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Theses and Dissertations 1. Thesis and Dissertation Collection, all items
1988-09
The effect of the covariance factor on the Procurement Problem Variance of net leadtime demand
Adams, Keith T.
http://ndl.handle.net/10945/23190
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' (8 D U DLEY research materials and institutional publications created by the NPS community. : Calhoun is named for Professor of Mathematics Guy K. Calhoun, NPS'‘s first ath KNOX appointed — and published — scholarly author.
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NAVAL POSTGRADUATE SCHOOL Monterey , California
THESIS
THE EFFECT OF THE COVARIANCE FACTOR ON THE PROCUREMENT PROBLEM VARIANCE OF NET LEADTIME DEMAND by Keith T. Adams
september 1988
Thesis Advisor: Alan W. McMasters
Approved for public release; distribution is unlimited
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|. TITLE (include Security Classification) THE EFFECT OF THE COVARIANCE FACTOR ON THE PROCUREMENT PROBLEM VARIANCE OF NET LEADTIME DEMAND
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|. PERSONAL AUTHOR(S) | ADAMS, Keith T.
Ja. TYPE OF REPORT) 13b TIME COVERED 14. DATE OF_REPORT (Year, Month, Day) [15 PAGE COUNT Master's Thesis FROM TO 1988 September 44
.. SUPPLEMENTARY NOTATION The views expressed in this thesis are those of the autho
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Defense: or the U.S. Government.
| COSATI CODES 18 SUBJECT TERMS (Continue on reverse if necessary and identify by block number) FIELD Covariance, Variance, Standard deviation,
: fT tC CLeadtime, Demand, Repairables, inventory models, |. AP ICP's, Inventory Control Points, Wholesale
. ABSTRACT (Continue on reverse if necessary and identify by block number) | An analysis is made of the formulae used by the Navy's Inventory Control Points in calculating the variance of Net Leadtime Demand of repairable items. A new formula is then derived, which makes use of actual Icalculations of covariance between regenerations and demands. The resulting variance values derived from the new formula are compared with the variance Ivalues resident on the Navy's Ships Parts Control Center data base and are Ishown to produce lower variances. The new formula is also compared to the Joption path formula to determine which formula produces the smallest Ivariance. The comparison suggests an under-estimation of variance results when the option path with its estimate of the covariance is used. The thesis concludes with recommendations for implementation of the new formula.
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Approved for public release; distribution is unlimited
The Effect of the Covariance Factor on the Procurement Problem Variance of Net Leadtime Demand
by Keith T. Adams Lieutenant Commander, Supply Corps, United States Navy
B.S., Purdue University, 1973 M.Ed., University of Missouri, 1975
Submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE IN OPERATIONS RESEARCH from the
NAVAL POSTGRADUATE SCHOOL
September 1988
ABSTRACT
An analysis is made of the formulae used by the Navy’s Inventory Control Points in calculating the variance of Net Leadtime Demand of repairable items. A new formula is then derived, which makes use of actual calculations of covariance between regenerations and demands. The resulting variance values derived from the new formula are compared with the variance values resident on the Navy’s Ships Parts Control Center data base and are shown to produce lower variances. The new formula is also compared to the option path formula to determine which formula produces the smallest variance. The comparison suggests an under-estimation of variance results when the option path with its estimate of the covariance is used. The thesis concludes with recommendations for
implementation of the new formula.
11
THESIS DISCLAIMER
The views and judgements presented in this thesis are those solely of the author. They do not necessarily reflect official positions held by the Naval Postgraduate School, the Department of the Navy, the Department of Defense, or any other US government agency or organization. No citation of this work may
include references or attributions to any official US government source.
1V
TABLE OF CONTENTS
MUS GPTG UTC TON occ ccccccscccccesccccc ccs ccacecoucccccccuccovceonccavscossesuecsseccessssscsscevsvsvsenve 1 POMOC OUND) ices cccsecoscorcstlepiatsscossccceosscccccccecsssssesssesesvees 1 MOURNS cig cccieyscecccveacccccesecscccosecseccssectsccsecsscessecssesssecsseessens ene 3 DICT, 3 Be cc eeccicceccecsassccsccssssessssessecssecssesseessesssessonssosssessees 3
I. FORMULA DEVELOPMENT.......cccccsscccsscccsscsssccsccseccsseessessecssesssessessreessesssesseess 4 PUMA IONAL, CAVEAT: ..n.c.ccccscccccccccscccsecoccccescssccosecssccsssssssssessssesseen 4 B. PROCUREMENT PROBLEM VARIABLE...ee.ccsscsssssssesssesosessessseeosee. 4 C. UICP VARIANCE FORMULA .o..cocccssccssessssssesssessesstesstsssesssesstessessece: 5 BAU VOR MMOL As cscscccscvcsccecssccccecoseccccsssecsscsuccscsssseccncsssccsucsseccsesees 7 E. FORMULA COMPARISONS. .eecccscsssscsscsssessecsssessesssessecsvesseesensevesseesees 9
II]. FORMULA COMPARISON METHODOLOGY .0.....::-ssssscscesssssssecessssssessessssvcce 12 AA, YATES AVCOTCMSIER (GIN. eae 12 B. FORMULA COMPARISON PROCEDURES. ..-.cccccccssssssessecssesssecesene 13 ©y AMAT FORMATE, c.cccccc.-ccccccsccsccecssecsscoscsasscssecssecssecssessseessevsee 15
po SB GUUIEINS) a rc 16
V. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS. .....scccsocssscssseees 21 (CUI CS Se 21 BO ONC WU STON GS, cic iccccsscccssccccsscccssecscscsvecssecssecseccoscsseccsscssscaneceeseen 21 C. RECOMMENDATIONS .ovcceccssscssssssscosecssessscssecssessesssessscarsessessessessseese 22 D. RELATED FURTHER STUDY .oeccccccccscsssccosssssssssscssecessesesssessstsnecsasce: 23
MMMSNO)E REFERENCES, ......cccc ccc cccccccceccccssscssescsocesscsessessssousecsecsssssussssessestsensevsres. 24
V
APPENDIX A - DEN/NOMECLATURE Of DATA ELEMENTS 20 APPENDIN B - FORTRAN PROGRAM FOR VARIANCE CALCULATIONS.... 26 APPENDIX CG - DEVAILET) OUD PU als CIN ye 34
INITIAL DISTRIBUTION Ores iiss ccessecs ce 35
V1
TABLE OF ABBREVIATIONS
Variables
Z - Procurement Problem Variable (PPV)
Z - procurement problem random variable
V - Procurement Problem Variance
D - mean demand per quarter
d - quarterly demand random variable Var(d)- variance of quarterly demand
L - mean procurement leadtime
] - procurement leadtime random variable L, - net acquisition time
Var(])- variance of leadtime
B - mean regenerations per quarter (CR)(SR) b - quarterly regeneration random variable T - mean procurement problem turn around time
(or mean repair cycle time) t - repair cycle time random variable Var(t)- variance of repair cycle time
Abbreviations
A/O - Application/Operation
ASO - Aviation Supply Office, Philadelphia, PA
COG - Cognizant Activity
DEN - Data Element Number
1G - Inventory Control Point
ICPDAT - Inventory Control Point Data
IHF - Inventory History File
FMSO - Fleet Material Support Office, Mechanicsburg, PA MAD - Mean Absolute Deviation
NICN - Navy Identification Code Number
NIIN - National Item Identification Number
NPS - Naval Postgraduate School, Monterey, CA
NSF - Navy Stock Fund
OPTION - Option path formula for variance calculations at ICPs PVAR - Mathematically correct formula for variance calculation SAS - Statistical Analysis System
SIG - Selective Item Generator
SPCC - Ships Parts Control Center, Mechanicsburg, PA
UICP - Uniform Inventory Control Point
Vil
I. INTRODUCTION
A. BACKGROUND
In the U.S. Navy there are approximately 228,800 items classified as repairables. The responsibility for managing these items is shared between the Navy’s two inventory control points (ICPs), the Aviation Supply Office (ASO) in Philadelphia, PA., and Ships Parts Control Center (SPCC) in Mechanicsburg, PA. The tota] dollar value of these items is in excess of $28 billion with an