application of the Theory | 158 |

617 Problems | 159 |

SPECIAL TOPICS IN PERIODIC SUPPLY | 163 |

72 Availability over Different Cycle Lengths | 164 |

Orbit | 165 |

74 Failures due to Wear Out | 167 |

75 Numerical Example | 170 |

76 Multiple Wear Out Failures at one Location during a Cycle | 172 |

19 Field Test Experience | 10 |

110 The Item Approach Revisited | 13 |

111 The System Approach Revisited | 14 |

112 Summary | 17 |

113 Problems | 18 |

SINGLESITE INVENTORY MODEL FOR REPAIRABLE ITEMS | 19 |

22 Mean and Variance | 20 |

23 Poisson Distribution and Notation | 21 |

24 Palms Theorem | 22 |

26 Stock Level | 24 |

27 Item Performance Measures | 25 |

28 System Performance Measures | 29 |

210 Marginal Analysis | 30 |

211 Convexity | 33 |

212 Mathematical Solution of Marginal Analysis | 34 |

213 Separability | 37 |

215 Summary | 41 |

216 Problems | 42 |

METRIC A MULTIECHELON MODEL | 45 |

32 METRIC Model Assumptions | 46 |

33 METRIC Theory | 48 |

34 Numerical Example | 49 |

35 Convexification | 53 |

36 Summary of the METRIC Optimization Procedure | 54 |

37 Availability | 55 |

38 Summary | 56 |

DEMAND PROCESSES AND DEMAND PREDICTION | 59 |

42 Poisson Process | 61 |

43 Negative Binomial Distribution | 62 |

44 MultiIndenture Problem | 65 |

45 MultiIndenture Example | 67 |

47 MultiIndenture Example Revisited | 71 |

48 Demand Rates that Vary with Time | 72 |

49 Bayesian Analysis | 73 |

410 Objective Bayes | 75 |

411 Bayesian Analysis in the Case of Initial Estimate Data | 80 |

412 JamesStein Estimation | 81 |

413 JamesStein Estimation Experiment | 83 |

414 Comparison of Bayes andJamesStein | 85 |

416 Demand Prediction Experiment Results | 87 |

417 Random Failure versus Wearout Processes | 89 |

418 GoodnessofFit Tests | 92 |

419 Summary | 95 |

420 Problems | 96 |

VARIMETRIC A MULTIECHELON MULTIINDENTURE MODEL | 101 |

MultiEchelon Theory | 103 |

53 Definitions | 106 |

54 Demand Rates | 107 |

55 Mean and Variance for the Number of LRUs in Depot Repair | 108 |

56 Mean and Variance for the Number of SRUs in Base Repair or Resupply | 109 |

57 Mean and Variance for the Number of LRUs in Base Repair or Resupply | 110 |

58 Availability | 111 |

59 Optimization | 112 |

511 Generalization of the Poisson Demand Assumption | 113 |

512 Common Items | 114 |

514 Numerical Example | 120 |

515 Item Criticality Differences | 122 |

516 Availability Degradation due to Maintenance | 123 |

517 Availability Formula Underestimates for Aircraft | 124 |

518 Summary | 125 |

MULTIECHELON MULTIINDENTURE MODELS WITH PERIODIC SUPPLY AND REDUNDANCY | 128 |

62 Chapter Overview | 130 |

63 Maintenance Concept | 131 |

64 Availability as a Function of Time during the Cycle | 132 |

65 Probability Distribution of Backorders for an ORU | 133 |

66 Probability Distribution for Number of Systems Down for an ORU | 136 |

67 Probability Distribution for Number of Systems Down | 139 |

68 Availability | 140 |

69 Numerical Example for one ORU | 141 |

610 Optimization | 142 |

611 Multiple Resource Constraints | 143 |

612 REDUNDANCY BLOCK DIAGRAMS | 145 |

613 Numerical Examples | 147 |

614 Other Redundancy Configurations with 50 ORUs Operating | 153 |

615 Summary of the Theory | 156 |

77 Common Items | 177 |

78 Condemnations | 178 |

79 Dynamic Calculations | 179 |

711 Problems | 180 |

MODELING OF CANNIBALIZATION | 181 |

82 Single Site Model | 183 |

83 MultiIndenture Model | 186 |

84 Optimization of Availability | 188 |

85 Comparison of Objective Functions for Cannibalization | 190 |

86 Generalizations | 193 |

87 DynaMETRIC and the Aircraft Sustainability Model | 194 |

88 DRIVE Distribution and Repair in Variable Environments | 195 |

810 Model Assumptions with DRIVE | 197 |

811 Implementation Problems with DRIVE | 199 |

812 Distribution Algorithm for DRIVE | 200 |

813 Field Test Results for DRIVE | 201 |

814 OVERDRIVE Separate Distribution and Repair Models | 202 |

815 Current Status of DRIVE | 206 |

816 Summary | 207 |

817 Problems | 208 |

APPLICATIONS | 210 |

92 Airline Applications | 212 |

93 Redistribution and Sale of Assets | 213 |

Flyaway Kits | 214 |

96 Items that are Sometimes RepairedinPlace | 215 |

97 Contractor Repair | 216 |

99 Sites that are Both Operating and Support | 218 |

911 Systems Composed of Multiple SubSystems | 219 |

912 Items with Limited Interchangeability and Substitutability | 220 |

914 Unsatisfied Demand may not be a Backorder | 221 |

IMPLEMENTATION ISSUES | 223 |

102 Comparison of VARIMETRIC with Other Stockage Policies | 225 |

104 Robust Estimation | 226 |

105 Assessment of Alternative Support Policies | 227 |

106 Model Implementation Air Force | 228 |

107 Model Implementation Army | 230 |

108 Model Implementation Navy | 231 |

1010 Model Implementation Worldwide | 232 |

1012 System Approach Revisited One More Time | 234 |

1013 Problems | 235 |

PALMS THEOREM | 237 |

A2 Preliminary Mathematics | 238 |

A3 Proof of Palms Theorem | 239 |

A4 Extension of Palms Theorem to Finite Populations | 241 |

A6 Problems | 242 |

MULTIECHELON SYSTEMS WITH LATERAL SUPPLY | 244 |

B2 Background | 246 |

B3 Simulation Description | 247 |

B4 Parameter Values | 249 |

B5 DepotRepairableOnly Items | 250 |

B6 BaseRepairable Items | 257 |

B7 Number of Lateral Shipments | 258 |

DEMAND PREDICTION STUDIES | 261 |

C2 Appendix Overview | 263 |

C3 Description of the Demand Prediction Experiment | 264 |

C4 Results of the Demand Prediction Experiment for C5 Airframe | 269 |

C5 Results of the Demand Prediction Experiment for A10 Airframe | 274 |

C6 Results of the F16 Demand Prediction Experiment | 275 |

C7 Demand Prediction for F16 using Flying Hour Data | 276 |

C8 Correlations | 281 |

Items | 285 |

C10 Summary | 286 |

PREDICTING WARTIME DEMAND FOR AIRCRAFT SPARES | 290 |

D2 Desert Storm Experience | 292 |

D4 Proposal for a Controlled Experiment | 293 |

D5 Data Analysis F15 CD Aircraft | 294 |

D6 Analysis of Other Data Sets | 296 |

D7 Summary | 298 |

VMETRIC MODEL IMPLEMENTATION | 301 |

E2 VMetric Screens | 302 |

DEMAND ANALYSIS SYSTEM | 315 |

321 | |

326 | |

### Other editions - View all

Optimal Inventory Modeling of Systems: Multi-Echelon Techniques Craig C. Sherbrooke Limited preview - 2006 |

Optimal Inventory Modeling of Systems: Multi-Echelon Techniques Craig C. Sherbrooke No preview available - 2013 |