NAVAL POSTGRADUATE SCHOOL * Monterey, California (OF DTIC MELECTE APR 0 8 THESIS y E AN ANALYSIS OF THREE AVCAL INVENTORY MODELS USING THE TIGER SIMULATION MODEL C> by LLJ Mark David Sullivan ._J cSeptember 1984 9 Thesis Advisor: F.R. Richards Approved for public release; distribution unlimited. t o-.. . . .* . . .. ... . ....... "-"....... . . . . .. . . . . .. . . . . .
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NAVAL POSTGRADUATE SCHOOL* Monterey, California
(OF
DTICMELECTE
APR 0 8
THESIS y E
AN ANALYSIS OF THREE AVCAL INVENTORY MODELSUSING THE TIGER SIMULATION MODEL
C> by
LLJ Mark David Sullivan._JcSeptember 1984
9 Thesis Advisor: F.R. Richards
Approved for public release; distribution unlimited.
4. TITLE (and Subtitle) S TYPE OF REPORT & PERIOD COVEREC
An Analysis of Three AVCAL Inventory Master's Thesis;September 1984
Models Using the TIGER Simulation Model -PERFORMING ORG. REPORT NUMBER
7. AUTHOR(s) B CONTRACT CR GRAN' NUMBER(I)
Mark David Sullivan
9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASKAREA & WORK UNIT NUMBERS
Naval Postgraduate SchoolMonterey, California 93943
$I. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE
Naval Postgraduate School Sept mber 1984Monterey, California 13. NUMBER OF PAGES
14. MONITORING AGENCY NAME & ADDRESS(If different from Controlling Offce) 15. SECURITY CLASS. (of thl report)
Unclassified
1S. DECLASSIFICATtON, DOWNGRADINGSCHEDULE
16. DISTRIBUTION STATEMENT (of this Report)
Approved for public release; distribution unlimited
17. DISTRIBUTION STATEMENT (of the ebstract entered In Block 20, it different from Report)
". 1
IS. SUPPLEMENTARY NOTES
I9. KEY WORDS (Continue on reverse side if neceesey ard Identify by block number)
AVCAL inventory models
RIMAIR TIGER
ACIM operational availability
simulation
20 ABSTRACT (Continue on reverse ede If neceeeary and Identify by block number)
This thesis investigates the effectiveness of threeAViation Consolidated Allowance List (AVCAL) inventorymodels in achieving aircraft system operationalavailability. The three models studied are the Aviation
*• Supply Office (ASO) Model, the Repairables Integrated Model
for Aviation (RIM-AIR), and the Availability CenteredInventory Model (ACIM). TIGER, a simulation model developed
DD I FJAN M 1473 EDITION OF I NOV 65 1 O.SOLETE
S N 0102- LF. 04. 6601 1*SECURITY CLASSIFICATION OF TNIS PAGE (VIn Dell ntered)
SECURITY CLASSIFICATIO14 OF THIS PAGE (ftaR Data Ent*V.*4-
by Naval Seas Systems command, is amended to accommodatesimulation of multiple aircraft sorties with a realisticparts pipeline operation. AVCAL model inventory levels
are compared over a ninety day period utilizing availabilitystatistics computed by TIGER.
5 N 0 102- LF- 0 14- 66012 _______________________
SECURITY CLASSIFICATION Of THIS PAOE(Whe" Data Entotod)
Approved for public release; distribution unlimited
An Analysis of Three AVCAL Inventory Models Using the TIGERSimulation Model
by
Mark David SullivanLieutenant Commander, United States Navy
B.S., University of Louisville, 1974
Submitted in partial fulfillment of therequirements for the degree of
There are many scenarios in which these two ratios will not
be equal. For example, a system with high failure rate parts
will tend to have a lower A ratio. But these same parts may
not decrease ratio B to the same degree if adequate spares are
available. AVMUP emphasizes part criticality and reliability
more than AVA. For this study, AVMUP was consistently several
percentage points less than AVA.
Another set of statistics used in this thesis was the < -
Critical Equipments Summary produced by TIGER. This is an
optional printout that points out parts that are "worst
offenders". Parts that caused the system to go to a down
status or parts that failed while the system was already in
a down status are listed in this output.
Table I provides an example of this summary. It depicts
the events in a 90 hour mission, using a three part system,
System Y. At time 8.96 hours, Part A fails, but since System
Y is still up, no system downtime is recorded. At time 34.04
hours, part B fails, causing System Y to fail. TIGER counts
19
TABLE I
Critical Equipments Computation
Part A Part B
MTBF=50 MTBF=50
SYSTEM Y
Part CMTBF=30
1. TIGER events occurring in 90 hour mission, System Y
Total System
Time Event System Status Downtime
0.00 Mission start UP 0.008.96 Part A fails UP 0.00
34.04 Part B fails DOWN 0.0061.02 Part C fails DOWN 26.9890.00 Mission end DOWN 55.96
2. Breakdown of total system downtime among CriticalEquipments contributing to system downtime.
Period of System Downtime DividedTotal System Number of Among Down PartsDowntime Parts Down A B C
34.04-61.02 2 (A,B) 13.49 13.49 0.00(26.98)
61.02-90.00 3 (A,B,C) 9.66 9.66 9.66(28.98)
Total Downtime 23.15 23.15 9.66
Percent of Total 41.37 41.37 17.26System Downtime
20
I•
both parts A and B as critical equipments because both
contribute to system downtime. At time 34.04, system down-
time begins and continues until the end of the mission at
time 90.0. Thus total system downtime is
90.0 - 34.04 = 55.96 hours
At time 61.02, Part C fails. Part C is also considered
to be a critical equipment for the period from 61.02 to 90.0
(28.98 hours) even though System Y is in a down status during
this period. As shown in Part 2 of Table I, TIGER divides
system downtime during the period 34.04 to 61.02 (26.98 hours)
between the two parts (A and B) that are in a down status.
Parts A and B are each credited with 1/2 of 26.98 hours, or
13.49 hours each during this period. TIGER then divides the
system downtime for the period 61.02 to 90.0 (28.98 hours)
between parts A, B and C because all three parts are in a
down status during this period. Parts A, B, and C are each
credited with 1/3 of 28.98 hours, or 9.66 hours each during
this period.Iq
Therefore, total system downtime is divided between the
three parts A, B, and C as follows: A: 23.15 hours, B:
23.15 hours, and C: 9.66 hours. These hourly total are also
converted to percentages of total system downtime by part.
Parts that are large contributors to system downtime can be
easily identified through the Critical Equipments Summary and
inventory models can then be analyzed to isolate possible
weaknesses. Explanations of the other TIGER statistics can
be found in the TIGER Manual [Ref. 4].
21
I
3. TIGER Subroutines
TIGER in its present form at the Naval Postgraduate
School is written in FORTRAN, utilizing subroutines as major
subdivisions of the program. A short summary of the purpose
of each subroutine is presented below.
MAIN Program: The majority of data is input.TIGER statistics are calculated once after eachmission completion and again after all missions arecompleted.
Subroutine PACK: Equipment configuration dataand phase operating rules are input. Inventorylevels are computed.
Subroutine RUN: TIGER next event calculationsare done. This subroutine is called at the start ofeach new phase within a mission.
Subroutine TTE: Random numbers are generatedto provide times for part failures or repairs.Inventory levels are monitored. Major changes tothis subroutine were made for this study.
Subroutine STATUS: .Equipment(s) are reviewedafter each event for status (up or down) of the mainsystem and all parts.
Subroutine STANDBY: TIGER program arrays areindexed.
Subroutine EVENT: Events (part failures,repair, etc.) are sorted to find earliest time.Major changes to this subroutine were made forthis study.
Subroutine APPLE: Statistics generated duringa mission are summarized.
Subroutine SPARES: This subroutine is used toinput inventory levels to the main program.
Subroutine ASPARE: ASO Manual inventory levelsare computed. This is a new Subroutine.
Subroutine RIMAIR: RIMAIR inventory levels arecomputed. This is a New Subroutine.
22
C. TIGER CHANGES
1. Aircraft Sortie Simulation
One of the major changes made to TIGER permitted
the simulation of multiple aircraft sorties over a period of
ninety days. Since TIGER was originally desicned to test
ship systems that underwent a few lengthy phases, variable
dimensions had to be changed to allow for the many more
phases that were required. With these new changes a 24-hour
period may be divided up into as many as four phases. Figure
2.1 shows a sample combination of phases that can be arranged.
This combination was then replicated once for each day in
the mission.
Phase 1 Phase 2 Phase 3 Phase 4
<-4 > 8 ><-- 3 > -- 9 ---
Fly Ondeck Fly Ondeck
Figure 2.1. Phase Sequence Combination.
During each phase a number of aircraft may be onerated.
Since this version of TIGER does not allow for separate
aircraft (systems) to be operated in different phase
sequences, aircraft were operated simultarneously. For this
study three aircraft were operated in 'series" operation.
That is, three identical aircraft systems were operated
23
with the requirement that all aircraft must be in an up
status for the combined trio system of aircraft to be in
up status.
2. Equipment: Repair and Resupply
TIGER was modified so that parts that failed and
were removed from the aircraft, known as carcasses, could be
tracked through the repair and resupply system. The inventory
algorithms studied assumed a one-for-one repair policy; for
each part turned in, another is issued. Figure 2.2 shows a
schematic of the overall repair and resupply pipeline. When
a part fails, it has two different pipelines it can follow.
P (BCM) - io Part Ordered Off Ship
Part Failure -- 0.
1-P (BCM) - Part Repaired on Ship
Figure 2.2. Part Pipelines.
With a probability = P (BCM), it will be considered
"beyond the capability of local maintenance". In this case
the part will be shipped to the depot level repair center
off-ship, and a replacement part will be ordered. The time
to receive a replacement part is known as the order and
shipping time, OST. This time can vary depending on the
stock level of the part at the depot, the location of the
ship, and whether or not resupply to the carrier is possible
(wartime scenario). Tiger will assign an exponentially
24
L. .
distributed CST, with mean equal to the SRTIM parameter of
the part. SRTIM is defined as the off-ship order and
shipping time of the specific part type. This time is
placed in a new event time queue, RFITIM. Each part type
has its own RFITIM queue that tracks all parts placed in
the pipeline.
The exact number of parts in the pipeline is limited to
the number of parts originally stocked. This computation is
done through the NOP (number of parts) array. Whenever the
NOP level equals the original inventory level, no more parts
are available until a part is resupplied or repaired. The
RFITIM queue is sorted to find the earliest repair time.
The failed part can also be placed in the repair pipeline,
with a probability of 1-P (BCM). This corresponds to the
part being repaired at the ship repair facility, the Aviation D
Intermediate Maintenance Department (AIMD). The part is
assigned an exponentially distributed repair time, with mean*
equal to the REPTIM parameter of the part. REPTIM is defined I
as the on-ship repair time for the specific part type. This
time is also placed in the RFITIM event queue. This queue
runs independently of the main TIGER event chain, known as I
ETIME; but RFITIM does follow phase type rules outlined
previously.
3. New TIGER Subroutines
Two new subroutines were introduced into TIGER. The
first, ASPARE, calculates inventory levels based on ASO
Units per Component/Aircraft (UPA): Number of partsof type X installed on each aircraft. An individualUPA exists for each part type X.
Planned Operating Hours: Planned aircraft utilizationper month in hours.
Number of Aircraft: Number of aircraft supported bythis ARR.
Maintenance Replacement Factor (MRF) : For repairableitems, the number of times that an item will be BCM atorganizational (squadron) and Intermediate (AIMD)levels during one MC.
MRF = # BCM's/(MC * UPA)
Rotatable Pool Factor (RPF) : Predicted number ofremoval/IMA repair cycles in one MC.
RPF = (Predicted # of repairs)/(MC * UPA)
Turn Around Time (TAT) : Average number of days between . -
removal of a repairable item for processing at the AIMDand return to Ready For Issue (RFI) condition. Thisestimate includes time to schedule, fault isolate,disassemble, repair, assemble, and test a repairableassembly.
The candidates for inclusion in the AVCAL are chosen as
follows. The attrition quantity in any ninety day period is
determined as follows:
(1) Compute Flight Hour Factor (FHF) for aircraft:
FHF = (avg. # of Aircraft)* (Operating Hrs./Qtr.)
(2) Compute Expected number of Maintenance Cycles per
Using these calculations, an RPQ of 0.11 is the minimum
value that will require an RPA of one. Below the 0.11
level a stock quantity of zero satisfies the 90% protection, 0
and no part is stocked for the pool.
C. MODEL LIMITATIONS
The ASO model is the oldest of the three models discussed
in this thesis. It is the only model developed before data
automation and powerful computers became widespread in the
Navy. This partially explains the model's simple approach
to the inventory problem. Procedures are simple enough that
inventory levels could be calculated by hand for each part,
one at a time, with the use of one short table from the ASO
Manual. One noteworthy weakness in the model is the omission
of the concept of budget. The only direct reference to dollar
amounts is in the use of $5000 as a cutoff amount for attri-
tion allowance. But even this figure has become completely
arbitrary because there is no provision for its change or
update and because it applies to inventories with parts
typically ranging in price from a few hundred dollars to over
several hundred thousand dollars.
Mitchell [Ref. 11] pointed out that limiting TAT to twenty
days is not a true reflection of the real repair pipeline
operation. A breakdown of the TAT elements is shown below in S
Figure 3.2. The limit values were developed at ASO in a study
conducted in 1977 [Ref. 121. The limit values tend to under-
state the problems encountered in the repair pipeline. The
37
: ..oi i -<. i . , -. . ., _.i.._ - ;. .. :,. .. :i;. - .i . . il . . ;i.i ... .. i.i . -_ i i ;. _ ,- . , _.-. - - . . .. ,i: ,.
values are applied across all parts, although the complex
equipments encounter longer times than the simple parts.
TAT element Limit (days)
IP: In-process time 1SKD: Scheduling time 3RPR: Repair time 8AWP: Awaiting parts time 20
TAT: Total time 20
Figure 3.2. TAT Elements.
The ASO model is tasked to achieve material availability
goals and stockage criteria promulgated in OPNAVINST 4441.12A
[Ref. 13]. For ships, the objective for overall AVCAL per-
formance is to fill 75% of all demands and to provide overall
availability of 85% for items stocked. But as noted in the
Navy Fleet Materials Support Office RIM-AIR Study [Ref. 14],
the ASO model has historically failed to do this. Fleet
aircraft availability is often achieved only through a
constant process of selective cannibalization of squadron
aircraft parts. For example, in an E-2C squadron with four
aircraft aboard a carrier, one aircraft is designated the
"parts locker" in order to overcome shortcomings in both the
repair and requisition pipelines.
38
There is a disadvantage in the ASO criteria that
attrition and repair demand be segregated. Separate range
criteria are applied to determine attrition and repair
pool support. This splitting of demand results in non-
stockage of items that would have been stocked had demand
been combined. This contributes to the overall conservative
approach that characterizes ASO Manual AVCAL levels.
3 9
S ' ' ' "- - - "i . i . . . . . . , l i _ . ' " " " "
IV. RIMAIR MODEL
A. MODEL DESCRIPTION
During the Seventies all DOD budget policies came under
close scrutiny by civilian government leaders. The DOD
Retail Inventory Management and Stockage Policy (RIMSTOP)
Study was issued in 1976 to set guidelines for retail level
inventory support provided by the military services [Ref. 14].
Out of RIMSTOP originated DOD Directive 4140.44 (Supply
Management of the Intermediate and Consumer Levels of
Inventory), and DOD Instructions 4140.45 (consumable items),
4140.46 (repairable items) and 4140.47 (war reserves).
DODI 4140.46 [Ref. 151 dictates that:
"the following levels will be computed for eachrepairable item to be stocked at the intermediatelevel on a demand-supported basis:
(1) Repair Cycle Level (RCL). The RCL is a functionof the anticipated number of maintenance replacementsthat will be repaired locally and the item's repaircycle time.
(2) Order and Shipping Time Level (OSTL). The OSTLis a function of the anticipated number of maintenancereplacements that will require supply from externalsources and the item's order and shipping time.
(3) Safety Level (SL). The SL is a function of thecapabilities that the repair cycle time will be exceeded,the order and shipping time will be exceeded, the main-tenance replacement rate will be higher than forecasted,and a number of maintenance replacements, anticipatedfor repair at the activity, will require resupply fromexternal sources.
40
(4) Operating Level (OL). The OL is an EconomicOrder Quantity (EOQ) and is a function of the cost toorder and the cost to hold an item of inventory.
(5) Replenishment. Replenishment action will betaken when the asset position reaches the reorder point."
In addition, DODI 4140.47 (Secondary Item War Reserve
Requirements Development) authorizes increments to the order
and ship time, repair cycle and safety levels to satisfy
wartime recurring demands over and above the peacetime
demands. An additional Resupply Delay Time (RDT) level is
also authorized to provide material coverage of anticipated
delays in the wartime retail level supply pipeline.
Commander, Naval Supply Systems Command (COMNAVSUPSYSCOM)
proposed a pipeline model that would adhere to these DOD
policies while attaining Navy availability goals. This model
was designated Repairables Integrated Model for Aviation
(RIMAIR). In addition to the levels mentioned above, RIMAIR
added a level of stock that assures a self-supporting capa-
bility for a prescribed period of time, known as an "endurance
delta". The same assumptions stated for the ASO model apply
to this model.
RIMAIR produces a total depth of stock that equals:
Incorporation of these concepts into the essentiality code
is difficult. For this study an item essentiality code
equal to one was assumed for all parts. One reason for this
was because all parts were considered equally essential for
aircraft mission performance.
The Lagrange multiplier provided control for budget
levels as discussed above. By decreasino lambda the inven-
tory cost would increase, or by increasina lambda the
inventory cost would decrease. This budaet control function
was discrete. The actual inventory cost could vary from the
target budget by as much as the cost of a single part.
The RIMAIR algorithm was included within the TIGER
program as a separate subroutine. First, RIMAIR inventory
levels are computed in the subroutine and second, TIGER
simulates aircraft flights with these RIMAIR stocks as
input. Lambda values are included in the input data file,
external to the TIGER program. Lambda values are changed
and new budget levels are then examined to see if they meet
the target budget.
The RIMAIR and ASO models share some of the same weak-
nesses because they are based on the same underlying assump-
tions. The problem that the ASO model encountered with TAT,
discussed in III.C, is also present in RIMAIR. This points*Iout that there are problems in the inventory decision process
that exist above the model level. In this case, it is with
the Navy process of data collection of TAT.
52
Another comparison can be made between the two models
as far as workload required to support it. The RIMAIR model
j| increases the workload compared to the ASO model because
RIMAIR introduces two new parameters, the item essentiality
code and the lambda value. The problem with the essentiality
code, as mentioned above is how to assign it7 faulty coding
can result in unbalanced AVCALs. Time must be spent assigning
and updating these codes. Since the lambda value is assianed
external to the RIMAIR subroutine, time is spent checking
budget levels and resetting lambda values. One improvement
to the present algorithm would be to include a loop in the
* program that would change the lambda value depending on
proximity to target budget.
Both the ASO and RIMAIR models are retail level, single
echelon models. This means that they calculate AVCALs only
for the organizational level facility. Multi-echelon models
have been developed that spell out stock levels at organiza-
tional, intermediate and depot level facilities. The next
chapter will examine one of these multi-echelon models, ACIM,
that can also be used for the single-echelon case.
53
. °
V. ACIM MODEL
A. MODEL DESCRIPTION
The Naval Sea Systems Command's Availability Inventory
Model (ACIM) was developed after the Chief of Naval
Operations directed that "a sophisticated availabil'ity-
based sparing technique be developed and applied on a
selected basis for equipments which require a level of
readiness above that which standard policies can provide
[Ref. 16]."
In response to this CNO direction, the Chief of Naval
Material issued NAVMATINST 3000.2. This instruction
established Operational Availability (A ) as the primary0
measure of material readiness for Navy weapons systems
and established policy for A analytical techniques.
Subsequently CHNAVMAT recommended, and CNO approved, a
standard availability centered optimization model for use
by all program managers in determining consumer level
stockage quantities for selected equipments. This ACIM
0model develops repair parts allowances to achieve a
specified A at the minimum possible inventory cost.
0
This thesis will investigate ACIM model version 2.0,
developed by CACI-Inc Federal and implemented by Henry J.
Watras for use on the NPS IBM 3033. This chapter will
describe the ACIM model as it applies to AVCAL determination
54
14
in this thesis. A more detailed analysis of this model can
be found in McDonnell [Ref. 17] and in the ACIM Handbook
*[Ref. 16].
The underlying assumptions of the ACIM model are
listed below.
1. Included parts are organized in terms of anequipment with topdown breakdown. Multiple units of apart within a given next higher assembly are representedonly once in the breakdown. However, if the same partappears in different locations in the structure, eachappearance is treated as a unique item in the operationof the model.
2. External demands upon supply are stationary andcompound-Poisson distributed.
3. All stockage locations use a continuous review,(S-l,S) ordering policy.
4. Mean times to repair are defined as constantswhich include all equipment repair related down timesthat are not supply related.
5. Component failures are independent.
6. No further demands for parts can occur when oneor more parts are in down status. That is, when a partfails the system does not operate again until the failedpart is replaced.
A top-down breakdown is one which starts with the
highest level unit, in this case the E-2C aircraft. The
next level down is the WRA level, which are the individual
parts discussed in this study. Below the WRA level is the
Shop Replaceable Assembly (SRA) level, the sub-SRA level,
and on down until the smallest diode or resistor has been
itemized. This multi-level approach is also called a
multi-identured approach. For this study only WRA level
55
. - - ,,
inventories will be computed although ACIM can compute
stocks down to the lowest level.
The ACIM definition of availability is the same as
that used in the TIGER simulation model; namely,
A UPTIMEo UPTIME + DOWNTIME
ACIM replaces uptime by MTBF and downtime by Mean
Time To Repair (MTTR) plus Mean Supply Response Time
(MSRT). So, A° can be reexpressed as:
A =MTBF
o MTBF + MTTR + MSRT
The MTTR and MTBF parameters are inputs to the ACIM
model. The MSRT factor depends on the stockage levels and
ACIM uses this dependency to achieve a target value of A0
ACIM actually attempts to minimize MSRT in order to
maximize A0
B. INVENTORY DETERMINATION
1. ACIM Solution Equations
The model is defined recursively by considering an
arbitrary item in the system and an arbitrary facility.
The system is the aircraft, and the items are the individual
parts (WRAs). The structure of the model is civen by the
following set of definitions and equations:
a. Let i be an arbitrary item in equipment e (whichmay be e itself). Let u 0 represent an arbitrary facilityin the support system.
56
b. M. = DEL + RiU IU iu'
M. = mean time to return a failed item i atM. location u to a serviceable condition7
DEL. = expected delay per demand for item i
at location u, experienced in the
repair and requisition pipelines-
R. = mean time to repair item i at userlU location u (for on-equipment repair)7
= 0 if location u does not operate theequipment.
1C. DEL. = (X-S i ) * p(X; Y * T iu)iu X> S .u
where S. = stock level of item i at location7S lU
Y. = expected number of demands upon inventorylU for item i at location u;
p(X; Y iu*T ) = probability of X units of stock reductionfor item i at location u; the distribution
may be Poisson, Normal or Negative Bino-mial, depending on the mean and varianceof the part;
T. = mean resupply time (time to replace aniu inventory loss) for item i at location u.
d. T = P iu(Liu + L' iu) + (1-P.u) * (Riu + R' iu),
where Piu = probability that a demand for item iupon inventory at location u results ina loss (discard or sent elsewhere forrepair) which must be replaced throughresupply;
Lu = average resupply lead time assuminq stockis available at the resupply source;
L'iu = additional resupply lead time due toexpected shortages at the resupplysource;
57
+ . , . , . .,.
R : average shop repair cycle time assumingiu availability of spares for items within
i at the next lower indenture level;
R'iu= additional shop repair cycle time due toexpected shortages of srares for itemswithin i at the next lower indenturelevel.
The values of Liu, R iu' T iu' and Yiu are inputs to the
model.
D iv for u = 0
e. L
D io for u = 1,2,...,U,
where v is the resupply source for location 0 and v=0 if
the location 0 has no resupply source.
f. R' . Y. M U/ Y YjjCi ]l j C U u
where j identifies items within i at the next lowerindenture level; j = 0 if i has no subordinate parts.
g. A =/(i + Y *M ) ,eu eu eu
where A fraction of time equipment e is available foreu
use at location u (defined only for locations u whichoperate the equipment).
2. Objective Function
The overall objective of ACIM is to determine
stockages levels for all items and all stockage facilities so
that the expected operational availability of the equipment
is maximized for a given inventory budget or, conversely, to
find levels which achieve a given operational availability
at least cost. This objective can be explicitly stated as
follows:
Find values for Sk for all items k and locations v in the
58
support system which minimize DEL = DELeu for all user
locations u subject to:
SckSk < B,
k,v
where ck = unit cost of item k7
B = given budget for spares procurement.
A similar statement can be written for the converse
objective of achieving a given value for A at least cost.eu
The ACIM solution to the problem defined above is S
found by a recursive procedure based upon equations b-g.
First, however, a subproblem is defined and a solution
procedure is given for the subproblem. A recursive appli- 0
cation of the subproblem is then used to solve the original
problem.
The subproblem is set up as follows. Substituting
equation d in c, the expected delay per demand is given by
DEL. i DEL (S iv L iv, R'iDiv ,v ,v i
where the stock level S iv, additional resupply time L'iv,
and additional repair cycle time, R' iv, are considered as
decision variables for an arbitrary item ice and arbitrary
location v in the support system. Suppose that values for
Si are given for all items and locations v. The subproblem
is to find a particular item and location such that a one
unit increase in its stock level will yield the laraest
decrease in DELeu per dollar investment for some user
12 Indenture14-42 Part number/nomenclature43-44 Cognizance45-50 Number per next higher assy $/cents60-64 SMR&R codes65-71 Best Replacement factor per year
bE 72-75 Minimum Replacement unit76 Military essentiality code77 Override code78 Override amount
Format I Record Example
1 1072 HF POWER AMP000000000111111111122222222223333333333123456789012345678901234567890123456789
IR 6 3494000 OG 8.4050 114444444444555555555566666666667777777777801234567890123456789012345678901234567890
Figure 5.3. Format I Data Elements and Record Example.
69
0 "• • . .. . .. • ...
iI
after the first should be assigned a code of 2.
Part Number. Enter the NIIN/NICN or other part or
stock number for item identification purposes. Part
number field size is defined in Format A. The rest of the
field entries are for Nomenclature.
Nomenclature. Enter textual data that identifies or
describes the item.
Cognizance Code. Enter a code identifying the manage-
ment cognizance of the item.
Number Per Next Higher Assembly. Enter the number of
units of the item in the equipment.
Unit Cost. Enter the estimated unit procurement cost
of the item in dollars and cents. There is an implied
decimal point between columns 57 and 58 (cents occupy
columns 58-59).
SM&R Codes. The Source, Maintenance and Recoverability
codes are given. Entries for the maintenance codes are
mandatory, others are optional.
Application Replacement Factor. Enter the actual
anticipated number of times that the item will be replaced
during one year of operation. This value represents an
average over all items (of this type) in the system.
Minimum Replacement Unit (MRU). Enter a value for
the MRU if different than 1. For this study 1 was used.
Military Essentiality Code (MEC). Enter a 1.
70
o .- , . ° . .
Override Code. The only override code used was Y,
which was assigned to indenture level 1 equipment (total
system). This code includes the item in all model processes
but a zero stock level is assigned.
Override Quantity. Not applicable.
C. MODEL LIMITATIONS
The ACIM model is the most flexible model of the three
inventory models discussed so far. ACIM's flexibility lies
in its ability to solve either of the following problems for
multi-echelon or single echelon supply systems:
1. Select a minimum cost collection of spares for a
system so that the system will achieve a given availability
target.
2. For a given budget select a'collection of spares
that will produce maximum availability for the system.
For this study ACIM was usually operated with a budget
constraint. This was primarily due to the fact that the
RIMAIR algorithm provided for control of the budget only.
Therefore, the two models were compared on a equal budget
basis. After running ACIM at a specific budget level the
resulting inventory levels are manually input into the
input data file for the TIGER simulation model.
ACIM, like the other two models, is a steady-state
model. This means that the model operates on the assump-
tion that all flows through the repair and requisition
71
pipelines have stabilized. The inventory system is
assumed to be operating at a constant rate over a long
period of time. This means that the model cannot be used
to investiaate surge demand periods.
This model does have a few computational approximations
that should be noted. The first concerns ACIM's approxima-
tion of availability. ACIM assumes that no failures can
occur after the first failure occurs. In actual aircraft
systems, a single part failure will usually only degrade
the system performance rather than cause the entire system
to shut down. Parts usually continue to operate and con-
tinue to experience failures after one part fails. In
addition, the process of minimizing MSRT does not yield the
same stockage decisions as maximizing availability. For
some systems the results may be similar, but for other
systems there may be large differences.
Another peculiarity of the model is that it assumes that
the yearly operating tempo input for a system represents
operating tempo per "available year". For example, if an
aircraft is scheduled for 1000 flight hours per year and 50%
availability target is assigned, ACIM tacitly assumes it
flies 500 hours per year.
When using the ACIM model to match a target budget (or
availability), the iterative process only approximates the
target goal. The ACIM algorithm will always exceed the
target because it adds an item to the inventory until the
72
target is reached. Due to the discrete nature of the
problem, the budget goal may be exceeded by an amount almost
equal to the least expensive part7 and that may be significant.
The ACIM model does present a sianificant increase in the
workload required for data input. The exact topdown break-
down of parts, parts parameters, and maintenance facility
information is required. Nevertheless, ACIM appears to be a
useful tool and can be expanded to encompass many repair
facilities at different levels, handling inventory problems
1-4 14 JCC No. of timeline iterationsto be run for the datadeck.
5-80 19A4 RUNID Alphanumeric run identifier.
5. Statistical Parameter Card.
To run a predetermined # of missions, set NOPT & NMAX equal
to the no. of missions, and PL = 1.0. A value of XK = 1.28
corresponds to 90% lower confidence limit.
Columns Format Variable Description
1-4 14 NMAX Max no. of missions to be
* run (may not exceed 1000)
5-8 14 NOPT Optimal no. of missions tobe run (may not exceed MAX)
9-12 F4.0 PL Reliability spec. required
13-16 F4.0 XK Std.Dev. for lower conf.limit
17-20 14 ISEED Random number seed
21-24 14 NPH No. of phase types (max of6)
9
94
6. Phase Type and Duration Cards.
This card specifies the type of phase and duration of eachphase. A phase is time period with both a repair policy anda system operation policy. Two phase types were used: type1, flight phase; and type 2, ondeck repair phase. One cardcorresponds to a 24-hour period. Duration is in hours.System is presently configured for four phases per day.
This card determines the scenario under which a simulationcan be run. The default values will allow TIGER to simulatea mission under the same conditions under which theinventory models will calculate planned inventory levels.So if the ASO model, for example, plans for a 1000 flight-hour quarter with pipeline times equal to ten days, TIGERwill simulate a 90 day mission with these same parameters.By changing the default values on this card, inventorylevels will be calculated under parameters entered onprevious cards, but TIGER will simulate under conditionsdefined by this card. This permits investigation ofinventory policy during periods of abnormally high tempoflight operations or lengthened pipeline times. NDAYS canbe varied from 0-90 days. NWAR is a 2-state variable: 0means previous inventory parameters will be used, 1 meanswartime scenario and new parameters will be used. One ofthe new wartime parameters is BCMFAC, which increases theBCM rate for all parts. Another is REPFAC, which willincrease the on-ship repair time for all parts. NTIME willbe the higher system operational time for the war scenario,equal to the flight time expected for one A/C in 90 days.
Columns Format Variable Description
1-4 14 NDAYS Length of scenario (0-90days)
5-8 14 NWAR Sets wartime scenario:0: original parameters
(no change)1: new values for SRTIM,
BCM & NTIME will becomputed
9-12 14 NOAC No. of A/C used in scenario
13-16 16 NTIME A/C flight hours in wartime
17-21 F5.1 BCMFAC Fractional change in BCMrate
22-26 F5.1 REPFAC Fractional change in on-shiprepair times during war
5: to specify printoutusing the KS variables(see below)
6: TIGER/MANNING completedetails printout
If KOPT=5, select from the following output options asneeded (otherwise leave the fields blank)
5-8 14 KS(l) = 1: Input data
9-12 14 KS(2) = 1: equip. downtime attime of missionfailure
13-16 14 KS(3) =1: downtime at end ofphase
17-20 14 KS(4) =1: abort messages
21-24 14 KS(5) =1: all events
25-28 14 KS(6) =1: ETIME matrix
29-32 I4 KS(7) =1: not used
33-36 14 KS(8) =1: not used
37-40 14 KS(9) =1: not used
41-44 14 KS(10) =1: system & subsystemstatus
45-48 14 KS(II) =1: TIGER/MANNINGdebugging
49-52 14 KS(12) =1: status of all groups
53-56 14 KS(13) =1: downtime messages
97
I . -
................................
9. Phase Repair Card.
This this study repair option 0 was used to simulate flightops and repair option 2 simulated A/C on deck under repair.
Columns Format Variable Description
1-4 14 IFLAG(l) Repair option for each phasetype, up to 6:= 0 if onboard repair allowed
in the phase= 1 if no on-board repair
allowed in the phase= 2 on-board repair allowed
but failure inhibited
5-8 14 IFLAG(2)
9-12 14 IFLAG(3)
13-16 14 IFLAG(4)
17-20 14 IFLAG(5)
21-24 14 IFLAG(6)
10.. Repair Policy Card.
REPOL was set to 1.0. Normally it determines what fractionof repairs will be done on-ship. In this study thisfraction was determined by BCM(I) instead. TAD2 specifieshow long a system can operate in a down state before systemfailure. For this study mission allowable downtime = 0.XM and XT were set at their default values = 1.0.
Columns Format Variable Description
1-4 F4.0 REPOL Decimal fraction of repairsto be performed aboard ship
These cards define the parameters for each type equipment.X is the time to replace a WRA from the A/C if a spare ison hand, arbitrarily set = 2.0 hours. V is used in thisstudy to specify the onboard repair time at the AIMD level.
Columns Format Variable Description
1-4 14 I Equipment type numbers, tobe assigned sequentially,from 1 to a maximum of 200
5-20 4A4 DUM(J) Equipment type description
21-28 F8.0 X Mean time between failure
29-32 F4.0 Y Mean time to repair/replace
33-36 F4.0 U Duty cycle utilization
37-40 F4.0 V AIMD part repair time
41-44 F4.0 W Admin delay time (depot/ship)
45-58 14 IDUM Not used
12. * Blank Card *** (Signals the end of equip. cards)
13. Equipment Cards.
These cards, one for each type equipment list individualparts by number, according to the equipment type. The firstnumber is equipment type, the numbers following it on thesame line are the individual parts for each type equipment.
Columns Format Variable Description
1-4 14 NTYPE The type no. associated withthe part numbers following it
5-8 14 LOAD(l) Part numbers, 19 per linemax. Numbers begin at 1 and
9-12 14 LOAD(2) may not exceed 500. No gapsallowed in numbering parts.
77-80 14 LOAD(19)
99
.....................
14. *** Blank Card *** (Signals the end of equipment cards)
15. Spares Model Card.
The only option used on this card was "999." (columns 21-24)
Column Format Variable Description
21-24 F4.0 SX Used to call Spares sub-routine to determineallowance levels
16. ACIM Inventory Card.
This card will input ACIM allowance levels. If XFLAG=0.0 is
selected on card #i, TIGER will simulate with this input.Any arbitrary inventory levels may be input on this line.
Column Format Variable Description
1-2 12 ISPARE One allowance is entered foreach equipment type, up to a
3-4 12 ISPARE max of 31.
61-62 12 ISPARE
17. System Card.
Columns Format Variable Description
1-4 A4 ID Any alphanumeric e.g. SYST,to identify the specificsystem
5-8 14 LL Phase Type number (sequen-tial) maximum value is 6
9-12 14 NSS No. of subsystems in thephase (varies only from 1to 31)
13-16 14 ISS System identification number,usually last group number onthe configuration matrixcards
17-24 F8.0 SSTIME System allowable downtime.100000 inhibits aborts.
One for each subsystem - up to 31. At least 1 subsystem
is required.
Columns Format Variable Description
1-4 A4 ID Any alphanumeric, e.g., theliteral SSl, SS2, ... SS31
5-8 14 LL Phase type number
13-16 14 ISS Subsystem identification no.This is a group # for a groupdefined on a ConfigurationMatrix Card. Each designatedsubsystem group must be agroup that, upon its failure,causes the system to fail.
17-24 F8.0 SSTIME(2) Subsystem allowable sustaineddowntime. To inhibit abortsuse a value of 100000.
19. Configuration Matrix Card.
One card for each group, up to 300 cards.
Columns Format Variable Description
1-4 14 NRO No. of members in the groupdefined on this card that arerequired to be operating andin an up status.
5-8 14 IB(l) The group no. assianed to thegroup of members defined onthis card. It may vary from501 to 1000 in any order.
101
Configuration cards cont'd.
Column Format Variable Description
9-12 14 IB(2) The numbers of the equipment &groups which make up the group
13-16 14 IB(3) defined on this card. Themax. no. of members in a group
17-20 14 IB(4) is unlimited; but if there aremore than 7, a continuation
21-24 14 IB(5) card is required of the sameformat. The no. required and
25-28 14 IB(6) master group must be identicalon all continuation cards.
29-32 14 IB(7)
33-36 14 IB(8)
20. * Blank Card *** (Signals the end of phaseconfiguration cards.)
NOTE: For each phase type, a set of the above System,Subsystem and Configuration Matrix Cards areentered, each set separated by a blank card.
21. Optional Output Card.
Columns Format Variable Description
1-4 A4 SPRS Place any alphanumeric, e.g.,SPR, in this field if a tableof spares usage is desired.
5-8 A4 APPL Place any alphanumeric, e.c.,APL, in this field if a sum-mary table of equipment thatcaused mission failures(unreliability) and systemdown times (unavailability)is desired.
9-12 A4 GMMA Not used
13-16 A4 DEMO Not used
102
pq
APPENDIX B
TIGER INPUT DATA FOR SERIES SYSTEM
This appendix contains the input data file representing
the series system configuration. The TIGER program reads
this file and proceeds with the simulation as defined in the
data file. Part parameters for Appendix B are identical
with those for the parallel system listed in Appendix C.
Input data cards 17, 18, and 19 are the only data cards that
are different for the series and parllel system data files.
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154
LIST OF REFERENCES
1. Chief of Naval Operations Instruction 5442.4H(OPNAVINST 5442.4H), "Aircraft and Training DevicesMaterial Condition Definitions, Mission-EssentialSubsystems Matrices, and Mission Descriptions",pp. 101-104, 20 May 1983.
2. Leather, J.E., An Evaluation of the Effect of SparesAllowance Policy Upon Ship Availability andReliability, M.S. Thesis, Naval Postgraduate School,Monterey, CA., September 1980.
3. O'Reilly, P.J., An Evaluation of AllowanceDetermination Using Operational Availability,M.S. Thesis, Naval Postgraduate School, Monterey, CA,June, 1982.
5. Naval Postgraduate School Report NPS55-81-005, NavalPostgraduate School Random Number Package LLRANDOMII,Lewis, P.A.W., Uribe, L., February 1981.
6. Boatwright, B.O., RIMAIR VS. Current ASO Policy: AComparative Analysis of Two Methods For DeterminingAvcal Stockage Levels, pp. 76-84, M.S. Thesis, NavalPostgraduate School, Monterey, CA, September, 1983.
7. Naval Operations Analysis, 2nd ed., pp. 262-272, UnitedStates Naval Institute, 1979.
8. Fleet Material Support Office, ALRAND WorkingMemorandum 352, Aviation Supply Support ofOperating Forces, 14 March 1980.
9. Ross, S.M., Introduction to Probability Models,New York, Academic Press, 1980.
10. Naval Aviation Supply Office Instruction 4423.32 CH-l,ASO Provisioning Manual, pp. 111-3-1, 111-3-15,27 November 1978.
11. Mitchell, M.L., A Retail Level Inventory Model forNaval Aviation Repairable Items, M.S. Thesis, NavalPostgraduate School Thesis, Monterey, CA, March, 1983.
12. Aviation Supply Office letter to Naval Supply SystemsHeadquarters ACA-I: JPB: mec 4790, Subj: Turn AroundTime Constraints, 2 November 1977.
155
.° .0 -.
*-77 --
13. Chief of Naval Operations Instruction 441.12A, SupplySupport of the Operating Forces, Enclosure (5), pg. 6,9 August 1973.
14. Fleet Material Support Office Report 155, RIM-AIR Study,pg. 1, Operations Analysis Department, 30 June 1983.
15. Department of Defense Instruction 4140.46, StandardStockage Policy for Repairable Secondary Items at theIntermediate and Consumer Levels of Inventory, pp. 3-4,7 April 1978.
16. Naval Seas Systems Command, Availability CenteredInventory Model Consumer Level Allowance DevelopmentHandbook, May 1983.
17. McDonnell, J., LAMPS MK III Pack-Up Kit SparesSelection As Depicted By the Availability CenteredInventory Model (ACIM), M.S. Thesis, Naval PostgraduateSchool, Monterey, CA, March, 1984.
156
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No. Copies
1. Defense Technical Information Center 2Cameron StationAlexandria, Virginia 22314
2. Library, Code 0142 2Naval Postgraduate SchoolMonterey, California 93943
3. Assoc. Professor F.R. Richards, Code 55Rh 2Naval Postgraduate SchoolMonterey, California 93943
4. Assoc. Professor A.W. McMasters, Code 55Mg 1Naval Postgraduate SchoolMonterey, California 93943
5. Mr. Peter Evanovich 1Center for Naval Analysis2000 North Beauregard St.Alexandria, Virginia 22311
6. LCDR Mark David Sullivan 24921 Whitewood LaneVirginia Beach, Virginia 23464