Optimal Inventory Modeling of Systems

Dedication. List of Figures. List of Tables. List of Variables. Preface. Acknowledgements. 1: Introduction. 1.1. Chapter Overview. 1.2. The System Approach. 1.3. The Item Approach. 1.4. Repairable vs. Consumable Items. 1.5. "Physics" of the Problem. 1.6. Multi-Item Optimization. 1.7. Multi-Echelon Optimization. 1.8. Multi-Indenture Optimization. 1.9. Field Test Experience. 1.10. The Item Approach Revisited. 1.11. The System Approach Revisited. 1.12. Summary. 1.13. Problems. 2: Single-Site Inventory Model For Repairable Items. 2.1. Chapter Overview. 2.2. Mean and Variance. 2.3. Poisson Distribution and Notation. 2.4. Palm's Theorem. 2.5. Justification of Independent Repair Times and Constant Demand. 2.6. Stock Level. 2.7. Item Performance Measures. 2.8. System Performance Measures. 2.9. Single-Site Model. 2.10. Marginal Analysis. 2.11. Convexity. 2.12. Mathematical Solution of Marginal Analysis. 2.13. Separability. 2.14. Availability. 2.15. Summary. 2.16. Problems. 3: Metric: A Multi-Echelon Model. 3.1. Chapter Overview. 3.2. METRIC Model Assumptions. 3.3. METRIC Theory. 3.4. Numerical Example. 3.5. Convexification. 3.6. Summary of the METRIC Optimization Procedure. 3.7. Availability. 3.8. Summary. 3.9. Problems. 4: Demand Processes And Demand Prediction. 4.1. Chapter Overview. 4.2. Poisson Process. 4.3. Negative Binomial Distribution. 4.4. Multi-Indenture Problem. 4.5. Multi-Indenture Example. 4.6. Variance of the Number of Units in the Pipeline. 4.7. Multi-Indenture Example Revisited. 4.8. Demand Rates that Vary with Time. 4.9. Bayesian Analysis. 4.10. Objective Bayes. 4.11. Bayesian Analysis in the Case of Initial Estimate Data. 4.12. James-Stein Estimation. 4.13. James-Stein Estimation Experiment. 4.14. Comparison of Bayes and James-Stein. 4.15. Demand Prediction Experiment Design. 4.16. Demand Prediction Experiment Results. 4.17. Random Failure versus Wear-out Processes. 4.18. Goodness-of-Fit Tests. 4.19. Summary. 4.20. Problems. 5: Vari-METRIC: A Multi-Echelon, Multi-Indenture Model. 5.1. Chapter Overview. 5.2. Mathematical Preliminary: Multi-Echelon Theory. 5.3. Definitions. 5.4. Demand Rates. 5.5. Mean and Variance for the Number of LRUs in Depot Repair. 5.6. Mean and Variance for the Number of SRUs in Base Repair or Resupply. 5.7. Mean and Variance for the Number of LRUs in Base Repair or Resupply. 5.8. Availability. 5.9. Optimization. 5.10. Generalization of the Resupply Time Assumptions. 5.11. Generalization of the Poisson Demand Assumption. 5.12. Common Items. 5.13. Consumable and Partially Repairable Items. 5.14. Numerical Example. 5.15. Item Criticality Differences. 5.16. Availability Degradation due to Maintenance. 5.17. Availability Formula Underestimates for Aircraft. 5.18. Summary. 5.19. Problems. 6: Multi-Echelon, Multi-Indenture Models With Periodic Supply and Redundancy. 6.1. Space Station Description. 6.2. Chapter Overview. 6.3. Maintenance Concept. 6.4. Availability as a Function of Time during the Cycle. 6.5. Probability Distribution of Backorders for an ORU. 6.6. Probability Distribution for Number of Systems Down for an ORU. 6.7. Probability Distribution for Number of Systems Down. 6.8. Availability. 6.9. Numerical Example for one ORU. 6.10. Optimization. 6.11. Multiple Resource Constraints. 6.12. Redundancy Block Diagrams. 6.13. Numerical Examples. 6.14. Other Redundancy Configurations with 50% ORUs Operating. 6.15. Summary of the Theory. 6.16. Application of the Theory. 6.17. Problems. 7: Special Topics In Periodic Supply. 7.1. Chapter Overview. 7.2. Availability over Different Cycle Lengths. 7.3. Availability Degradation due to Remove/Replace in Orbit. 7.4. Failures due to Wear Out. 7.5. Numerical Example. 7.6. Multiple Wear Out Failures at one Location during a Cycle. 7.7. Common Items. 7.8. Condemnations. 7.9. Dynamic Calculations. 7.10. Summary. 7.11. Problems. 8: Modeling of Cannibalization. 8.1. Chapter Overview. 8.2. Single Site Model. 8.3. Multi-Indenture Model. 8.4. Optimization of Availability. 8.5. Comparison of Objective Functions for Cannibalization. 8.6. Generalizations. 8.7. Dyna-METRIC and the Aircraft Sustainability Model. 8.8. DRIVE - Distribution and Repair in Variable Environments. 8.9. Purpose of DRIVE. 8.10. Model Assumptions with DRIVE. 8.11. Implementation Problems with DRIVE. 8.12. Distribution Algorithm for DRIVE. 8.13. Field Test Results for DRIVE. 8.14. OVERDRIVE - Separate Distribution & Repair Models. 8.15. Current Status of DRIVE. 8.16. Summary. 8.17. Problems. 9: Applications. 9.1. Chapter Overview. 9.2. Airline Applications. 9.3. Redistribution and Sale of Assets. 9.4. Periodic Resupply. 9.5. No Resupply: Flyaway Kits. 9.6. Items that are Sometimes Repaired-in-Place. 9.7. Contractor Repair. 9.8. Probability Distribution of Delay Time. 9.9. Sites that are Both Operating and Support. 9.10. Large Systems where Indenture Information may be Lacking. 9.11. Systems Composed of Multiple Sub-Systems. 9.12. Items with Limited Interchangeability and Substitutability. 9.13. Redundancy. 9.14. Unfilled Demand May Not Be a Backorder. 9.15. Summary. 10: Implementation Issues. 10.1. Chapter Overview. 10.2. Comparison of VARI-METRIC with Other Stockage Policies. 10.3. Use of Standards versus Measured Quantities. 10.4. Robust Estimation. 10.5. Assessment of Alternative Support Policies. 10.6. Model Implementation - Air Force. 10.7. Model Implementation - Army. 10.8. Model Implementation - Navy. 10.9. Model Implementation - Coast Guard. 10.10. Model Implementation - Worldwide. 10.11. Model Hierarchies. 10.12. System Approach Revisited One More Time. 10.13. Problems. Appendix A: Palm's Theorem. A.1. Appendix Overview. A.2. Preliminary Mathematics. A.3. Proof of Palm's Theorem. A.4. Extension of Palm's Theorem to Finite Populations. A.5. Dynamic Form of Palm's Theorem. A.6. Problems. Appendix B: Multi-Echelon Systems with Lateral Supply. B.1. Appendix Overview. B.2. Background. B.3. Simulation Description. B.4. Parameter Values. B.5. Depot-Repairable-Only Items. B.6. Base-Repairable Items. B.7. Number of Lateral Shipments. B.8. Summary. Appendix C: Demand Prediction Studies. C.1. Background. C.2. Appendix Overview. C.3. Description of the Demand Prediction Experiment. C.4. Results of the Demand Prediction Experiment for C-5 Airframe. C.5. Results of the Demand Prediction Experiment for A-10 Airframe. C.6. Results of the F-16 Demand Prediction Experiment. C.7. Demand Prediction for F-16 using Flying Hour Data. C.8. Correlations. C.9. Smaller Smoothing Constant for Low-Demand Items. C.10. Summary. Appendix D: Predicting Wartime Demand For Aircraft Spares. D.1. Appendix Overview. D.2. Desert Storm Experience. D.3. Literature Review. D.4. Proposal for a Controlled Experiment. D.5. Data Analysis - F-15 C/D Aircraft. D.6. Analysis of Other Data Sets. D.7. Summary. Appendix E: VMETRIC Model Implementation. E.1. Chapter Overview. E.2. VMetric Screens. Appendix F: Demand Analysis System. References. Index.