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Theses and Dissertations 1. Thesis and Dissertation Collection, all items 


1987 


Wholesale replenishment models: model evaluation. 


Hammer, Roger Elliot, Jr. 


http://ndl.handle.net/10945/22584 


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NAVAL POSTGRADUATE SCHOOL 


Monterey, California 





aE =f Sled bo 


WHOLESALE REPLENISHMENT MODELS: 
MODEL EVALUATION 


by 
Roger Elliot Hammer, Jr. 


June 1987 





Thesis Advisor: Alan W. McMasters 


Approved for public release; distribution is unlimited. 


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WHOLESALE REPLENISHMENT MODELS: MODEL EVALUATION 





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Hammer, Roger Elliot Orc 

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—s we eee eee 


COSATI COOES 18 SUBJECT TERMS (Continue on reverse if necessary and identify by block number) 

- EO Repairables, Depot Level Repairables, Repairables Models, 
—— Pee aes Wholesale Level ee Mean Supply 

SE a E: ables System 


<8STRACT (Continue on reverse if necessary and identify by san oor 






This thesis analyzes a new wholesale level repairables replenishment model 
proposed for implementation by the U. S. Navy. The new model uses the total 
investment level as its measure of effectiveness with a mean supply response time 
(MSRT) goal as a constraint. In addition, the new model requires that procurement 
and repair order quantities be specified as input parameters. The importance of 
the model is that it relates resources to readiness, an area of primary concern to 
Congress and the Department of Defense. Tests with actual data were conducted 
between the current Navy repairables model and the new model. The results of these 
tests indicate that the new model would consistently out-perform the current model 
for investment levels and system material availability (SMA). 


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Professor Alan W. McMasters 408-646-2678 Code 54Me 
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Approved for public release; distribution is unlimited, 
Wholesale Replenishment Models: Model Evaluation 
by 


Roger Ek. Hammer, Jr. 
Lieutenant Commander, Supply Corps, United States Navy 
B.A., University eof NOetn Garouinameecy. 


Submitted in partial fulfillment of the 
requirements for the degree of 


MASTER OF SCIENCE IN MANAGEMENT 
PEOn. Ene 


NAVAL POSTGRADUATE SCHOOL 
June 1987 


ABSTRACT 


This thesis analyzes a new wholesale level repairables 
replenishment model proposed for implementation by the U.S. 
Navy. The new model uses the total investment level as its 
measure of effectiveness with a mean supply response time 
(MSRT) goal as a constraint. In addition, the new model 
requires that procurement and repair order quantities be 
specified as input parameters. The importance of the model 
is that it relates resources to readiness, an area of primary 
concern to Congress and the Department of Defense. Tests 
with actual data were conducted between the current Navy 
repairables model and the new model. The results of these 
tests indicate that the new model would consistently out- 
perform the current model for investment levels and system 


material availability (SMA). 


eas: 


ele 


IV. 


TABLE OF CONTENTS 


INTRODUCTION 

A. BACKGROUND. ..........5 220 5 2 ee 8 
B. OBJECTIVES. .. 2.0... 060 5 vue ere 10 
C. PREVIEW... . 2... 6. es ee ee 10 


THE NAVY SUPPLY SYSTEM 


A. THE NAVY LOGISTICS ORGANIZATION......... aa 12 
B. SUPPLY SYSTEM OVERVIEW. °°...) en 14 
C. THE NAVY STOCK FUND. ye 18 
D. THE REPALRABLES SYSTEM, . 7... 20 
E. SUPPLY SYSTEM PERFORMANCE MEASURES... 9. 23 


THE REPATRABLES MODELS 


A. MODEL DEVELOPMENT............. ccc cee eceeueeeeeas 30 
B. THE MSRT MODEL............0900...) ee , 40 
C. UICP INTEGRATED REPAIRABLES MODEL................ 49g 


MODEL PERFORMANCE COMPARISON 


A. MODEL PROGRAMMING. ........ 3232 =) 
B. MODEL PROGRAMMING CHANGES. 7.0 eee 62 
C. PERFORMANCE TEST RESULTS......2 323 64 


REPAITRABLES MODEL SIMULALATIONS 


A. SIMULATION PROGRAMMING...........3..0 ee 67 
B. OCCURRENCE OF BACKORDERS. |... 22 69 
C. DEMAND DURING THE RESUPPLY CYCE. ee 74 
D. SENSITIVITY ANALYSIS FOR Q AND Koo ee 80 
E. RECURRING INVENTORY PATTERNS — 2 30 86 


VI. SUMMARY AND CONCLUSIONS 


fs SIOPeh SDC ge so 91 
POMC MOINS 45 ee es ss Mies 6 6 oe ee we 92 
C. RECOMMENDATIONS FOR FURTHER RESEARCH.............. 93 
APPENDIX A: PROGRAM TO TEST PROPOSED WHOLESALE .......... 96 


REPATRABLES REPLENISHMENT MODEL AGAINST THE 
CURRENT UICP INTEGRATED REPAIRABLES MODEL 


APPENDIX B: VARIABLE LISTING FOR REPAIRABLES SIMULATION. . 110 
APPENDIX C: PROGRAM LISTING FOR REPAIRABLES SIMULATION... 112 


LIST OF REFERENCES........... ccc cccccceccecceceeecneeeee. 122 


LIST OF TABLES 


TEST RUN SAMPLES ............-55 2) =e 61 
UICP/MSRT MODELS PERFORMANCE COMPARISON -............ 65 
SPCC MANAGED DLR'S 

UICP/MSRT MODELS PERFORMANCE COMPARISON -............ 66 
ASO MANAGED DLR'S 

PERFORMANCE STATISTICS FOR Q CONSTANT/R VARIED....... 82 
PERFORMANCE STATISTICS FOR R CONSTANT/Q VARIED....... 83 


bo 
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ouww wom Om Mm WwW Ww WD WD WwW 
Oo wm F&F WwW HO fF WN & WO NO F&F 


. 10 


LIST OF FIGURES 


Depot Level Repairables Inventory System............. 22 
CONUS ACWT and Gross Availability Goals.............. 27 
(IPG I and II Requirements) 

iRvshonulio= lolly (Cy olll je. . GE ee ee 0 32 
Datermmictaic Modelewathenow Batching..........08..... 36 
Deterministic Model With Batching.................... oe 
The Concept of Time-Weighted Units Short............. 45 
i eeinedonmoeehESKe ae Men... ....-- EY: 
Simulation Events File Excerpt No. 1................. 72 
Simulation Events File Excerpt No. 2................. tke 
Demand During Resupply Histogram No. l............... 77 
Demand During Resupply Cee Nom. = 719 
Demand During Resupply Histogram i (Coa ee ie... aes 719 
Simulated MSRT as a Function of Procurement.......... 84 
Quantity 


Samulated MSRT and SMA as a Function of O when R=i... 85 


Simulated MSRT and ADDDR as a Function of R.......... 87 
Simulated Net Inventory as a Function of Time -...... 89 
Plot No. 1 
Simulated Net Inventory as a Function of Time -...... 90 
Plot No. 2 


I. INTRODUCTION 


A. BACKGROUND 

In early 1977, the Naval Supply Systems Command (NAVSUP) 
began planning for a major project to replace all ADP system 
hardware and software at the Navy's two inventory control 
points (ICP's). Although the primary objective of this 
resystemization effort, known as Project Resolicitation, was 
to upgrade obsolete computer hardware at the Aviation Supply 
Office (ASO) in Philadelphia, Pennsylvania and the Ships 
Parts Control Center (SPCC) in Mechanicsburg, Pennsylvania, 
it also provided the opportunity to reevaluate the existing 
peacetime wholesale level inventory models used at these 
activities. [Refs.1,2,3] | 

In the spring of 1982, NAVSUP requested the Naval 
Postgraduate School to evaluate the existing wholesale 
provisioning and replenishment models for secondary items and 
make recommendations for improvements or changes. Throughout 
1982 and 1983, Richards and McMasters investigated the 
question of an appropriate wholesale provisioning model 
because improvements to the existing models had been given 
top priority by NAVSUP planners. They concluded that a new 
model should be developed around an objective function which 
directly relates resources to combat readiness as Congress 
and the Department of Defense were placing considerable 
emphasis on this relationship. [Refs.2,3] 

The new wholesale provisioning model proposed by Richards 
and McMasters was accepted for implementation by the Navy in 
December 1984. This model minimizes the aggregate mean 


supply response time (MSRT) for the total population of 


repair parts purchased for a new weapon system subject to an 
overall budget constraint. The MSRT model was selected over 
other proposed models because of its direct relationship to 
operational availability (A,) as defined by the Department of 
Defense and the fact that this is the only variable in the 
definition that the supply system can affect. [Refs.2,4] 
Following development of the provisioning model, 
attention shifted to the wholesale repairables replenishment 
model. Repairables, or more specifically depot level 
repairables (DLR's), presently account for over 80 percent of 
the estimated $28.0 billion wholesale inventories managed by 
ASO and SPCC [Refs.5,6]. As such, they are the focus of 
considerable management attention both within the Navy and 
the Department of Defense. DLR's are categorized as 
relatively high value components which have been determined 
to be more economical to repair than to replace when they 
fail in use [Ref.7]. ) 
In order to- provide a smooth transition from the 
initially provisioned inventory to the follow-on 
replenishment process, it was logical that the _ new 
repairables model be developed using a theoretical framework 
similar to that used in the new provisioning model. During 
1984, Apple, working with Richards and McMasters, developed 
the first formulation for a new wholesale repairables 
replenishment model which used minimization of MSRT in the 
objective function ([Ref.8]. The Apple model was a mlti- 
echelon model which attempted to incorporate the effects of 
not stocking a particular item at the shipboard level. As 
such, this model could not be easily implemented at the 
wholesale level because the ICP’'s do not currently maintain 
precise information about the range and depth of repair parts 


stocked by fleet operating units. 


9 


Throughout 1985 and 1986, both Gormly and Pearsall, also 
students of Richards and McMasters, continued work on the 
repairables model developed by Apple. Gormly converted 
Apple's multi-echelon model to an aggregate demand model 
which could be used at the ICP level with the existing ICP 
demand forecasting programs [Ref.9]. Pearsall investigated 
the potential impact of the Gormly MSRT model on ICP 
procurement workload and tested the model with selected real 
world data provided from ASO and SPCC data bases [Ref.10]. 


B. OBJECTIVES 

The primary objective of this thesis is to compare the 
theoretical performance of the wholesale repairables model- 
currently used by the ICP's against that of the Gormly 
aggregate demand MSRT model. The performance measures used 
for this comparison are total investment in wholesale stock 
and system material availability (SMA). Secondly, this 
thesis attempts to verify some of the underlying assumptions 
for the MSRT model and examine the effects of various 
stocking, repair and procurement policies on mean supply 
response time and material availability through the use of 


inventory simulation. 


C. PREVIEW 

Chapter II of this thesis provides an overview of the 
Navy Supply System including sections on the Navy Stock Fund, 
the repairables system and supply system performance 
measures. This is followed by a detailed presentation of the 
Gormly aggregate demand MSRT model and the current ICP 
integrated repairables model in Chapter III. Chapter IV 


discusses results from the performance comparison tests 


10 


conducted using actual inventory management data provided by 
ASO and SPCC. Chapter V describes the repairables model 
similation programmed for the MSRT model and discusses 
results of simulation test runs. The final chapter 
summarizes results of research conducted during the first 
half of 1987 for the MSRT repairables model and provides 


recommendations for areas requiring additional study. 


11 


II. THE NAVY SUPPLY SYSTEM 


The purpose of this chapter is to acquaint the reader 
with the current management organization and policies of the 
Naval Logistics and Supply Systems. The first section 
provides an overview of the present Navy § logistics 
organization and discusses the roles of the major logistics 
commands. This section is followed by a more complete 
discussion of the military supply system and the roles and 
responsibilites of activities under the cognizance of the 
Commander, Naval Supply Systems Command (NAVSUP). The second 
half of the chapter includes sections on the Navy Stock Fund, 
the Repairables System and Supply System Performance 
Measures. These sections are included to provide the reader 
with a better understanding of factors influencing 


development of the new repairables inventory model presented 


in Chapter III. 


A. THE NAVY LOGISTICS ORGANIZATION 

Within the Navy, primary responsibility for logistics 
support of operating forces rests with the Chief of Naval 
Operations (CNO). As the senior military officer in the 
Navy, the CNO is responsible for planning and determining all 
material support needs of operating forces including 
equipment, weapon systems, materials, supplies, facilities, 
Maintenance and supporting services [Ref.11]. Under the 
Chief of Naval Operations, there are five major systems 
commands assigned logistics management responsibilities: the 
Naval Air Systems Command (NAVAIR), Naval Sea Systems Command 
(NAVSEA), Space and Naval Warfare Systems Command (SPAWAR), 


12 


the Naval Facilities Engineering Command (NAVFAC) and the 
Naval Supply Systems Command (NAVSUP). Until 1985, the five 
systems commands were part of the Naval Material Command 
(NAVMAT) under the administrative control of the Chief of 
Naval Material. The Naval Material Command was dissolved in 
1985 by the Secretary of the Navy, and NAVMAT administrative 
responsibilities were assumed by the Office of the Secretary 
of the Navy (SECNAV), the Office of the CNO (OPNAV) and the 
Systems Commands. 

Three of these commands, NAVAIR, NAVSEA and SPAWAR, known 
as Hardware Systems Commands (HSC' s), have overall 
responsibility for acquisition and maintenance of weapon 
systems and major end items used by the Navy's operating 
forces. The HSC's act as the eentral technical authorities 
on all matters relating to support and maintenance of weapon 
systems for which they are responsible. Additionally, the 
HSC's have inventory management responsibility for selected 
secondary items of supply stocked within the Naval Supply 
system. [Refs.7,11] 

NAVFAC performs a similar function for the facilities 
requirements of the Navy shore establishment. NAVFAC has 
responsibility for administration of the military 
construction progran, shore facilities planning and 
maintenance, and material support for construction and 
transportation equipment. [Ref.11} 

NAVSUP, as the lead agency responsible for coordination 
of supply support for all operating forces and _ shore 
activities, performs a wide variety of functions including 
administration of the Naval Supply System, the Navy Resale 
Program, publications and printing, the Navy Stock Fund, the 
field contracting system and the Navy Transportation System. 
Additionally, NAVSUP administers the Navy Food Service 


13 


Program and exercises management control over all Navy 
material handling equipment (MHE) and special clothing. 
[Ref .11] 


B. SUPPLY SYSTEM OVERVIEW 

Conceptually, the Navy Supply System is described as a 
multi-echelon system in which responsibility for inventory 
Management of secondary items of supply is cooperative effort 
involving a large number of activities operating on the 
local, regional and national/worldwide level. The majority 
of these are end-use consumer activities (ships, aviation 
squadrons and shore facilities) which stock material 
inventories exolusively for their own consumption. The 
remainder are comprised of regional and national stock points 
and inventory oontrol points operated by the Navy, the 
Defense Logistics Agency, the General Services Administration 
and the other military services. Within the the larger DOD 
Supply System, approximately 4 million items of supply valued 
at over $100 billion are stocked in support of operating 
forces. Of these, the Navy uses approximately half or 2 
million items [{Ref.11]}. 

The Naval Supply System is concerned exclusively with 
inventory management of secondary items of supply, as opposed 
to complete weapon systems or principal end items. Secondary 
items are by definition "Consumable and repairable items and 
those end items not classified as principal end items.” 
(Ref.12] Seoondary item requirements are determined by the 
inventory control point (ICP) which has been assigned 
management responsibility for the item and are based on 
either observed/estimated demand or non-demand based 


insurance levels. Item attrition is based on normal in- 


14 


service wearout or consumption rates. Procurement of 
secondary items is financed with either stock funds or 
appropriated/investment funds depending on such factors as 
unit price, expected item life and item recoverability. 
Budget formulations for secondary items are based upon 
standard levels setting techniques and - stratification 
projections. Finally, issues to end-use activities are 
subject to established allowances determined by the ICP’s but 
are not usually restricted if the activity has a valid 
requirement for the item. [Ref.13] 

In contrast, a principal end item is defined as "A final 
combination of end products, component parts and/or material 
which is ready for its intended use (e.g. ship, aircraft, 
truck, mobile machine shop, etc.)." [Ref.12] Principal end 
items are specifically designated as such by the CNO, with 
responsibility for requirements planning and procurement 
delegated to the Systems Commands. Budget formulations for 
principal - end items are accomplished separately. from 
secondary items through material planning studies, cost 


benefit analysis and principle item stratifications. 


Procurements are financed exclusively with 
appropriated/investment funds under specific programs 
approved by Congress. Principal item attrition is based 


solely on major/total destruction, intended destructive use, 
or planned retirement. Issues to end-use activities are 
strictly limited to established allowances or by special 
authorization from the appropriate Systems Command. [Ref.13] 
There are three levels of inventory managed within the 
Navy Supply System: Retail-Consumer, Retail-Intermediate and 
Wholesale [Ref.12]. As already indicated, Retail Consumer 
inventories are held by operating units and shore facilities 


not having supply support as a primary mission. Only those 


IS 


items of supply required to support the primary mission of 
the unit are carried in stock at the Retail Consumer level. 
Material held at the organizational level includes both 
demand based items, and non-demand based insurance items, 
which are stocked to reduce the probability of extended down 
time for mission essential equipment. 

The Retail Intermediate Level, or first echelon of 
resupply within the Navy, includes inventories stocked by 
ships of the Mobile Logistics Support Force (fleet issue 
ships, tenders, repair ships), Naval Supply Depots (NSD's) 
located overseas, Naval Supply Centers (NSC'’s) located in the 
United States, selected shore activities having special 
missions (e.g., Naval Shipyards) or other activities located 
close to fleet customers {e.g., Naval Air Stations). Mobile 
Logistics Support Force (MLSF) ships and. overseas depots have 
primary responsibility for supply support of deployed 
operating units and shore activities located overseas. 
Regional supply centers and Naval Air Stations (NAS's) 
located in the United States are responsible for supply 
support of operating units and shore activities located in 
their designated geographical areas. Naval Shipyards (NSY's) 
stock retail inventories exclusively for their own needs. 
[Ref. 7] 

The Wholesale Level, or second echelon of resupply within 
the Navy, is oriented toward providing supply support at the 
national and worldwide level as opposed to the regional and 
local level. Physical inventories of wholesale material are 
stocked at six Defense Supply Depots and eleven GSA Supply 
Centers located throughout the United States,.and at the 
seven Naval Supply Centers {in addition to their Retail 


Intermediate inventories). Under the DOD Integrated Material 


16 


Management Program implemented for the wholesale level, each 
item of supply is assigned to a single inventory manager so 
that no two ICP’s have responsibility for the same item of 
supply. [Ref.7] | 

Within the Navy, the Aviation Supply Office (ASO) and the 
Ships Parts Control Center (SPCC) are the two inventory 
control points assigned wholesale level inventory management 
responsibilities. The Navy ICP'’s have two primary functions 
relative to the management of secondary items of supply: 
supply support and program support. The supply support 
function is commodity oriented and involves inventory 
Management of secondary items used exclusively by the Navy, 
as well as some items used by the other services. Supply 
support functions include inventory levels setting, material 
identification and cataloging, consolidated allowance list 
preparation, maintenance of item planning and technical data, 
and arrangements for financing of system stocks. [Ref. 7] | 

Program support is weapon system oriented as opposed to 
commodity oriented and involves coordination of all supply 
Support arrangements for weapon systems and equipment in the 
Navy inventory. Program support functions include secondary 
item cataloging, initial provisioning, allowance list 
preparation, arrangements for material repair and 
replenishment, and monitoring the overall logistic support 
status of assigned equipment and systems [Ref.7]. As many 
items of supply required for support of Navy systems at the 
wholesale level are managed by non-Navy activities, the 
program support manager is responsible for ensuring that 
these activities procure sufficient stock to meet the Navy's 


planned requirements when new weapon systems are fielded. 


17 


C. THE NAVY STOCK FUND 

The Navy Stock Fund (NSF) is a working capital revolving 
fund established by Congress for purchase of secondary items 
ef supply stocked within the Navy Supply Systen. Items of 
supply purchased with NSF money are held in suspense in the 
Navy Stock Account (NSA) on the inventory records of Navy 
stock points until they are issued or “purchased” by an end 
use activity. When NSA stock is issued or "sold" by a stock 
point, the Navy Stock Fund is reimbursed for the cost of the 
material with funds transferred from the Operation and 
Maintenance (O&M) appropriation of the requisitioning 
activity. Although the ratio of materials to cash in the 
Navy Stock Fund is constantly changing over time, the fund 
maintains a relatively constant total asset value. This 
total asset value of money and material is often referred to 
as the “corpus” or body. [Refs.7,14] 

In order to recover all costs associated with inventory 
management of supplies purchased with stock fund money, a 
surcharge is added to the price of each item issued from 
stock. The surcharge is designed to reimburse the fund for 
material losses due to damage, obsolescence or physical loss; 
transportation charges for material moving between stock 
points and to customers; and anticipated price increases for 
material purchased from commercial vendors. {[Refs.7,14] 

Administration of the Navy Stock Fund is_ the 
responsibility of NAVSUP. NAVSUP, in turn, has assigned 
Management control for NSF money to the two Navy ICP’s, ASO 
and SPCC, and to the Navy Retail Office (NRO) at the Fleet 
Material Support Office (FMSO) located in Mechanicsburg, 
Pennsylvania. ASO and SPCC use stock fund money to purchase 
new repair parts and consumables directly from manufacturers 


and to fund repair of depot level repairables (DLR’s) at both 


18 


Navy and commercial repair activities. Wholesale material 
purchased by the Navy ICP’s is “pushed” to designated stock 
points where it is held in inventory along with the 
activity's own retail stock. [Ref.7] 

The Navy Retail Office allocates NSF money to Retail 
Stock Points for purchase of materials and supplies stocked 
for eventual resale to their own customers. Sources of 
supply for NSA material purchased by Retail Stock Points 
include both DLA and GSA wholesale level activities, ASO and 
SPCC, as well as commercial vendors. Material purchased from 
wholesale level activities for stocking at the retail level 
is “pulled” from the wholesale system by registering customer 
demands with the inventory control points. [Ref.7] 

Until 1981, all depot level repairables (DLR's), due to 
their relatively high unit cost, were classified as 
investment items and were procured and repaired with funds 
appropriated annually by Congress. As system stocks of DLR's 
had already been paid for with investment funds, the 
customers' operating budgets were not charged when a 
repairable was issued from system stocks. On i April i981, 
all non-aviation DLR's managed by SPCC were capitalized into 
the Navy Stock Fund under a pilot program designed to improve 
system-wide asset management of repairables ([Ref.7]}. The 
primary reason for transferring DLR's to the stock fund was 
to provide increased funding flexibility to repair or 
reprocure system assets as required without having to go 
through the lengthy annual budget process. The pilot program 
was so successful that a major portion of aviation DLR's 
managed by ASO were also transferred to the Navy Stock Fund 
on 1 April 1985 [Refs. 5,7]. 


19 


In order to reimburse the stock fund for the cost of 
repairs and replenishments for DLR's, a dual pricing system 
was implemented in which the customer is charged either a 
reduced "repair price" or full reprocurement price depending 
on whether a repairable carcass is turned-in to the supply 
system. The new pricing system has had the added benefit of 
improving management of repairable assets at the user level 
as customers are now charged the full reprocurement price for 


failing to turn items in promptly. [Ref.7] 


D. THE REPAITRABLES SYSTEM 

Within the Navy, a system component is designated as a 
repairable if its repair cost is less than one hundred 
percent of its replacement cost and/or its repair time is 
less than its procurement lead time [Ref.10]. A component is 
initially designated as a repairable during the design phase 
of development for a new weapon system through a process 
known as level of repair analysis (LORA). The LORA process 
not only determines whether a system component will be a 
repairable, but also the level of maintenance at which it 
will be repaired. An item designated as a repairable 
continues to be managed separately during initial 
provisioning for the new weapon system and subsequently 
during the repair and reprocurement cycles until it no longer 
meets the criteria for being a repairable or the weapons 
system is phased out. 

There are three levels of maintenance at which repair 
action may occur: (1) the organizational level (i.e., a 
ship); (2) the intermediate level (i.e., tender, aircraft 
carrier or shore intermediate maintenance activity); and the 
depot level (i.e., Naval Shipyard, Naval Air Rework Facility 


or commercial repair activity). Repair of Navy depot level 


20 


repairables (DLR's) is centrally managed at the wholesale 
level by the two ICP’s: ASO and SPCC. Figure 2.1 illustrates 
the flow of transactions and movement of material for depot 
level repairables. [Ref.7] 

The cycle begins when a customer submits a requisdtden 
(demand) for a DLR to the nearest stock point (e.g., NSC, 
NAS). In the normal situation, the customer will also ship a 
failed component to the stock point within a few days 
following submission of the requisition. If the requested 
item is available for issue at the stock point, it is shipped 
directly to the requisitioner. Otherwise, the requisition is 
referred to the inventory manager at the ICP having 
responsibility the material. If the item is available at 
another stock point, the inventory manager refers’ the 
requisition to that activity for issue. Once the item has 
been shipped from a stock point, the transaction is reported 
to the cognizant ICP by means of a transaction item report 
(TIR). If a ready-for-issue (RFI) component is not available 
within the system, the demand will be recorded as a backorder 
against material which is due in from repair or procurement. 

At the wholesale level, the inventory manager's primary 
responsibility is to ensure that an adequate number of units, 
both REI and not-ready-for issue (NRFI), are available within 
the system to fill programmed requirements and expected 
future. demands from customers. This is no easy task given 
the rapid advancements in weapon systems technology which 
often make repair parts obsolete in a relatively short period 
of time. The repairables management problem is further 
complicated by the fact that procurement lead times for these 
high dollar value items often exceed four years. 


Consequently, the inventory manager must constantly be alert 


21 


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22 


to changes in demand patterns which would result in either an 
overstockage situation or critical shortage of material. 

At present, the ICP's major areas of concern are carcass 
tracking and repair turnaround times. Recently, a new 
Repairables Management Data System has been implemented at 
ASO and SPCC to maintain more positive control of repairable 
assets moving through the system and to monitor repair 
progress at designated overhaul points (DOP’s). The purpose 
of the system is to reduce repair turnaround times and 
improve carcass return rates [Ref.7] Recent discussions with 
SPCC repairables managers indicate repair turnaround times 
for non-aviation DLR's have been reduced by 44 percent over 
the past 4 years and now average just over 120 days [Ref.15]. 

While repair management occupies the majority of the 
inventory manager's time, he must still actively monitor 
system attritions and promptly initiate reprocurement action 
with the manufacturer when a _ shortfall is projected. 
Currently, the Supply Demand Review (SDR) application is used 
at the ICP's to identify candidates for reprocurement. SDR 
is part of a larger group of computerized inventory modeling 
applications and files collectively known as the Uniform 
Inventory Control Program (UICP). As indicated above, long 
procurement leadtimes for many repairables coupled with low 
attrition rates make procurement forecasting more an art than 
a science. Often a manufacturer for a particular item has 
already ceased production and would have to expend 
considerable effort to reconfigure his current production 


line to make the small number of items required by the Navy. 


E. SUPPLY SYSTEM PERFORMANCE MEASURES 
In order to ensure the military's operating forces 


maintain a high degree of material readiness, the Secretary 


23 


of Defense, in consultation with the military services and 
the Defense Logistics Agency has established uniform 
inventory management policies and minimum performance goals 
for both the wholesale and retail levels of supply. The CNO 
has also established minimum performance goals for weapon 
system operational availability which includes supply support 
as a key parameter. The following is a detailed discussion 
of the measures of performance used by the Naval Supply 
System to guage mission effectiveness. Definitions and 
formulas in this section are taken from NAVSUP Publication 
953 [Ref.7] unless otherwise indicated. 

Performance measures used by the supply system fall into 
two major interrelated categories: material availability and 
supply response time (or delay time). Material availability 
Measures include System Material Availability (SMA) or Gross 
Availability, computed at the wholesale level; and Gross and 
Net Availability, computed at the Retail Level. Supply 
response time measures include Average Days Delay (ADD), 
Average Days Delay for Delayed (backordered) Requisitions 
(ADDDR) and Average Customer Wait Time (ACWI), also known as 
Mean Supply Response Time (MSRT). 

SMA (or Gross Wholesale Availability) is defined as the 
percentage of customer requisitions received at the wholesale 
level which are filled from on hand stock. SMA can be 


computed as: 


Backorders Established | 


SMA(%) = 100 ~ Ween) Nomande af blo Whoo 
(4) : [1 Total Demands at the Wholesale Level 


The SMA goal established by the CNO for the wholesale level 
is presently 85 percent [Ref.12]. 


24 


Both Gross Availability and Net Availability are 
performance measures established by DOD for the Retail 
Intermediate and Consumer Levels oof supply. Gross 
Availability, also called Point of Entry (POE) effectiveness 
at Navy stock points, is defined as the percentage of total 
demands for both stocked and non-stocked items that are 
satisfied from on hand inventory. Gross Availability at the 
retail level is computed in the same manner as SMA is 
computed for the wholesale level. The Gross “Availability 
goal-for the Retail Intermediate Level is presently set at 70 
percent. ([Ref.12]} At the Retail Consumer Level, Gross 
Availability aoa are 65 percent for ships and shore 
aotivities receiving intermediate level support, and 75 
percent for aviation units [Ref.12]. 

Net Availability is the percentage of total of demands 
received for stocked items that are filled from stock at the 


supplying activity: 


Demands Filled for Stocked = | 


Net Availability(%) = 100 
r= CYS) | Total Demands for Stocked Items 


The Net Availability goal for both Retail Intermediate and 


Consumer activities is currently set at 85 percent [Ref . 12]. 


ADD is a measure of how long it takes to fill requisition 
received at the wholesale level from available system stock. 
As the ICP's do not presently collect times required to fill 
individual requisitions, the ADD caloulation is approximated 
by: 

ADD = Backorders at the End of the Month 
Requisitions Processed During the Month 


25 


ADDDR attempts to measure how long it takes to fill a 
backordered requisition. ADDDR is computed using the 


following approximation: 


Backorders at the End of the Month 


Aven ies Backorders Established During the Month 


Average Customer Wait Time (ACWT) is defined as _ the 
average time, in days, required to fill a customer demand 
regardless of whether or not the item is stocked in the 
supply system. For the Navy, the CNO has established an ACWT 
goal of 125 hours for critical maintenance requirements 
requisitioned by end-use activities located in the 
continental United States (CONUS) and 135 hours’ for 
activities outside the United States (OUTCONUS) [Ref.12}. 
The system-wide ACWI goal of 125 hours is computed by 
weighting the supply response time goals established for each 
of the three levels of supply by their respective material 
availability goals as shown in Figure 2.2. [Ref. 12] 

Mean Supply Response Time (MSRT) as defined in NAVMATINST 
3000.2 is a weighted average of supply response times from 
organizational level stocks and from the supply system. This 
definition is analogous to the definition for ACWT. The 
importance of MSRT as a measure of supply system performance 
is demonstrated through the following discussion of 
Operational Availability, ‘which is the official measure of 
weapon system performance for the Navy. [Ref.4] 

Operational Availability (Ag) represents the expected 
percentage of time that a weapon system or equipment will be 
ready to perform satisfactorily in an operating environment 
(Ref .4]. Alternatively, A, is also defined as _ ‘the 
probability that a weapon system or equipment, when used 


under stated operating conditions in an actual operating 


26 


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environment, will operate satisfactorily when called upon” 


[Ref.16,p.65]. A, is expressed mathematically as: 


_ Up Time _ MTBF 
ch Up Time + Down Time MTBF + MITR + MSRT 


where, 
MTBF = Mean Time Between Failures; 


MTTR= Mean Time to Repair. 


MTBF is primarily a function of system reliability which 
is designed in during the engineering design phase of weapon 
systems development. MTTR is a function of a variety of 
Maintenance support factors including personnel availability 
and training, availability of tools and test equipment and 
system maintainability ({i.e., ease of repair). As already 
indicated, MSRT is a function of availability of repair parts 
and other materials required to perform preventative and 
corrective maintenance actions. MSRT is the only variable in 
the A, equation which can be controlled by the supply systen, . 
and as such, is now considered to be the primary performance 
measure for the Navy Supply System. [Ref.16] 

In the next chapter, the new wholesale repairables 
inventory model proposed for implementation at the ICP's is 
presented along with the current repairables model. The 
mathematical models presently used to compute inventory 
levels at the Navy's ICP's were adapted from models developed 
for the commercial sector. These models attempt to minimize 
the total annual variable costs associated with procuring, 
stocking and backordering material. As such, they directly 
relate to the CNO's stated performance objectives for supply 


response time and operational availability. The new model 


28 


proposed for use at the ICP’s is fundamentally different from 
the current models in that it determines the amount of 
inventory required at the wholesale level to meet a specified 
MSRT goal. As such, this model would provide the ICP'’s with 
the aenne to directly control MSRT at the wholesale level in 
consonance with the CNO's and Congress’ stated goal of 


relating resources to combat readiness. 


29 


IIl. THE REPALRABLES MODELS 


The purpose of this chapter is to present the underlying 
mathematical theory for the new repairables model and discuss 
the procedure used to compute inventory levels. The current 
UICP repairables model is also presented for comparison 
mucosa The opening section describes the Navy repairables 
cycle and the-methodology used to develop the formulas for 
resupply cycle time and demand during the resupply cycle. 
This discussion is followed by a detailed presentation of the 
aggregate demand MSRT model. In the final section, the 
computational algorithms used in the current UICP integrated 


repairables model are discussed. 


A. MODEL DEVELOPMENT 

The first step in developing a mathematical model which 
reflects the relevant characteristics of a dynamic system 
such as the repairables inventory system is to identify key 
events along with their associated times and  inter- 
dependencies. Figure 3.1 graphically depicts the key events 
in the resupply cycle for the repairables system. Times 
associated with these events are as follows: 

int = _ Carcass turn-in time: the time it takes for a NRFI 


carcass to be received at the collection point 
(stock point) after a demand =has_ been 


registered; 

T2 = Carcass waiting time: average time an NRFI carcass 
waits at the collection point before being sent 
for repair; 


30 


figs = Shipping time for a carcass from the collection 
point to the repair activity (DOP); 


T4 = Procurement waiting time: average time an 
inventory deficiency exists due to attrition 
before an order for replacement units is placed 
with the manufacturer. 


jigs) = Shipping time for an RFI unit from the DOP or 
manufacturer to the stock point; 


T6 = Shipping time for an REI unit from the stock point 
to the customer; 


RTAT = Repair Turnaround Time: time required for the DOP 
to repair a batch of one or more items and return 
them to RFI condition; 

ALT = #£=Administrative Leadtime: time required by the ICP 
to prepare purchase documentation and place an 
order with the manufacturer for replacement items; 

PLT = #£=Production Leadtime: time required by the 
manufacturer to produce the quantity of items 
purchased; 

PCLT = Procurement Lead Time: ALT + PLT + 15; 

CTT = Carcass Turnaround Time: Tl + T3 + RTAT + T5. 


For this model development, it is assumed that a 
continuous inventory review policy is followed and current 
information is always available concerning the status of all 
Material assets in the inventory system. Procurement actions 
are initiated each time the number of carcass attritions 
equals the specified order quantity; and NRFI carcasses are 
sent for repair each time the number of carcasses turned in 
to the supply system equals the specified repair batch 
quantity. Additionally, it is assumed that the repair 
facility has infinite production capacity and will induct and 


repair all repair batches when received. 


31 





Figure 3.1 Repairables Cycle 


As inventory management at the wholesale level is 
primarily concerned with meeting system-wide demands as 
opposed to an individual customer's needs, the model used to 
predict system requirements is built on aggregate forecasts 
for demand, carcass return rates and repair survival rates. 
Forecasts for these parameters are generated quarterly at the 
ICP's using various constrained exponential smoothing models 
and historical demand data from previous quarters [Ref.7}. 

In both the UICP integrated repairables model and the 
MSRT model, the probability that an NRFI item will be 
returned to the system and survive the repair process is 
approximated by the product of carcass return rate (CRR) and 


the repair survival rate (RSR), where, 


32 


CRR = #£=Forecasted percentage of NRFI carcasses that will 
be returned to the wholesale inventory system for 
repair; 


RSR = #£=Forecasted percentage of NREI carcasses that will 
survive the repair process. 


The CRR and RSR forecasts are multiplied by the quarterly 
demand rate (D) to obtain a forecast for the quarterly 


regeneration rate (G): 


G = D*CRR*RSR 


where, 
D = Forecasted quarterly demand rate (or failure 
rate); 
G = Forecasted quarterly regeneration rate: average 


number of RFI units returned to inventory from 
the repair process. 


The following approximation can now be used to represent the 
probability that an NRFI item will be returned to the system 


and survive the repair process: 


CRR*RSR = 


OIQ 


Similarly, the probability that an item will be lost through 
attrition and must be purchased can be represented by: 


1 —- CRR*RSR = 1 -= : 


As defined above, the carcass turnaround time (CTT), or 
time required to process an NRFI carcass through the repair 
cycle and return it to a stock point in RFI condition, is the 
sum of T1, T3, RTAT and T5. The total procurement lead time 


(PCLT), or time required to replace an item lost to the 


33 


inventory system through attrition, is the sum of ALT, PLT 


and TS5. In the situation where carcasses are inducted for 
repair on a one-for-one basis as they are turned in to the 


system, carcass waiting time at the stock point is negligible 
and assumed to be zero. Similarly, if a procurement order is 
placed each time an attrition occurs, procurement waiting 
time (T4) is also relatively small and assumed to be zero. 
Using these two assumptions, the total expected resupply 
cycle time when items are procured and repaired on a one for 


one basis can be represented by: 


« 


L = (1 - CRR*RSR)PCLT + (CRR*RSR)CTT , 


or equivalently, 
1 = [4 _ = | peur + [=] err 


As shown in the above equations, the repairables system 
resupply cycle time is a weighted average of the procurement 
lead time and the carcass turnaround time. The resupply 
cycle time represents the expected amount of time required to 
replenish a unit of wholesale system stock which has been 
requisitioned (demanded) by a customer. Resupply cycle time 
begins when a demand is recorded against system stock and 
ends when the issue corresponding to that demand is replaced 
in the RFI inventory either through repair or procurement 


action. 


When items are procured or repaired in batches as opposed 
to one for one replacement, waiting times for procurement and 


repair (T2 and T4) must now be taken into account and the 


34 


repairables problem becomes somewhat more complex. Consider 
the following deterministic examples proposed by Apple 
fRef.8] to illustrate the repairables problem first without 
batching and then with batching. 

Figure 3.2 depicts the situation where items are repaired 
on a one-for-one basis as failures occur. In this example, 
it is assumed that all NRFI units are returned to the system 
and repaired at the DOP. The total time required to turn in 
an NRFI carcass to the inventory system, repair it at the DOP 


and return it to the stock point in RFI condition is: 
CTT(R=1) = Ti + T3 + RTAT + T5 


The total amount of stock required in the wholesale inventory 
system to preclude the occurrence of a stockout, denoted by 
SW, is: 


se, = [TEED 


where, 


+ 
Time between demands or failures and [ ] 
denotes rounding up to the next whole integer. 


AT 


In figure 3.2, AT = 0.5 years, RTAT = 0.875 years, T1 = 
0.375 years, and T2 = T5 = 0.25 years. CTT is therefore 1.75 
years and SW, is equal to 4. 

The situation where NRFI carcasses are allowed to 
accumulate before repair action is initiated is depicted in 
figure 3.3. The equation for the total time required to 
accumulate R units, repair them at the DOP and return them to 


the stock point in RFI condition now becomes: 


CTT(R>1) = T1 + T2 + T3 + RTAT + TS 


where, 


35D 


X = Failures 


5 


Time (in years) 
a, se RTAT T5 


TL 13 TAT Seis 


TL Ta) RATS 


Ds Re eerie 





Figure 3.2 Deterministic Model With No Batching. 


x = Failures 


4 
Tine 
(in years) 


ae 


IT3 RTAT TS 


ITS REAR as 


—-—-— Waiting tine 


oW = 6 





Figure 3.3 Deterministic Model With Batching. 


36 


(R-1)AT 


T2 2 


The total amount of stock required in the inventory system 


- when carcasses are accumulated prior to repair now becomes: 


- + 
SH = [SE | 7 fae wed | 


In Figure 3.3, Tl = .375 years, T3 = T5 = .25 years, AT 


0.5 years and RTAT = .875 years as before. However, with R 
3, CTT is now 2.25 years and SW, = 6. 

A similar line of reasoning can be followed for the 
procurement half of the problem where attritions occur at a 
constant rate until QO units have accumilated and an order is 
placed with the manufacturer. For this derivation it is 
assumed that all units are lost through attrition. Here the 


total procurement cycle time is: 
PCLT(Q>1) = T4 + ALT + PLT + TS ; 


and the amount of system stock required to preclude a 


stockout is: 


+ 


SW 


eons _ f PERE (O+) . al 


AT 2 


In the actual situation where demands, attritions and all 
associated times are random variables, the expected increase 
in resupply cycle time resulting from batch procurements and 


repairs (W(T)) can be represented by: 
G 
wT) = [1 - = | ¥(0) A [=] wR) 


37 


where, 


W(Q) = Average amount of time an attrition waits in the 
queue at the ICP before procurement action is 
initiated. 

W(R) = Average amount of time an NRFI carcass waits in 


the queue at the stock point (or DOP) before 
repair action is initiated. 


Under the assumption that times between failures are 
exponentially distributed, demands at the wholesale level 
eccur according to a Poisson process. Again, looking first 
at the repair half of the problem, the time between arrivals 


in the carcass queue can be expressed as: 


Qe 


The number in the repair queue ranges from 0 to R-1 units as 
shown in the deterministic example and constitutes a 
continuous Markov chain [Ref.7] The average number of units 
in the repair queve at a random point in time is: 


R-1 


2 e 


and the average time an NRFI carcass waits in the repair 


queue now becomes: 


R-1 
W(R) = 3G 


For the procurement half of the problem, the average time 
between arrivals (or attritions) is represented by: 
i 
AT = = 
D-G 


38 


where, 


DG = The quarterly attrition rate. 


The average number of attritions in the procurement queue is: 


Q-1 
2 & 


and the average waiting time in the procurement queue is: 


Q-1 


W(O) = 2(D-G) ‘ 


As determined previously, the expected cycle time or 
resupply time when units are procured or repaired on a one 
for one basis is represented by i Accordingly, the total 
expected resupply time when batching of repairs’ and 


procurements is allowed can be expressed as: 
te G G , 
L=L + [1 - =] wo) + [=] we 


By substituting in the full expressions for W(Q) and W(R) and 
collecting terms, the total expected resupply cycle time 
becomes: | 


* Q-1 Rt 
L=L + 2D 





and mean demand over this resupply time is: 





DL =p[L + —s + =! 








39 








where, 


ree. 
PPV = DL and is called the Procurement Problem Variable 
in the current ICP integrated repairables model. 


This is the formula for mean demand over resupply cycle time 


for the aggregate demand model presented by Gormly [Ref.9]. 


B. THE MSRT MODEL 

The aggregate demand MSRT model presented by Gormly is a 
time-weighted units short model which attempts to minimize 
the total investment level for a particular group of 
repairable items subject to a specified mean supply response 
time goal. Alternatively, the Gormly model can be used to 
compute the aggregate minimum MSRT attainable for a group of 
items when an investment level constraint is imposed. The 
first form of the model uses marginal analysis to determine 
the wholesale stock level for each item by comparing the 
ratio of reduced response time to the additional investment 
cost incurred when one more unit of stock is added to the 
wholesale inventory. Unlike the current ICP model which 
attempts to determine the optimal procurement and repair 
reorder points and order quantities for each item 
independently, this model determines the total amount of 
wholesale stock required in the system to achieve a specified 
response time goal using repair and procurement order 
quantities as input parameters. 

The formal statement of the aggregate demand MSRT model 
is to find the wholesale stock level (SW,) for each item i, 


for i= 1,2,3...n, Which: 


minimizes: > CSW, , 


2 D,E,MSRT, (SW, } 


subject to: I a |S MSRT Goal 
> DE, 
i=l 

where, 

Cy = Unit procurement cost for item i; 

SW, = Wholesale stock level for item i; 

D; = Quarterly demand rate for item i; 

E, = Essentiality weight for item i; 


'MSRT,(SW,;) = Mean supply response time for item i when 
stocked at a level SW. 


The total investment level in this equation is equivalent 
to the value of the repairables portion of the Navy Stock 
Fund corpus as discussed in Chapter II. The essentiality 
weight (E,) is included as required by DOD Instruction 
4140.39, “Procurement Cycles and Safety Levels of Supply for 
Secondary Items", and is used to determine the relative 
importance of items with respect to one another ([Ref.17]}. 
For a more detailed discussion of the essentiality weight, - 
the reader is referred to Gormly [Ref.9]}. 

In order to find the optimal inventory level for each 
item which minimizes the total investment in wholesale 
stock, an equivalent expression for MSRT,(SW,) is needed. 
Apple drew upon Hadley and Whitin's expression for expected 


time-weighted units short per unit of time to develop an 


41 


equivalent expression for MSRT,(SW,) [Ref.9]. Unfortunately, 
while Apple's use of Hadley and Whitin's time-weighted units 
short concept was theoretically correct, the formula he 
derived for use in the original MSRT model was subsequently 
found to be inconsistent with that presented by Hadley and 
Whitin in dnalysis of Jnaventory Systems {Ref.18]. The 
correct formla for the steady-state time-weighted units 
short adapted for use in the MSRT model is described in the 
following paragraphs. 

As shown by Hadley and Whitin [Ref.18,pp.181-182}, the 
inventory position for a lot size reorder point model with 
stochastic demands ranges from the reorder point to the 
reorder point plus the order quantity. For the proposed 
repairables model, the order quantity is Q if a procurement 
is made and R if a repair batch is inducted. The expected 
order quantity (E(OR) ) for a resupply cycle is a weighted 
average of O and R, where weighting is a function of the 
demand rate (D) and the regeneration rate (R) (subscripts are 


dropped for convenience): 
E(OR) = [1-Z]o + [=]R . 


This formula shows that Q units will be ordered for that 
fraction of the total resupply cycle time corresponding to 1l- 
(G/D), and R units will be ordered for that fraction of the 
total resupply cycle time corresponding to G/D. These 
fractions also correspond to the probability that an NEE 
carcass will be lost to the system (i.e. not returned by the 
customer or not repairable) and the probability that an NRFI 


carcass will be returned and repaired, respectively. 


42 


As a procurement is made each time Q attritions 
accumulate, and a repair batch is inducted each time R NREI 
carcasses accumulate, the expected reorder point can be 


written as: 


ROP = SW — E(OR). 

The expected inventory position for the repairables 
problem then varies between (SW-[E(OR)+1]) and SW. According 
to Hadley and Whitin [Ref .18,p.182} the associated 
probability distribution for the inventory position is 


uniform with each possible value having a probability of: 


i 
E(OR) 





Using the assumption that demand during resupply time is 
described by the Poisson probability distribution with a mean 
of DL", Hadley and Whitin [{Ref.18,pp.184-185] showed that the 
expected number of backorders at a random point in time can 


be expressed as: 





B(SW,E(QR);DL ) = aa [ Bc ROP) = B(sw) | 


where, 
DL 1 
B(x) = (Pe Yast) - (on )¢x) [Hex] + SRty(x-1) ; 
H(x) = Dy p(u:DL ) ; 
u=X 
: DL u DL 
p(u;DL ) ( -= 5 leat A) a 


In situations where DL” is sufficiently large (say > 20.0) 


the Normal approximation may be used for B(x): 


2 
B(x) = 2 { (ey fase? - corey 





where, 
DL = oO (the standard deviation) is assumed; 
* 
x—DL 
t = ; 
n 
DL 
o(-) is the standardized Normal density function with 
mean of zero and standard deviation of one; 
O(- ) is the complementary cumulative distribution 


function for the standardized Normal distribution; 


Hadley and Whitin [Ref.18,p.184] also argued that the 
expected number of backorders at a random point in time is 
computationally equivalent to the expected time-weighted 
units short per unit time (TWUS): 


TWUS = B(SW,E(OR);DL” ) 


Phe time-weighted units short concept can be illustrated 
graphically as shown in Figure 3.4. In Figure 3.4, the 
shaded area at the end of the resupply cycle time (L*) 
represents the expected time-weighted units short (i.e., the 
expected number of unit shortage-quarters in a resupply 
cycle). 

Returning to the equation for MSRT(SW,); by dividing the 
expected time-weighted units short by the quarterly demand, 
Gormly [Ref.9] obtained the average time delay per failure or 


hey 


mean supply response time (expressed in quarters): 


TWUS , (SW, ) 


D, 


MSRT,(SW,) = 


To convert to the ICP convention of days, we mltiply by 91, 
the average number of days in a quarter: 


91(TWUS , (SW, )) 


Dy 


MSRT,(SW,) (days) = 


a" 
© 
> 
@ 

onl 

ha 
2 | 
Oo 
re) 
if 3 | 





Figure 3.4 The Concept of Time-Weighted Units Short. 


The aggregate MSRT value for n items (ignoring essentiality) 
is given by: 


n 


= D MSRT, (SW, ) 
MSRT(SW) = ————_—_—__—__ , 


or, 


n 
91> THUS, (SW, ) 


MSRT(SW) = —— 


Leal 


As already shown, the key parameters in this relationship 
are DL* (PPV), Q and R. Input parameters required to compute 
the procurement problem variable are available in the data 
bases maintained by ASO and SPCC. Repair induction 
quantities (R) and procurement order quantities (Q) are input 
parameters to the MSRT computation determined by procurement 
workload constraints and/or economical lot size 
considerations. 

The procedure used to determine the optimal wholesale 
stock level (SW,) for each item in the corpus begins by 
setting SW, = 0 and computing the expected time-weighted units 
short (TWUS,) for each item. An initial aggregate MSRT can 
then be computed directly by summing the calculated time- 
weighted units short values for each item and dividing that 
sum by the sum of all items' quarterly demand forecasts. The 
attained MSRT is then compared to the MSRT goal. 

If the computed MSRT exceeds the MSRT goal on the first 
try, the process ends at that point and no items are selected 


for stocking. As this is rarely the case in the real world 


46 


situation, the marginal analysis process is initiated by 
incrementing SW, for all items to one and computing a 


cost/benefit ratio (WT,) for each item: 


C, 


WT, = TwWOS(sw-1) — TWUS(SW,) 
This ratio relates the increase in investment cost incurred 
by adding one more unit of stock to the wholesale level to 
the benefit obtained in reduced response time. 

After weights for all items have been computed, the stock 
depth for the item having the smallest ratio is increased by 
one. The aggregate MSRT value is then recomputed and 
compared to the goal. If the goal has not been reached, the 
weight for the item whose stock level was incremented is 
recomputed and the process continues until enough units of 
each item have been added to just aesofar Ge MSRT goal. 

The final step in the procedure is to compute the total 
investment level for the corpus. This is easily done by 
summing the product of the unit cost and the computed stock 
level over all items. Since the optimal stock level for each 
item has already been determined through the marginal 
analysis procedure, this value is the minimum amount of 
investment required to obtain the specified mean supply 
response time goal. 

Because projected system material availability (SMA) is 
also of interest to the ICP’s, this performance measure can 
also be computed using Hadley and Whitin's equation for the 
expected number of baokorders per unit time [Ref.18,p.184]: 


D 


PB(SW,E(QR),DL ) — 





[a@(ROP) - a(Sw) | 


where, 


47 


x 
Q(x) = H(x)(DL -x] + xp(x) for the Poisson distribution; 
Or, 


« 
@(x) =VDL [ oct) - tD(t) | for the Normal approximation. 


The aggregate expected number of backorders per unit time 


(again ignoring essentiality) is: 


nm 

x 

EBO(SW) = > EB, (SW,,E(QR),;DL, ) 
ial 


Since SMA is the expected fraction of demands filled per unit 


of time, it can now be computed as: 


EBO(SW) 


n 


SMA = 1 - 


C. UICP INTEGRATED REPAIRABLES MODEL 

The current UICP repairables model is an essentiality-— 
weighted requisitions short model based on the lot size 
reorder point model of Hadley and Whitin [Ref.18]. The 
objective function for this model attempts to consider all 
the expected total annual variable costs associated with 
ordering, holding and backordering a unit of wholesale stock, 


that is, 
TVC = Ordering Costs + Holding Costs + Backorder Costs. 


Ordering costs include internal administrative costs incurred 
by the ICP to negotiate a procurement contract with the 


manufacturer and any set-up costs incurred by = the 


45 


manufacturer to go into production. Holding costs are those 
costs associated with maintaining on hand inventories. 
Holding costs include costs of storage, obsolescence, damage 
or pilferage and opportunity costs. Shortage costs attempt 
to estimate the cost to the system for incurring backorders. 
Since the actual shortage cost is impossible to determine, 
the shortage cost computed in the UICP model is an imputed 
cost which is used to set inventory levels to meet a 
specified SMA performance goal. 

The goal of the UICP integrated repairables model is to 
determine the optimal procurement and repair quantities for 
each item stocked at the wholesale level and their associated 
reorder points which minimize the total expected annual 
variable costs. While this can be easily done via standard 
calculus for a consumables model where there is only one 
order quantity and one reorder point, the repairables problem 
is much- more complex. Consider the full mathematical - 
expression for the repairables model objective function where 
the three major terms represent order costs, holding costs 


and backorder costs respectively: 


wen of $] 8 [S]]- fg] cof] -< tol] - net 


where G and D and Q and E are defined as before, and 


Q, = Repair order quantity; 
Cc = Expected item procurement cost; 
C, = Expected item repair cost; 
fe 
Cc = Expected cost to the system to repair or replace a 


unit of stock; 


A = Average procurement order/setup cost per order; 


49 


A, = Average repair order/setup cost per order; 


it = Holding cost rate (currently set at $0.21 per 
dollar of unit value per year for repairables); 

SL = Safety level; 

A = Shortage cost parameter used by the ICP's to 
adjust inventory levels to meet a specified SMA 
goal 

BOR = #£=Expected number of backordered requisitions. 


Both the safety level (SL) and the expected number of 
backordered requisitions are a function of the expected 
number of units backordered during a resupply cycle. Rather 
than attempting to derive a mathematical formula for the 
expected number of backorders in a resupply cycle, the Navy 
has chosen to borrow selected formulas from the UICP 
consumables model. In an attempt to “gatisfy material 
availability goals and procurement workload constraints, .a 
‘large number of constraints on repair and Droste 
quantities and their reorder points. 

The actual formulas and computational algorithms used in 
UICP to compute repair and reorder quantities and reorder 
points at ASO and SPCC are detailed in the Computation and 
Research Evaluation System (CARES III) programming algorithms 
maintained by the Fleet Material Support Office 
(FMSO) [Ref.19]. These are described below. 

The levels determination process for repairables begins 
with calculation of unconstrained procurement and repair 
order quantities using two variations of the Wilson Economic 


Order Quantity (EOQ) formula: 


, 8(D-G)A 
IC 


for the Economic Procurement Quantity, 


30 


g[MIN(D,G)] A, 
IC 





for the Economic Repair Quantity. 
2 


The procurement order quantity is then constrained to ensure 
that at least one but no more than three years worth of 


attrition demand are purchased: 
- 
ee « 
Q = wmv 12¢0-6),max[4(0-6).2 1} 


And the repair order quantity is constrained to be at least 
one but no larger than the expected number of repair demands 
between scheduled repair reviews: 

ne 7 + 

@, = max [1.(RRCTXG).Q, | *, 
where, © 


RRCT = Repair Review Cycle Time, an ICP set parameter. 


UICP calls these two quantities the Basic Order Quantity and 
Basic Repair Quantity, respectively. 


Now the unconstrained stockout risk is computed as: 


MCD + ARE 


x = 
where C is defined as before and computed by the following 


equation: 
G G 
C = [1=]c. [=], 
and, 
¥ = Requisition frequency (D/Average Requisition 


Size). 


a1 


RISK represents the probability that demand during 
resupply cycle time will exceed the reorder point. Assuming 
that demand during a resupply cycle follows the Normal 
distribution, RISK" can be represented graphically as the 


area to the right of DL" + ZO as shown in Figure 3.5. 





ts tae” 
DL DL + Zo 


Figure 3.5 Definition of RISK. 


x 
In the above figure, DL is the mean demand over the resupply 
cycle (PPV), Z is the standard Normal deviate and GO is 
standard deviation for demand during resupply time. The 


safety level (SL) is defined as the product ZO. 


x 
At both ICP's, RISK is constrained to be no less than 
0.01 and no larger than a specified value determined 


separately for different categories of items: 
Pipa . % 
RISK = MIN [ max RISK, MAX(0. 01, RISK )] 


The upper bound for RISK is imposed to ensure that the system 
is not subject to too high a probability of a stockout. The 


upper bound for all ASO managed items is currently set at 


ae 


0.5. Upper bounds for SPCC managed items vary from 0.3 to 
0.99 for different categories of items classified by a four 
digit cognizance symbol. 

. Next the Basic Reorder Level for procurement is computed 
using either the Normal or Negative Binomial probability 
distribution. For all items at ASO and most items at SPCC 


the Normal distribution is used to calculate the procurement 


R=ppy+2z jo, 


reorder point: 


where, 

Z = Number of standard deviations corresponding to the 
item's acceptable stockout risk (standard Normal 
deviate). 

ae = Forcasted demand variance over the resupply cycle. 


When the Negative Binomial distribution is used (PPV less 
than an ICP established break point), SPCC uses a recursion 
equation to find the smallest R such that: 


R 
1 -— RISK « a p(x) 
x=0 
where, 
p(x) = Probability that demand during resupply time is 
equal to x, calculated as follows, 
k 
p(O) =p 
and, 
X+k-1 
p(x) = [==] (1-p)p(x-1) BOD = 1,259 <6 6% R. 
2 
Orr 


Th te 1 —— 
@ parameter P 18s equal to PPy ’ 


03 


(PPV) 


and the parameter k is equal to: - 
Gar PY 


Now the fully constrained repair quantity is determined 


according to the following algorithm: 


+ 
Q, = MAX 1 mmr {8,.[400xsm) = naxco.i-rev)] 


SHLF = An ICP specified shelf life parameter (not 
applicable to non-deteriorative items). 
The Basic Reorder Level for procurement is next 
constrained in oonsideration of shelflife restrictions, 


Minimum safety level requirements and the number of policy 


receivers: 
+ 
3 (HSLS/3){D) + PP¥ 
R = MAX | PPV, NSO. MIN | [4(D)(SHLF) + PPY | - 4(D-G) 
MAX(R+k, PRS) 
where, 

NSO = Numerical stocking objective, an ICP low limit 
parameter determined independently for each item; 

MSLS = Months of safety level stock, an ICP parameter 
presently set to 99.0); 

PRS = Number of policy receivers (i.e. number of 
wholesale stock points designated to reoeive 
assets due in from repair or procurement) ; 

k = Repair option, an ICP parameter used to augment 


the Basic Reorder Level (presently set to 0). 


04 


And the Constrained Order Quantity for procurement is 
constrained to be at least one unit but no larger than the 


Basic Order Quantity: 
+ 
Q = MAX 1.1m {a [40-cxsm) 7 rax«o.8-rev)| 


Finally, the Basic Repair Level and Constrained Repair 
Level are determined by adding the procurement safety level 
to the expected demand during repair turnaround time and 
making a final check for shelflife restrictions and policy 


receivers: 


R= [DRTAT + mAx(0.R-PPY+k)]”. 


op 
R, = MAX | 0, NSO. man { [cox + (DRTAT-1)], naxci, 22s} 


where, 
DRTAT = Expected demand during repair turnaround time; 
k = Repair option as defined previously (k=0). 


In the actual repairables levels calculations performed 
by UICP, four separate repair levels are computed. The four 
computed levels (levels 1-4) attempt to model the real world 
Situation where repairable assets are severely constrained 
and repair scheduling is accomplished on a priority basis. 
Level 1 repairs are for high priority backordered 
requirements needed to repair a critical system casualty at 
the consumer level (CASREP, NMCS requisitions); level 2 


repairs are for other high priority but less immediate 


=) 


backordered requirements (established Planned Program 
Requirements (PPR’'s) and other end use backorders); level 3 
requirements are for stock replenishment  backorders, 
projected PPR’'s and Pre-positioned War Reserve Stock (PWRS); 
and level 4 requirements are for stock in anticipation of 
demand. Levels 2 through 4 are used by CARES to make steady- 
state performance projections for SMA, ADD and ADDDR. For 
purposes of comparison between the UICP and MSRT models, only 


level 4 is used. 


36 


IV. MODEL PERFORMANCE COMPARISON 


Prior to 1987, performance analyses of the aggregate 
demand MSRT model were conducted under controlled conditions 
using small samples of selected inventory management data to 
evaluate the effects of varying procurement (Q) and repair 
(R) lot sizes [Refs.9,10]. The logical next step was to 
perform head-to-head performance comparison tests for the 
MSRT and UICP models using larger samples of actual inventory 
management data provided by the _ ICP's. This chapter 
summarizes results of performance comparison tests for the 
MSRT and UICP repairables models conducted during the spring 
or 1987. 


A. MODEL PROGRAMMING 

During January and early February 1987, the MSRT model 
and an approximation of the UICP Integrated Repairables model 
were programmed in FORTRAN 66 on the IBM 3033 mainframe 
computer at the Naval Postgraduate School. The program was 
designed to compute inventory levels for up to 1000 items of 
stock extracted from 3 CARES work tapes provided by ASO and 
SPCC. Two of the tapes were provided by SPCC and contained 
inventory management data for 174,472 consumable and 
repairable items. Although the data from SPCC dated from 
1984, it was considered valid for test purposes. A third 
tape was provided by ASO and dated from 1986. It included 
inventory management data for 211,168 items (both consumables 
and repairables). 

Test runs were made using data samples from the 7G, 7H 


and 7R cognizance categories. 1G and 7H items are non- 


a¢ 


aviation depot level repairables (DLR's) managed by SPCC. 7G 
items are exclusively electronic repairables while 7H items 
are hull. mechanical and electrical (HM&E) repairables. 7R 
items are aviation DLR's managed by ASO. The total numbers 
of items on the tapes for these three categories are as 


follows: 


1G - 12,269 
TH - 30,884 
TR = 39,258 


TOTAL - 82,411 


In order to facilitate processing, separate files for 
each of the three cognizance groups were established on the 
IBM 3033 mass storage system. Additionally, a fourth file 
containing input parameters used by the ICP's for comput eee 
of levels in the UICP model was also established. Selected 
data from one of the three DLR files and the input parameter 
file were read in at the beginning of the program to be used 
for levels computations. | 

Thirteen groups of items were selected for analysis from 
the total item population on the basis of four-digit 
cognizance symbols. ‘The four-digit cognizance symbol (or 
COG) is used by the ICP's to segregate items within each 
major category into smaller management groups of similar 
items for levels setting. The first two digits of the four- 
digit COG are the same as the two-digit cognizance symbol 
(e.g. 7G, 7TH). The last two digits indicate the subgroup to 
which the item is assigned. In UICP, inventory levels are 
computed separately for each item using different shortage 


cost parameters (A's) determined for each four-digit COG 


group. 


08 


Policy for grouping of items for levels computations is 
fundamentally different at the two ICP's. At SPCC, items are 
grouped according to three major criteria: item essentiality, 
frequency of demand and weapons system segmentation. The 
third digit in the SPCC four-digit COG is the Item Mission 
Essentiality Code (IMEC). The IMEC is an integer code from 0 
to 4 assigned to each item to give some indication of the 
relative importance of the item in the system. IMEC's are 
not actually used in the levels computation process as they 
are only subjective indicators and do not quantify the 
relative essentiality of items with respect to one another 
(i.e., an item with an IMEC code of 4 is not necessarily four 
times as important as an item with an IMEC code of 1, 4 being 
the highest code assigned). | 

The fourth digit in the SPCC four-digit COG indicates the 
demand frequency range and whether the item is weapon system 
segmented. Codes A and D correspond to a quarterly 
requisition frequency (RF) of three or more. Codes B and E 
correspond to a quarterly requisition frequency of less than 
three but greater than or equal to one. Codes C and F 
correspond to a quarterly requisition frequency of less than 
one. Weapon system segmented items are those secondary items 
identified for support of a single weapon system, while non- 
weapon system segmented items are common to more than one 
system. Codes A, B and C are used for non-weapon system 
segmented items while D, E, and F are used for weapon system 
segmented items. 

At ASO, all secondary items are weapon systems segmented. 
Additionally, neither requisition frequency or item 
essentiality are considered in the four-digit cognizance 
groupings. Instead, ASO uses the item Special Material 


Identification Code (SMIC) for the last two digits of the 


99 


four-digit cog. The SMIC either identifies the item to a 
specific weapon system (e.g. P-3, A-6, F/A-18 aircraft), or, 
if the item is used in more than one system, to a group of 
common equipments (e.g. landing gear, avionics, etc.). 

Prior to the computation of levels, each group was 
screened for items with unusual parameters and life of type 
buy (LOT) material. All items with zero quarterly demand 
rates (D), regeneration rates (G), procurement lead time or 
repair turnaround time variances (0*) were eliminated, as were 
items with excessively high quarterly demands (2 250,000). 
Finally, all items having zero or very small ($5.00 Or less) 
repair costs were eliminated. All LOT material was also 
eliminated as cyclical levels are not computed for these 
items. 

Four groups of items from each of the 7G and 7H 
Sospieoerec categories were selected. Six of the eight groups 
contained high demand items (RF>3) and the other two 
contained medium demand items (1<RF<3). Four-digit COG 
groups having more than 500 items were not selected to keep 
computer run times to 30 minutes or less. Five sae of 
items were selected from the 7R cognizance category. These 
corresponded to major aircraft (EP-3E, A6E, A7, ATE .and F/A- 
18). The larger number of items in some these groups did not 
cause run time problems as many of the items had very low 
demand rates or were life of type buy items. The largest 
group was 7RSF and its run time was still under 30 minutes. 
The final COGS used in the performance test runs are listed 
in Table 4.1. The second colum lists the total number of 
items in the group and the third column lists the number of 


items passing the parameters screen. 


60 


TABLE 4.1 TEST RUN SAMPLES 


TOTAL NUMBER NUMBER OF ITEMS 

4 DIGIT COG OF ITEMS IN COG PASSING SCREEN 
71GOB 114 92 
1G1A 165 107 
1G2B 176 158 
1G4A 75 73 
TH1A 145 139 
TH2A 147 142 
7H3D 255 249 
7H4D 131 130 
TREP (EP-3E) 674 74 
TRGA (A7) 1 ia 421 
TRRA (AGE) 427 266 
IRSF (F/A-18) 1538 615 
TRTA (ATE) 534 290 


After reading in and screening inventory data for unusual 
parameters, the program computed procurement order quantities 
and order points for all items using the UICP model. Next, 
the computed order quantities and order points were added 
together to obtain the wholesale stock level (SW,) for each 
item. The resulting SW, values were then used to determine 
expected MSRT values for each item. Finally, the aggregate 
_MSRT, SMA and total investment level for the group were 
calculated. The process was repeated in the second half of 
the program running the same items through the MSRT model and 
using the attained aggregate MSRT from the UICP model as the 
MSRT goal. In both models, the repair order quantity (R) was 
set to one. The value of one was chosen for R because both 
ICP's have a current policy of inducting carcasses for repair 
on a one-for-one basis as they become available. 

Three sets of test runs were made for each group to 
observe the effects of varying the procurement lot sizes and 


MSRT goals. In the first set of runs, the procurement 


61 


quantity (Q) for the MSRT model was set equal to the UICP 
computed procurement quantity (Q-UICP). For the second set 
of runs, Q in the MSRT model was set to one. In the third 
set of runs, Q for the MSRT model was fixed at Q-UICP and the 
MSRT goal was varied from 0.01 days to 10.0 days. 


B. MODEL PROGRAMMING CHANGES 

The first set of performance comparison tests was 
conducted in February 1987 and the results looked very 
favorable for the MSRT model. However, in subsequent 
discussions with operations research personnel at ASO, SPCC 
and FMSO in late February, a number of questions were raised 
concerning the validity of performance measures computed for 
the two models as well as the assumptions used for 
computation of demand during the resupply cycle for the MSRT 
model (i.e. MSRT values appeared to be too small and SMA 
values too large). Performance results for these tests were 
subsequently imac seed When the formula for time-weighted 
units short for the MSRT model was found to be inappropriate 
for the steady-state conditions of replenishment. 

Between February and June 1987, the MSRT model was 
carefully reviewed and reformated as described in Chapter 
iil. Programming for UICP model levels computations was 
completely revised to conform with the algorithms used in 
CARES as outlined in Application D, Operation 56 maintained 
by FMSO ([Ref.19]. CARES modules for computation of 
performance statistics (SMA, ADD and ADDDR) were also added. 
These will not be presented here, however, because they serve 
no purpose in the performance comparisons. The revised 
program code is contained in Appendix A. It should be noted 


that the CARES subroutines for SMA and ADD were not used for 


62 


the second series of comparison tests conducted in June as 
additional debugging was required. 

Performance tests using the reformated programs were 
conducted in the same manner as the earlier tests. The UICP 
model was run to compute both the procurement and repair 
quantities for that model. The procurement reorder points 
for each item were also computed. Next, the aggregate order 
quantity for each item was computed using the formla for 
E(QR) described in Chapter III. The inventory position for 
each item under the UICP model was assumed to vary from the 
procurement reorder point (ROP) to ROP+E(OQR). The aggregate 
MSRT was then computed and used as the goal for the MSRT 
model. The total investment level for each item's maximum 
inventory position (ROP + E(QR)) was then determined. These 
values were summed to obtain the total investment level for 
the group. Aggregate SMA computations were also made using 
the formula described in Chapter III. . 

The marginal analysis approach described in Chapter III 
was used by the MSRT model to compute the optimal maximm 
inventory position (SW) for each item. The aggregate 
attained MSRT, total investment levels and SMA were then 
computed in the same manner as for the UICP model. An item's 
reorder point for the MSRT model was assumed to be SW-E(QOR) 
for computation of performance measure values. 

Two sets of test runs were made for each sample group. 
In the first set of runs, MSRT model values for Q and R were 
set equal to the UICP computed procurement and repair 
quantities. For the second group of runs, Q and R values for 
the MSRT model were both set equal to one. Results of the 
test runs are summarized in Tables 4.2 and 4.3 and the end of 


this chapter. 


63 


C. PERFORMANCE TEST RESULTS 

In the first set of test runs where UICP computed values 
for QO and R were used for both models, the MSRI model 
consistently out-performed the UICP model, both in terms of 
total investment levels required and attained SMA's. The 
average reduction in investment level for all sample groups 
was 5.1 percent. The range of saving was from a low of 1.3 
percent for the 7G1iA and 7G4A groups, to a high of 12.3 
percent for 7RGA group. For 12 of the 13 groups, SMA was 
marginally higher for the MSRT model. The average increase 
in SMA for all groups was 1.0 percent. 

When procurement and repair quantities for the MSRT model 
were reduced to one, the savings in investment levels ranged 
from a low of 6 percent for 7RSF to a high of 35 percent for 
7G2B. The average reduction in investment level for all 
groups was 25 percent. Additionally, SMA values for ii of 
the 13 samples were better than those computed for the UICP 


model. 


64 


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66 


V. REPALRABLES MODEL SIMULATIONS 


This chapter summarizes supplemental research conducted 
during the spring of i987 for the aggregate demand MSRT 
model. In order to gain a better understanding of the actual 
repairables process and verify some of the underlying 
assumptions for the MSRT model, a single item simlation was 
programmed in April 1987. The goals for programming the 
simulation were to: (1) determine where in the repairables 
cycle backorders were most likely to occur; (2) isolate and 
identify the probability distribution(s) for demand during 
resupply time resulting from a stream of Poisson demands; (3) 
conduct sensitivity analysis to examine the effects of batch 
procurements and repairs on MSRT and SMA; and (4) identify 


any discernable recurring patterns in the repairables cycle. 


A. SIMULATION PROGRAMMING 

The single item repairables simulation was programmed in 
FORTRAN 77 on the IBM 3033 mainframe computer at the Naval 
Postgraduate School. The program was designed to simulate 
all events in the life of a repairable item under steady 
state conditions under the following assumptions: 


1. Demands were generated randomly according to the 
Poisson distribution; 


2. Attritions were generated randomly using a Bernoulli 
distribution; 


3. Procurement leadtimes and repair turnaround times were 
held constant at their forecasted mean values; 


4. Procurement action was initiated each time the number 


ef attritions occurring since the last order equalled 
the established order quantity (0); 


67 


9. Repair inductions were made each time the total number 
of NREFI carcasses on hand equalled the established 
repair batch quantity (R); 


6. All units in each repair batch were inducted, repaired 
and returned to RFI status as a group; 


7. More than one repair or procurement order could be 
outstanding at the same time; 


8. The depot repair facility had infinite repair capacity. 


The MSRT model simulation was designed to record all 
individual events occurring in the resupply cycle for a 
maximum of thirty years. Input parameters were wholesale 
stock level (SW), demand rate (D), regeneration rate (G), 
procurement leadtime (PCLT), repair turnaround time (RTAT) 
and repair survival rate (RSR). Their values were set at the 
beginning of the program and held constant for the entire 
simulation. Random demands and attritions were generated 
using the LLRANDOMII Random Number Generator contained in the 
non-IMSL subroutine library of the IBM 3033. Performance 
statistics were generated at the end of each run for SMA, 
MSRT (ADD) and average days delay for delayed requisitions . 
(ADDDR ) . Statistics were also computed for average demand 
(D), regeneration rate (G), carcass return rate (CRR) and 
repair survival rate (RSR) to provide a check on values 
generated by the random number subroutine. 

Options for both long and short reports were included. 
The long report included inventory position, on-hand RFI 
inventory, number of items in the repair and procurement 
queues, number of items in repair and on order and the number 
of backorders for each discrete event in the resupply cycle. 
A second long report option was also included to generate 
data for plotting of net inventory and inventory position 


using the DISSPLA graphics application. The short report 


68 


option included only summary performance statistics and was 
used when making comparative runs in which the parameters for 
Q and R were varied. 

At the beginning of each run, on-hand inventory was set 
equal to SW with no units in the pipelines for either repair 
or procurement. As NRFI carcasses and = attritions 
accumulated, queues were established for both repair and 
procurement. Procurement action was initiated each time Q 
attritions occurred and repair inductions occurred each time 
R carcasses accumulated. Variable definitions for the 
Simulation program are listed in Appendix B and the full 


program code is contained in Appendix C. 


B. OCCURRENCE OF BACKORDERS 

The first objective for programming the simulation was to 
generate sufficiently large samples of inventory data to 
determine where stockouts were ocourring in the repairables 
cycle. As the number of individual events occurring over a 
thirty-year simulation is extremely large (as much as 2400 
for an item with a quarterly demand of 10) it was not 
practical to include the full printouts from the events files 
in this thesis. Selected excerpts from the full events files 
are included in this chapter for illustration purposes. 

Prior to running the first simulations, it was 
conjectured that stockouts were most likely to occur near the 
end of a procurement cycle. While this conjecture was not 
proved invalid by the simulations, it did prove to be an over 
Simplification of the actual situation which resulted. In 
virtually all of the simulation test runs, the occurrence of 
stockouts was more the result of a complex combination of 


factors with the key determinant being the number of items in 


69 


the procurement pipeline at random points in time. This 
phenomenon 18 easiest to explain through the use of two 
examples taken from one of the test runs. Figures 5.1 and 
9.2 are excerpts from a thirty-year event profile for an item 


having the following characteristics: 


D 8.0 units/qgtr. 
G = 7.6 units/qtr. (15% attrition rate) 
Q = 5= 1 year's attrition demand(4(D-G) ) 
R = 1 
PCLT = 10.2 qtrs (928 days) 
RTAT = 1.2 gtrs. (109 days) 
SW = £30 units 


These parameters resulted in an SMA of approximately 90 
percent, an MSRT of 2.4 days and an ADDDR of 22.4 days. 

Figure 5.1 shows the inventory system status over a 136 
day period overlapping years three and four. The times shown 
correspond to the last third of the procurement cyole for the 
first order, the middle of the procurement cycle for the 
second order and a third order is pending. The two 
outstanding orders of five units each are due in on days 
1780 and 2207 (end of year four and beginning of year six 
respectively). Additionally, four attritions have already 
occurred since the last order was placed on day 1278 (deficit 
column). A third order will be placed on day 1542 when the 
fifth attrition ocours. Backorders begin occurring 
intermittently on day 1405, shortly after the third and 
fourth attritions are recorded, and continue through day 
1461. In this example, the relatively large number of units 
in repair (17-18) in combination with the two outstanding 
procurement orders contributes to the occurrence of 


stockouts. Note that in this example the backorders are of 


70 


relatively short duration (1 to 8 days) as requisitions are 
filled promptly from material returning from repair. 

Figure 5.2 shows a somewhat different situation in the 
middle of year nine. In this example we are at the end of 
the procurement cycle for the oldest order, the middle of the 
procurement cycle for two orders and the beginning of the 
cycle for a fourth order. The oldest outstanding order is 
received on day 39518. The other two orders are due in on 
days 3779 and 4101 (middle of year 10 and beginning of year 
11 respectively). The fourth order is placed on day 3455 
when the fifth attrition occurs. Backorders begin occurring 
steadily as soon as the fourth order is placed and terminate 
promptly when the oldest order arrives on day 3518. -During 
this same time frame, the number of units in the repair cycle 
has also increased substantially from four units on day 3375 
to a high of sixteen units on day 3480. Here again, the 
combination of outstanding procurement orders and _ the 
increase in the number of units in repair each contribute to 
the stockout situation. Note that the average number of 
outstanding backorders in this instance is significantly 
larger (4-5 units), and the average days delay for filling 
requisitions is approximately 21 days. 

These two examples are fairly typical of the inventory 
patterns observed in all of the simulation runs for items 
having a quarterly demand of 5 or more units. Unless the 
demand rate was set fairly low (D < 2/qtr.), there were 
almost always at least two procurement orders outstanding by 
the end of the third year and the repair pipeline was never 
empty. When 50 to 60 percent of SW was in the procurement 
pipeline, stockouts occurred intermittently until the oldest 


outstanding order was received. In instances when the number 


ra 


1401. 


1413. 
1418. 


1418 


1436. 


1434. 


143?. 


1461. 
1461. 


1474. 


1497. 
1310. 
1512. 
1512. 
1514. 
1322. 


18 


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Figure 5.1 Simulation Events File Excerpt No.1 


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SRRRRRRRAERRRRRRRRKERKRREKRRKRRERRRRBRRBE SB 


3433 .04 
3445 .03 
3495.6? 
2457.79 
3453.45 
3459. 74 
3471.34 
3473.15 
3480. 13 
3434.35 
3485 . 34 
3456.33 
2492.78 
3492.33 
3494.0? 
3494 . SS 
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3514.96 
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3519.96 
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3379.54 
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3335.65 
3395 .63 
3401.59 
3405.22 
3410.76 
3416.22 
3421.16 


Figure 5.2 Simulation Events File Excerpt No.2 


#3 


of units in the procurement cycle exceeded 70 percent of SW, 
stockouts occurred continuously until this percentage dropped 
back down to just over 50 percent. The average amount of 
time a backorder was outstanding also increased Significantly 
during these periods. Conversely, stockouts were rarely 
observed when less than 50 percent of the wholesale stock was 
in the procurement pipeline. It should be noted that these 
percentages would increase or decrease depending on the value 


of SW. 


C. DEMAND DURING THE RESUPPLY CYCLE 

In both the UICP and MSRT models presented in Chapter 
III, a key assumption is that the demands occurring during 
the resupply cycle can be described by a single probability 
distribution. The distribution for demand during the 
resupply cycle in the repairables case can not be derived 
easily because it is a function of the quarterly demand, 
procurement lead time, eeeore regeneration rate and the 
repair turnaround time. While past use of the Poisson 
assumption provides a convenient method for computing a 
mathematical solution for the distribution of demand during 
the resupply cycle, this theory has never been validated for 
the repairables case. Here the repairables simulation proved 
to be extremely useful for isolating the dastributions 
resulting from a single stream of Poisson demands. 

Prior to generating the first resupply cycle time demand 
samples, it was conjectured that the resulting distribution 
would be Poisson with a mean which was the demand during the 
resupply cycle if the procurement lead time and repair 
turnaround time were assumed to be constant. However, the 


Situation where queues were allowed to form for the repair 


74 


and procurement pipelines complicated the problem and it was 
not known if the Poisson assumption would be valid for this 
case. 

In order to collect samples for demands occurring during 
each resupply cycle, an additional subroutine was added to 
the original simulation program in May 1987. This routine 
computed the total number of demands occurring between the 
time a demand was received by the system and the time the 
corresponding issue was replaced in inventory either through 
procurement or repair action. Thirty~year inventory 
simulations were used to generate sufficiently large samples 
for statistical analysis. Raw demand data generated by the 
Simulation program was transferred to an Apple Macintosh PC 
file to compute statistics, perform goodness of fit tests and 
generate histograms for demand during the resupply cycle. 
The Statworks application program was used for statistical 
analysis and to generate histograms. Two separate FORTRAN 77 
routines were written to perform Chi squared (x7) goodness of 
fit tests for the Poisson distribution. The first routine 
used a Poisson recursion equation to perform the re goodness 
of fit test. The second program used a Normal approximation 
to perform the fit test. 

A total of twelve separate simulations were run for 
analysis. Input parameters for D, PCLT, RTAT, and SW were 
held constant at the following values for all samples: 


D = 10.0 units/qtr 
PCLT = 10.2 qtrs (928 days) 
1.2 qtrs. (109 days) 
39 units 


wy 
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Six of the runs were made with Q=4 and R=5. The other six 
runs were made with Q=1 and R=1. The first two runs for each 
group were made using a 10 percent attrition rate (i.e., G/D 
= 0.90). In subsequent runs, attrition rates of 50, 70 and 
90 percent were used. This was done both to observe the 
effects of routing more units through the procurement cycle 
and to generate sufficient numbers of observations to perform 
reliable goodness of fit tests. Each simulation run 
generated between 1100 and 1200 observations which was more 
than sufficient in the majority of cases to perform x? 
goodness of fit tests at the 95 percent confidence level. 

Figure 5.3 shows the histogram for the first simulation 
with Q=4, R=5 and a 10 percent attrition rate. Like all the 
similation runs using PCLT=10.2 quarters and RTAT=1.2 
quarters, two distinct demand distributions resulted. The 
tall distribution on the left corresponds to demands that 
occurred during repair turnaround times (DRTAT). The flat 
distribution on the right corresponds to demands that 
occurred during procurement lead times (DPCLT). 

Because the actual distribution for during the resupply 
cycle could not be obtained directly from the simlation, 
each of the two distinct distributions were checked 
Separately for a fit to the Poisson distribution. If both 
were found to fit, then the distribution of demand during the 
resupply cycle is also Poisson since it is a _ convex 
combination of the two separate distributions. 

Equations used to compute the means for the null 


hypothesis are as follows: 


2 ? 





(DRTAT) = (D)(RTAT) + 


and, 


76 


Q-1 
2 





.(DPCLT) = (D)(PCLT) + 


For all observations associated with Q=4/R=5, the 
computed means for the null hypotheses were 14.0 and 103.5 
for DRTAT and DPCLT respectively. When Q=1/R=1 was used, the 
computed means for the DRTAT and DPCLT null hypotheses were 
12.0 and 102.0, respectively. 


<oOzmecoman 





Pigure 5.3 Demand During Resupply Histogram No.1 


For each of the four simulations in which the attrition 
rate was set at 10 percent, the DRTAT half of the histogram 
consistently matched the Poisson probability distribution at 
the 95 percent confidence interval regardless of whether R=1 


or R=4. The DPCLT half of the histogram for the 10 percent 


C7 


attrition runs had too few observations to obtain any 
reliable results. As the attrition rate was increased from 
70 to 90 percent in subsequent runs, the sample sizes for 
DPCLT eventually became large enough to compute reliable 
statistics. However, of the four DPCLT simmlations using a 
90 percent attrition rate, only one provided a fit to the 
Poisson distribution at the 95 percent confidence interval. 
The other three simulations did not even provide good fits at 
the 50 percent confidence interval. 

Figures 9.4 and 5.5 show the resulting demand during 
resupply cycle histograms generated using a 50 percent 
attrition rate. The hastogram in Figure 5.4 was generated 
using Q=1/R=1 and the histogram in Figure 5.5 used Q=4/R=5. 
These two histograms are included to provide a better picture 
of the demand during procurement lead time half of the 
distribution. The horizontal scale for demand in both. 
histograms uses the same scale to facilitate comparison. 

There are several observations worthy of comment in these 
two figures. First of all, the medians for DRTAT and DPCLT 
in both figures are very close to the theoretical means (12.0 
and 102.0 for Q=1/R=1 and 14.0 and 103.5) for Q=4/R=5) 
Secondly, the variances for the Q=4/R=5 distributions in 
Figure 5.5 are visibly larger than those for Q=1/R=1. 
Thirdly, when comparing the variances for DRTAT and DPCLT in 
each of the respective figures, the variance for DRTAT is 
noticeably smaller in each case. This observation is 
consistant with the theoretical Poisson variance which is 
equal to the square root of the mean. Although less obvious, 
the DPCLT plots have a significantly higher number of demands 
centered around the mean than is normal for a Poisson 
distribution with a mean close to 100. This could be seen 


more clearly when comparing the theoretical expected values 


18 


F 
R 
E 
Q 
U 
E 
MN 
C 
Y 


<Oozmecoman 





r ; = | 


\; mln. | In 
aj og 


Figure 5.4 Demand During Resupply Histogram No.2 (Q=1/R=1) 


= ' 





Figure 5.5 Demand During Resupply Histogram No.3 (Q=4/R=5) 


79 


for DPCLT with the observed values when the goodness of fit 
tests were made. Finally, the right tail for DPCLT in 10 of 
12 simmulations was significantly longer than the left tail. 
In only one histogram were demands recorded below 80 for 
DPCLT . 

As results for DPCLT goodness of fit tests did not 
satisfy the hypothesis of a Poisson distribution for most of 
the simulation runs, the distribution of demand during the 
resupply cycle could not be shown to be Poisson, even when 
procurement lead time and repair turnaround time are assumed 


to be constant. 


D. SENSITIVITY ANALYSIS FOR Q AND R 

As discussed in Chapter III, when procurements and 
repairs are batched, the wholesale stock level must be 
increased to compensate for the additional time NRFI 
carcasses and attritions spend waiting in their respective 
queues prior to orders being initiated. The focus of this 
affort was to observe the effects various combinations of Q 
and R had on SMA, MSRT and ADDDR using the single item model 
similation. For this analysis, input parameters were the 
same as those used in the first example of this chapter 
except that the values for Q and R were varied for each run.. 

Three simulations were run for each combination of Q and 
R using different random number seeds. Although the number 
of runs for each combination of Q and R values was not 
sufficient to compute reliable statistics, results were 
relatively consistent between runs and were considered 
satisfactory for this sensitivity analysis. 

Performance results from one full set of simulations 


using the same random number seed are summarized in Tables 


80 


ol amd 5.2. For the first group shown in Table 5.1, Q 
values were held constant while R was varied from 1 to 8. In 
the second group shown in Table 5.2, R values have been held 
constant and QO varied from i to 8. Performance results for 
MSRT were consistent with those obtained using’ the 
theoretical model. In each case, as the number of units in 
either the repair or procurement batches increased, model 
’ performance decreased for all three statistics, although not 
at the same rates. As expected, setting © and R equal to one 
consistently resulted in the best overall performance. 
Finally, it is interesting to note that regardless of whether 
Q or R was varied while the other remained fixed, the 
performance results were very similar. This may be the 
result of the combination input parameters used and should 
not be generalized for all cases. 

As discussed by Pearsall [Ref.10], the size of the 
procurement order quantity is a variable of primary concern 
for the ICP's as Q has a direct effect on procurement 
workload. While the optimal order policy for the MSRT model 
is one-for-one replenishment, this policy is impractical if 
an item experiences a large number of demands or has a high 
attrition rate. | 

Referring again to Table 5.2 where Q was incremented, 
MSRT and SMA values for Q>1 are not significantly larger than 
for Q=1, providing R is relatively small (2 to 3 units). 
However, as Q and/or R become larger, MSRT increases at an 
increasing rate. This observation is illustrated graphically 
in Figures 5.6 and 5.7. Figure 5.6 depicts the MSRT plots 
for the five runs in which R was held constant and Q varied. 
Data for this plot was taken directly from Table 5.2. 

Figure 5.7 shows a comparative plot of MSRT versus SMA 
for R=1 and Q varied from i to 8. Note here that SMA 


G1 


TABLE 5.1 PERFORMANCE STATISTICS FOR Q CONSTANT/R VARIED 


Q R MSRI (days) ADDDR (days ) SMA(%) 
ih il 0.960 18.928 94.93 
at 2 1.101 18.405 94.02 
ib 6) 1.544 20.297 92.39 
1 4 1.7 6oo 20.780 91.08 
i J 2.427 22.159 89.05 
1 6 2.970 23.431 37 Woe 
aL 7 4.089 26.348 84.48 
1 8 4.747 Pte olf il 82.66 
2 1 1.223 18.845 93.51 
2 2 1.440 ee 92.49 
2 3 2, Ona 20.504 90.16 
2 4 2.391 21.633 88.95 
2 ro) 3.073 Zona 87.12 
2 6 Be fey 24.111 84.58 
2 7 9.062 29.396 82.15 
2 8 St 740, 28.483 719.92 
5 il aoe 18.195 91.58 
3 2 1.852 18.266 89.86 
S 3 2.609 20891) 87736 
3 a 3.4123 ape 2). EE: ; 86.00 
ve < 3.890 24.589 84.18 
3 6 4.60? 25.238 81.74 
6: 7 6.349 29.670 78.60 
3 8 7.108 JOR ooo 16aa0 
4 1 1.859 19.713 90.57 
2 2 2.216 20.805 89.35 
4 2 3.011 22.840 86.82 
2 4 Bors 23.896 85.29 
4 2) 4.342 24.892 82.56 
it 6 9.396 Pao) (/)0)1L 197 Onl 
2 7 UGS 30.076 76.47 
4 8 7.989 507651 713.94 
9 iL 2.412 22.439 89", 25 
= 2 2.837 Aso 87.83 
S 3 3.663 235,916 84.69 
=; 4 4.413 24.306 81.85 
9 9 Bi 310) fi 27.286 19.82 
= 6 6.5941 25.492 74.34 
9 7 8.917 30.742 10.99 
5 8 9.731 . - 31.252 68.76 


82 


TABLE 5.2 PERFORMANCE STATISTICS FOR R CONSTANT/Q VARIED 


Q R MSRT (days)  ADDDR(days) SMA(%) 
1 1 0.960 18.928 94.93 
2 1 1.223 18.845 93.51 
3 1 1.532 18.195 91.58 
4 1 1.859 19.713 90.57 
5 i 2.412 22.439 89.25 
6 1 3.573 24.133 85.19 
7 1 4.452 26.842 83.89 
8 1 5. 806 29.209 80.12 
1 2 110d 18.405 94.02 
2 2 1.440 19.182 92.49 
3 2 1.852 18.266 89. 86 
4 2 2.216 20.805 89.35 
5 2 2.837 23.312 86.83 
6 2 4.162 26.140 84.08 
7 2 5.073 27.484 82. 66 
g 2 6.786 29.608 77.08 
1 3 1.544 20.297 92.39 
2 3 2.017 20.504 90.16 
3 3 2.609 20.917 87.53 
4 3 3.011 22.840 86.82 
5 3 3.663 23.916 84.69 
6 3 5.338 29.079 81.64 
7 3 6.358 29.549 77.82 
g 3 8.361 31.828 73.73 
1 4 1.855 20.780 91.08 
2 4 2.391 21.633 88.95 
3 4 a, 123 22.313 86.00 
4 4 3.514 23.896 85.29 
5 4 4.413 24.306 81.85 
6 4 6.053 28.833 79.01 
7 4 7.255 29.358 75.27 
g 4 9.639 32.999 70°. 79 
1 5 2.427 22.159 89.05 
2 5 3.073 23.857 87.12 
3 5 3.890 24.589 84.18 
4 5 4.342 24.892 82.56 
5 5 Sey 27.286 79.82 
6 5 7.156 30.283 76.37 
: : 8.676 31.565 73.04 


> 
— 
fh 
OV 
~J 
to 
wn 


.954 68.66 


83 


Gey 
dal 
Cal 
omy 
bey 


PPR? & 


Ot 





Ayryuents ywemerans01g Jo uotyoung & ce LAST peyetnuts 9°g9 aanstyzZ 


(O> ALILNYND LNSWSYNIOdd 


8 9 Y A 


CSAUO> LUSH 


84 


(23> US 


Ws + 
LYSW + 


08 


06 


00} 


Ol 


Tay usu O JO uoTJOUNZ & Se YS pue LYS peyernuts 2°9 eanbty 


CO> ALILNYND LNSWSYdNIOdd 


8 9 P f 


CSAMO> LYSH 


35 


decreases in a roughly linear fashion as values for OQ 
increase. SMA does not decrease at the same rate that MSRT 
increases because SMA only considers the number of backorders 
and not the average length of time that a backorder exists. 
This is the primary reason for using MSRT as opposed to SMA 
to measure system performance. 

Referring now to Figure 5.8, this graph shows 
corresponding MSRT and ADDDR values for three runs in which Q 
was held constant and R was varied. The bottom plots in the 
respective MSRT and ADDDR groups are for Q=1. The middle 
plots in each group are for Q=5 and the top plots are for Q=8 
(Q=8 data was not included in Table 5.1). Note here that, as 
expected, ADDDR increases in proportion to MSRT for each pair 
of plots. This is due to the fact that MSRT is a function of 
the total backorder time experienced during the resupply 
cycle, or more precisely, time-weighted units short. 
Additionally, note the large increase between the Q=5 and Q=8 
plots for both MSRT and ADDDR. When the value for Q was 
changed from 5 to 8, MSRT increased by over 100 percent for 
all corresponding values of R. ADDDR for the same Q values 


increased approximately 35 percent as R varied from i to 9. 


E. RECURRING INVENTORY PATTERNS 

A secondary objective of the simulation runs was to 
identify any recurring patterns in the repairables cycle. 
Graphical analysis was used to detect any discernable 
patterns as the amount of data outputted to the events files 
was too large to screen visually. 

Twenty-five simulation runs were plotted in conjunction 
with other analyses and screened for obvious patterns. 


Sample outputs are contained in Figures 5.9 and 5.10. Input 


36 


8=0 YoddY 
S=D woddy 
t=O YoodY 
B=) LUSH 
S=D LUSH 
b=} LUSH 


ee a 


aq yO uotzound 6 co ydddy pue LASW peyetTnuts g°q sanbty 


CH) ALILNUND YWIibdSy 





CSAU0> YOOOU / LUSH 


of 


parameters are indicated on the two graphs. None of the 
plots generated contained any consistant patterns in the 
repairables cycle once the model simulation approached steady 
state (i.e. procurement and repair pipelines filled and RFI 
units being returned to stock from both repair and 
procurement). As noted in Section B of this chapter, there 
are a significant number of situations in which the large 
number of units in both the procurement and repair pipelines 
at the same time results in a period of prolonged stockouts. 
In Figure 5.9, a prolonged stockout situation occurs during 
year 20. In Figure 5.10, stockouts occur almost continuously 
from the middle of year 10 through year 13. It is important 
to note that the on hand inventory never returns to SW as 
there are always units in both the repair and procurement 


pipelines. 


88 


T ‘ON 0Td - OWTL JO UoTJOUMY e Ge ATOWUSAUT YON PEWeTNUTS 6°S 9anbTT 


(SYUSA NI) SWIL 
0°0£ 0°82 0°92 O42 O°@2 0°02 o's! 0°91 ov o°z1 o'0l 0°8 09 o°F 0°2 0'0 





4 
4 


SHiD 2° 
SHiD Z ‘Ol 
SLINN O€ = MS 


ft ow 
RE 
ae 
Ok 
Oo. 


D 
HiD/9°2 = 9 
HiD/O'8 = 0 


r2 22 «(O 


0 sc 


AYOLINSANI LN 


39 


JOTd - OUT], JO UOTJOUNY @ Ge AIOPUSAUT JON PayetNUts OTS sanBbry 


(SYUGA NI) SWIL 


0°0¢ 0°82 0°92 0°32 O’7¢2 0°02 o’st o°sl -O°bl 0°21 0’°Or 0°a 0°93 O'F 0°¢ 0°0O 
i 
H | ud oD 
| 

SYlD Zt = LULH rN 
SHLD Z'Ol = L719d 
SLINN O& = MS 
Ley 
8) 18) 
yID/g'2 = 9 
yI0D/O'8 =a 


XYOINSANI LON 


90 


VI. SUMMARY AND CONCLUSIONS 


A. SUMMARY | 

Chapter II provided an overview of the Navy Supply System 
including discussions on the Navy logistics organization, the 
Navy Stock Fund, the repairables system and supply system 
performance measures. This chapter served as a prelude for 
the detailed presentation of the current and proposed 
wholesale repairables inventory models in Chapter III. In 
Chapter III, we discussed the resupply cycle and reviewed the 
underlying mathematical theory for the proposed wholesale 
level model as originally presented by Apple [Ref.8] and 
Gormly [Ref .9]. The proposed model is fundamentally 
different from the current model in that it directly relates 
resources to operational readiness by determining the minimum 
total investment in wholesale inventory required to meet a 
specified mean supply response time (MSRT) goal. As such, 
this model is consistent with the DOD's and CNO's established 
policy objectives for supply system performance as outlined 
in OPNAVINST 4441.12B [Ref.12]}. Furthermore, the proposed 
model provides for a smooth eaeseon from the Navy's new 
wholesale initial provisioning model. In contrast, the 
current repairables model, which attempts to minimize the 
total annual costs associated with supply system operations, 
does not consider total investment levels or MSRT. Neither 
does it provide for an easy transition from the new 
provisioning model. 

In Chapter IV, results of the initial performance 
comparison tests between the two models using actual 


inventory management data were presented. These tests showed 


91 


that the proposed model consistently requires less investment 
in wholesale system stock to achieve the same MSRT goal 
attained with the present model using the same input 
parameters. These tests also demonstrated that by reducing 
the lot sizes for procurement (Q) and repair (R), significant 
Savings in total investment level could be realized without 
affecting supply response time or system material 
availability. 

Chapter V discussed the results of supplemental research 
conducted on the proposed model using a single item inventory 
' gimulation. Inventory simulations served to increase our 
understanding of the dynamics of the repairables inventory 
system and verify the theoretical performance of the new 
model. We were able to identify the conditions which lead to 
the occurrence of stockouts and isolate the probability 
distributions for demands occurring during procurement lead 
time and repair turnaround time using the assumptions for the 
proposed model. Sensitivity analysis conducted using 
Simulation provided additional insight into the effects of 


increases in procurement and repair lot sizes on MSRT and 


SMA. 


B. CONCLUSIONS 

Although the proposed model still requires additional 
testing to better understand the effects of changes in 
procurement and repair lot size policies, the initial 
performance tests have demonstrated that this model is 
capable of out-performing the current model by a sufficiently 
large margin to merit serious consideration for 
implementation at the Navy's inventory control points. While 
it can be argued that the proposed model is too simplistic in 


that it does not consider many of the costs associated with 


92 


supply system operations, we as military logistics managers 
must always be receptive to new ideas which have _ the 
potential to improve overall supply system efficiency and 
responsiveness without tieing up scarce financial resources 
in unneeded inventory. By considering the relative costs and 
benefits associated with stocking an entire inventory of 
items, the proposed model attempts to optimize system 
performance as a whole without having a significant impact on 
other system costs associated with ordering and holding 
stock. In fact, it can be argued that the proposed model 
provides inventory managers with increased flexibility to 
control other system costs by keeping them independent of the 
levels computation process. 

First of all, the proposed model provides the flexibility 
to select Q and R values to take advantage of economical lot 
Size procurements and repairs and in consideration of IcP 
workload and other constraints. Secondly, the proposed model 
avoids the need to indirectly quantify unknown 
backorder/stockout costs as the MSRT goal controls the extent 
of backorders directly. Thirdly, by minimizing the total 
amount of stock required at the wholesale level, holding 
costs as computed in the current model will also be reduced. 
Finally, and most importantly, the aggregate MSRT goal, as an 
input parameter for the proposed model, can be set to meet 
established objectives for any new weapon system's 


operational availability. 


C. RECOMMENDATIONS FOR FURTHER RESEARCH 
There are four major areas in which additional research 
should be conducted to gain a better understanding of the 


dynamics of the proposed model and the repairables system. 


93 


As already indicated, additional tests must be conducted to 
provide a better understanding of the effects of procurement 
workload constraints and ordering policies on investment 
levels and the MSRT goal. As it has already been 
demonstrated that the proposed repairables model can out- 
perform the current UICP model using the UICP determined Q 
and R quantities, additional research should concentrate on 
evaluating the cost savings obtainable through quantity 
discount buys against the increase in investment level for 
wholesale stock. The Q-Star program currently being 
evaluated at SPCC would provide a convenient mechanism for 
analyzing these cost tradeoffs for the proposed model. 

Secondly, additional research should be conducted to 
determine appropriate MSRT goals for the wholesale level. As 
has already been suggested by both Gormly [Ref.9] and 
Pearsall {Ref.10], setting MSRT goals by IMEC category 
appears to the logical approach to this problem, but 
additional analysis is required to determine what these goals 
should be. 

Thirdly, as the single item model simulation proved to be 
of significant value in increasing our knowledge of the 
dynamics of the repairables system and the resupply cycle, 
work in this area should continue on a larger scale. The 
initial results from goodness of fit tests conducted on 
sample distributions for demands occurring during procurement 
lead time and repair turnaround time failed to confirm the 
assumption that the probability distribution for demand 
during the resupply cycle follows the Poisson distribution. 
Additional research using simulations is required to identify 
the resulting probability distributions and understand the 
changes that occur in them as attrition rates increase and Q 


and R values are varied. It is also recommended that a 


94 


multi-item simulation be programmed to evaluate overall model 
performance and analyze the effects of procurement workload 
and other constraints. 

Finally, as the proposed repairables model is easily 
converted to a consumables model, performance tests should 
also be conducted against the current UICP consumables model 
using actual inventory data. If results from these tests are 
favorable, consideration should also be given to implementing 
the proposed model as the new wholesale level consumables 
model. This would provide a single model for both 


consumables and repairables. 


95 


QAADAANO 


O 


- APPENDIX A 


RARKRRKRARKAKRKRKRKKRRKAKRRRKRRARKRKRRARRRRRRARKRRRRRRRRRRRRRRRRRRRRRRERRRKKRRRKRRKKEKR 


*xkk PROGRAM TO TEST PROPOSED WHOLESALE REPAIRABLES REPLENISHMENT *** 
xk MODEL AGAINST THE CURRENT UICP INTEGRATED REPAIRABLES MODEL KKK 
RRRRRRRRKRRARRRRRRRRRRRRRRRRRRRRKRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRKX 
xkk MAIN PROGRAM 
REAL*8 NAME2(3)/'MIN INVE','STMENT L','EVEL'/ 
REAL*8 NAME3(3)/'MIN MSRT',' ',' '/ 
REAL*8 NAME1(3)/'UICP INT','EG. REPA','IRABLES'/ 
REAL Q1/'1 '/,02/'4D '/,93/'EOQ '/,04/'D '/,Q5/'UICP'/ 
REAL RQ1/'1 '/,RQ2/'4D '/,RQ3/'EOQ '/,RQ4/'D '/,RQS/'UICP'/ 
INTEGER STOP(1000) ,MARK(1000) ,LOT(1000) ,MD,PBP,RLC 
INTEGER X(1000) ,NSO(1000) ,QMIN(1000) ,NRPR(1000) 
INTEGER NPO,NOPT,N,NN,NI 
REAL D(1000),G(1000) ,PCLT(1000) ,RTAT(1000) ,LAM,SLC(1000) 
REAL H,Z(1000) ,T(1000) ,Q(1000) ,QQ(1000) 
REAL CT(1000) ,C1(1000) ,C2(1000) ,cOG1(1000) ,COG2(1000) ,RSR(1000) 
REAL A2(1000) ,DMAD(1000),RF(1000) ,C11(1000) ,E(1000) , RMIN, RMAX 
REAL RVAR(1000) ,DRTAT(1000) ,TOV(2),QR(1000) ,QRI(1000) ,QRR(1000) 
REAL MODMST ,MODNSF ,MSRTG(10) ,MSRTGG, PVAR(1000) 
REAL QQR(1000) ,AS1(1000) ,CRT,COGG1 ,COGG2 
REAL BB(10),QM,QMR 
REAL*8 B . 
COMMON SN(1000,9) 
EXTERNAL MODMST ,MODNSF 
*kk THE NEXT PARAMETER MUST BE SPECIFIED WHENEVER A NEW COG IS 
xkk INTRODUCED. THIS NUMBER IS PROVIDED BY THE PRINTOUT FROM 
xkk REPDATA PROGRAM WHICH ESTABLISHES A TEMPORARY DATA SET ON MVSO004. 
N=39 


C *** THE NEXT NUMBER SPECIFIES FULL TABLE LISTING(NPO=0) OR ONLY 


MaAaANA 


kkR A SUMMARY (NPO=1). 
NPO=1 


kkk THE VALUES OF THE PROCUREMENT AND REPAIR QUANTITIES MUST BE 
kkK SELECTED. PROGRAM PARAMETERS ARE SET TO CORRESPOND TO THE DESIRED 
kkk QUANTITIES. THE PROGRAM PARAMETERS AND VALUES ARE: MQ=1 FOR Q=1, 
kkX R=1, MQ=2 FOR Q=QUICP,R=RUICP. ALSO PARAMETERS QM AND QMR MUST BE 
kK SET; QM=Q1 OR Q2, AND QMR=RQ1 OR ROQ2. 

MOQ=5 

QM=Q5 

QOMR=RQ5 


*k*X THE APPROPRIATE MODEL MUST BE SELECTED. NOPT=1 IS MIN INVESTMENT 
**kX LEVEL AND NOPT=2 IS MIN MSRT. THE TESTS REPORTED HERE USED NOPT=1 
*x*X*X ONLY. NN IS THE NUMBER OF MEASURES OF PERFORMANCE; IF MSRT AND 
**X*X SMA ARE BOTH USED THEN NN=2. 

NOPT=1 


96 


22 


898 


CQ xxx 


Om & U) 


C xx 


NN=2 
CRT IS THE CARCASS RETURN TIME FROM CUSTOMER TO DEPOT. IT IS NOT 
NOT PART OF CARES DATA. GORMLY ESTIMATE AS OF 1/12/87 IS 40 DAYS. 
CRT=40./91. 
THE ANNUAL HOLDING COST FOR REPAIRABLES IS 21¢ PER DOLLAR HELD. 
H=0.21 
NI IS A COUNT OF VIABLE ITEMS (NOT HAVING STRANGE DATA). 
NI=0 
THE FOUR-DIGIT GOG PARAMETERS ARE READ. THEN EACH ITEM'S DATA IS 
READ. THE NOTATION IS THE ICP STANDARD USED IN VARIOUS DOCUMENTS. 
READ(10,2)RMIN,RMAX,LAM,PBP,RLC 
FORMAT (4X,2F4.2,F7.0,12,I11) 
DO 23 I=1,N 
READ(10,898,END=24)COG1(I) ,COG2(I) ,MARK(I),(SN(I,J),J=1,9),SLC(I), 
*E(I),PCLT(I),RSR(I),RTAT(I),NRPR(I),C1(I),C11(1I),D(I),G(I), 
XPVAR(I),RF(I),AS1(I),RVAR(I),DRTAT(I), 
*C2(I),A2(I),DMAD(I) ,LOT(I) ,NSO(I) ,QMIN(I) 
FORMAT (2A2,11,9A1,Al1,F3.3,F4.2,F3.2,F4.2,14,6F10.2, FS. OSE. 2, 
*F8.2,F10.2,218, 15) 
THE FOLLOWING STATEMENTS ARE SCREENS TO ELIMINATE STRANGE DATA. 
baht )enO.250000.)GO TO 22 
IF(D(I).EQ.0.0)GO TO 22 
Pe (eZmeLh 5.0 )GO TO 22 
IF(G(I).EQ.0.0)GO TO 22 
MECoC dT ieth.G(L))GO TO 22 
IF(PVAR(I).EQ.0.0)GO TO 22 
IF(RVAR(I).EQ.0.0)GO TO 22 
IF(LOT(I).NE.0)GO TO 22 
NI=NI+1 
CONTINUE 
WRITE(6,444)NI 
FORMAT (4X, 'NI=' ,I8) 
COGG1=C0G1(1) 
COGG2=C0G2 (1) 
THE PPV VALUE IS COMPUTED FOR EACH ITEM. 
DO 5 I=1,NI 
CT(I)=CRT 
STOP(I)=0 
T(I)=RTAT(I) + CT(I) 
TFAD(1) .LE.G(I))GO TO 3 
Z2(I)=(D(I)-G(I))*PCLT(I) + G(I)*T(TI) 
GO TO 4 
Z(I)=D(1I)*T(I) 
IF(PVAR(I).GT.Z(I))PVAR(I)=Z(I) 
CONTINUE 
MSRTGG=0.0 
THE CURRENT ICP MODEL IS CALLED TO PROVIDE THE BASIS FOR THE 


o7 


kkk TESTS. THIS MODEL PROVIDES THE GOAL MSRT VALUE, THE UICP VALUES 
kkk FOR Q AND R, AND THE MAXIMUM INVENTORY POSITION AND INVESTMENT 
kkk FOR EACH ITEM FOR THE ICP MODEL. 
CALL ICPMOD(NI,H,B,X,Z,RTAT,C1,C11,C2,D,G,90,NRPR,RF,PVAR,LOT, 
*DMAD ,E,LAM, MARK, PBP, SLC, RMIN, RMAX,RLC,NSO,COGG1,AS1,A2,QRI,QQR) 
C *** THE PERFORMANCE OF THE ICP MODEL IS COMPUTED AND PRINTED. 
CALL PRTOUT(1,NAME1,0M,B,QQ,QRI,QQR,N,NI,NN,X,Z,C11,D,G,MSRTGG, 
*COGG1 , COGG2 ,NPO, TOV, QMR) 
MOD=1 7 
C *** THE PROPOSED MODEL'S GOAL IS COMPUTED. 
MSRTGG=TOV (2) 
C *** THE VALUES OF THE PROPOSED MODEL'S Q AND R (QRR) ARE ESTABLISHED. 
C *k* THE EXPECTED ORDER QUANTITY ,QR, IS ALSO COMPUTED. 
DO 40 I=IN 
Oia! fe 
IF (MQ.EQ.2)0(I)=00(I) 
QRR(I)=1.0 
IF (QMR.EQ.RQ2)QRR(E)=QRI(I) 
OR(I)=Q(I)*(1.-G(I)/D(I) )+QRR(I)*(G(I)/D(I)) 
40 CONTINUE 
MOD=2 
C *** THE PROPOSED MODEL IS CALLED AND EACH ITEM'S MAX INVENTORY 
C **k POSITION IS COMPUTED VIA MARGINAL ANALYSIS. 
CALL MODOPT(NI,NN,B,MODNSF,X,Z,D,QR,C11,STOP,MSRTGG , MOD) 
C *** THE PERFORMANCE OF THE PROPOSED MODEL IS COMPUTED AND PRINTED. 
CALL PRTOUT(2,NAME2,0M,B,Q,QRR,QR,N,NI,NN,X,Z,C11,D,G,MSRTGG, 
*COGG1 , COGG2, NPO , TOV, QMR) 
1000 CONTINUE 
99 STOP 
END 


qa 


c 
C **k ROUTINE TO FIND MIN X SUCH THAT CDF(X).GE.(1-RISK) 
INTEGER FUNCTION NFX(ZZ,PVAR,RISK,PBP,MARK) 
REAL 2Z,R,RISK,TT,PVAR 
INTEGER NX,NB,MARK,PBP 
BP=FLOAT(PBP) 
R=1.-RISK 
NX=0 
C ***k IF(MARK.EQ.0)GO TO 10**** MARK 0 IS IGNORED FOR- REPAIRABLES. 
IF(ZZ.GE.BP)GO TO 12 
in (Zz0LT BP) Gor TO) 
10 CALL CDFP(ZZ,NX,P,C,CC) 
TR(C,GE LR) GO. 10120 
NX=NK+1 
GO TO 10 
11 CALL CDFB(ZZ,NX,PVAR,C,NB) 
IF(NB.EQ.1)GO TO 12 


98 


IF(C.GE.R)GO TO 20 
NX=NX+1 
GO TO! 11 
20 NFX=NX 
RETURN 
12 CALL CDFN(R,TT) 
NFX=ZZ+TT*SORT (PVAR)+0.9999 
RETURN 
END 


C *** ROUTINE TO CALCULATE POISSON CDF AND MASS 
C **X CUMULATIVE POISSON DISTRIBUTION 
SUBROUTINE CDFP(ZZ,K,P,C,D) 
REAL*8 2ZZZ,PP,CC,CC1,DD 
REaieaane ,.C,/D 


INTEGER K,I 7 
IF(K.LT.0)GO TO 12 
ZZZ=ZZ 

PP=DEXP (-Z2ZZ) 

CC=PP 

CC1=0.0 


IF(K.EQ.0) GO TO ll 
KK=5*IFIX(ZZ+0.5). 
IF(ZZ.GT.10.0.AND.K.GT.KK)GO TO 15 
ee) MG) enh 
CC1=CC 
PP=PP*ZZZ/DFLOAT (I) 
CC=CC+PP 

10 CONTINUE 

11 P=PP 
C=CC 
DD=1.0-CCl 
D=DD 
RETURN 

12 P=0.0 

- C=0.0 
D=1.0 
RETURN 

15 P=0.0 
C=1.0 
D=0.0 
RETURN 
END 


C *** ROUTINE TO CALCULATE NEGBINOMIAL CDF 


SUBROUTINE CDFB(ZZ,K,PVAR,C,NB) 
REAL 2Z,C,PVAR 


99 


@ 
C AK* 


C xk* 


REAL*8 ZZZ,PP,CC,BR,R,BK,S22,B,BQ 
INTEGER K,I,NB 

NB=0 

2ZZ=22 

S22=PVAR 

BR=ZZZ/$22 

BQ=S22/Z2ZZ 
IF(BQ.LE.1.0)GO TO 8 

R = 1.0-BR 

BK=(ZZZ**2) /($22-2Z2ZZ) 
IF(BK*DLOG(BQ).GT.9.0)GO TO 8 
PP=BR**BK 

CC=PP 

Tho 0) Gounod 
GO -To.9 

NB=1 

RETURN 

DO 10 I=1,K 
B=DFLOAT(I-1) 
PP=PP*R*(B+BK) /DFLOAT(I) 
CC=CC+PP 

CONTINUE 

c=cc 

RETURN 

END 


ROUTINE TO CALCULATE NORMAL DEVIATE GIVEN R. 
SUBROUTINE CDFN(R,TT) 

INTEGER IER 

REAL R,1T 

CALL MDNRIS(R,TT,IER) 

RETURN 

END 


THE CURRENT ICP INTEGRATED REPAIRABLES MODEL 
THIS SUBROUTINE COMPUTES ONLY THE PROCUREMENT Q AND ROP. 
SUBROUTINE ICPMOD(N,H,B,X,Z,RTAT,C1,C11,C2,D,G,Q0,NRPR,RF, PVARe eee 


*DMAD,E,LAM,MARK,PBP,SLC,RMIN,RMAX,RLC,NSO,COG,AS1,A2,Q0R,QQR) 


INTEGER N,X(N),NRPR(N) ,LOT(N) ,MARK(N) ,¥(1000) ,R121,08,09 
INTEGER ROP(1000) ,NSO(N) ,RLC, PBP,Q22,021,02C,0S 

REAL Z(N),C1(N),C2(N),D(N),G(N),RF(N) ,PVAR(N) , DMAD(N) ,AS1(N) 
REAL SL(1000) ,RMIN, RMAX,C3(1000) ,RISK(1000) ,E(N),SLC(N) ,H 
REAL 01,02,03,04,05,06,07,0(N) ,COG,LAM,R,R11,R12,R13,R1,C11(N) 
REAL QQR(N),QR(N),A2(N) ,AA,AC,QR1,RRCT,QR2,0R3,QSL 

REAL*8 B 

REAL A7/'7R!/ 

B=0.0 


100 


C *** DETERMINE THE PROCUREMENT REORDER POINT. 


2 


3 


DO 5 I=1,N 


MeDCry.LE.G(r))GO TO 3 
IF(LOT(I).NE.O.AND.Z(I).LE.0.0)GO TO 2 

Saree) ecw ie (Gil), Gl) wecl(r)*(1. -(G(1)/D{(TI))) 
RISK (I)=H*C3(I)*D(I)/(H*C3(I)*D(I) + E(I)*LAM*RF(I)) 
RISK(I)=AMIN1 (RISK(I) , RMAX) 
RISK(I)=AMAX1(RISK(I) , RMIN) 

¥(I)=NFX(Z(I) ,PVAR(I),RISK(I) ,PBP,MARK(I)) 
R121=MAX0(Y(I),NRPR(I)) 

R12=FLOAT(R121) 

CALL SHFLIF(SL(I),SLC(I)) 
IF(SL(I).EQ.100.)R11=R12 

Mist REO. 100.)GO TO 1 
Bl1=4.*(D(1)-G(1))*SL(I) + Z(I) - (D(I)-G(I))*4. 
R13=33.*D(I)+Z(I) 

R1=AMIN1(R11,R12,R13) 
R=AMAX1(R1,FLOAT(NSO(I)),Z(I)) 
ROP(I)=IFIX(R+0.999) 

GO TO 5 

ROP(I)=0 

GO To 5 

ROP(I)=IFIX(Z(I)+0.999) 


5 CONTINUE 


C ***k COMPUTE PROCUREMENT QUANTITY NEXT. - 


10 
Lt 


DO 12 I=1,N 


IF(LOT(I).NE.0)GO TO 10 

Ml) LE.G(1))GO TO 9 
Q1=SORT(8.*(D(I)-G(I))*(1970.+AS1(I))/(H*C1(I))) 
IF(COG.NE.A7)GO TO 7 
Q1=SORT(8.*(D(I)-G(I))*(1530.+AS1(I))/(H*C1(I))) 
Q2=4.*(D(I)-G(I)) 

Q3=AMAX1 (01,92) 

Q4=12.*(D(I)-G(I)) 

Q5=AMIN1 (93,04) 

IF(SL(I).EQ.100. )Q6=05 

IF(SL(I).EQ.100.)GO TO 8 

Q6=4.%*(D(I)-G(I) )*SL(I)-AMAX1(0., (FLOAT(ROP(I))-Z(I))) 
Q7=AMIN1(Q5,06) 

Q8=IFIX(07+0.999) 

Q9=MAX0(1,98) _ 

Q(I)=FLOAT(Q9) 

Go To ii 

O(I)=1.0 

GO TO 11 

Q(I)=FLOAT(LOT(I)) 

BE OCl yeh 1. 0)0(L)=2.0 


101 


C ***k COMPUTE CONSTRAINED REPAIR QTY (B021A=02C)FOR THE ICP MODEL. 
Ac=660. 
IF (COGG1.EQ.A7)AC=133. 
IF(C2(I).EQ.0.0)OR(I)=0.0 
IF(C2(I).EQ.0.0)GO TO 20 
OR1=SORT(8.*(AC+A2(I))*G(I)/(H*C2(I))) 
RRCT=0.0 
IF (COGG1 .EQ.A7)RRCT=0.08 
OR2=RRCT*G(I) 
OR3=AMAX1(1.,QR1,0R2) 
Q22=IFIX(QR3+0.999) 
CALL SHFLIF(SL(I) ,SLC(I)) 
QSL=4.*D(I)*SL(I)-AMAX1(0.0, (FLOAT(Y(I))-Z(I))) 
QS=IFIX(QSL+0.999) 
Q21=MINO(Q22,0S) 
Q2C=MAX0(1,021) 
_ QR(I)=FLOAT(Q2C) 
20 IF(QR(I).EQ.0.0)GO TO 21 
C *** THE EXPECTED ORDER QUANTITY IS COMPUTED. 
QOR(1I)=Q(1)*(1.-G(I)/D(I) )+QR(I)*(G(I)/D(T)) 
GO TO 22 
21 QOR(I)=Q(I) 
Cc ***k THE INVENTORY POSITION AND INVESTMENT COST IS COMPUTED. 
22 X(I)=ROP(I)+IFIX(QQR(I)+0.5) 
B=B+C11(I)*FLOAT(X(I) ) 
12 CONTINUE | 
RETURN 
END 


C *** THE SHELF LIFE CODE IS CONVERTED TO THE COMPUTATIONAL FACTOR. 

SUBROUTINE SHFLIF(SL,SLC) 

REAL*4 A/'A Bf 8 Wee) UG '/ Dye '/ BOE ie 
AB /'F 7, 
nG/*G a) as em OS) / Ki Kees o/h ae 
AN/'N  '/,P/'P '/,0/'9 '/,R/'R N/ 7) oor ee 
*AL/'1 \/ Aer 2 Wns tS '/ ,A4/'4 ly ASS ae 
*A6/'6 are ke) By ees As) 1/7 ,A9/'9 b/ ,A0/ 1G iy 
REAL*4 SL,SLC 

IF(SLC.EQ.A0)SL=100. 

IF(SLC.EQ.A0)GO TO 50 

IF(SLC.EQ.A)SL=1./3. 

IF(SLC.EQ.A)GO TO 50 

IF(SLC.EQ.B)SL=2./3. 

IF(SLC.EQ.B)GO TO 50 

IF(SLC.EQ.C.OR.SLC.EQ.A1)SL=3./3. 
IF(SLC.EQ.C.OR.SLC.EQ.A1)GO TO 50 

IF(SLC.EQ.D)SL=4./3. 


102 


ol @) 


ANANANNANA 


IF(SLC.EQ.D)GO TO 50 
IF(SLC.EQ.E)SL=5./3. 
IF(SLC.EQ.E)GO TO 50 
IF(SLC.EQ.F.OR.SLC.EQ.A2)SL=6./3. 
IF(SLC.EQ.F.OR.SLC.EQ.A2)GO TO 50 
IF(SLC.EQ.G.OR.SLC.EQ.A3)SL=9./3. 
IF(SLC.EQ.G.OR.SLC.EQ.A3)GO TO 50 
IF(SLC.EQ.H.OR.SLC.EQ.A4)SL=12./3. 
IF(SLC.EQ.H.OR.SLC.EQ.A4)GO TO 50 
IF(SLC.EQ.J)SL=15./3. 
IF(SLC.EQ.J)GO TO 50 
IF(SLC.EQ.K.OR.SLC.EQ.A5)SL=18./3. 
IF(SLC.EQ.K.OR.SLC.EQ.A5)GO TO 50 
IF(SLC.EQ.L)SL=21./3. 
IF(SLC.EQ.L)GO TO 50 
IF(SLC.EQ.M.OR.SLC.EQ.A6)SL=24./3. 
IF(SLC.EQ.M.OR.SLC.EQ.A6)GO TO 50 
IF(SLC.EQ.N)SL=27./3. - 
IF(SLC.EQ.N)GO TO 50 
IF(SLC.EQ.P)SL=30./3. 
IF(SLC.EQ.P)GO TO 50 

' IF(SLC.EQ.Q.0R.SLC.EQ.A7)SL=36./3. 
IF(SLC.EQ.Q.OR.SLC.EQ.A7)GO TO 50 
IF(SLC.EQ.R.OR.SLC.EQ.A8)SL=48./3. 
IF(SLC.EQ.R.OR.SLC.EQ.A8)GO TO 50 
IF(SLC.EQ.S.OR.SLC.EQ.A9)SL=60./3. 
IF(SLC.EQ.S.OR.SLC.EQ.A9)GO TO.50 
SL=100. 

50 RETURN 

END 


kkk THE PROPOSED MODEL'S ALGORITHM 
SUBROUTINE MODOPT(N,NN,B,AMODEL,X,2N,D,QR,C1,STOP,GOALG,MOD) 
**kk PERFORM OPTIMAL ALLOCATION FOR GIVEN MODEL USING 
*kX MARGINAL ANALYSIS METHOD AND LOWER BOUNDING. 
kK N=NO. ITEMS 
kK B=INVESTMENT LEVEL OF STOCK FUND 
kk BRMODEL=ENTRY POINT FOR MODEL TO USE (STANDARDIZED ARGUMENTS) 
kk X=OPTIMAL ALLOCATIONS PER ITEM 
kkk ZN= MEAN DEMAND DURING RESUPPLY TIME OR PPV 
kk C1=PROCUREMENT COST FOR EACH ITEM 
kkk RR=WORK VECTOR TO STORE RATIOS 
INTEGER N,1I,K,MK,STEP, X(N) ,STOP(N) 
REAL ZN(N),QR(N) ,D(N) ,MR,RR(1000),SR,TRY 
REAL MODNSF,MODMST,C1(N) ,GOALG 
REAL*8 B 
SR=0. 


103 


ARK 


30 


ARK 


ARK 


40 
RAK 


ARK 
ARK 


10 


KK=1 
INITIALIZE 
B=0. 
aye) til, a=, fa 
X(I)=0 
INITIALIZE STOP BEFORE OPTIMIZING ON INVESTMENT LEVEL(STOP=1 MEANS 
THAT THE LEVEL HAS HIT THE ITEM MSRT BOUND). 
STOP (I)=0 
RR(I)=AMODEL(ZN(I),D(I),QR(I) ,C1(I),X(I)+1,STOP(I)) 
CONTINUE 
STEP=0 
DO UNTIL MSRT OR BUDGET GOAL IS REACHED 
CONTINUE 
STEP=STEP+1 
MK=0 
MR=10000000. 
IF(MOD.EQ.3)MR=0. 
DO 30 K=1,N - 
IF(STOP(K).EQ.1)GO TO 30 
IF(RR(K).GE.MR)GO TO 30 
MR=RR(K) 
MK=K 
CONTINUE 2 
IF(MK .EQ. 0) GO TO 40 
ALLOCATE ONE MORE UNIT OF ITEM MK IF POSSIBLE. 
B=B+C1 (MK) 
X(MK)=K(MK)+1 , 
NEXT CHECK TO SEE IF GOAL HAS BEEN ATTAINED. 
CALL GOALM(X,N,ZN,D,QR,TRY,GOALG) 
IF(TRY.EQ.0.0)GO TO 40 
SR=MR 
RR(MK)=AMODEL (ZN (MK) ,D(MK), QR(MK) ,C1 (MK) ,X(MK)+1, STOP (MK) ) 
GouTo: 20 
RETURN 
END 


ROUTINE TO MINIMIZE INVESTMENT LEVEL OF STOCK FUND 
REAL FUNCTION MODNSF(ZZ,D,QR,C,K,STOP) 
COMPUTE MARGIN ANALYSIS RATIOS ASSUMING 
POISSON DEMAND. 

REAL ZZ,QR,D,C,MSRT,MSRTD,TS1,TS2 
INTEGER K,STOP 

IF(ZZ.NE.0.0)GO TO 10 

MODNSF=0.0 

MSRT=-0.0001 

GO TO 12 

TS1=TWUS(ZZ,OR,K-1) 


104 


eZ 


tgs 
15 


10 


20 


TS2=TWUS (ZZ,QR,K) 
IF(TS1.EQ.TS2)GO TO 13 
MODNSF= C/(TS1-TS2) 
MSRT=TS2/D 
MSRTD=91.*MSRT 

IF (MSRTD.LT.0.001)STOP=1 
GO TO 15 

MODNSF=C 

RETURN 

END 


ROUTINE TO CALCULATE THE EXP TIME WTD UNITS SHORT FOR K UNITS 


REAL FUNCTION TWUS(ZZ,QR,K) 


Roeeecaet i,k 2, ON, Re VOR, Po,es,Fo,Po,Gbl ,CDZ,CD3,CD4, CDS, CD6 


Ree CCDl,CCDzZ,CCD3 ,CCD4,CCD5,CCD6, BETA] ,BETAZ 


REAL~S PHIL PHIz ,DCD!,DCD2,D1,D2,T1,12,2,DBETAl ,DBETA2 


INTEGER K 
SW=FLOAT (K) 

Z=20 

RP=SW-OR 

KRP=K~-IFIX(QR+.5) 
fiezzeGR. 20. )GO TO 20 

CALL CDFP(2Z,KRP-1,P1,CD1,CCD1) 
CALL CDFP(Z2Z,KRP,P2,CD2,CCD2) 
CALL CDFP(ZZ,KRP+1,P3,CD3,CCD3) 
CALL CDFP(ZZ,K-1,P4,CD4,CCD4) 
CALL CDFP(ZZ,K,P5,CD5,CCD5) 
CALL CDFP(ZZ,K+1,P6,CD6,CCD6) 
IF (CCD1.LT.0.000001) GO TO 10 
BETA1=(CCD1*ZZ**2) /2.-CCD2*ZZ*KRP+CCD3*KRP* (KRP+1)/2. 
IF (BETA1.LT.0.000001)BETA1=0.0 

IF (CCD4.GE.0.000001) GO TO 7 

BETA2=0.0 

Gonzous 
BETA2=(CCD4*ZZ**2) /2. -CCD5*ZZ*K+CCD6*K* (K+1)/2. 
IF (BETA2.LT.0.000001)BETA2=0.0 
TWUS=(BETA1-BETA2)/QR 

RETURN 

TWUS=0 .0 

RETURN 

S=FLOAT(K)+0.5 

T1=(RP-ZZ) /SQRT(ZZ) 

IF(DABS(T1).LE.7.)GO TO 21 

PHI1=0.0 

IF(T1.GT.7.)D1=0.0 

IF(TL.LT.(-7.0))D1=1.0 

GQ TO 22 


105 


21 PHI1=(DEXP(~(T1**2)/Z.))/SORT(Z.*ayielogzecr 
CALL MDNORD(T1,CD1) 
D1=1.0-CD1 | 

22 DBETA1=Z*(D1*(1.0+T1**2)-T1*PHI1)/2. 
T2=(SW-ZZ) /SQRT(ZZ) 
IF(DABS(T2).LE.7.)GO TO 23 
PHI2=0.0 
TF (T2-GT.7 6) D2=0n0 
TR(T2eLT, (=) 0 D210 
GOTO 25 

23 PHI2=(DEXP(-(T2**2)/2.))/SORT(2.*3.14159265) 
CALL MDNORD(T2,CD2) 
D2=1.0-CD2 

25 DBETA2=Z* (D2*(1.0+T2**2)-T2*PHI2)/2. 
TWUS=(DBETA1-DBETAZ)/QR 
RETURN 
END 


C *k* ROUTINE TO SEE IF GOAL HAS BEEN ATTAINED. 
SUBROUTINE GOALM(X,N,Z,D,QR,TRY ,MSRTG) 
INTEGER N,X(N) ,XI 
REAL Z(N),VO(1000) ,TV,SLT,D(N),QR(N),MSRTG, TRY 
REAL MSRTC,MSRT 


TV=0.0 
SLt=0. 
DO 10 I=1,N 
" IF(Z(I).EQ.0.0)GO TO 16 
KI=Rct) 
SLT = SLT + D(I) 
14 MSRTC=TWUS (Z(I),QR(I) ,XI)/D(I) 
MSRT=AMAX1 (MSRTC,0.0) 
Go 1om1s 
16 MSRT=0.0 
18 VO(I) = 91.*MSRT 


TV = TV + VO(I)*D(I) 
10 CONTINUE 
TV=TV/SLT 
TRY = 1.0 
IF(TV.LE.MSRTG)TRY = 0.0 
22 RETURN 
END 
C 
Cc **k ROUTINE TO EVALUATE PERFORMANCE AND PRINT OUT RESULTS 
SUBROUTINE PRTOUT(MD,NAME,QM,B,Q,ORR,OR,NT,N,NN,X,Z,C1,D,G,MSRTG, 
kCOG1,COG2,NPO, TOV, QMR) 
INTEGER X(N) ,ROP(1000) ,NPO,NT 
REAL Z(N) ,0V(2,1000) ,TOV(2) ,C1(N) ,MSRTG, BSW(1000) 


106 


REAL COG1,C0G2,0(N),D(N),G(N),QRR(N) ,OR(N) 
REAL*8 B,NAME(3) 
COMMON SN(1000,9) 
DO 1 I=1,N 
BSW(I)=C1(I)*X(I) 
1 ROP(I)=X(I)-IFIX(QR(I)+0.5) 
C ***x THE PERFORMANCE ROUTINE IS CALLED NEXT. 
CALL OBJECT(X,N,NN,Z,D,OR,OV, TOV) 


WRITE (6,900) 
900 BHORMAT Ci // 7, ' KKKKKKKKKKKRKKRKKRKKRKKKK RK KKK KKRKKKKKKKAAKKKKE 


KUAKKKAKAKKKKKKKK KK KKKKKKKKKKKKKKK KA KKKKKKKKKEKKRRK RRR KAKKKKKKKRKKE | 
KIAKKAKKAAKKKKKEZ | ) 


WRITE (6,901)MD,NAME ,COG1 ,COG2,MSRTG,OM,QMR 

901 FORMAT('0',1X,!' MODEL (',I1,')',2X,3A8,2X,'COG: ',2A2,8X, 
*xIMSRT GOAL:',F8.2,' DAYS',4X,'OP: ',A4,4X,'OR:',A4) 

c *kk TF ONLY A SUMMARY TABLE IS DESIRED SKIP TO STATEMENT 907. 

IF(NPO.EQ.1)GO TO 907 
WRITE(6,902) 

902 FORMAT('0',5X,'NIIN',7X,'DEPTH' ,5X, 'MSRT(DAYS)' , 4x, 
xVINVEST. LVL.',3X,'UNIT COST! ,6X,'QP', 6X, 
*'ROP! 6X, 'PPV! 9X, 'D',9X,'G!, 9X, 'OR') 
WRITE(6,903) ((SN(I,J) ,J=1,9) ,X(I) ,OV(2,1) ,BSW(Z), c1(Z), aan), 
*ROP(I),Z(I) ,D(I),G(1) ,ORR(I) , I=1,N) 

PeSmEORMAT (3X, 9Al,2X,16,2X,F12.3,5X,F12.2,2X,F10.2,2X,F7.2,18,2X%, 
*F10.3,F10.3,F10.3,F10.3) 

906 WRITE(6,904)TOV(2),B,TOV(1)° 

904 FORMAT('0' ,4X,'OVERALL PERFORMANCE:! ,2X,F9.3,4X,'$!,F12.2,5X, 
*ISMA:! ,F8.2) 
GO TO 909 

907 WRITE(6,908)TOV(2),B,TOV(1),NT,N 

908 FORMAT('0',4X,'OVERALL PERFORMANCE:! ,2X,F9.3,4X,'$!',F12.2,5X, 
*'SMA:',F8.2,4X, 'N/NI=',18,'/',18) 

909 WRITE(6,905) 

905 FORMAT('0O!',' RKRKKRKKRKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKKKKKKKKKKKKK 


KIVAKKKKKRKARKKARAKKKKKKKKK KKK KKKKKAKKKAKKKKK KKK KKK KKKRAKRKKKRAKKKKKKRKE NV 
AUAKKKARKRER | ) 


RETURN 
END 


C *** ROUTINE TO COMPUTE THE MSRT AND SMA VALUES FOR A GIVEN ALLOCATION. 
SUBROUTINE OBJECT(X,N,NN,Z,D,QR,OV,TOV) 

INTEGER N,NN,X(N) ,XI 

REAL Z(N),OV(NN,N) , TOV(NN) ,SLT,MSRT,OV1,D(N),QR(N) 
REAL CD,P,MSRTC,BO,BOT,DD 

TOV(1)=0. 

TOV(2)=0. 

BO=0.0 


107 


BOT=0 .0 


5 CONTINUE 

SLT=0. 

DO 10 I=1,N 
TFiZ( 1 GEOR O40) GO) Lore 
XI=X(I) 

SLT = SLT + D(TI) 
OV(1,1I)=0. 


C *x* THE EXPECTED NUMBER OF BACKORDERS IS COMPUTED. 
CALL EBO(Z(I),XI,D(I) ,QR(I),OV1) 
MSRTC=TWUS(Z(I) ,QR(I) ,XI)/D(I) 

MSRT=AMAX1 (MSRTC,0.0) 
OV(1,I)=AMIN1(OV1,1.0) 


GO TO 7 

6 OV(1,1)=0.0 
MSRT=1.0 

7 OV(2Z 1) = Si aisks 


TOV(2) = TOV(2) + OV(2,I)*D(I) 
BO=BO+0V(1,I) 
10 CONTINUE 

IF (SLT.EQ.0.0)SLT=1.0 

BOT=B0/SLT 

TOV(1)= (1.-BOT)*100. 

TOV(2)=TOV(2)/SLT 

RETURN : 

END 


C **x THE ROUTINE TO COMPUTE THE EXPECTED NUMBER OF BACKORDERS. 
SUBROUTINE EBO(Z,X,D,0R,OV1) 
REAL Z,D,QR,OV1,ALPHAI1 ,ALPHA2,X1,X2,CD1,CD2,CDD1,CDD2,P1,P2 
REAL PP1,PP2,PHI1,PHI2 
INTEGER X 
K1=X-IFIX(QR+0.5) 
X1=FLOAT(K1) 
X2=FLOAT(X) 
K2=IFIX(X2) 
ME 62, GI 204) Gor roe 10 
CALL CDFP(Z,K1,P1,CD1,D1) 
CALL CDFP(Z,K2,P2,CD2,D2) 
ALPHAL=D1*(Z-X1)+X1*P1 
ALPHA2=D2*(Z-X2)+X2*P2 
IF (ALPHA1.LT.0.0)ALPHA1=0.0 
IF (ALPHA2.LT.0.0)ALPHA2=0.0 
GO TO 20 
10 T1=(Cd-=2) sort) 
IF(ABS(T1).GT.7.0)GO TO 12 
PHI1=(EXP(- (T1**2)/2.))/SORT(2.*3.14159265 ) 


108 


iz 


In: 


14 


£5 


20 


CALL MDNOR(T1,CD1) 

D1=1.0-CD1 

GO TO 13 

iF (Tl .G1.7.0)D1=0.0 

IF(T1.LT. (-7.0))D1=1.0 
PHI1=0.0 

T2=(X2-Z)/SOQRT(Z) 
IF(ABS(T2).G6T.7.0)GO TO 14 
PHI 2=(EXP (-(T2**2)/2.))/SOQRT(2.*3.14159265) 
CALL MDNOR(T2,CD2) 

D2=1.0-CD2 

GO TO 15 

PE(T2.GIe7 ean 2—one 

gt GeAepepe, 07) OO Mwah Ae 
PHI2=0.0 
ALPHA1=(PHI1-T1*D1)*(SQRT(Z) ) 
ALPHA2=(PHI2-T2*D2)*(SOQRT(Z)) 
IF (ALPHA1 .LT.0.0)ALPHA1=0.0 
IF (ALPHA2.LT.0.0)ALPHA2=0.0 
OV1=(ALPHA1-ALPHA2)*D/OR 
RETURN 

END ~ 


109 


aegngeee™ 


PE DPELCLECEL) ML BEEBE L- 


F 


APPENDIX B 


VARIABLES LISTING FOR REPATRABLES SIMULATION 


QUARTERLY DEMAND RATE 

QUARTERLY REGENERATION RATE 
PROCUREMENT ORDER QUANTITY 

REPAIR ORDER QUANTITY 

WHOLESALE STOCK LEVEL 

PROCUREMENT REORDER POINT 
PROCUREMENT LEAD TIME © IN QUARTERS) 
REPAIR TURNAROUND TIME CIN QUARTERS > 
PROCUREMENT LEAD TIME <IN DRYS> 
REPAIR TURNAROUND TIME ¢CIN DAYS) 
REPAIR SURVIVAL RATE 

CRRACRSS RETURN RATE 

INVENTORY POSITION 

CARCRSS REGENERATION RATE 

READY FOR ISSUE UNITS ON-HAND 

NOT REAROY FOR ISSUE UNITS ON-HAND 
UNITS IN PROCUREMENT 

UNITS IN REPAIR 


ATTRITIONS OCCURRING SINCE LAST PROCUREMENT ORDER 
OUTSTANDING BACKORDERS 


TOTAL NUMBER OF ATTRITIONS FOR SIMULATION 
TOTAL NUMBER OF CARCASSES INDUCTED FOR REPAIR 
TOTAL NUMBER OF DEMANDS FOR SIMULATION 
TOTAL NUMBER OF REPAIR BATCHES INDUCTED 
TOTAL NUNBER OF PROCUREMENT ORDERS PLACED 
INDIVIDUAL BACKORDER TIMES 

TOTAL BACKOROER TIME FOR SIMULATION 
AVERAGE NUMBER OF BACKORDERS PER YEAR 
AVERAGE NUBER OF UNITS REPAIRED PER YEAR 
AVERAGE NUMBER OF UNITS PURCHASED PER YEAR 
COMPUTED MEAN SUPPLY RESPONSE TIME 

AVERAGE DAYS DELAY FOR BACKORDERED REQUISITIONS 
COMPUTED SYSTEM MATERIAL AVAILABILITY 
NUMBER OF YEARS USED FOR SIMULATION 

REPORT PRINTOUT OPTION 

SIMULATION CLOCK 

TIME BETWEEN DEMANDS 

REPAIR BATCH INDUCTION TIMES 

PROCUREMENT ORDER PLACEMENT TIMES 
BACKORDER STRAT TIMES 

NUMBER OF UNITS IN A PROCUREMENT BATCH 


B3B8533 
mmm 


NUMBER OF REPAIRABLE CARCASSES IN A REPAIR BATCH 
NUMBER OF DEMANDS OCCURRING PRIOR TO AN ATTRITION DEMAND 
NUMBER OF DEMANDS OCCURRING PRIOR TO A REPAIR DEMAND 


110 


rye iy sae 


DRO OR DPG FOR DORCT SUBROUTINE 

NUMBER OF UNITS INDUCTED IN A REPAIR BATCH 
ATTRITIONS OCCURRING AT DOP 

NUMBER OF BACKORDERS FILLED BY A REPAIR OR PROCUREMENT 
DEMANDS OCCURING DURING REPAIR CYCLES 

DEMANDS OCCURING DURING PROCUREMENT CYCLES 

DEMANDS OCCURING DURING THE RESUPPLY CYCLE 

CARCASS RETURN ATTRITION GENERATOR CRANDOM NUMBERS > 
REPAIR ATTRITION GENERATOR (RANDOM NUMBERS > 

NUMBER OF REPAIR BATCHES OUTSTANDING 

NUMBER OF PROCURENENT ORDERS OUTSTANDING 

DORCT SELECTION INDEX 


STORAGE ARRAY INDEX 

DEMAND CURING REPAIR INDEX 
DEMAND DURING PROCUREMENT INDEX 
REPAIR ATTRITION INDEX 
BACKORDER INDEX 


APPENDIX C 


PROGRAM LISTING FOR REPAIRABLES SIMULATION 





ited SIMULATION OF WHOLESALE REPAIRABLES REPLENISHMENT ae 
+** INVENTORY MODEL WITH POISSON DEMANDS (SINGLE ITEM) + 





toeeee 


Ue Roe Ce OL Pp RRO LG) SR Se aoc ininininininiaiaininininisininininicniininininicic ini 


INTEGER C¢ 1500), E¢ 1500), IP¢2500>, RF 1<2500>, NRF 1<2500>,TR/O/, 
*DEF (2500), PCMT (2500 >, REP (2500 >, B0¢(2500),0,R,SW,ROP,POPT, |, TRON/O/, 
*1X,0/1/,M/1/,N/2500/,NN/1500/,NYRS, TREP /0/, TBUY /0/ 

REAL CLK(2500>, TIME< 1500),D,G,PLT,RTAT, CRR, RSR, PCLT, TAT, RGR, 


O1 

Q=1F 1X<4*(D-G >+ .99) 

SELECT NUMBER OF YEARS FOR SIMULATION (1-30) RRR EEREEEE EEE Ere 
NYRS=30 

SELECT PRINTOUT OPTION CPOPT=0 FOR SHORT, POPT=1 FOR LONG AND ++ 
POPT = 2 FOR NET INVENTORY PLOT *ttetetetetciesicitinieisicieieiieinisiniosieictntaiaiciniaiak 
POPT=1 

SELECT INITIAL SEED FOR RANDON NUMBER GENERATOR 9 errr 
CANY INTEGER BETWEEN 1 AND 2°*31-1) ‘RRR EEEEEEEEEEEEET 


Hai 


GENERATE TIME BETWEEN DEMANDS, CARCASS RETURNS AND REPAIR SURVIVALS 
CALL RANDOMCTIME, CRR,RSR,C,0,E,NN, 1X) 
INITIALIZE STORAGE ARRAYS 
DO 10 1=1,N 
IPCI =O 
RF ICI =O 
NAF I C1 =0 
DEF ¢ 1 =0 


i] 


112 


10 


20 
Cee 


aa 


MOO 1 © 


ii 


10 


{ 


*TR,C,D,£,G,0,R,SH,ROP,J,H,N,NN, TOUT, TRON, TREP, TBUY> 





PRINT OUT RESULTS 


CALL PRINT(CLK, IP,RFI,NRFI,OEF,PCHT,REP,60,0,R,SW,ROP,D,G,CRR, 
*RSR RGR, PCLT, TAT, BOT, POPT, TRON, TREP , TBUYV, NYRS, J,M,N,NN,AT, TR 
STOP 
END 





* ROUTINE TO GENERATE RANDOM DEMANDS, CARCASS RETURNS AND * 
* REPAIR SURVIUALS USING THE LLRANI! RANDOM NUMBER GENERATOR * 





SUBROUTINE RANDOM<TIME,CRR,RSR,C,0,E£,N, 1X) 
INTEGER C(N>,E¢(N>, CC< 1500), 2Z2¢ 1500),W,X, 1X,N, MUL, ISORT 
REAL TIMECN>,AC1500>,B8¢ 1500), T< 1500),2¢ 1500), CRRA, RSR,D 
SELECT MULTIPLIER FOR RANDOM RANDOM NUMBER GENERATOR 9 eeeeesseccee 
(HUL=1 FOR 16807 OR MUL=2 FOR 397204094> 
MUL=1 
SPECIFY SORT OPTION (O FOR NO SORT OR 1 FOR ASCENDING ORDER SORT> 
ISORT=0 
CALL SRNDCIX,A,N,MUL, ISORT> 
DO=9 1.0/0 
DO 10 1=1,N 
T¢1>=ABS(LOG(ACI >>*DD> 
IFC1.EQ. 1>THEN 
TIMECI2=TCH> 
ELSE 
TIME C1 =TIMECI-1>4TC1> 
ENDIF 
CONT INUE 
CALL SRNDCIX,8,N,MUL, ISORT> 
W=1F I X<CRR* 1000+0.5) 
DO 20 1=1,N 
BC) =B¢1 #1000. 
CCCIEHIFIXCBC1 40.5) 
IFCCC¢1>.LT.W THEN 
C<1>=0 
ELSE 
Ccl=1 
ENDIF 
CONT I NUE 


113 


Cere 


OOOO © 


10 
Cree 


1 


GENERATE REPAIR SURVIVAL RATES steers 
CALL SRNDCIX,2,N,MUL, ISORT>) 
X=1F 1X<RSR* 1000+0 . 5) 
DO 30 I=1,N 
Z2¢ 1 ZC 1 9 1000. 
220 1 IF IXCZ0 1940.5) 
IFC22¢19.LT.X THEN 
Ecl=1 
ELSE 
Ec] =0 
ENDIF 
CONT INUE 





= ROUTINE TO MANAGE SIMULATION EVENTS = 





SUBROUTINE EVENTCCLK, TIME,BOT, IPX,RFIX, NRF IX, DEFX,PCHIX,REPX,BOX, 


*PLT,RTAT,AT,TR,C,D,E,G,0,R, SH, ROP, J,M,N,NN, TOUT, TRON, TREP, TBUY > 


INTEGER CCNND,ECNND, IPXCN), RF IXCND, NRF IXCN), DEFXCND, BOXCN), TR, 


*PCMTX(N>, REPX(N), IP,RFI,SH,0,R,NRFI/0/,AT/O/,DEF /0/,PCHT/0/, 
*REP /0/,60/0/,1,J5,K/1/,L/1/,M, IK/O/, IL/0/, K/1/,¥/0/,2/0/,N,NN, 
*TRON , TREP , TBUY , ROP, RR< 1500, 00¢ 1500>, DRO< 1500), DPA< 1500), 
*DRST¢ 1500) 


REAL CLK(N>, TIME<(NN>, RTIME< 1500>, PTIME< 1500>,BTIME< 1500>, BOT<NND, 


*PLT ,RTRT, TOUT 


INITIALIZE OPENING INVENTORY VALUES theme 
IP=SH 
RF I=SH 
ROP=SH-0 
INITIALIZE STORAGE 
DO 10 1=1,NN 
BTIMEC1>=0.0 
PT IMEC 1 =S0000. 
RTIME< 1 >=50000. 
Q0< 1>=0 
RRC 1 =O 
DROQ< 1 =0 
DPO< 1 =0 
DRST<1=0 
CONT INUE 
CALL ARRAYCCLK, IP, RFI ,NRE!,DEF,PCNT,REP,BO, IPX,RFIX, NRF IX, DEFX, 





*PCNTX, REPX, BOX, J,N> 


DO 20 1=1,NN 
IFCCTIMEC1>.GE.RTIMECK>>. AND. CTIMECI >.LT.PTIMECL >>>THEN 
CALL ROUEINCCLK,RTIME,BTIME,RFI,REP,60,B80T,RR,1,J,K,M,N,NN,Y, 


* DRQ, DRST > 


GO TO 2 
ELSE IFCCTIMECI>.GE.PTIMECL)). AND. CTIMECID.LT.RTIMECK))> THEN 


114 


28 


NOM000 


CALL POUEINCCLK,PTIME,BTIME,RFI,PCMT,B0,60T,00,1,J,L,4,4,NN,Z, 
DPQ, DRST > 
GO To 2 
ELSE IFCCTIMEC!>.GE.RTIMECK>>. AND. CPTIMECL).LE.ATIMECK>> THEN 
CALL POUEINCCLK,PTIME,BTIME,RF!,PCNT,60,B0T,QQ,!,U,L,4,N,NN,Z, 
* DPQ,DRST> 
GO To 2 
ELSE IFCCTIMEC!.GE.PTIMECL>>. AND. CRTIMECK>.LE.PTIMECL >> >THEN 
CALL ROUEINCCLK,RTIME,BTIME,RFI,REP,60,B0T,RR,1,J,K,M,N,NN,Y, 
DRO, DRST > 
GO TO 2 
ELSE 
GO To 3 
ENDIF 
CALL ARRAYCCLK, IP, RFI ,NRFI,DEF,PCHT,REP,BO, IPX,RFIX, NRF IX, 
2 DEFX , PCMTX, REPX, BOX, J,N> 


# 


% 





GO TO 1 
CALL DEMANOCCLK, TIME, RTIME,PTIME,BTIME, IP,RFI,NRFI,AT,DEF,PCHT, 
- REP ,BO,0,R,RR,00,RTAT,PLT,C,E,1,J0,K,L,4,4,NN,¥,2, 7R,ORO,0PQ, 
* IK, IL,JK> 
CALL ARRAYCCLK,IP,RFI,NRFI,DEF,PCHT,REP,BO, IPX,RFIX,NRFIX, 
’ DEFX, PCMTX, REPX, BOX, J,ND 
IFCCLK(J).GE.TOUT>GO TO 99 
CONT 1 NUE 
TRON | 
TREP=K*R-AT 
TBUY=AT-DEF 
RETURN 
END 
* ROUTINE TO RECORD DEMAND, CHECK FOR BACKORDER CONDITION, * 
* AND INITIATE PROCUREMENT OR REPAIR ACTIONS “ 





SUBROUTINE DEMANDCCLK, TIME, RTIME,PTIME,BTIME, IP,RFI,NRE IAT, DEF, 
*PCHT , REP ,B0,0,R,RR,00,RTAT,PLT,C,E£,1,J,K,L,4,N,NN, ¥,2, TR, ORG, DPQ, 
#1K,1L,JK) 
INTEGER IP,RFI,NRFI,AT,DEF,PCNT,REP,BO,!,K,L,M,N,Y,Z,CCNND, IK, IL, 
*NN, J,0,8, RRCNN, ECNN>, GOCNN), DROCNN), DPQCNND, TR, UK 
REAL CLKCN>, TIME CNN), RTIME CNN, PTIMECNND, BTIMECNND, PLT, RTAT 
J+ 1 
CLKCU=TIMNECI > 
REGISTER DEMAND AND DETERMINE IF NRF! CARCASS WILL BE RETURNED ** 
IFCCC1 >.£0.0)THEN 
NAF I=NRF I+ 1 
TR=TR+ 1 
ELSE 
AT=AT+ 1 
DEF=DEF + 1 
ENDIF 
IFCCCC1>.EQ.0).AND. (NRF! .GE. 1>>THEN 
IK=1K+1 


115 


OoOanam 


DROQC IK =I 
ENDIF 


IF CRE I .LT.OTHEN 
RF 1=0 
BT IMECM+B80=TIMECI> 
BO=B0+ 1 
ENDIF 
INITIATE REPAIR ACTION IF SUFFICIENT NRFI UNITS ARE AVAILABLE = 
IF (NRE I .EQ.R>THEN 
CALL REPRIRCCLK,RTIME, IP, NRFI,AT,DEF,REP,E,J,K,R,RR,Y,RTAT,N,NN, 
* UK) 
ENDIF 
IFCCCCL>.EQ. 1). AND. (DEF .GE. 1>>THEN 
IL=IL+1 
DPQCIL >=! 
ENDIF 
INITIATE REPROCUREMENT ACTION IF REORDER POINT HAS BEEN REACHED +* 
IF (DEF .GE.Q)>THEN 
CALL PROCMT(CLK,PTIME, IP,DEF,PCMT,PLT,QQ,J,L,N,NN,Z> 
ENDIF 





SUBROUTINE REPAIRCCLK,RTIME, IP,NRFI,AT,DEF,REP,E,J,K,R,RR,Y,RTAT, 
+N NN, JK) | 
INTEGER RRCNN>, IP, NRFI,AT,DEF,REP,1,J,K,N,NN,ECNND,Y,R, AQ, RO, UK 
REAL CLK(N),RTIMECNND, RTAT 
RO=0 
DO 10 I=JK,JK+(R-1) 
RO=RO+E C1 > 


RACK+Y =RO 

RT IME CK+¥ 59=CLK(C J >+RTAT 

IFCROQ.LT.ROTHEN 
DEF=DEF +AQ 
IP=1P—-AQ 
AT=AT+AQ 

ENDIF 

K=K+R 

Y=V+ 1 

RETURN 

END 


116 





ROUTINE TO INITIATE REPROCUREMENT ACTION * 





OOO 
% 


SUBROUTINE PROCHT<CCLK,PTIME, IP,OEF ,PCNT,PLT,GQ,J,L,N,NN,2Z) 
INTEGER IP,DEF ,PCMT,QQ<NN>,J,L,N,NN,Z 

REAL CLK<(N), PTIMECNN),PLT 

PCNT=PCNT+DEF 

|P=1P+DEF 

Q0¢(L+2 >=DEF 

PT IMECL42Z 2=CLK¢ J >+PLT 





ROUTINE TO RECEIVE RFI UNITS FROM REPROCUREMENT = 





OOM OO 
% 


SUBROUTINE POUEINCCLK,PTIME,8TIME,RFI,PCMT,80,80T,0,1,J,L,4,N,NN, 
*2 DPQ, DRST> 

INTEGER RFI ,PCMT,B0,Q<NN>,RO,J,LL,M,N,NN,2Z, DRSTCNND, DPQCNND, |, X 
REAL CLK(N>,PTIME<NN), BTIMECNN>, BOTCNN> 


10 CONTINUE 

CLK(J0=PTIMECL? 

PCMT=PCMT-O<L> 

RF I=RF1+Q<L> 

RQ=Q<L > 

CALL DORCT<DRST,DPO,RQ, | ,X,NND 

DETERMINE DISTRIBUTION OF RFI ASSETS eeeeerereererece 
DUE IN FROM PROCUREMENT <STOCK AND/OR UNFILLED ORDERS > ‘eeeeeiemic: 
IF(BO.GT.O>THEN 

CALL BKOROR<CLK,BTIME,BOT,RFI,B0,RO,J,4,N,NN> 

ENDIF 

L=L+1 

RETURN 

END 


iv 





ROUTING TO RECEIVE REPAIRED UNITS FROM REPAIR - 





OO © 2 © 
% 


SUBROUTINE ROUEINCCLK,ATIME,BTIME,RFI,REP,80,80T,R,1,J,K,M,N,NN,Y, 
*0RO, DRST> 

INTEGER RFI,REP,B0,R(NN>,RO,1,J,K,M,N,NN,Y, DRSTCNN >, DROCNND, X 
REAL CLK(N>,RTIMECNN>, BTIMECNN>, BOTCNND 

X=0 


11? 


iP 


OOM © 


10 


NO0N0 1 © 


Y=¥- 1 














J=J+ 1 
CLK(J=RTIMECK> 
REP=REP-R(K) 
RF I=RFI+RCK> 
RO=RCK > 
CALL DORCT<DRST ,DRO,RQ,1,X,NND 
DETERMINE DISTRIBUTION OF RFI ASSETS * eres 
DUE IN FROM REPAIR <STOCK AND/OR UNFILLED ORDERS)  eectetececcice 
IF(BO.GT.O>THEN 
CALL BKORDR<CLK,BTIME,BOT,RFI,80,R0,J,4,N,NND 
ENDIF 
K=K+ 1 
RETURN 
END 
* ROUTINE TO DETERMINE DISTRIBUTION OF RFI ASSETS DUE IN FROM * 
* REPAIR OR PROCUREMENT AND COMPUTE BACKORDER TIMES oa 
SUBROUTINE BKORDR(CLK,BTIME,B0T,RFI,60,60,J,¢,N,NND 
INTEGER |,J,4,NB0,N,NN,80,RFI,B0 
REAL CLK(N>, BTIMECNN), BOTCNND 
IF(BO.LE.BQ THEN 
RF I=RF 1-80 
NBO=B0 
BO=0 
ELSE 
NBO=BQ 
BO=80-80 
RF I=0 
ENDIF 
Wor Uye Lehi os OF SAL KURDEP (8) em 2 eomininiokwomiainininicinininksn nine 
DO 10 I=M,M+<(NBO-1) 
BOT¢ 1 =CLK(J>-BTIMECI> 
CONT | NUE 
M=M+NBO 
RETURN 
END 
* ROUTINE TO COMPUTE DEMAND DURING RESUPPLY CYCLE TIME ws 
SUBROUTINE DORCT CORST,DQ,RQ,1,X,N> 
INTEGER DRST(N>,DQCN),1,J,K/1/,L,M/1/,RQ, DRSTR¢ 1500 >, DRSTP¢ 1500), 
*X VIS 17 


1F¢X.EQ.0 THEN 
0G 10 J=K,K+CRO-1) 
DRSTRCJ>=¢C1-1>-00¢5) 
DRST¢ 11 =DRSTRC > 
WRITECG , 34 DRSTCI ID 


118 


OOOO © 


OOM © © 


10 


*CRR, ASR, RGR, PLT,RTAT,BOT,POPT, TRON, TREP, TBUY,NYRS,J,4,N,NN, 


Li=11+4 
CONT 1 NUE 
K=K+RO 
ELSE 
DO 20 L=M,M+¢(RO-1> 
DRSTPCL =< 1-1>-DQ<L> 
DRST C11 =DRSTPCL> 
WRITE<6, 34 ORSTCI1> 
bi=11+1 
CONT 1 NUE 
M=tt+RO 
ENDIF 
FORMAT <2X, 14> 





* ROUTINE TO STORE INDIVIDUAL EVENTS : * 






a ee pen eee ee ee ee ee ee ee a ee ee ee ee 





ea we eee eee Se Se ee ee ee ee es a ee an on a ch oni fe ee nt On ee tS oir 


SUBROUTINE ARRAYSCLK, IP, REI,NRFI,OEF ,PCHT,REP,BO, IPX, RF IX, NRF IX, 


*DEFX, PCMTX, REPX, BOX, | ,N> 


INTEGER IPX<N),RFIX¢(N), NAF IX<N>, DEFX<N), PCHTX<N>, REPX<ND, 


*B0X<(N>, IP,RFI,NRFI,AT,DEF,PCHT,REP,BO,1,N 


REAL CLK<CN> 
IPX¢1=IP 

RE IX¢ | =RF | 
NRF 1 X¢ 1 =NRF | 
DEFX¢ | =DEF 
PCMTX¢ | =PCHT 
REPX¢ | =-REP 
BOX< | =B0 
RETURN 

END 


-_— ee ee rer ee ee ee ee ee Trtllhlc Ol Ohl OCUlc OlUlc OhClc Ohl OhUhlh Ohl POhlhlU PO Ol HPhOlhlUl Plc OlhlhlUr rl OOhlhlUhrOChlClcrlhUlUch OO OChlUcr OCU HhlUlh Hhhlh HPhlUlc OOlhlUh rOhlhlUhr ThlhlUh ChlUhrOChlUlc TCU rOCUClUCUCOCUhClUchOlhUhClCUc OOChUClCUc OCUlUc OOhClUlUrPChChlUh OClUcU OPThlClU OChCUc HOC Ol OrlUCUlUh Ch HOU Ohhh HOmUhUhUh}HLUhUhHD 


* ROUTINE TO. COMPUTE PERFORMANCE STATISTICS AND PRINTOUT RESULTS * 





SUBROUTINE PRINTCCLK, IP,RF1,NREI,DEF,PCMT,REP,80,0,R,SN,ROP,D,G, 
T,TR> 
INTEGER IP(N>,RFI(N),NRFICN),DEFCN), PCMTCN), REP(N),BOCN),Q, 


+f, SH, ROP, 1,J,NYRS, TRON, TREP, TBUY M,N, NN, AT, TR, POPT, x 


REAL CLK(N>,BOTCNN>, CRR,RSR,RGR,PLT,RTAT,0,G,MSRT, ADDBO, ARON, SMA, 


*ABO , TROT , AREP , ABUY 


IF <POPT .EQ.2.9G0 TO 55 


Cee COMPUTE TOTAL BACKORDER TIME FOR SIMULATION PERIOD etree 


TBOT=0 

IF CH.EQ.0>THEN 
TBOT=0.0 
MSRT=0 .0 
ADDBDO=0 .0 
StHA= 100.0 


119 


10 


— 
An Ub 


ABO=0 
ELSE 
DO 30 1=1,M 
TBOT=TBOT+B80T< I> 
CONT INUE 
MSRT=TBOT /TRON 
ADDBO=TBOT M1 
SMA= 100. *< 1.0-FLOAT<M>/TRON> 
ABO=FLOAT<M>/NYRS 
ENDIF 
ARON=FLOAT < TRON > /NYRS 
AREP=FLOAT<TREP > /NYRS 
ABUV=FLOAT <TBUY > /NYRS 
WRITE(6, 120,G,SW,ROP,0,R 
WRITE6, 2>PLT,RTAT,CRR,RSA,RGR 
IF<POPT.EQ.09GO0 TO 50 
WRITE<6, 11> 
WRITE<6,9> 
WAITE<6,3> 
WRITE6,4> 
WRITEC6,9> 
DO 10 1=1,J 
IF<POPT .EQ.2>THEN 
CLK¢ 1 =CLK¢ 1/364. 
WRITE(6, S2CLKCI>, IPCI), RFICI> 
ELSE 
WRITEC6, 12 2CLKC1>, IPC 1>, RE IC 1, NREIC I>, DEF I>, REPCID, 
~ PCMT<1>,BOCI> 
ENDIF 
CONT I NUE 
IFCPOPT.EQ.2>THEN 
GO TO $8 
ENDIF 
WRITE<6,9> 
WAITE<6, 11> 
WRITE<6, 6 ARON, ABO 
WRITE<6, 7 AREP , ABUY 
WRITE<6, 8 SMA, MSRT, ADDBO 
WRITEC6, 11> 
WRITE<6,9> 
FORMAT (2X, 'D:',F6.2,° QTRS',3X,‘G:',F6.2,° QTRS’,4X, ‘SH:',14,4X, 
**ROP:',14,4X, 'Q:°,14,4X, ‘R:', 14) 
FORMAT (2X, ‘PCLT: ‘,F6.2,° QTRS',3X, ‘ATAT:‘,F6.2,° OTRS*,3X,‘CRR:', 
*F6.2,2X, ‘RSR:',F6.2,2X%, ‘RGR: ',F6.2> 
FORMAT <14X, ‘INU POS‘ 8X, ‘O/H NRFI‘',8X, ‘IN REPAIR , 7X, 
** BACKORDERS* > 
FORMAT (5X, ‘DAY’, 14X, ‘O/H AFI’ ,9X, ‘DEFICIT’ ,8X, ‘ON ORDER‘ > 
FORMAT (FS .2, 14, 14) 
FORMAT <2X,F8.2,4X, 14, 4X, 14, 4X, 14, 4X, 14, 4X, 14, 4X, 14, 4X, 14 
FORMAT <2X, "AUG. NO. OF DEMANDS AYR: *,F?.2,9X, 
**AUG. NO. OF BACKORDERS/VR: ‘ ,F?.2> 
FORMAT (2X, ‘AUG. NO. OF REPARIRS/VR: *,F?.2,9X, 


120 


** RUG. NO. OF BUYS/VEAR:',4X,F?.2> 
§ FORMATC2X, ‘SMA:',F?.2,° ®°,9X, ‘MSRT:°,F8.3,° DAYS", 12X, 
** ADD /B0:',F8.3,° DAVS'> 
9 FORMATC' ‘> 
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11. FORMAT 1X, ° 
* hbo ese ae 
88 RETURN 
END 


121 


LIST OF REFERENCES 


Naval Supply Systems Command, "ICP Resolicitation, System Policy 
and Concepts", Red Task Group Report, Phase I, February 1978. 


Richards, F.R., and McMasters, A.W., Wholesale Provisioning 
Models: Model Development , Naval Postgraduate School Report No. 
NPGS5-83-026, Monterey, CA, September 1983. 


McMasters, A.W., AMholesale Provisioning Models: Model 
Evaluation, Naval Postgraduate School Report No. NPS 55-86-011, 
Monterey, CA, May 1986. 


Naval Material Command, "Operational Availability of Weapon 
Systems and Equipment; Definitions and Policy”, NAVMAT 
Instruction 3000.2, 21 January 1981. 


Ziegler, F.,ASO Code SDB4-A, Telephone interview, 22 May 1987. 
Sicari, J., SPCC Code 014, Telephone interview, 8 June 1987. 


Naval Supply Systems Command, Javentory Management: A Basic 
Guide to Requirements Determination in the Navy , NAVSUP 
Publication 553, 1984. 


Apple, C.L., 4 Systems Approach to TJnaventory Management of 
Repatrables in the Navy, Masters Thesis, Naval Postgraduate 
School, Monterey, CA, March 1985. 


Gormly, R.L., Analysis of an Aggregate Demand epairables 
Model, Masters Thesis, Naval Postgraduate School, Monterey, CA, 
December 1985. 


Pearsall, G.H., Analysis of a Proposed Wholesale Repairables 
Replenishment Model, Masters Thesis, Naval Postgraduate School, 
Monterey, CA, December 1986. 


Department of Defense, DOD Supply Management Reference Book, DA 
PAM 700-1, NAVSUPINST 4400.78C, MCO 4400.163, AF PAM 67-2, DLAM 
9105.5, 1 January 1985. 


Office of the Chief of Naval Operations, "Retail Supply Support 


of Naval Activities and Operating Forces", OPNAV Instruction 
4441.12B, 25 May 1983. 


122 


roe 


14. 


a 


16. 


ae 


18. 


19. 


Seebeck, R.N., The Effects of the Stock Coardination Program 
Upon Inventory Management at the Naval Electronic Systems 
Command, Master's Thesis, Naval Postgraduate School, Monterey, 
CA, June 1978. 


McComb, 5.R., /uading Depot Level Hepairables in the Navy Stock 
fund: The Effect on H.C.4.S. Jwakuni, Japan, Master's Thesis, 
Naval Postgraduate School, Monterey, CA, June 1982. 

Bellevue, M., SPCC Code 0503X, Telephone interview, 21 May 1987. 


Blanchard, Benjamin $., Logaistacs Lngineering and Management , 
3rd ed., Englewood Cliffs, NJ: Prentice-Hall, 1896 


Department of Defense, "Procurement Cycles and Safety Levels of 
Supply for Secondary Items", DODINST 4440.23, 17 July 1970. 


Hadley, G. and Whitin, 1.M., Analysis of Inventory Systems, 
Englewood Cliffs, NJ: Prentice-Hall, 1963. 


Fleet Material Support Office, “Application D, Operation 56, 


CARES (Computation and Research Evaluation System) III", 3 
August 1984. 


123 


10. 


INITIAL DISTRIBUTION LIST 


Defense Technical Information Center 
Cameron Station 


Alexandria, VA 22304-6145 


Defense Logistics Studies Information Exchange 
U.S. Army Logistics Management Center 
Fort Lee, VA 23801 


Library Code 0142 
Naval Postgraduate School 
Monterey, CA 93943-5002 


Commander 

Naval Supply Systems Command 
Attn: Code 042 

Washington, DC 20376 


Commanding Officer 

Fleet Material Support Office 
Attn: Code 93 

Mechanicsburg, PA 17055 


Commanding Officer 

Navy Ships Parts Control Center 
Attn: Code 0412 

Mechanicsburg, PA 17055 


Commanding Officer 

Navy Aviation Supply Office 
Attn: Code SDB4-A 
Philadelphia, PA 19111 


Assoc. Professor Alan W. McMasters, Code 54MNg 
Naval Postgraduate School 
Monterey, CA 93943 


Asst. Professor Thomas P. Moore, Code 54Mh 
Naval Postgraduate School 
Monterey, CA 93943 


LCDR Roger E. Hammer, Jr., SC, USN, Code 100 


Naval Supply Center 
Charleston, SC 29406 


124 


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