Optimal Inventory Modeling of Systems: Multi-Echelon Techniques

350 Pages·2004·14.673 MB·English

by  Craig C. Sherbrooke Ph.D (auth.)

OPTIMAL INVENTORY MODELING
OF SYSTEMS
Multi-Echelon Techniques
Second Edition
Recent titles in the
INTERNATIONAL SERIES IN
OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Frederick S. Hillier, Series Editor, Stanford University
Ramík, J. & Vlach, M. / GENERALIZED CONCAVITY IN FUZZY OPTIMIZATION
AND DECISION ANALYSIS
Song, J. & Yao, D. / SUPPLY CHAIN STRUCTURES: Coordination, Information and
Optimization
Kozan, E. & Ohuchi, A. / OPERATIONS RESEARCH/ MANAGEMENT SCIENCE AT WORK
Bouyssou et al. / AIDING DECISIONS WITH MULTIPLE CRITERIA: Essays in
Honor of Bernard Roy
Cox, Louis Anthony, Jr. / RISK ANALYSIS: Foundations, Models and Methods
Dror, M., L’Ecuyer, P. & Szidarovszky, F. / MODELING UNCERTAINTY: An Examination
of Stochastic Theory, Methods, and Applications
Dokuchaev, N. / DYNAMIC PORTFOLIO STRATEGIES: Quantitative Methods and Empirical Rules
for Incomplete Information
Sarker, R., Mohammadian, M. & Yao, X. / EVOLUTIONARY OPTIMIZATION
Demeulemeester, R. & Herroelen, W. / PROJECT SCHEDULING: A Research Handbook
Gazis, D.C. / TRAFFIC THEORY
Zhu, J. / QUANTITATIVE MODELS FOR PERFORMANCE EVALUATION AND BENCHMARKING
Ehrgott, M. & Gandibleux, X. /MULTIPLE CRITERIA OPTIMIZATION: State of the Art Annotated
Bibliographical Surveys
Bienstock, D. / Potential Function Methods for Approx. Solving Linear Programming Problems
Matsatsinis, N.F. & Siskos, Y. / INTELLIGENT SUPPORT SYSTEMS FOR MARKETING
DECISIONS
Alpern, S.& Gal, S. /THE THEORY OF SEARCH GAMES AND RENDEZVOUS
Hall, R.W./HANDBOOK OF TRANSPORTATION SCIENCE - Ed.
Glover, F. & Kochenberger,G.A./HANDBOOK OF METAHEURISTICS
Graves, S.B. & Ringuest, J.L. / MODELS AND METHODS FOR PROJECT SELECTION:
Concepts from Management Science, Finance and Information Technology
Hassin, R. & Haviv, M./ TO QUEUE OR NOT TO QUEUE: Equilibrium Behavior in Queueing
Systems
Gershwin, S.B. et al/ ANALYSIS & MODELING OF MANUFACTURING SYSTEMS
Maros, I./ COMPUTATIONAL TECHNIQUES OF THE SIMPLEX METHOD
Harrison, T., Lee, H. & Neale,J./THE PRACTICE OF SUPPLY CHAIN MANAGEMENT: Where
Theory And Application Converge
Shanthikumar, J.G., Yao, D. & Zijm,W.H./STOCHASTIC MODELING AND OPTIMIZATION
OFMANUFACTURING SYSTEMS AND SUPPLY CHAINS
Nabrzyski, J., Schopf, J.M., J./ GRID RESOURCE MANAGEMENT: State of the Art
and Future Trends
Thissen, W.A.H. & Herder, P.M./ CRITICAL INFRASTRUCTURES: State of the Art in Research
and Application
Carlsson, C., Fedrizzi, M., & Fullér, R./ FUZZY LOGIC IN MANAGEMENT
Soyer, R., Mazzuchi, T.A., & Singpurwalla, N.D./ MATHEMATICAL RELIABILITY: An
ExpositoryPerspective
Talluri, K. & van Ryzin,G./ THE THEORY AND PRACTICE OF REVENUE MANAGEMENT
Kavadias, S. & Loch,C.H./PROJECT SELECTION UNDER UNCERTAINTY: Dynamically
Allocating Resources to Maximize Value
Sainfort, F., Brandeau, M.L., Pierskalla, W.P./ HANDBOOK OF OPERATIONS RESEARCH AND
HEALTHCARE: Methods and Applications
Cooper, W.W., Seiford, L.M., Zhu, J./ HANDBOOK OF DATA ENVELOPMENT ANALYSIS:
Models and Methods
* A list of the early publications in the series is at the end of the book *
OPTIMAL INVENTORY MODELING
OF SYSTEMS
Multi-Echelon Techniques
Second Edition
by
Craig C. Sherbrooke, Ph.D.
KLUWER ACADEMIC PUBLISHERS
NEW YORK,BOSTON, DORDRECHT, LONDON, MOSCOW
eBookISBN: 1-4020-7865-X
Print ISBN: 1-4020-7849-8
©2004 Kluwer Academic Publishers
NewYork, Boston, Dordrecht, London, Moscow
Print ©2004 Kluwer Academic Publishers
Boston
All rights reserved
No part of this eBook maybe reproducedor transmitted inanyform or byanymeans,electronic,
mechanical, recording, or otherwise, without written consent from the Publisher
Created in the United States of America
Visit Kluwer Online at: http://kluweronline.com
and Kluwer's eBookstoreat: http://ebooks.kluweronline.com
Dedication
This book is dedicated to
Rosalie, the next generation of
mathematicians Andrew and
Evan, and the following
generation Joshua and Michael
Contents
Dedication v
List ofFigures xv
List ofTables xvii
List ofVariables xix
Preface xxiii
Acknowledgements xxix
1INTRODUCTION 1
1.1 CHAPTER OVERVIEW 1
1.2 THE SYSTEM APPROACH 2
1.3 THEITEMAPPROACH 3
1.4 REPAIRABLE VS. CONSUMABLEITEMS 4
1.5 “PHYSICS” OF THE PROBLEM 6
1.6 MULTI-ITEMOPTIMIZATION 7
1.7 MULTI-ECHELONOPTIMIZATION 8
1.8 MULTI-INDENTUREOPTIMIZATION 9
1.9 FIELDTESTEXPERIENCE 10
1.10 THEITEMAPPROACHREVISITED 13
1.11 THESYSTEMAPPROACHREVISITED 14
1.12 SUMMARY 17
1.13 PROBLEMS 18
viii Optimal Inventory Modeling of Systems
2SINGLE-SITE INVENTORY MODEL FOR REPAIRABLE ITEMS 19
2.1 CHAPTEROVERVIEW 19
2.2 MEAN AND VARIANCE 20
2.3 POISSONDISTRIBUTION AND NOTATION 21
2.4 PALM’STHEOREM 22
2.5 JUSTIFICATION OF INDEPENDENTREPAIRTIMES AND
CONSTANTDEMAND 22
2.6 STOCKLEVEL 24
2.7 ITEMPERFORMANCEMEASURES 25
2.8 SYSTEMPERFORMANCEMEASURES 29
2.9 SINGLE-SITEMODEL 29
2.10 MARGINALANALYSIS 30
2.11 CONVEXITY 33
2.12 MATHEMATICALSOLUTION OF MARGINAL ANALYSIS 34
2.13 SEPARABILITY 37
2.14 AVAILABILITY 37
2.15 SUMMARY 41
2.16 PROBLEMS 42
3 METRIC: A MULTI-ECHELON MODEL 45
3.1 CHAPTER OVERVIEW 45
3.2 METRICMODELASSUMPTIONS 46
3.3 METRIC THEORY 48
3.4 NUMERICALEXAMPLE 49
3.5 CONVEXIFICATION 53
3.6 SUMMARY OF THE METRIC OPTIMIZATIONPROCEDURE 54
3.7 AVAILABILITY 55
3.8 SUMMARY 56
3.9 PROBLEMS 56
4 DEMAND PROCESSES AND DEMAND PREDICTION 59
4.1 CHAPTEROVERVIEW 59
4.2 POISSONPROCESS 61
4.3 NEGATIVEBINOMIALDISTRIBUTION 62
4.4 MULTI-INDENTUREPROBLEM 65
4.5 MULTI-INDENTUREEXAMPLE 67
4.6 VARIANCE OF THE NUMBER OF UNITS IN THE PIPELINE 67
4.7 MULTI-INDENTUREEXAMPLEREVISITED 71
4.8 DEMANDRATES THAT VARY WITH TIME 72
4.9 BAYESIANANALYSIS 73
4.10 OBJECTIVEBAYES 75
Contents ix
4.11 BAYESIANANALYSIS IN THE CASE OF INITIALESTIMATE
DATA 80
4.12 JAMES-STEINESTIMATION 81
4.13 JAMES-STEINESTIMATIONEXPERIMENT 83
4.14 COMPARISON OF BAYES AND JAMES-STEIN 85
4.15 DEMANDPREDICTIONEXPERIMENT DESIGN 85
4.16 DEMANDPREDICTIONEXPERIMENTRESULTS 87
4.17 RANDOMFAILUREVERSUSWEAR-OUTPROCESSES 89
4.18 GOODNESS-OF-FITTESTS 92
4.19 SUMMARY 95
4.20 PROBLEMS 96
5 VARI-METRIC: A MULTI-ECHELON, MULTI-INDENTURE MODEL
101
5.1 CHAPTEROVERVIEW 101
5.2 MATHEMATICALPRELIMINARY:MULTI-ECHELONTHEORY103
5.3 DEFINITIONS 106
5.4 DEMANDRATES 107
5.5 MEAN AND VARIANCE FOR THE NUMBER OF LRUS IN
DEPOTREPAIR 108
5.6 MEAN AND VARIANCE FOR THE NUMBER OF SRUS IN
BASEREPAIR OR RESUPPLY 109
5.7 MEAN AND VARIANCE FOR THE NUMBER OF LRUS IN
BASEREPAIR OR RESUPPLY 110
5.8 AVAILABILITY 111
5.9 OPTIMIZATION 112
5.10 GENERALIZATION OF THE RESUPPLYTIMEASSUMPTIONS 112
5.11 GENERALIZATION OF THE POISSONDEMANDASSUMPTION 113
5.12 COMMONITEMS 114
5.13 CONSUMABLE AND PARTIALLYREPAIRABLEITEMS 114
5.14 NUMERICALEXAMPLE 120
5.15 ITEMCRITICALITYDIFFERENCES 122
5.16 AVAILABILITYDEGRADATIONDUE TO MAINTENANCE 123
5.17 AVAILABILITYFORMULAUNDERESTIMATES FOR AIRCRAFT124
5.18 SUMMARY 125
5.19 PROBLEMS 125
6 MULTI-ECHELON, MULTI-INDENTURE MODELS WITH PERIODIC
SUPPLY AND REDUNDANCY 129
6.1 SPACE STATIONDESCRIPTION 129
6.2 CHAPTEROVERVIEW 130
6.3 MAINTENANCECONCEPT 131
6.4 AVAILABILITY AS A FUNCTION OF TIMEDURING THE CYCLE132
x Optimal Inventory Modeling of Systems
6.5 PROBABILITYDISTRIBUTION OF BACKORDERS FOR AN ORU133
6.6 PROBABILITYDISTRIBUTION FOR NUMBER OF
SYSTEMSDOWN FOR AN ORU 136
6.7 PROBABILITYDISTRIBUTION FOR NUMBER OF
SYSTEMS DOWN 139
6.8 AVAILABILITY 140
6.9 NUMERICALEXAMPLE FOR ONE ORU 141
6.10 OPTIMIZATION 142
6.11 MULTIPLERESOURCECONSTRAINTS 143
6.12 REDUNDANCY BLOCK DIAGRAMS 145
6.13 NUMERICALEXAMPLES 147
6.14 OTHERREDUNDANCY CONFIGURATIONS WITH 50%
ORUSOPERATING 153
6.15 SUMMARY OF THE THEORY 156
6.16 APPLICATION OF THE THEORY 158
6.17 PROBLEMS 159
7 SPECIAL TOPICS IN PERIODIC SUPPLY 163
7.1 CHAPTEROVERVIEW 163
7.2 AVAILABILITY OVER DIFFERENTCYCLELENGTHS 164
7.3 AVAILABILITYDEGRADATION DUE TO REMOVE/REPLACE
INORBIT 165
7.4 FAILURES DUE TO WEAROUT 167
7.5 NUMERICAL EXAMPLE 170
7.6 MULTIPLEWEAROUTFAILURES AT ONE LOCATION DURING
ACYCLE 172
7.7 COMMONITEMS 177
7.8 CONDEMNATIONS 178
7.9 DYNAMICCALCULATIONS 179
7.10 SUMMARY 179
7.11 PROBLEMS 180
8MODELING OF CANNIBALIZATION 181
8.1 CHAPTEROVERVIEW 181
8.2 SINGLESITE MODEL 183
8.3 MULTI-INDENTUREMODEL 186
8.4 OPTIMIZATION OF AVAILABILITY 188
8.5 COMPARISON OF OBJECTIVEFUNCTIONS FOR
CANNIBALIZATION 190
8.6 GENERALIZATIONS 193
8.7 DYNA-METRIC AND THE AIRCRAFTSUSTAINABILITY
MODEL 194
Contents xi
8.8 DRIVE- DISTRIBUTION AND REPAIR IN VARIABLE
ENVIRONMENTS 195
8.9 PURPOSE OF DRIVE 195
8.10 MODELASSUMPTIONS WITH DRIVE 197
8.11 IMPLEMENTATIONPROBLEMS WITH DRIVE 199
8.12 DISTRIBUTIONALGORITHM FOR DRIVE 200
8.13 FIELDTESTRESULTS FOR DRIVE 201
8.14 OVERDRIVE - SEPARATEDISTRIBUTION & REPAIRMODELS
202
8.15 CURRENT STATUS OF DRIVE 206
8.16 SUMMARY 207
8.17 PROBLEMS 208
9APPLICATIONS 211
9.1 CHAPTEROVERVIEW 211
9.2 AIRLINEAPPLICATIONS 212
9.3 REDISTRIBUTION AND SALE OF ASSETS 213
9.4 PERIODICRESUPPLY 213
9.5 NO RESUPPLY: FLYAWAYKITS 214
9.6 ITEMS THAT ARE SOMETIMESREPAIRED-IN-PLACE 215
9.7 CONTRACTOR REPAIR 216
9.8 PROBABILITYDISTRIBUTION OF DELAYTIME 216
9.9 SITES THAT ARE BOTHOPERATING AND SUPPORT 218
9.10 LARGESYSTEMS WHERE INDENTUREINFORMATION MAY
BELACKING 218
9.11 SYSTEMSCOMPOSED OF MULTIPLESUB-SYSTEMS 219
9.12 ITEMS WITH LIMITEDINTERCHANGEABILITY AND
SUBSTITUTABILITY 220
9.13 REDUNDANCY 220
9.14 UNFILLED DEMAND MAY NOT BE A BACKORDER 221
9.15 SUMMARY 221
10IMPLEMENTATION ISSUES 223
10.1 CHAPTEROVERVIEW 223
10.2 COMPARISON OF VARI-METRIC WITH OTHER
STOCKAGEPOLICIES 225
10.3 USE OF STANDARDS VERSUS MEASUREDQUANTITIES 225
10.4 ROBUSTESTIMATION 226
10.5 ASSESSMENT OF ALTERNATIVESUPPORTPOLICIES 227
10.6 MODELIMPLEMENTATION – AIRFORCE 228
10.7 MODELIMPLEMENTATION - ARMY 230
10.8 MODELIMPLEMENTATION - NAVY 231
10.9 MODELIMPLEMENTATION – COASTGUARD 231