(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Children's Library | Biodiversity Heritage Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "Basic techniques of inventory management with possible applications to improve the existing inventory control of the Hellenic Navy."

DUDLEY KNOX LIBRARY 

? : DUATE SCHOOL 

MO [ - ;ALIFORMIA C >43 



NAVAL POSTGRADUATE SCHOOL 

Monterey, California 




THESIS 



BASIC TECHNIQUES OF INVENTORY MANAGEMENT 
WITH POSSIBLE APPLICATIONS TO IMPROVE THE 
EXISTING INVENTORY CONTROL OF 
THE HELLENIC NAVY 

by 

Demos D. Sarris 

December 1985 



Thesis Advisor; 
Co-Advisor : 



John W. Creighton 
Roger D. Evered 



Approved for public release; distribution unlimited 



T226829 



CURITY CLASSIFICATION OF THIS PAGE 



REPORT DOCUMENTATION PAGE 



. REPORT SECURITY CLASSIFICATION 

UNCLASSIFIED 



lb. RESTRICTIVE MARKINGS 



SECURITY CLASSIFICATION AUTHORITY 



DECLASSIFICATION / DOWNGRADING SCHEDULE 



3 DISTRIBUTION /AVAILABILITY OF REPORT 

Approved for public release; 
distribution unlimited. 



PERFORMING ORGANIZATION REPORT NUMBER(S) 



5. MONITORING ORGANIZATION REPORT NUMSER(S) 



. NAME OF PERFORMING ORGANIZATION 

faval Postgraduate School 



6b OFFICE SYMBOL 
(If. applicable) 

Code 54 



7a. NAME OF MONITORING ORGANIZATION 

Naval Postgraduate School 



. ADDRESS (City, State, and ZIP Code) 

[onterey, California 93943-5100 



7b. ADDRESS (City, State, and ZIP Code) 

Monterey, California 93943-5100 



NAME OF FUNDING /SPONSORING 
ORGANIZATION 



8b. OFFICE SYMBOL 
(If applicable) 



9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER 



ADDRESS (City, State, and ZIP Code) 



10 SOURCE OF FUNDING NUMBERS 



PROGRAM 
ELEMENT NO 



PROJECT 
NO 



TASK 
NO 



WORK UNIT 
ACCESSION NO 



A T S T ^ /n WcS'fC?U ( B^ 5, ^f' 0, i , NVENTORY MANAGEMENT WITH POSSIBLE APPLICATIONS TO 
MPROVE THE EXISTING INVENTORY CONTROL OF THE HELLENIC NAVY 

PERSONAL AUTHOR(S) 

iarris , Demos" D. 



i TYPE OF REPORT 

aster's Thesis 



13b TIME COVERED 
FROM TO 



14 DATE OF REPORT (Year, Month, Day) 

1985 December 



15 PAGE COUNT 
113 



SUPPLEMENTARY NOTATION 



COSATI CODES 



FIELD 



GROUP 



SUB-GROUP 



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

Inventory 



1 ABSTRACT (Continue on reverse if necessary and identify by block number) 

The Hellenic Navy faces many difficulties concerning the finding and 
supplying of materials due to the variety of causes. The main emphasis of 
this thesis is to introduce into the Hellenic Navy some basic inventory 
techniques used by the United States Navy. These techniques could be 
ipplied and implemented in the Hellenic Navy after a degree of modification.; 
Application of these techniques would improve and update the inventory 
:ontrol of the secondary (or auxiliary) items . Emphasis has also been 
Placed on minimizing the average annual inventory costs. 



I DISTRIBUTION /AVAILABILITY OF ABSTRACT 
■ 2 UNCLASSIFIED/UNLIMITED □ SAME AS RPT □ OTIC USERS 



21 ABSTRACT SECURITY CLASSIFICATION 

UNCLASSIFIED 



J NAME OF RESPONSIBLE INDIVIDUAL 

'ohn W. Creighton 



22b TELEPHONE (Include Area Code) 

646-2048 



22c. OFFICE SYMBOL 

54Cf 



IFORM 1473, 84 MAR 



83 APR edition may be used until exhausted 
All other editions are obsolete 



SECURITY CLASSIFICATION OF THIS PAGE 



Approved for public release; distribution unlimited. 



Basic Techniques of Inventory Management with Possible 
Applications to Improve the Existing Inventory Control 

of the Hellenic Navy 

by 

Demos D. Sarris 
Lieutenant Commander, Hellenic Navy 
B.A., Graduate School of Industrial Studies, 1966 
B.S., Hellenic Naval Academy, 1970 



Submitted in partial fulfillment of the 
requirements for the degree of 

MASTER OF SCIENCE IN MANAGEMENT 

from the 

NAVAL POSTGRADUATE SCHOOL 
December 1985 



ABSTRACT 

The Hellenic Navy faces many difficulties concerning the 
finding and supplying of materials due to the variety of 
causes. The main emphasis of this thesis is to introduce 
into the Hellenic Navy some basic inventory techniques used 
by the United States Navy. These techniques could be 
applied and implemented in the Hellenic Navy after a degree 
of modification. Application of these techniques would 
improve and update the inventory control of the secondary 
(or auxiliary) items. Emphasis has also been placed on 
minimizing the average annual inventory costs. 



TABLE OF CONTENTS 

I. INTRODUCTION — 9 

A. DIFFICULTIES CONCERNING THE FINDING 

AND SUPPLY OF THE MATERIALS 11 

B. DIFFERENTIATION OF MATERIALS ■ 12 

C. PROCEDURES TRANSACTIONS 13 

D. SYSTEM OF ORDERING ITEMS; WHEN SHOULD 

WE ORDER? HOW MANY SHOULD BE ORDER? 14 

E. OBJECTIVES ■ 16 

F. INVENTORY TECHNIQUES 17 

G. DEVELOPMENT OF INVENTORY MODELS 19 

H. INVENTORY CONTROL 23 

I. SCOPE OF THE THESIS 24 

II. DEVELOPMENT OF ABC ANALYSIS 26 

A. CLASSIFICATION OF THE MATERIALS 32 

B. CRITICAL VALUE ANALYSIS (CVA) 37 

C. SUMMARY 39 

III. PROVISIONING ■ 40 

A. INTRODUCTION 40 

B. DEFINITION ■ 41 

C. PROVISIONING METHODS 42 

D. PROGRAM DATA 43 

E. TIME WEIGHTED AVERAGE MONTH'S PROGRAM 44 

F. DEMAND PROPERTIES 47 



G. DEMAND SIZE 48 

H. BASIC INVENTORY THEORY 49 

I. NON-DEMAND BASED INVENTORIES 49 

J. DEMAND BASED ITEMS 51 

K. FUNCTIONS OF INVENTORY 51 

1. The Decoupling Function 51 

2. Pipeline Inventories 51 

3. Buffer or Safety Stock Inventories 52 

4. Review Cycle Inventories 52 

L. THE COST DIFFERENCE FORMULA (COSDIF) 52 

M. DETERMINING THE PURCHASE QUANTITY AND 

BUDGET 56 

1. Example 57 

IV. INVENTORY CONTROL MODELS 61 

A. GENERAL INFORMATION 61 

B. PERPETUAL OR CONTINUOUS REVIEW MODELS 61 

C. REORDER POINT 73 

D. PERIODIC REVIEW MODELS 74 

E. MATERIAL REQUIREMENTS PLANNING (MRP) 76 

F. AN EOQ-MRP COMPARISON 84 

V. FORECASTING 87 

A. THE IMPORTANCE OF THE FORECAST 87 

B. FORECASTING PRINCIPLES 88 

C. MAKING A FORECAST 88 

D. WHAT TO EXPECT FROM A GOOD FORECASTING 

SYSTEM 88 



E. AGGREGATE LONGER' TERM FORECASTS • 90 

F. TIME SERIES ANALYSIS 92 

G. INDIVIDUAL ITEM SHORT TERM FORECASTS*- 93 

1. Moving Average ■ ■ •-- 93 

2. Exponential Smoothing or Exponentially 
Weighted Average ■ 96 

H. FORECASTING ERRORS 98 

I. FORECASTING LEAD TIME 99 

J. PROBABILITY DISTRIBUTIONS 101 

K. NORMAL DISTRIBUTION ■ 101 

L. POISSON DISTRIBUTION 104 

VI. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 106 

A. SUMMARY 106 

B. CONCLUSIONS 108 

C. RECOMMENDATIONS 109 

LIST OF REFERENCES 111 

INITIAL DISTRIBUTION LIST 112 



LIST OF TABLES 

1. ABC ANALYSIS 34 

2. ABC ANALYSIS 35 

3. TOTAL COST FOR VARIOUS EOQ AMOUNTS 71 

4. MRP PLAN FOR 100 UNITS OF PRODUCT A IN PERIOD 8 85 

5. COMPARISON OF FIXED ORDER SIZE AND MRP SYSTEMS 86 

6. HISTORICAL DATA (MOVING AVERAGE) 95 



LIST OF FIGURES 

1. Pareto's Law of Maldistribution 28 

2. Characteristics of ABC Groups ■ ■ ■ 32 

3. ABC Analysis ■ 36 

4. A Provisioning Decision Matrix 54 

5. Carrying Cost 65 

6. Order or Setup Cost ■ 65 

7 . Total Annual Cost ■ ■ 66 

8. Sawtooth Model 68 

9. Total Annual Cost of EOQ Example 72 

10. Inventory Model Under Conditions of Uncertainty 75 

11. A Periodic Inventory System 77 

12. Typical Product Structure 81 

13. Typical Product Structure 83 

14. Classification Scheme of Forecasting Methods 91 



I. INTRODUCTION 

Greece is a seafaring nation. Over 80 percent of Greece 
borders the sea and thousands of islands surround 
continental Greece. It has a long naval tradition and 
frequently the "wooden walls," as the ancients called the 
vessels, secured the independence and the wealth of the 
country. Even today, the Hellenic Navy has the 
responsibility of guarding the country's borders. 

The present situation in Greece, of course, is different 
from past years. In older times, naval ships and equipment 
were internally produced and se 1 f -sus t a ined . The wooden 
walls were manufactured from local material by artistic 
carpenters and the crews were excellently trained in the 
nautical arts. Today the nautical tradition continues but 
the material is very much different. In the sector of 
material, Greece, as well as most other nations, is no 
longer self-supporting. Greece has the ability to build 
ships but does not have the means to arm them, principally 
because of the rapid advancement of weapons systems and the 
evolution of electronic warfare. 

Competition between different nations manufacturing 
weapons systems has resulted in a great variety. Thus, 
Greece, in order to cover its needs must, from time to time, 
be supplied with material from the United States of America, 



as well as from various European nations. Supply of 
material and spare parts depends a great deal on these 
nations. In the Hellenic Navy, many problems arise that do 
not exist in the United States Navy. The time needed for 
search and transport of each individual spare part varies 
from part to part, from order to order, and from country to 
country. The cost of purchase of each material is increased 
greatly by the cost of packaging, loading, transporting, 
insuring, etc. The problem becomes ever more accute if the 
wrong item or an unsuitable part is received. 

Sources of material required for the support of the 
Naval Forces are listed as follows: 

1. Indigenous or local sources. 

2. European sources. 

3 . U.S.A. sources . 

Handling and supplying the materials requires a great 
deal of attention and carries high responsibility. The 
limited money available demands that a priority checklist be 
made of the needs and consequent stock level requirements. 
A timely forecast will result in the lowering of the cost of 
supply. Also, the techniques of inventory management, which 
are discussed in the next chapters, will assist in the 
control of surpluses (reserve stock), thereby keeping the 
total yearly cost at a low level. 



10 



The major problem in meeting these objectives is that 
they are basically in conflict. Better customer service can 
be provided if inventories are at high levels, but a high 
level of stock results in high inventory cost. Inventories 
can be kept low if customers are forced to wait for needed 
supplies . 

Most of the problems can be lessened by sound economic 
judgement, and cost-optimization principles can be used to 
establish most inventory policies. There is, however, still 
resistance to the increased use of mathematical and 
statistical techniques in an area once thought to be 
governed by experience and common sense. 

A. DIFFICULTIES CONCERNING THE FINDING AND SUPPLY OF 
MATERIALS 

As mentioned before, Greece faces many difficulties 

concerning the finding and supplying of materials due to the 

variety of their origins. These may be classified in the 

following categories: 

1. Political: Prohibition of sales of materials to 
countries that do not belong to the same allied 
coalition . 

2. Legal: A nation may have the material, but due to an 
agreement that it may have signed with other 
countries, the nation having a potential supply cannot 
offer the material to a third nation. 

3. Anachronistic: Part of the material that is used by 
the Hellenic Navy is no longer manufactured, 
anachronistic, and at times almost obsolete. It 
happens often that the nation or the factory that 



11 



prepared the material is discontinuing the manufacture 
of that material and thus it becomes costly to ._ 
re-supply . 

4. Economic: There is a Greek saying, "Lack of Funds, 
Stoppage of Runs." Namely, lack of mon_e_y, may cause 
the discontinuation of supply. 



B. DIFFERENTIATION OF MATERIALS 

The materials are differentiated into two major 
categories : 

1. Principal Items 

2. Secondary Items 

Principal items are items of great value, such as 
vessels, airplanes, helicopters, weapons systems, radar, 
electrical apparatus, etc. These items are programmed, 
ordered and monitored by the Hellenic Navy Staff. 
Frequently, the principal items of lesser importance and 
value are monitored by the Hellenic Navy Center of Supply 
under authorization of the Hellenic Navy Staff. 
Secondary items are items that are not categoried as 
principal items. 

The secondary items are broken down into two categories: 
1 . General i terns 
2. Reserved items 

The one label we can use for the remunerated items is 
that these items have a specific purpose. What the Hellenic 
Navy calls Main Items are those items which the United 



12 



States Navy terms as Principal Items, while both Navies use 
the term Secondary Items. 

The main emphasis of this thesis is to develop some 
basic inventory techniques that could improve the inventory 
control of the secondary items in the Hellenic Navy. The 
secondary items are stored in various areas in different 
parts of Greece. It is from these various places that 
vessels and services order and receive the items necessary 
for their needs. 

C. PROCEDURES TRANSACTIONS 

The Naval Supply Center is the appropriate source for 
the re-supply of the stock of items for all Naval Stores 
Depots. The re-supply of the stock depends on data obtained 
from the historical file and future requirements projection 
files. Based upon this information, the items may be 
classified as demand-based or non-deraand-based items. This 
classification will be discussed later. 

Naval Stores Depot procedure for providing timely 
information to the Naval Supply Center concerning stock 
status is described in the following paragraphs. 

The vessels and services submit their paper work 
concerning the items they need to the Naval Stores Depot. 
The Depot, if it has the items to satisfy the customer 
orders, sends them to the customer and at the same time 



13 



sends a copy of the customer's request, including the 
quantity of items received, to the Naval Supply Center for 
their records. If the Depot does not have the item, it 
informs the customer and sends a request to the Navy Supply 
Center requesting that item. The Navy Supply Center, 
according to the degree of priority of the request, will 
proceed to an immediate purchase or spot procurement, or 
will inform the customer that a waiting period is needed 
until the item arrives. 

When the Navy Supply Depot receives the item, they draw 
up a document of arrival, or receipt of delivery, of the 
items. A copy of the receipt of delivery is submitted to 
the Navy Store Center to enable the current level of stock 
to be specified. In the future, this procedure will take 
place at a center of computer terminals at the Navy Supply 
Depot . 

D. SYSTEM OF ORDERING ITEMS: WHEN SHOULD WE ORDER? 
HOW MANY SHOULD WE ORDER? 

The ordering of items is usually on an annual basis, but 
when a need arises, it may be more frequent, usually 
quarterly . 

The quantities that will be ordered are based on 

1 . an average use 

2. annual analysis of the five past years, called an 
Average Annual Consumption (M.E.A. in Greek). 



14 



The information on consumption derives from the existing 
electronic calculator or computer-based records. The 
quantity that will be ordered and is forecast to cover the 
needs for the coming year is determined as follows: 

The figure representing the total consumption of the 
fifth and most recent year is multiplied by five. The 
figure representing the sum of the fourth year is multiplied 
by four, the third year's by three, the second year's by two 
and the figure of the first year, by one. The sum of the 
five year items after the above mentioned multiplications is 
divided by the sum of the multipliers of the five years, and 
thus the final figure represents the quantity of items that 
will be ordered for the next year. 

For example, let us suppose that we are at the end of 
1985 and we wish to calculate a consignment for 1986; the 
consumption of the last five years respectively was: 

- for 1985, 10 items 
for 1984, 14 items 

- for 1983, 8 items 

- for 1982, 16 items 

- for 1981, 8 items 

Consequently, the consignment for 1986 will be 12 items: 

10 "5+14 '4+8 '3+16 -2+8'l 170 , . , 
5+4+3+2+1 T5 ~ 12 ltenfs 



15 



Of course, the consignment is placed when the average of 
the stock sits at a p r e-de t ermined level of re-ordering, 
based on a determination of a lead time and some degree of 
safety, or emergency, stock. 

E. OBJECTIVES 

The Naval Supply System of the U.S. Navy is similar to 
the operations of large corporations of the private sector 
in providing goods and services to a variety of customers. 
One of the primary objectives of both the private sector and 
the Naval Supply System is the attainment and retention of 
satisfied customers. Satisfied customers in the Navy system 
equates to enhanced combat readiness of our national defense 
forces. In order to achieve this objective, the supply 
system tries to maintain a proper mix of items in the 
inventory of the Naval Stores Depot. The accomplishment of 
these objectives is charged to the Naval Supply Center in 
our Navy. 

The Naval Supply Center is responsible for the secondary 
items as well as for the requirements determination and 
stocking at all Naval Stores Depots to meet the requisitions 
of the customers. 

In the U.S. Navy, such items managed by the Naval Supply 
Center are categoried as consumables or repairable s. As the 
term implies, consumable items are consumed in use or cannot 



16 



be repaired economically when they fail to function. On the 
other hand, repairables are permanent in nature and can be 
repaired economically by either the base repair facility or 
the customer. 

F. INVENTORY TECHNIQUES 

Many people believe that inventory techniques consist 
only of keeping records of commodities and stock levels. 
They think an inventory problem is the determination of 
which details to record, who should make the entries into 
the records, where and when to make the entries, etc. [Ref. 
l:pp. 1-2] 

Others take an overall point of view when looking at 
inventory techniques. They view inventory techniques, not 
as dealing with specific commodities, but rather with the 
totality of the commodities and investments in all the 
stock's inventory. For them, the problems are inventory 
turnover, financing investments tied up in stock, etc. 
Their concerns lie with inventories which are too large and 
the problem of reduction. [Ref. l:pp. 1-2] 

Still others have another point of view, concerning what 
items to stock, when to stock them, how much to stock, etc. 
Other concerns of these individuals are labor stability, 
utilization of equipment and facilities, and customer 
relations. [Ref. l:pp. 1-2] 



17 



Because there is such a wide variety of viewpoints 
regarding this subject, it is necessary to provide 
definitions of inventory terms. [Ref. l:pp. 1-2] 

An inventory technique in which the following costs are 
significant and where two or more are subject to control 
will serve as the definition of inventory techniques in this 
thesis : 

1. The cost of carrying inventories, or holding cost. 
This cost consists of the investment in inventories, 
cost of storage, handling items in storage, 
obsolescence, theft, and other related costs. 
Carrying cost is usually expressed as a percentage of 
the on-hand-inventory dollar value. 

2. The cost of incurring shortages, stockout cost, or 
backorder cost includes costs due to lost sales, loss 
of good will, overtime payments, special administra- 
tive efforts, etc. The stockout cost is the actual 
cost, conceptually, of not having an item in stock in 
the Navy, including the non-availability of a vessel 
for exercises due to lack of materials. It is 
impossible to calculate the damage such an occurrence 
would have on the Navy. In a military operation, all 
demands must be satisfied eventually. [Ref. l:pp. 1- 
2] 

3. The cost of replenishing inventories, or ordering 
cost. This cost is primarily administrative, 
consisting of salaries for personnel in inventory 
control and contracting, costs for supplies and data 
processing in order to determine and process 
purchases, and the storage costs of the materials. 
[Ref. 2:pp. 1-9] 

4. The procurement cost, or cost of buying the 
inventories. While the above costs are considered 
variable, depending on the circumstances, this cost is 
fixed. The sum of all the costs is called the total 
cost. Inventory techniques are intended to keep total 
annual inventory costs as low as possible. [Ref. 2: 
PP. 1-9] 



18 



Before implementing an inventory technique of any level 
of sophistication or complexity, the knowledge base of all 
who will be involved with the technique must be developed. 
Obtaining cooperative responses from the various levels of 
the hierarchy when introducing a new technique may be quite 
difficult and a great potential exists for alienating those 
who perhaps are not motivated towards the technique. Thus, 
the benefits of the new system may be offset by a lack of 
r ece p t i venes s , or hostility, towards the technique on the 
part of those who will be implementing the system. [Ref. 2: 
PP. 1-9] 

G. DEVELOPMENT OF INVENTORY MODELS 

There has been a rapid growth of interest within the 
last four decades in what is referred to as scientific 
inventory control, generally understood to consist of using 
mathematical models to determine the rules of operation for 
inventory systems. Such is the popularity of, and interest 
in, this subject that some knowledge of inventory models is 
expected from every serious student in management science or 
industrial engineering. 

Originally, practical applications were the immediate 
goals of inventory control models and this is still true to 
a large extent. However, with greater development and 
exploration in this area, the theoretical problems of 



19 



mathematics involved in inventory models are increasingly 
becoming the primary interest for many individuals. Such 
people are contributing greatly to the future of inventory 
management by providing a greater number of more versatile 
applications for inventory-related models. Today, work on 
inventory models is being carried on at many different 
levels, from a concentration solely on practical problems, 
to a focus on the purely mathematical properties of the 
models and projecting for future needs. [Ref. 3: preface, 
v] 

While inventory problems have existed throughout 
history, attempts to apply analytical techniques in the 
study of these problems dates only to the turn of the 
century. The simultaneous growth of the various branches of 
engineering, especially industrial engineering, and the 
manufacturing industries seems to have provided the initial 
impetus for the application of mathematical models to 
inventory analysis. The first, real, recognized need for 
inventory analysis occurred in industries which had a 
combination of problems with production scheduling and 
inventory, e.g., in situations where items were produced in 
lots with a fairly high cost of set up and where the items 
were then stored at a factory warehouse. [Ref. 3:p. 2] 

In 1915, Ford Harris of Westinghouse Corporation 
developed the earliest derivation of what is usually called 



20 



the simple lot size formula. Since then, this formula has 
been developed by many individuals, apparently 
independently. Another often-used name for this formula is 
the Wilson Formula because H. Wilson also derived it as an 
integral part of an inventory control plan which he sold to 
many organizations. F.E. Raymond wrote the first full- 
length book about inventory problems while he was at M.I.T. 
The book contains no theory or derivations, but rather, 
attempts to explain practical uses for various extensions of 
the simple lot size model. [Ref. 3:p. 3] 

It was only after World War II, when the operations 
research and management sciences fields emerged, that 
attention was focused on the variable nature of inventory 
problems. Problems had been treated as if they were 
deterministic up until that time, with the exception of a 
few isolated cases, as in the work of Wilson, where some 
probabilistic considerations were incorporated. [Ref. 3:p. 
3] 

Analytical techniques for solving inventory problems 
were first required in industry where engineers were looking 
for the solution for practical problems. Economists, 
interestingly enough, were not the first to take an active 
interest in inventory problems, in spite of the important 
role played by inventories in the study of dynamic economic 
models. It was because of the very real "need to know" on 



21 



the part of the engineers that interest in inventory 
problems evolved. However, now, both schools are actively 
participating in contributing to the field of inventory 
management. [Ref. 3:p. 3] 

The development and application of inventory models 
became, with time, quite widespread. "A significant role in 
the applications of inventory models is played by computers 
in tasks ranging from the military's very innovative and 
progressive uses to those of inventory management's early 
pioneers, the manufacturing and retail industries. [Ref. 3: 
p. 3] 

The United States Navy, having as a basic starting 
point, the Harris Wilson formula, has developed formulas 
that correspond more efficiently to its needs and various 
categories of materials. The United States Navy spends 
large amounts of money in. operation research. The policy 
that has been developed is a product of long and detailed 
examination, analysis, and a trial and error process for 
every condition and problem. This work is executed by 
expert task groups, more specifically by the joint efforts 
of a group of qualified experts who establish and develop 
uniform criteria for a more efficient management policy. 

Each of the military services provides data to this 
working group. The working group reviews the supply 
management practices and makes recommendations for 



22 



management improvements which are considered compatible with 
current technology. The working group also produces 
directives and instructions, which are reviewed by the 
services and are formally signed by the Office of the 
Secretary of Defense (O.S.D.). Because the inventory policy 
is not static, but dynamic, and differs not only from one 
geographic location to another, from one type of a vessel to 
another, and, more importantly, from peacetime periods to 
wartime periods, it is necessary that the different models 
and techniques that are applied in the inventory policy 
express a specific policy that is applied accordingly. The 
milestone for such an application is found in the existing 
historical facts. 

H. INVENTORY CONTROL 

Inventory control is the scientific art of ensuring that 
sufficient inventory or stock is held by an organization in 
order for it to economically meet both its internal and 
external demand commitments without holding any more stock 
then is absolutely necessary. Both too large and too small 
holdings of inventory are disadvantageous. Therefore, the 
primary goal of Inventory Control is to obtain the optimum 
balance or compromise between the two extremes. [Ref. 4:p. 
97] 



23 



There are important applications for inventory control 
in virtually all facets of business, including non-profit 
organizations. The basic tenets of controlling inventory 
remain the same for all applications. The changes occur in 
the magnitude of responsibilities and the range of 
variables, or, in other words, the range of the inherent 
complexities. The technique of maintaining stock at optimum 
levels is also a function of Inventory Control, whether the 
items be raw materials, work-in-progress, or finished goods. 

Much as in top management in multinational corporations, 
top commands in most military services are becoming 
cognizant of the existing inventory situations within the 
organization, and their links to the overall efficiency of 
the operation of the command or service. Thus, the services 
have an increasing need for personnel with a knowledge of 
mathematical inventory theory for the analyzing and 
controlling of stocks. 

I. SCOPE OF THE THESIS 

This thesis will explore and describe some pertinent 
techniques of inventory management which were taught during 
the course of studies at the Naval Postgraduate School. 
These techniques could be applied and implemented in the 
Hellenic Navy with certain modifications and adjustments. 
Application of these techniques would improve and update the 



24 



inventory control systems. For this purpose, both the 
discussion and the approach have been kept as simple as the 
elements of inventory theory will allow. Effort has been 
made to keep away from complex day-to-day inventory 
management problems and address only the foundations of 
Inventory Management as applicable to the Hellenic Navy. 



25 



II. DEVELOPMENT OF ABC ANALYSIS 

There is a plethora of materials* that move in the Navy, 
according to inventory management techniques, for the 
support of various units in the Navy. Because of that, a 
detailed and updated follow-up of the movements of every 
piece of material is not only difficult, but also expensive. 

The daily follow-up of all the transactions of materials 
and the maintenance of the stock at the greatest level of 
efficiency requires a great deal of personnel, sophisticated 
inventory models and, consequently, a great expense. 

Therefore, for effective management that will yield 
favorable and cost-effective results for efficient control, 
the inventory should be classified into categories in 
accordance with the priority of the materials. The 
techniques used must isolate items which require precise and 
extremely detailed control from items which do not need to 
be controlled as strictly. 

In relation to this problem, Pareto's Principle of 
Maldistribution is important. This principle is as follows: 



*When the writer uses the term "materials," it will 
encompass items such as components, instruments, and other 
equipment . 



26 



Very often a small number of important items dominate the 
results while at the other end of the line are a large 
number of items whose volume is so small that they have 
little effect on the results. [Ref. 5:p 20] 

This principle is illustrated in Figure__l and is the 
basis for the ABC analysis. [Ref. 5, p: 21] 

ABC Analysis has never been used fully in spite of the 
fact that it is an old technique. Many specialized 
inventory management techniques are based on this method. 
It allows items to be classified according to stockout 
costs, cash flows, relative sales volume, and lead time. 
[Ref. 5:p. 7] 

The methodology of any inventory management technique 
should avoid overselling formulas and must leave a systems 
base that does not lock the operating management into a 
rigid system, but allows for minor variations based on 
judgement . 

Many managers believe that the most rewarding study 
technique they have ever used is the ABC Analysis. Such an 
analysis is applicable to value engineering, sales planning, 
quality control, cost estimating and other operations, not 
merely to inventory control. [Ref. 5:p. 20] 

Efficient inventory control should effectively control 
the inventory at the least possible cost. For small, low- 
cost items which are used in bulk, such as paper clips and 
rubber bands, it is usually very costly to monitor 



27 



S 

Oh 
2 



3 



o 



O 



O 



o 

CO 



o 
o 



o 

o 



o 
rvi 



o 

CO 



o 
"3- 



o 



o 

CO 



o 
o 













1 2: 

n 










1 5 

1 -w 














g 

















o 

o 



o 

CO 



o 

U3 



~S\ 



o 



o 



o 



o 

u3 



O 



o 



i3^^^:> 



b '-n <, <3 ^ 



-«. «», -t. 



Figure 1 . 
Pareto's Law of Maldistribution 

28 



consumption closely. In such a case, it is more practical 
to keep a supply on hand at all times and allow people to 
help themselves. Any waste can be absorbed more easily than 
the cost of controlling usage. [Ref. 6:p. 173] 

Of course, important items should not receive such loose 
control. Rather, one must make a decision, clarifying which 
items are unimportant, requiring loose controls, and which 
need to be monitored more closely. Therefore inventory 
controllers should carefully check stock records item by 
item, classifying them into groups. [Ref. 6:p. 173] 

The proper classification of items is clear on an ABC 
curve, which shows that a few of the items are responsible 
for most of the value of all materials and parts used. 

Large investment items fall into category A, the vital 
few. These ten percent of the items may easily account for 
70 percent of the money spent on materials. These are the 
materials whose usage should be carefully monitored as to 
the specific quantity needed to support the system. The 
need should be calculated in advance according to the period 
of use. The schedule of manufacture or purchase should 
usually be timed so that they arrive just before they are 
needed. These are the items which are most suitable for 
ordering by the computerized MRP methods, which are 
described in detail in Chapter IV. Usually, inventories of 



29 



these items should be held down by frequent ordering of 
small quantities. [Ref. 6:pp. 173-174] 

B-category materials are the 15 to 20 percent of the 
items which make up approximately 15 percent of the 
investment. These items are expensive enough to require 
careful records of their use, but are less important than A- 
category materials and do not require the same degree of 
careful monitoring. Standard reorder quantities and minimum 
stock limits may be set and followed for these items. When 
the stock of an item gets down to its established reorder 
point, replenishment orders can then be made out. In this 
case, Economic Order Quantities (see Chapter IV) might be 
used to advantage. [Ref. 6:p. 174] 

The many trivial items which commonly make up 75 percent 
of the items in inventory while accounting for only ten 
percent of the value of the materials fall into category C. 
The items in this category should receive minimal attention 
and can be carried in large safety stocks. They can often 
be on a reorder point system, rather than in the 
computerized MRP system. C-items can be made readily 
available in the workplace where they may be obtained 
without the use of requisitions. Usually, these items are 
charged to an overhead account, rather than to products 
individually. [Ref. 6:pp. 174-175] 



30 



Looser controls of C-category materials and stocking 
them with large safety margins would increase costs of 
investment from shelf wear, obsolescence, and wasteful use. 
However, the costs of controlling them more tightly would be 
even greater. However, sufficient control must be exercised 
to be sure not to run out of critical, low-cost items. 
[Ref. 6:p. 175] 

For a summary of the characteristics of each category 
and its treatment, see Figure 2. 

The background for the ABC system can be summarized by 
the "80-20 Rule," where 20 percent of the items account for 
80 percent of the value. This rule applies frequently to 
other situations besides inventory management. For 
instance, in marketing, 20 percent of customers may account 
for 80 percent of the sales, or at a university, 20 perce.nt 
of the courses offered may account for 80 percent of the 
total student credit hours. [Ref. 5:p. 137] 

The decision steps for classifying items into the A, B, 
and C categories are actually relatively simple. First, one 
must set the criterion for developing the ranking. This 
criterion can be sales volume or value of the materials, 
etc. Items should then be ranked in descending order of 
importance according to this criterion. Next, the sum of 
the total value of the ranking criterion should be recorded 
with the total number of items. Beginning from the most 



31 



important item, at the top, one must calculate the number 
and percent of the total ranking criterion represented by 
each individual item and its total, including all the items 
above it. This procedure is developed in more detail below. 
[Ref. 5:pp. 137-138] 

Figure 2. Characteristics of ABC Groups 



Maintain close Maintain moder- Maintain looser 

control ate control control 

Based on calculated Based on calcu- When supply 

requirements lated require- reaches order 

ments or past point, order 

usage more 
Keep records of 
receipts and use Keep records and 

receipts Few checks against 

needs 
Close check 
on schedule Some checks on 

revisions changes in mind 

Continual Expediting for Little or no 

expediting prospective expediting 

shortages 

Low safety Moderate safety Large safety 

stock stock stocks 



A. CLASSIFICATION OF THE MATERIALS 

In order to classify the materials into A, B, and C 
categories, initially a list that will include all items 



32 



must be made. This list will include columns of the 
following elements: (Table 1) 

1. Number of item for identification of the material. 

2. Item code, stock number, part number, or some sort of 
description . 

3. Number of items used per year. 

4. Unit cost of the item. 

5. Usage value, which is the number of items times unit 
cost . 

Once this list is completed with all the materials, it is 

reorganized by arranging the items in order of priority 

based on the highest demand of annual usage for each item. 

In addition to the above categories, the following 

information should now be included: (Table 2) 

Cumulative percentage of items. 

Cumulative usage value. 

Cumulative percentage of usage value. 
In the next step, results are plotted on graph paper. 
The X axis shows the cumulative percent of the total items, 
and the Y axis the cumulative percent of total usage value. 
See Figure 3. 

The assignment of the materials into their respective 
ABC groups is the last and most difficult step because there 
is no simple technique for doing so. Rather, the decision 
is to a large extent arbitrary, a subjejctive judgement by 
the decision-maker. Often, significant natural breaks will 



33 



TABLE 1 
ABC ANALYSIS 



(1) 

Number of 
Items 


(2) 
Item 
Code 


(3) 

Number of 

Items per 

Year 


(4) 
Unit Cost 


(5) 
Usage 
Value 


1 


4710-00- 
2776101 


3 


12 


36 


2 


-11-2778703 


12 


0.25 


3 


3 


-11-2785411 


4 


4 


16 


4 


-11-5422909 


30 


0.05 


15 


5 


-11-5422918 


20 


0.1 


2 


6 


4720-00- 
2889751 


5 


0.5 


2.5 


7 


4730-NT- 
AA21753 


14 


2 


28 


8 


4730-NT- 
AA45761 


20 


60 


1200 


9 


4730-00- 
1720045 


7 


9 


63 


10 


4730-00- 
1874191 


600 


.50 


300 


11 


4730-00- 
1892624 


16 


0.5 


8 


12 


4730-00- 
1892628 


1000 


1 


1000 


13 


-11-1899735 


2 


60 


120 


14 


-11- 1892552 


260 


0.5 


130 


15 


-11- 1892583 


10 


20 


200 



34 



TABLE 2 
ABC ANALYSIS 



(1) 

Number 

of 

Items 


(2) 
Item 
Code 


(3) 

Number 

of 

Items 

per 

Year 


(4) 
Unit Cost 


(5) 
Usage 
Value 


(6) 
Cumula- 
tive 
Percent 
of Itmes 


(7) 
Cumula- 
tive 
Usage 
Value 


(8) 
Cumula- 
tive 
Percent- 
age of 
Usage 
Value % 


1 


4710-00- 
2776101 


20 


60 


1200 


6.7 


1200 


38.5 


2 


-11-2778703 


1000 


1 


1000 


13 


2200 


71 


3 


-11-2785411 


600 


.5 


300 


20 


2500 


80 


4 


-11-5422909 


10 


20 


200 


27 


2700 


87 


5 


-11-5422918 


260 


.5 


130 


33 


2830 


91 


6 


4720-00- 
2889751 


2 


60 


120 


40 


2950 


95 


7 


4730-NT- 
AA21753 


7 


9 


63 


47 


3013 


97 


8 


4730- NT- 
AA45761 


3 


12 


36 


53 


3049 


98 


9 


4730-00- 
1720045 


14 


2 


28 


6 


3077 


99 


10 


4730-00- 
1874191 


4 


4 


16 


67 


3093 


99.4 


11 


4730-00- 
1892624 


16 


.5 


8 


73 


3101 


99.7 


12 


4730-00- 
1892628 


12 


.25 


3 


80 


3104 


99.8 


13 


-11- 1899735 


5 


.5 


2.5 


86 


3106.5 


99.9 


14 


-11- 1892552 


20 


.1 


2 


93 


3108.5 


99.95 


15 


-11- 1892583 


30 


.05 


1.5 


1000 


3110 


100 



35 



c 
u 

M 

u 

L 
A 

T 

I 
V 
E 

P 
E 
R 
C 

E 
N 
T 



F 

U 
S 
A 
G 
E 

V 
A 
L 
U 
E 



100 



80 



60 



20 




20 



jo 



60 



Items C 



SO 



100 



A 



CUMULATIVE PERCENT OF ITEMS 

Figure 3 
ABC Analysis - The SO -20 Rule 



36 



appear during the examination of the rankings. However, 
this is not always the case, and at such times a decision 
must be made based on balancing the material's importance 
with the cost of its control. [Ref. 5:p. 138] 

Thomas (1968) proposed a simple method for roughly 
dividing materials into which of the A, B, and C categories 
they will most likely belong without the necessity of 
performing a complete Pareto analysis of all items in stock. 
He suggested that an item which has a usage value (prime 
cost x yearly or monthly demand) that is more than six times 
the average value for all the items probably belongs in 
category A. Similarly, category C items would have a usage 
value of less than half the overall average. Therefore, all 
items with usage values between six times and half of the 
average value must belong in category B. [Ref. l:p. 92] 

B. CRITICAL VALUE ANALYSIS (CVA) 

From an inventory control perspective, the ABC analysis 
is not always completely satisfactory as some items in 
category C may not receive as much attention as they merit. 
These items with low usage values, if lacking, would create 
serious problems in the sales of a company or in the 
operations of a weapons system. For example, shoelaces may 
be classed as a category C item in the inventory of a 
distributor or wholesaler. However, if a stockout of 



37 



shoelaces were to occur, a loss of shoe sales could result. 
A small bolt or similar part may be a category C item for 
the manufacture of sophisticated consumer products, such as 
refrigerators or automobiles. But a stockout of that tiny 
part could close down an entire assembly line, causing 
greater losses than the cost of maintaining a larger 
inventory of that part. For that reason, some companies 
implement a plan, developed by the military, called Critical 
Value Analyusis. The basic function of CVA is to classify 
inventory materials on the basis of point values assigned in 
three to five categories, as in the following example: 

1. Top priority: no stockouts--cr itical items. 

2. High priority: essential, but limited stockout s 
permitted . 

3. Medium priority: necessary, but occasional stockouts 
permitted . 

4. Low priority: desirable, but stockouts allowed. 
Clearly, the combined usage of both ABC Analysis and CVA 

could produce a higher degree of control of inventory 
management. If all items are classified by the ABC and 
Critical Value Analysis approach, we could classify the low 
priority and high priority items, with the high priority 
items as A class items, the medium priority items as the B 
class items and the low priority items to the C class. 

The United States Navy has classified the material that 
is used by the end of the line consumers (retail, ships and 



38 



aircraft) into ten categories (VADCATS) according to the 
Value of Annual Demand (VAD). Items with the highest VAD 
are assigned to VAD category (VADCAT) A and would have a 
monthly order cycle, and items in the lowest VAD grouping 
are assigned to VADCAT J and are expected to be ordered once 
a year or less. 

C. SUMMARY 

Finally, one must remember that the ABC method for 
classifying inventory is subject to limitations as a control 
technique. On the other hand, as a system, it is easy to 
implement and allows the user organization to focus more 
attention on the more important items of inventory in order 
to more effectively utilize resources. Naturally, a company 
will wish to use the more sophisticated and therefore more 
expensive systems of inventory management in the situations 
where the best returns can be realized, that is, with the 
items in category A. In this regard, an understanding of 
the forms of basic inventory models will be helpful. 



39 



III. . PROVISIONING 

A. INTRODUCTION 

Initial supply support for complex weapons and equipment 
begins very early in the acquisition phases of a new weapons 
system through the provisioning process. In order for the 
weapons-system's operation, maintenance and supply system 
replenishments to be as effective as possible, a sort of 
pump-priming, in the form of initial provisioning must take 
place . 

The state of a system's functional readiness at a random 
point in time is described in terms of Operational 
Availability, which depends upon the weapons system's 
reliability, maintainability, and logistic suppor tability. 

For each system, the following elements must be provided 
and assigned: 

1. Maintenance Planning 

2. Support and Test Equipment 

3. Supply Support, including initial provisioning 
4 . Transportation and Handling 

5. Technical Data 

6 . Facilities 

7. Personnel and Training 

8. Funds for Logistic Support Resources 

9. Logistic Support Management Information 



40 



Initial provisioning brings together, at the right time, 
in the right combination, material, trained personnel, tools 
and test equipment in order to maximize operational 
readines . 

B. DEFINITION 

Provisioning may be defined as the process of 
determining the range and depth of the required parts for 
support of an end item for an initial period. The 
responsibility for provisioning is shared jointly by the 
Hardware Systems Commands, the in-service engineering 
activities, the vendor and the Ships Parts Control Center 
(SPCC). 

Another way to view provisioning is as the front end of 
Life Cycle Support. The development of an allowance list 
and the lay-in of material are the culmination of the 
provisioning process. In fact, the development of the 
allowance list serves as the bridge between the twin 
subjects of Provisioning and the COSAL (Coordinated 
Shipboard Allowance List). The end product of the 
provisioning process, the allowance list serves as the basic 
building block for the development of the COSAL. 

When an item is purchased, the contractor provides the 
Pro visioning -Technical Documentation, which includes: 
- Drawings down to the piece part level 

The contractor's recommended list of spares 



41 



Failure Rate Data down to the piece part level 
Technical Manuals 

C. PROVISIONING METHODS 

Now the question is, should all the spare parts 
suggested by the contractor be purchased? There are two 
systems which could be used to evaluate the contractor's 
recommendations for parts purchase. 

The first system is the manual or explored system, under 
which a basic maintenance plan or Lead Allowance Part List 
is used. Developed by the in-service activity, this 
document provides the basic maintenance plan and basic spare 
parts requirements to the Supply Center. The maintenance 
plans and basic spare parts requirements are the same 
regardless of manufacturer for many types of equipment such 
as valves, boilers, laundry equipment and the like. Only 
maintenance-worthy items, as identified by the 
manufacturer's Provisioning Technical Documentation and 
verified as being maintenance- worthy by the Lead Allowance 
Part List, are considered for stocking. The method is only 
appropriate for equipment that is relatively small and 
unsophisticated. 

For large and more sophisticated equipment, primary 
electronics, and ordnance, the second method is used. With 
this sytera, the contractor provides the provisioning 



42 



technical documentation in a mechanized format, which often 
identifies thousands of individual parts in a given system. 
A provisioning conference is usually held to review each 
item individually, rather than using a Lead Allowance Part 
List to identify those which are considered maintenance- 
significant . 

Representatives from the Supply Center, the in-service 
engineering activity, and the contractor participate in the 
conference. During this provisioning conference, decisions 
concerning the maintenance philosophy and' the classification 
of specific piece parts as maintenance-worthy are made and 
the information is subsequently loaded into the files. 

D. PROGRAM DATA 

The program data is developed by establishing a 
Preliminary Operational Capability (POC) date for the end 
item. This date is when repair and spare parts are first 
needed for the end item. 

Other necessary dates are the time to initiate the first 
replenishment purchase, POC+TR (TR = Time Replenishment), 
and the time when the first replenishment purchase is 
received, POC+TR+L (L = Procurement Lead Time). 

The primary concern of provisioning is the determination 
of the required number of units of each component of a 
system at the time of POC-L and POC. In order to avoid the 



43 



occurrence of a stockout, the provisioning purchase made at 
POC-L should be large enough to fulfill all anticipated 
requirements during the interval from POC to POC+TR+L. The 
provisioning problem would be fairly simple if the forecasts 
of demand that are available during that interval and for 
the time POC, TR, and L were clear and reliable. However, a 
great deal of uncertainty characterizes the provisioning 
problem with regard to the failure rates of new equipment, 
the procurement lead time, and the time TR. Additional 
units will be installed and the- amount of equipment will 
grow during the interval between POC and POC+TR+L. This 
will cause an increase in the aggregate failure rates over 
this interval of concern in the provisioning process. In 
addition, actual installation schedules can be subject to a 
great deal of uncertainty. Often the failure rate estimates 
are only engineers' theoretical guesses of the actual 
failure rates. Time lags can be very long. For instance, 
the time interval between POC-L and POC+TR+L may be four 
years or more. Therefore, the fact that the provisioned 
quantities often do not meet the demands is not surprising. 

E. TIME WEIGHTED AVERAGE MONTH'S PROGRAM 

The Department of Defense has developed a standard 
method for determining the program for requirement forecasts 
that is called the Time Weighted Average Month's Program 



44 



(TWAMP). The amount of program to be used in TWAMP is based 
on the Program Time Base (PTB), the value of which is 
dependent on the environment, but is usually twelve months. 
Simply put, the PTB is the number of months of program to be 
used in forecasting the demand for the first or following 
purchases . 

In order to compute the TWAMP, one must determine the 
area under the curve of the total installed population over 
time from POC to POC+TR+L and then divide it by the length 
of the PTB. The result is the average number of end items 
to be supported over the PTB. The designation of this 
average is the initial TWAMP or TWAMPi. 

The formulas below are provided for computing this 
initial TWAMP. By summing the vertical slices of the area 
spanning each month, they obtain the total area. The 
formulas assume that deliveries occur at mid-month, thus the 
cumulative program buildup (Dm) until and including the last 
month (m) in the PTB is defined as follows: 

For m=l, Dl=Il/2 

m-1 
For m>2, Dm (E Ik) +Im/2 
k=l 

where : 

m= the number of months after POC 

D= the area of the time slice of the curve described 
above for the month t 



45 



Ik= the number of units of the end item to be installed in 
month K. 

TWAMP over an integer PTB is given by: 

TWAMPi - Z DM/PTB for m=l,2, . . . PTB. 
m 

The initial annual demand rate for any given spare part 

can be computed with the following formula: 

Di=TWAMPi x N x BRF 

where : 

N= the number of units of a given replaceable part in the 
end item 

BRF=the Best Replacement Factor which is actually the 
estimated failure rate of a unit over the course of a 
year . 

Initially, the BRF is based on a Technical Replacement 
Factor (TRF), the contractor's estimate of the attrition 
rate . 

The Cost Difference (COSDIF) formula, which will be 
described in a following section (Demand Based Items), 
requires an initial estimate of the Steady State Annual 
Demand Rate (Dss), which is computed by determining, first, 
the total number of end items expected to be installed by 
the end of the procurement lead time: Dss=TWAMPss x N x BRF 

In order to develop the provisioning budget, which is 
discussed in a following section, one must compute an 
estimate of the initial demand during the procurement lead 
time (L) plus one quarter. The result is the purchase 



46 



quantity value, which is used to develop the budget. For 
consumable items, the formula is: 
D(L+1) = Di x (L+l)/4 



F. DEMAND PROPERTIES 

Four components are recognized in every inventory 
system: demand, replenishment, cost, and constraint. 
Briefly, demands are those things taken out of the 
inventory; replenishments are those items that are put in; 
costs are the pertinent measures associated with positive or 
surplus, and negative or shortage stockout inventories, and 
with raising the level of inventories; and constraints are 
the various factors, administrative, physical, and others, 
which place limitations on the other three components. 
[Ref. l:p. 21] 

The most important of the properties of an inventory 
system is the demand property. The reason inventories are 
kept is in order to meet demands, fill orders, and satisfy 
requirements. The only reason inventory problems exist is 
because of demands, otherwise, we would not have any 
inventory problems. [Ref. l:p. 21] 

For the most part, demands cannot be controlled 
directly, and often even indirect control is not possible. 



47 



Rather, they are generally dependent on decisions made by 

people outside of the organization that has the inventory 

problem. In the Navy, many times the demand depends on 

unweighed factors. While the demands themselves cannot be 

controlled, in general, it is possible to study their 

properties . 

- When do customers place their orders? 

How much do they require? 

Is the demand greater at the beginning of the month or 
at the end of the month? 

Is accurate information available, or is it necessary 
to estimate average demands and the ranges of demands? 

These are the significant properties which affect the 

solutions of inventory problems. [Ref. 1 : p . 22] 

G. DEMAND SIZE 

Demand size is used to denote the quantity necessary to 
satisfy the demand for inventory. We say the demand size is 
constant when it does not change from period to period, 
otherwise it is labelled as variable. The demand size, when 
we have precise advance information about it, is said to be 
known. Those inventory systems in which the demand size is 
known are referred to as deterministic systems. At times 
when the demand size is not known, we may ascertain its 
probability distribution. In these cases, we refer to the 
inventory systems as probabilistic systems. 



48 



H. BASIC INVENTORY THEORY 

The primary elements with which basic inventory theory 
begins are historical demand and demand averages. Theory 
makes the assumption that demand estimates are available. 
Items may be classified, for Navy purposes, as either demand 
based or non-demand bases. 

I. NON-DEMAND BASED INVENTORIES 

Those materials for which the decision to stock is not 
based on anticipated demand are called non-demand based 
items. [Ref. 2:pp. 1-4] 

The U.S. Navy classifies an item as demand based if it 
has an expected demand of equal to or greater than one in 90 
days. On a destroyer-sized ship, there are approximately 
2,300 demand based items. [Ref. 2:pp. 1-4] 

A non-demand based item that is essential and will not 
fail in normal usage is an insurance item if its failure or 
loss, without an easily-available replacement, would 
seriously hamper the operation of a weapons system. [Ref. 
2:?p. 1-4] 

For items whose predicted usage is too low to qualify 
them as demand based materials, but where the lack of 
replacement would seriously hinder the weapons system's 
operation, the Navy establishes Numeric Stock Objective 
(NSO) stock levels. For non-demand based items, the minimum 



49 



quantity needed for one maintenance action, or a quantity of 
one, usually determines the quantity of NSO. 

An item becomes an insurance item if it has an expected 
demand of equal to or more than one every four years (i.e., 
one fourth of one demand in one year, or ".25"). Aboard a 
DD-963 class ship, there are approximately 9,800 insurance 
items stocked. There are, in addition, about 4,100 items in 
stock on the ship because they are: 
- personnel safety items, or 

will satisfy planned maintenance requirements. 
The total stock number sequence list for on-board stocking 
amounts to approximately 16,200 items. 

Items also included in the Numeric Stockage Objective 
(NSO) category are: 

1. Items such as set assembly, non-repetitive overhaul 
programs that are needed to support specific programs 
that are sporadic or non-recurring in nature and where 
there is no r e p r o c u r e m e n t required after the 
completion of that particular program. 

2. Items that are procured on a life-of-type basis, or 
that are "bought-out" when a production program 
terminates . 

3. Items which should be retained after a one-time or 
non-repetitive program in which they are not fully 
consumed, for possible use at a future time on a 
similar program. 

Any item for which the Cost Difference (C0SDIF) equation 

shows that it is more costly to keep it in stock than to not 

stock it is a non-demand based item. 



50 



J. DEMAND BASED ITEMS 

For demand based items, the decision on whether or not 
to stock is based on anticipated recurring demands. Any 
item which does not fit into this category is a non-demand 
based item. 

K. FUNCTIONS OF INVENTORY 

The theory of inventory can be described as a theory of 
storage. Often, it is impossible to meet the demands for 
some items if the item has not been stored in anticipation 
of demands. The following functions of storage identify use 
of, and reasons for having an inventory. 

1 . The Decoupling Function 

Inventories make reliance on production facilities 
unnecessary, allowing missions or tasks to be performed 
independently. In manufacturing, inventory is used to 
separate or de-couple production capabilities from each 
other. For the Navy, maintenance of inventories allows for 
fleet operations to be carried out in remote locations for 
long periods of time without the need for resupply. 

2 . Pipeline Inventories 

The transportation time of the materials from the 
producer to the supply center is called the pipeline. If 
for no other reason, some inventory must be maintained in 
the inventory system to meet the demands of the customers 



51 



during the transit, handling, and shipping time of the 
items. For those items which are not in continuous 
production, the pipeline inventory must also account for the 
production lead time. 

3 . Buffer or Safety Stock Inventories 

In many inventory systems, the average demand and 
average lead time for the inventory pipeline are 
supplemented by enough stock to provide for a possible 
higher than average demand during the lead time. In order 
to determine reasonable or affordable levels of safety 
stock, the risk of stocking out is assessed including the 
cost and inconveniences involved. 

4 . Review Cycle Inventories 

Between inventory reviews, the inventory management 
scheme's order cycle or review time portion must provide 
enough material to support operations. A consideration of 
the amount of stock which will be used between inventory 
reviews must be included when the question of how much stock 
to order at once in such a periodic review system is 
decided . 

L. THE COST DIFFERENCE FORMULA (COSDIF) 

Demand-based items are identified by means of a cost 
equation referred to as the Cost Difference (COSDIF) 
equation, a probabilistic approach for comparing the 



52 



forecasted cost of keeping an item in stock with the 
projected cost of needing the item after not having stocked 
it. 

Alan Kaplan of the U.S. Army's Inventory Research Office 
was the first to introduce the COSDIF formula. This formula 
resulted from a simple decision model as illustrated in 
Figure 4. 

Here the demand development period (DDP) is assumed to 
be two years. The DDP is the initial two years in a new 
system's use. During this time Demand Data, in the form of 
replacement and resupply requisitions for each part of the 
system, is recorded and reviewed to develop demand 
projections based on real world use of the new system. 
After that time, it is expected that the observed demand 
will provide good forecasts. 

When all the costs and probability values are known for 
the states of nature, the expected cost for each decision 
can be evaluated. The optimal decision is that which 
creates the least expected expense. In order to decide 
whether to stock an item or not, it is convenient to use the 
difference between the projected expenses associated with 
each decision. For the rest of this section, this 
difference in expenses will be called the COSDIF. The 
differences in cost between the decision to stock or not to 
stock are analytically expressed in the following equation: 



53 



Decision 


States of Nature 


No demand during DDP 


Demand during DDP 


Make a 
provisioning 
buy 

Do not 
make a 
provisioning 
buy 


Cost of procurement plus two years' 
holding cost 

No costs 


Two years of average annual 
variable costs 

Costs of spot buys during 
first year and average annual 
variable cost for second year 



Figure 4 
A Provisioning Decision Matrix 



54 



COSDIF = (Do/Dss) x [A+2IC(R0P+Q) ] + (1-Do/Dss) x 

[4A D/Q + ICQ/2 + Dss x CI] - (1-Do/Dss) x 
[Dss x (CSP+K x PLT/4) + Dss x C x P] 

where : 

Dss= Steady state annual demand 

Do/Dss= Probability of no demand in two years, given an 

annual steady state demand forecast (total) of Dss 

A= Cost of procurement 

1= Carrying cost rate 

C= Unit price 

ROP= Reorder point quantity 

Q= Optimal order size 

Cl= Cost of issuing stock 

CSP= Cost of spot procurement 

PLT= Production lead time in quarters 

K= Shortage cost per unit per year 

P= Spot purchase premium rate. 

When the resulting COSDIF value is negative, the costs 
of not purchasing and stocking the item are greater than 
those faced if the purchase is made. In other words, it 
would be preferable to make the purchase. However, if the 
COSDIF value is positive, it would be less cost-effective to 
make the purchase. When the result is zero, either decision 
would be equally acceptable from an economic standpoint, but 



55 



it is less work for the provisioner to not buy, so the 
purchase is usually not made. 

In the development of the provisioning budget, the 
COSDIF formula is used as the range model, and is therefore 
highly important to managers when they determine their 
initial stockage priorities. 

M. DETERMINING THE PURCHASE QUANTITY AND BUDGET 

If, by the use of the COSDIF formula, it is determined 
that an item should be stocked, the quantity of the purchase 
must be decided. The U.S. Department of Defense stipulates 
that the quantity should be equivalent to the expected 
demand over the course of time that includes the forecasted 
replenishment procurement lead time plus one quarter. The 
provision of the extra quarter is to provide a cushion of 
safety stock. In order to compute this quantity, the 
following formula is used: 

D(L+l)=Di x (L+l)/4 
where L represents the procurement lead time. 

For those items which do not meet the COSDIF 
requirements, there is a re-examination in order to see if 
they should be classified as insurance or Numeric Stockage 
Objective (NSO) items. If they can be so classified, the 
quantity of purchase of these items is considered to be one 
Minimum Replacement Unit (MRU). 



56 



The cost of purchasing an item depends on whether the 
item is demand based or is an insurance or NSO item. In the 
format case the cost of C x D(L+1) and in the latter, just 
C. By summing the procurement costs of all the items, the 
total value of the provisioning package is determined, which 
amount is the proposed provisioning budget. 

In the U.S.A., the total value of the provisioning 
package is set as the "budget constraint," the monetary 
value which serves as the firm upper limit on the amount 
that may be spent to purchase the materials for the stock. 
While the actual range and purchase quantities of the 
materials for the stock may vary from the values used in the 
processing of the budget, the procedures used must be 
approved . 

1 . Example 

Suppose that the program installation schedule for a 
new weapons system MK-98 is as follows: 
Months: ONDJFMAMJJAS 



Year : 
1986 



1122223444 



Year : 

1987 6 7 7 7 8 8 9 

and PTB=12 months. 



57 



First we must determine the initial TWAMP and the steady 
state TWAMP. 

Cumulative Program Buildup 



Year, 1986 
























Months 


N 


D 


J 


F 


M 


A 


M 


J 


J 


A 


S 


Mo. # 




1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


Ik 1/ 




1 


1 


2 


2 


2 


3 


4 


4 


4 


4 


Dm 2/ 




.5 


1.5 


3 


5 


7 


9 


11.5 


15 


19 


23 


Year, 1987 
























Months 


N 


D 


J 


F 


M 


A 


M 


J 


J 


A 


S 


Mo. # 11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


22 


Ik 1/ 6 


7 


7 


7 


8 


8 


9 

















Dm 2/ 28 


34.5 


41.5 


48.5 


56 


64 


7 25 


77 


77 


77 


77 


77 



Therefore, steady state TWAMPss=77 since it represents the 
total installation to be made. 

The initial TWAMP for PTB=12 will be: 

E 

m Dm _ 0.5+1.5+3+5+7+9+11.5+15+19+23+2 8+34.5 



TWAMPi = 



PTB TT 

157 



12 



= 13.08 



Assume there are four demand based consumable repair 
parts for the Mark-98 which are being provisioned. Suppose 
that the data for each and the sign of the COSDIF value are 
as follows: 
Item No. COSDIF N BRF COST MRU 



1 


(-) 


3 


0.35 


150 


1 


2 


(-) 


10 


0.15 


10 


2 


3 


(-) 


1 


0.05 


30 


1 


4 


( + ) 


2 


0.10 


5 


1 



The L value is 5.4 quarters for all items 



58 



The following steps are involved in determining 
provisioning budget: 

1. Ignore items with positive (+) COSDIF 

2. Decide whether item is insurance or demand based item 

3. If it is an insurance based item, then buy one MRU 

4. The cost for the insurance items is computed by the 
following equation: 

C0ST= C x MRU 

5. If the item is a demand based item, then compute the 
initial annual demand by using the following formula: 

Di= TWAMPi x N x BRF 

6. Compute the initial demand during the procurement lead 
time (L) plus one quarter by using the following 
formula : 

D(L+1) = Di x (L+l)/4 

7. Finally, the cost of each item is computed by using 
the following equation: 

COST = C x D(L+1) 



According to these for the example given, the data we 
have is: 



Item #1: a. Di= 13.08x3x0.35=13.73 

b. D(L+l)=13.73x(5.4+l)/4=22 

c. Cost=150x22=$3,300 

Item #2: a. Di=13 . 08x10x0 . 1 5=19 . 62 

b. D(L+1)= 19.62x1.6=31 

c. Cost= 31x10=310 

Item #3 a. Di=l 3 . 08x1x0 . 05=0 . 654 

b. D(L+l)-0. 654x1. 6=1 

c. Cost= 1x30=3- 



59 



The Provisioning Budget will be 



For item 1 
item 2 
item 3 



22xl50=$3300 

31x 10=$ 310 

lx 30=$ 30 



Total budget 



$3,640 



60 



IV. INVENTORY CONTROL MODELS 

A. GENERAL INFORMATION 

The significant costs of inventory control techniques 
were introduced in the first chapter. Evolving from the 
considerations of costs, management control, and accounting 
procedures are two operating doctrines known as the 
continuous review and periodic review systems. 

The assumptions that are made have a direct bearing on 
the complexity and accuracy of the models. In general, a 
model becomes easier to work with and understand as more 
factors are assumed away in it. On the other hand, the 
results from such a simple model are more likely to be 
inaccurate. Thus, it becomes necessary to analyze the 
tradeoffs between the accuracy and the simplicity of the 
model. The user or the developer of inventory models tries 
to strike a balance between these two factors, creating 
models that are simple to understand and implement but also 
do not assume away reality to such a degree as to endanger 
their accuracy. [Ref. 4:pp. 1-9] 

B. PERPETUAL OR CONTINUOUS REVIEW MODELS 

It is possible to mathematically derive the answers to 
the questions of when and how much to order by use of the 
variable operating cost equations. The resulting solution, 



61 



basic and simplified, is the class of inventory models known 
as perpetual or continuous review systems. In these models, 
a transaction reporting system keeps the running totals of 
material on hand for each item in order to accurately 
determine the precise time for placing an order. 
Fluctuations in usage cause variations in the time between 
orders. The amounts of the purchase or order, however, are 
predetermined using the Economic Order Quantity (EOQ) 
formula. When the inventory drops to a predetermined re- 
order point, that critical level of stock that signals need 
for replenishment, an order for a fixed number of units is 
placed. The lead time for an order which is affected by 
such variables as transit time and cost, plays a large role 
in the determination of that re-order point. It is 
important to understand the assumptions, which are 
invariably made, of the inventory control models. To 
illustrate this, we shall list and discuss the assumptions 
of the Simple EOQ Model. This model incorporates the 
following simplifying assumptions: 

1. Demand is constant and continuous over time. 

2. Lead time for replenishment is known and constant. 

3. Backorders are not permitted. 

4. Price or cost is constant and independent of the 
order . 

5. No inventory is in transit. 



62 



6. Single item of inventory or no interaction between 
items. 

7. Infinite planning horizon. 

8. No limit on availability of capital. 

There is a very close relationship between the first 
three assumptions. We know precisely the amount that will 
be in demand for each relevant time span. Thus, in respect 
to the rate of usage over the course of time, demand is 
linear while the time span between placing the order and its 
receipt, the lead time, is constant. These factors preclude 
the possibility of stockouts and therefore end the concern 
over stockout costs. 

For some businesses, such as those where the variation 
in the demand is very slight, the extra accuracy achieved by 
a more complex model would be so small as to not be worth 
the added expense. The Simple EOQ Model is also a 
convenient beginning point for the available data in firms 
that are only beginning to implement inventory models. Some 
firms implement very sophisticated models in cases where the 
data is quite simple, thus getting virtually no greater 
accuracy than if they had used a simpler, less costly model. 

The assumption that there is no inventory in transit 
basically means that the transportation for delivery (FOB) 
is included in the purchase price of the item. This also 
means that there is no responsibility on the orderer's part 



63 



for the goods during transport because the title for them is 
not transferred until delivery. 

The constant cost assumption essentially implies that 
there are no volume discounts on prices and that the prices 
are relatively stable. 

These assumptions in the Simple EOQ Model leave only two 
types of costs to be considered: inventory carrying cost 
and ordering or setup cost. In the simple model, the 
resulting decision analyzes the tradeoffs between these two 
costs. Consideration of the inventory carrying cost alone 
would lead to a decision of ordering as little as possible 
at a time because this cost rises in direct proportion to 
increases in lot size (Figure 5). On the other hand, a 
decision based solely on the order or setup cost, which is 
fixed per order, would be to place fewer and larger orders 
in order to decrease the total order costs (Figure 6). A 
compromise decision must be reached balancing these two 
costs in determining the lot size with the aim of reducing 
the overall costs (Figure 7). 

A mathematical formulation of the total annual cost with 
the above assumptions is expressed as follows: 

K(Q) = %QIC + iA = C 

where : 

A = The annuual rate of demand or requirement for the 
period . 



64 



A 
N 
N 
U 
A 
L 

C 


S 
T 



12000 



8000 _ 



6000 _ 



4000 



2000 _ 




40 



80 



120 



160 



200 



A 

N 
N 
U 
A 
L 



8000 



6000 



c 



s 

T 



4000 



2000 



SIZE OF ORDER QUALITY 

Figure 5. Carrying Cost 



40 



80 



120 



120 



200 



SIZE OF ORDER QUALITY 



Figure 6. Order or SetuD Cost 



65 



Total Costs 



A 

N 
N 
U 
A 
L 

C 


S 
T 




/ 
/ 
/ 
/ 

' Carrying Cost 



Order/Setup Cost 



SIZE OF ORDER QUALITY 



Figure 7 

Total Annual Cost 



Q= The quantity ordered or lot size. 

A= The cost of placing an order or setup cost. 

C= The value or cost of one unit of inventory. 

1= Carrying cost per dollar value of inventory per year 
expressed as a percentage. 

The first terra of the equation refers to inventory carrying 

cost, that is equal to the average number of units in the 

economic order cycle (%Q) multiplied by the value per unit 

(C) and by the carrying cost (I). We can understand the 

logic of the equation looking at the so-called sawtooth 

model (Figure 8). The vertical line (Q) represents the 

amount ordered or produced for the economic order size. We 

start each period with this amount.. During the order cycle 

(t), we use up or sell this amount at the rate represented 

by the sloping line. The average number of items on hand 

during the period directly affects the cost of carrying the 

inventory through this period. Simply, the average number 

of items on hand, given a constant demand rate, is 

equivalent to one half of the starting amount (Q). The 

dashed horizontal line represents average inventory. The 

logic is proven quite simply. Assuming that Q equals 100 

items and the demand is 10 items daily, the 100 items would 

last 10 days (t). Halfway through the time period, after 

the fifth day, 50 items would be remaining, or one half of Q 

(% x 100). 



67 



Q 



Level of Inventory 




< — * — ►] 



ventory 



1/2 Q 



TIME 



Figure 8. Sawtooth Model 



68 



The equation's second term refers to the setup or order 
cost. An increase in the size of Q would result in few 
orders annually because the demand remains constant. 
Therefore, annual order costs would decrease with increased 
order quantities. 

The equation's third term represents the yearly purchase 
or manufacturing cost, which quite simply is equivalent to 
the annual demand multiplied by the per-unit purchase or 
manufacturing cost. 

The next step is the determination of the Q, the 
economic order quantity (EOQ). The EOQ equals that value of 
Q which minimizes the total annual cost (K(Q)). This can be 
done mathematically by differentiating the K(Q) function 
with respect to Q as follows: 

K(Q)=%QIC+ i A+^C 

dK(Q) IC _ AA 

Hq 2 qZ 

Setting dK(Q)/dQ equal to zero and solving for Q gives: 



2AA or Q-< 




Q i Vic 

This is the Harris and H. Wilson formula. For the U.S. 
Navy, A represents the average quarterly demand. So the 
optimal order quantity is: 

Q= 



8AA 



IC 



69 



For example, let us assume the following to show how the 
formula would work: 

C= $100 per unit 

1= 25% 

A= $200 

X= 3,600 units per year 

If we solve for Q, we will have: 

n 2AA 2 x 3600 x 200 0/n 

Q= TC" = 925 x 100 = 240 units - 

Reference to Table 3 and Figure 9 probably best 
demonstrates the nature of the tradeoffs and the logic of 
the above solution. These show the development of a range 
of different Q's from 100 to 500 with their accompanying 
inventory carrying cost and order cost in addition to the 
total cost. 

As the table illustrates, order costs are higher for 
lower values of Q, as predicted above, but the carrying 
costs are low. As the value of Q increases, up to 240, the 
ordering costs become lower because the number of orders per 
year decreases. On the other hand, the higher average 
inventories increase the carrying costs. For values of Q 
over 240, the decreases in the ordering costs become lower 
than the increases in the carrying cost, resulting in higher 
totalcosts. •* 



70 



TABLE 3 
TOTAL COSTS FOR VARIOUS EOQ AMOUNTS 



Q 


Order Cost 
A/Q 


Carrying 
Cost 1/2 QIC 


Total Cost 


100 


$7200 


$1250 


$8450 


140 


5140 


1750 


6890 


180 


4000 


2250 


6250 


220 


3270 


2750 


6020 


240 


3000 


3000 


6000 


260 


2770 


3250 


6020 


300 


2400 


3750 


6150 


340 


2120 


4250 


6370 


400 


1800 


5000 


6800 


500 


1440 


6250 


7690 



71 



A 

N 
N 
U 
A 
L 

C 



s 

T 



9000 



8000 



7000 



6000 



5000 



4000 



3000 



2000 



1000 



—Total Cost k(Q) 1/2 QIC 



Carrying Cost 




100 



200 



240 



300 



400 



500 



Order Quantity Q 
(Units Per Order) 



Figure 9. 

Total Annual Cost 
ofEOQ Example 



72 



By defining the optimum Q based on total costs, we are 
quickly able to determine from the table that the optimum Q 
is 240, according to the definition that has been 
established. The same result can be derived from Figure 9. 
Based on this EOQ system, expensive items and those for 
which the carrying cost (I) is high are ordered in small 
quantities at frequent intervals. But inexpensive and 
cheaply stored items will be ordered less frequently and in 
large quantities. 

C. RE-ORDER POINT 

In the above text it was pointed out that not only must 
one know the quantity to order, but also at which time to 
order. This point in time is generally called the re-order 
point, which is determined on the basis of a level of 
inventory or a number of units in stock. In accordance with 
the predetermined assumptions, there must be in inventory 
just enough stock to carry through the replenishment or lead 
time. Thus, when the lead time is known and constant, the 
amount of stock needed can be determined merely by 
multiplying the number of days of lead time by the daily 
demand. Then, when the level of inventory drops to this re- 
order point, an order is placed for the predetermined 
quantity. Under conditions of any uncertainty the re-order 
point must be redetermined to create an additional margin 



73 



called safety stock. Thus, the re-order point effectively 
amounts to the average demand during the lead time plus 
safety stock to allow for minor changes in demand. This 
principle is depicted graphically in Figure 10. 

So, based on the above example, if the lead time is 10 
days, the daily demand will be 10 units (3,600/360) and 100 
units will be the re-order point (10 days x 10 units). 

For the purposes of the U.S. Navy, the re-order level 
(RL) is a function of lead time demand, the variability of 
demand, and economic considerations. 

RL = D x L x SL 

where : 

D= Quarterly demand average 

L= The procurement lead time in quarters 

SL= Safety level, a function of demand and lead time 
variability and the desired level of service. 

D. PERIODIC REVIEW MODELS 

A policy of reviewing inventory and ordering at fixed 
regular intervals up to an optimal Requisition Objective 
(R0), is the basis of the periodic review model. Each order 
is intended to return the inventory level to a predetermined 
state. However, the size of the order may vary from 
interval to interval. At set intervals, the orders are 
placed without checking the stock level between orders. 
Thus, the inventory must provide for the expected demand 



74 



Inventory 
Level 



Recorder 
Point 



TV 

Q \ : 












A \ 

Safety \ 
Stock 

y 





TIME 

Figure 10 . 
Inventory Model Under Conditions of Uncertainty 



75 



between these intervals as well as allowing for some 
variations in the demand. Under this system, larger 
inventory levels must be maintained than in a continuous 
review system with similar demand and lead time. 

The target Requisition Objective must at least include 
sufficient quantities to cover the expected demand during 
the lead time plus the demand during one review time plus 
the Safety Stock, if any (Figure 11). The quantity ordered 
is determined by finding the difference between the RO and 
the inventory on hand at the time of the review. The 
additional costs generated by the higher investment level of 
this system are partially offset by lower clerical and data 
processing costs. For inexpensive items, a periodic review 
system may possibly be the most economical system. The U.S. 
Navy defines the RO as: 

RO=DxL+DxR+SL 
where : 

R= The length of the review period in quarters. 

For deterministic demand with no stockouts, the optimal 
review period R' is: 



R 



'-%, 



E. MATERIAL REQUIREMENTSS PLANNING (MRP) 

Production scheduling and inventory control are the 
concerns of material requirements planning (MRP). MRP 



76 



o 

N 

H 
A 
N 
D 



Requisitioning 
Objective (RO) 



Review 

T'me 

Demand 



Procure- 
ment 
Lead 
Time 

Demand 



Safety- 
Level 






t 
A 




A 



Q3 



Figure 11 

A Periodic Inventory 

Svstem 



77 



provides a precise scheduling system, an efficient material 
control system, and, in order to revise plans should changes 
occur, a rescheduling mechanism, while maintaining minimum 
levels of inventory and ensuring that necessary materials 
are available as they are required. The MRP system's major 
objectives are to simsul taneously : 

1. Ensure that materials, components, and products are 
available for planning production and for customer 
delivery . 

2. Maintain the inventory at the lowest possible level. 

3. Plan manufacturing activities, delivery schedules, and 
purchasing activities. 

The meaning of dependent and independent demand items 
was introduced in the third chapter. 

The demand pattern for dependent demand items is a lump 
pattern incompatible with the constant demand rate that is 
assumed in the basic EOQ Model. It was to better cope with 
these dependent demand items that MRP was developed. MRP 
begins with the scheduled completion dates, working backward 
to determine at which points dependent demand items will be 
ordered and the quantities to be ordered. 

The MRP system does not require forecasting of dependent 
demand items, but calculates the quantities from the master 
schedule. Except for lot sizing economies, it is important 
that these items are available at the precise time they are 
needed, not before and not after. Most inventory items in 



78 



manufacturing organizations are dependent and therefore 
should be managed by use of an MRP system. 

The MRP system's key features are the time phasing of 
requirements, generation of lower level requirements, 
planned order releases, and re-scheduling capability. The 
function of the time phasing of requirements is to determine 
the time period in which the material should be made 
available in order to meet the delivery date of the end 
product as denoted on the master schedule. Beginning with 
the end product, MRP controls all the necessary scheduling 
for the lower-level requirements. Planned order releases 
show the timing for placing orders by purchasing and 
manufacturing. When it becomes impossible to complete the 
work as scheduled, the MRP re-schedules planned orders to 
maintain realistic and meaningful priorities. 

The MRP system requires three major items of input. 
These items are the master production schedule, inventory 
status records, and the product structure records. 

This system takes the master production schedule for the 
end products and uses the product structure records to 
determine the gross quantities of components required. In 
order to obtain these gross quantities, the system uses a 
process of "exploding" the product structure record, 
breaking it down into its lower level requirements. This 
process simply multiplies the required amount of each 



79 



component for a single end product. Also identified by the 
explosion process are necessary components and the quantity 
of each needed to produce a certain number of the product. 
The term explosion is appropriate because the analysis of 
each level in the product schedule uncovers more 
requirements than in the previous one. The gross quantities 
are adjusted by referring to the inventory status records 
and subtracting from the gross quantities the number of 
items available in inventory. The "when," which is as 
important as "what" and "how many," is determined by setting 
back in time the lead times for each component. In this 
manner, each component's material requirements are phased 
over time in a pattern determined by lead times and parent 
requirements . 

A schematic representation of a product structure is 
shown in Figure 12. The structure of product A defines the 
relationship between the various items that make up the 
product in terms of levels as well as parent/component 
relationships. Th product has four levels of manufacture. 
The end product is designated by convention, as being at 
level 0, its immediate components at level 1, and so forth. 
The parent/component relationship indicates that A is the 
parent of the components B, C, and 10; B is the parent of 
components D and 20; C is the parent of components 30, 40, 
and 50; and D is the parent of components 60 and 70. The 



30 



Level C 



B(l 



10(3) 



C(l) 



Level 1 



r 



20(1) 



1 

D(2) 



r 



60(1) 



r 



30(2) 



1 



70(1) 



40(1) 



50(1) Level 2 



Level 3 



The letters represent assemblies/ subassemblies, and the numerals 
represent parts. The numbers in parentheses are the quantities 
required for assembly. 

Figure 12. Typical Product Structure 



81 



only item that is not a component is the independent demand 
item, A. The dependent demand items B,C, D, 10, 30, 40, 
50, 60, and 70, are components. Items B, C, and D are 
parents as well as components. 

For example, suppose we are to produce 100 units of 
product A in period 8 with the product structure shown in 
Figure 13. If no stock is on hand or on order, determine 
when to release orders for each component and the size of 
each order. Product A is made from components B and C; C is 
made from components D and E. By simple computation we can 
calculate our quantity requirements: 



Component B 

Component C 

Component D 

Component E 



(l)(number of A * s ) = 1 ( 100) = 100 

(2)(number of A ' s )=2( 100)=200 

(l)(number of C ' s )=1 ( 200)=200 

(2)(nuraber of C ' s )=2( 200)=400 
Now we must consider the time element for all the items. 
Table 3 creates a material requirements plan based on the 
demand for A. 

A material requirements plan has been developed for 
product A based on the product structure of A and the lead 
time needed to obtain each component. Planned order 
releases of a parent item are used to determine gross 
requirements for its component items. Planned order 

releases a requirement in the same time period for its lower 
level components. In order to complete 100 units of product 



82 



A(l) 
LT = 4 



Level 



B(l) 
LT = 3 




C (2) 
LT= 2 






i 

D(l) 

LT = 1 




i 

E(2) 
LT=1 



Level 1 



Level 2 



Figure 13. Typical Product Structure 



83 



A in period 8 it is necessary to release orders for 100 
units of B in period 1, 200 units of C in period 2, 200 
units of D in period 1, and 400 units of E in period 1. 
Planned order release dates are obtained by setting back in 
the lead times. A component's gross requirements time 
period is the planned order release period of its parent. 

F. AN E0Q-MRP COMPARISON 

There are many advantages to the MRP system as opposed 
to the fixed order size system in terras of controlling 
production of items. A comparison of the characteristics of 
these two inventory management techniques can be found in 
Table 4. The following are some of the disadvantages 
inherent in fixed order size systems: 

1. A. large inventory investment is necessary. 

2. With a highly varying demand rate it becomes 
unreliable . 

3. There is a large safety stock investment required. 

4. All items must be forecasted. 

5. It is based on past demand data. 

6. There is a greater chance of material obsolescence. 
When demand is dependent, the E0Q system can cause 

serious problems in the operation as well as an excessive 
inventory investment. A bill of materials explosion should 
be used to calculate demand for the dependent demand items. 
When demand can be calculated, there is no reason to use 



TABLE 4 
MRP PLAN FOR 1Q.Q UNITS OF PRODUCT A IN PERIOD 8 



Lead 
Time 






1 


2 


3 


4 


5 


6 


7 


8 


4 


A 


Gross 
require- 
ments 
















100 




- 


Planned 

order 

releases 








100 

































3 


B 


Gross 
require- 
ments 








100 














Planned 

order 

releases 


100 








































2 


C 


Gross 
require- 
ments 








200 














Planned 

order 

releases 




200 





































1 


D 


Gross 
require- 
ments 




200 


















Planned 

order 

releases 


200 








































1 


E 


Gross 
require- 
ments 




400 


















Planned 

order 

releases 


400 

















forecasting. While independent demand items must be 
forecasted, this is not the case for dependent demand items. 
Therefore, the latter should be calculated. Efficiency is 

v 

greatly enhanced when components are ordered based on 
product requirements and the component inventory is driven 
to zero between requirements. The result of implementing 
MRP will be to reduce inventory investment substantially for 
dependent demand items while at the same time removing the 
EOQ's built-in risk of shortages, thus greatly improving 
operational efficiency. The use of independent demand 
inventory models for dependent demand items generates 
excessive inventory at times when it is not needed and the 
risk of shortages and stockout when it is needed. 

TABLE 5. COMPARISON OF FIXED ORDER SIZE AND MRP SYSTEMS 



Fixed Order Size System 
EOQ 

Part oriented (every item) 

Independent demand 

Continuous item demand 

Continuous lead time demand 

Reorder point demand signal 

Historical demand base 

Forecast all items 

Quantity-based system 

Safety stock for all items 



MRP System 

Product/component oriented 
Dependent demand 
Discrete/lumpy item demand 
No lead time demand 
Time-phased ordering signal 
Future production base 
Forecast end items only 
Quantity and time-based system 
Safety stock for end items only 



86 



V. FORECASTING 

A. THE IMPORTANCE OF THE FORECAST 

Inventory control is concerned with the future because 
the past is beyond control. It is important to begin with 
the present position and to work from there to prepare for 
the future. In order to achieve this goal, one must assume, 
guess, or otherwise estimate what will occur in the future. 
With all other factors being equal, an organization is only 
able to survive if it can prepare itself to meet the needs 
of its customers. [Ref. 9:p. 13] 

In decision making, the avoidance of forecasting is 
impossible. An estimation of future demand is a 
prerequisite for every decision in production planning and 
inventory management. Forecasts are necessary to: 

1. Set up performance standards for customer service. 

2. Determine the allocation of the total inventory 
investment . 

3. Order replenishment stock. 

4. Identify the necessities for additional production 
capacity . 

5. Be able to choose among alternative operating 
techniques . 

After the decisions are made, there is only one thing 

that is certain — the forecasts will not be correct. The 

result is the need to determine the precise magnitude of the 



87 



errors and to ensure that past decisions are reviewed for 
any necessary alterations in response to those errors. 

B. FORECASTING PRINCIPLES 

It is important to establish the general principles of 
forecasting before discussing the techniques which are based 
upon them. Briefly, the most important of these principles 
are as follows: 

1. The accuracy of forecasts improves with larger groups 
of items . 

2. Shorter periods of time are more accurately 
forecasted . 

3. An estimate of error should be incorporated in each 
forecast . 

4. The forecasting methods should be tested before they 
are applied to any forecasting system. [Ref. 9:p. 18] 

C. MAKING A FORECAST 

There are three essential steps for forecasting: 

1. Preparation of the data. 

2. The actual making of the forecast and its accompanying 
error estimate. 

3. Tracking the forecast. 

D. WHAT TO EXPECT FROM A GOOD FORECASTING SYSTEM 

M.J. Netzorg, a management consultant who has nearly 
thirty years of experience, described the environment and 
situation in which forecasts of the demand for individual 
items are made : 



88 



we seldom have the time to make genuinely new 
forecasts . . .. For most items we get no market research 
support . . .. The only new information we get routinely 
is a month's net sales figures, by item, by region, to 
compare to the forecasts made earlier for that month . . . 
therefore one must not promise or even ai m~~f or accurate 
forecasts from month to month, but only forecasts that 
wouldn't crucify production and customer service. 

Netzorg suggests a simple 12-month moving average for 
forecasting very low volume or C items. The length of time 
for the moving decreases gradually to six months for the 
highest volume of B and A items among the slow movers. In 
agreement witli this standpoint, it is preferable that the 
more sophisticated forecasting models be applied only to the 
most important items, those in categories A and B, 

Therefore, an ideal forecast, from the viewpoint of 
effective inventory management and production planning, 
should : 

1. Estimate the demand to be expected in physical units. 

2 . Estimate the actual demand's probably range in 
reference to the expected value point (i.e., forecast 
error ) . 

3. Be timely by completing the forecast in time to allow 
for necessary decisions to be made. 

4. Update the forecast regularly so that prompt revisions 
can be made . 

5. Balance the costs of errors in the forecast against 
the costs of forecasting. 

6. Allow for overriding of the mechanical forecasts, 
whose main advantage is the ability to assimilate 
large amounts of information and historical data, by 
human judgement. 



89 



It is important to keep the number of items of 
information needed for forecasting at an absolute minimum. 
The forecasting technique's logic should be clear and easy 
to follow so that it is understood and usable by those who 
will supply the value judgements, thereby transforming the 
forecasts into predictions. 

There exist a great many techniques and systems for 
projecting past patterns onto the future for purposes of 
forecasting. These techniques are classified in many ways, 
one of which is based upon the time period involved: 

1. Aggregate Longer-Term Forecast. 

2. Individual Item Short-Term Forecast. 

One other classification scheme is illustrated in 
Figure 14. This scheme distinguishes between formally 
recognized forecasting techniques (formal) and approaches 
such as intuition and other similar "informal" techniques. 

E. AGGREGATE LONGER TERM FORECASTS 

An aggregate time series, which deals with the patterns 
of a group of products, is generally more stable than an 
individual item's sales pattern. However, in cases where 
the time series is not stable, or where the forecast deals 
with individual items, the use of the Individual Item Short 
Term Forecast is preferable. 



90 



Forecasting Methods 



Formal 



Qualitative 



Historical Analogy- 



Market Survey- 



Expert Opinion 



Delphi 



Life Cycle Analysis 



Informal (Intuitive) 



Quantitative 



[ 



Time Series Analysis 



Causal 



Simple Average 



Moving Average 



Exponential 
Smoothing 



Multiple 
Regression 



_ Econometrics 



Input-Output 



Multiplicative 

with 
Linear Trend 

(e.g. , by 
regress ion) 



Box- Jenkins 



Figure 14 
Classification Scheme of Forecasting Methods 



91 



F. TIME SERIES ANALYSIS 

A time series is "an ordered group of values of a 
variable measured at successive positions in time or for 
successive intervals of time." In this process we determine 
the number of items in the inventory at specific points in a 
range of time and also calculate the number of items sold 
over specific time intervals. The conclusion of the time 
series consists of developing a time series forecasting 
model which can become the basis for predicting future 
trends. [Ref. 10:p. 683] 

The Time Series Analysis makes the assumption that there 
are four component parts to the historical data: 

1. The trend, T. 

2. A seasonal variation, S. 

3. A cyclical variation, C. 

4. Random variation, R. 

The trend component consists of the long-term general 
developmental trends in the series, to include any constant 
amounts within the data. 

Seasonal variations are those variations due mainly to 
nature, but also affected by human behavior. 

It is only over a span of several years that a cycle or 
cyclical variation can be discerned. 

Those variations without specific determinable cause and 
without any pattern fall into the random variations 



92 



component. After the fact, however, these fluctuations may 
sometimes be explained. 

By use of the concepts one may develop a multiplicative 
model of a time series: 

Sales=(Trend)x(Seasonal)x(Cyclical)x(Random)=TxSxCxR 

Each of the four components can be isolated from any 
time series by application of related statistical 
procedures. Once the T, S, and C have been identified for 
a specific future time span, it is possible to generate a 
forecast with the multiplicative formula. 

There is an alternative forecasting technique. The 
Least Squares Regression Analysis may be substituted in 
order to forecast the aggregate sales. 

G. INDIVIDUAL ITEM SHORT-TERM FORECASTS 

There are two techniques for forecasting the quarterly 
demand when we are forecasting on an individual item basis 
or in a situation where the time series is unstable: 

- Moving average 

- Exponential smoothing. 
1 . Moving Average 

This technique forecasts for the subsequent period 
by averaging the actual demand for the last n time periods, 
where n is usually between 4 and 7. Thus, any data from 
before n previous time periods is ignored. The usual basis 
for determining the value of n is the expected seasonality 



93 



of the data, such as 4 quarters or 12 months in a year. By- 
making such a choice, one effectively eliminates the impact 
of seasonality in the data. At times n must be chosen 
arbitrarily, in which case it should be based upon the value 
which best describes the historical data when used in the 
model . 

The moving average is computed mathematically as: 
-, t 

t+1 n i=(t _ n+1) 

where : 

t= Period number for the current period 

F ,, = Forecast of demand for the next period 

Di= Actual demand for period i 

n= Number of periods of demand to be included, also 
called the "order" of the moving average. 

As an example, in order to forecast demand for the 

next quarter of this year (i.e., quarter 3 1985 or period 15 

from data of Table 6) using a moving average of order 4 

(that is n=4), we would compute: 



14 
14+1" 



F n/ . ,-,=%£ Di 



i=14-4+l 

or 



14 
-*2 



F-, c =kZ Di 



i=ll 

F 15 =(D 11 +D 12 +D 13 +D 14 )/4 

F 15 = (7, 500+15 ,000+13, 500+17 , 500)/4 



F 15 =13,375 



94 



TABLE 6 
HISTORICAL DATA (MOVING AVERAGE) 



Year 


Q' 


uarter 


Period Number 


# of I terns 


1982 




1 
2 
3 
4 


1 
2 
3 

4 


3,500 

8,000 

5,500 

10,000 


1983 




1 
2 
3 
4 


5 
6 
7 
8 


4,500 
6,000 
3,000 
5,500 


1984 


. 


1 
2 
3 
4 


9 
10 
11 

12 


5,500 

9,500 

7,500 

15,000 


1985 




1 
2 


13 
14 


13,500 
17,500 



95 



Thus, the next quarter's forecast would be 13,375 
items . 

There is a problem when an item is first introduced 

into the inventory system in that there i s ~n o available 

historical data to use. The data is still missing after the 

first three quarters. However, the use of an "initialized 

moving average" can easily overcome this shortcoming. This 

figure is determined by finding the sura of the available 

data and dividing it by the number of quarters from which 

that data is drawn, up until data has been accumulated for 

four quarters, at which time, use of the moving average 

formula is possible. 

2 . Exponential Smoothing of Exponentially Weighted 
Average 



When forecasting, it is usually preferable to make 
use of the most current available data, while also 
incorporating sufficient observations over time in the 
series in order to smooth out as much as possible the random 
fluctuations. The technique of exponential smoothing seems 
perfectly suited for achieving these goals. 

The formula below uses exponential smoothing to generate 
the forecast. If, for example, we consider demand data: 
New demand f orecast=( a )current demand+( 1-a) pre vious 

demand forecast, or: 
F t+1 - aDt+a-a)F 



96 



where a is a smoothing constant which has to be greater than 
or equal to zero and also less than or equal to one. The 
other symbols are illustrated in the following diagram. 



Period t-1 



D 



t-1 



t-1 



Period t 



XT 



F 



Period t+1 



17 



t+1 



time 



t+1 



The act of changing the value of a allows one to 
alter, at any time, the sensitivity of the exponentially 
weighted average. In order to place greater emphasis on the 
recent data, thereby increasing the sensitivity of the 
average, the value of a is increased. The reverse holds 
true for decreasing values of a, less emphasis is placed on 
the recent data. The sensitivity of the moving average is 
only able to be changed by the use of a different number of 
quarters as the basis on which the moving average is 
calculated . 

In the U.S. Navy, the value of a is set at 0.2 
unless they suspect a change in the mean of the distribution 
of the actual demand of the present period. In that 
situation, they set the value of a at 0.4. 

The U.S. Navy has found it practical when beginning 
a forecasting system with the exponentially weighted average 



97 



method, to use, as in the moving average technique, an 
initial estimate using the same moving average approach of 
1,2, 3, and 4 periods. The first forecasting demand value 
of the exponentially weighted model is then Che first full 
four quarter average. 

Change a based on a trend test, compute: 

T = 2(Dt + Dt-1) 



Dt + Dt-1 + Dt-2 + Dt-3 

The U.S. Navy changes the value of a from a=0.2 to 
a=0.4 if: 

T<0.9 and Dt<Ft 
T>1.1 and Dt^Ft 

and returns to a=0.2 when the value of T returns to: 
0.9<T<1.1 

H. FORECAST ERRORS 

When measuring forecast error, there are two common 
systems, the mean absolute deviation or MAD and the bias. 

1 n 1 n 

MAD=- Z Fi-Di| BIAS=- I (Fi-Di) 

n i-1 n i=l 

where : 

Fi= forecast of demand in period i. 

Di= Actual demand in period i. 

n= number of periods of data analyzed. 



98 



The MAD determines the average size of the error by 
summing the absolute values of the errors, adding both 
positive and negative errors to the sum. Thus, the manager 
receives a sense of the general accuracy of the forecasting, 
but is unable to determine if the error is above or below 
the forecast. 

On the other hand, the bias shows the typical trend of 
the forecast to be either too high or too low and by how 
much. By using the MAD, one determines the average size of 
the error while the bias determines the direction of the 
error. The best forecasting techniques are those which 
result in the least error measurements. 

I. FORECASTING LEAD TIME 

The lead time is that span of time beginning with the 
discovery by the inventory manager that the inventory has 
dropped below the re-order point and ending when the ordered 
material is received into the inventory. 

The lead time can usually be divided into two sections. 
The first is the time taken by the inventory manager and 
procurement personnel to prepare the order and negotiate 
with the manufacturer. The second block of time is that 
during which the manufacturer produces and delivers the 
order. The former period of time is generally labelled the 
administrative lead time (ALT), while the latter is called 



99 



the production lead time (PLT). The sum of both time 
periods is the total procurement lead time (L). 

There are two parts to be forecast. They are the L and 
the mean absolution deviation for L (MADL) . 

If we use L(n) to denote the computed forecast of L, the 
following equation can be used to determine its value, 
assuming the exponential weighting model: 

L(n+l)=a L(observed) + (1-a) L(n) 
where : 

L(observed)= the sum of the procurement lead times in days 
for purchases received during the observed period divided 
by the number of purchases received during the observed 
period multiplied by 91. 
The denominator is multiplied by 91 because a quarter 
consists of 91 days. 

For example, assume that two purchases arrived this 
quarter. One of these purchases took 265 days from the time 
it was initiated until the time it was received; the other 

took 310 days. We compute L(observed) as follows: 

T , , ,. 265 + 310 Q -, , 
L(observed) = — j n-T — =3.16 quarters 

The U.S. Navy bases the value of a on what they perceive 
as the validity of L(n), for S.P.C.C.: 

a=0.2 if previous purchase arrived in quarter N-l . 

a=0.5 if previous purchase arrived in quarters N-2 to N-4. 

a=1.0 if previous purchase arrived before N-4. 



100 



Although these values may not be directly applicable to 
the Hellenic Navy, they provide a general idea of the 
probable, preferable range of values for a. 

J. PROBABILITY DISTRIBUTION 

In the U.S. Navy, the fast moving or high demand items 
get normal distribution while the Poisson distribution is 
applied for the slow moving items. Based on experience, 75% 
to 80% of the entire spares requirement is shown to be slow 
moving while fast moving items account for only 15% to 20%. 
It is typical for 80% of the demands to be for the fast 
movers . 

K. NORMAL DISTRIBUTION 

By far the most important of the special probability 
densities used in statistics is the normal probability 
density, which is usually called the normal distribution for 
purposes of simplicity. In the eighteenth century, this 
normal probability was first studied when scientists 
discovered that the errors of measurement had an 
astonishingly high degree of regularity. They found that a 
continuous distribution, referred to as the "normal curve of 
errors" and attributed to the laws of chance, was what their 
observed patterns and distributionsn approximated most 
closely . 



101 



The equation for the normal distribution is called the 

density function and is represented by this formula: 

2 
2^ 1 .-%(^) 



f(x;m,a ) = 



2ttq 



-oo<x<°° 



with the parameters that: 

m= the mean, 

a= the standard deviation. 

The graph generated by the normal distribution is a 
bell-shaped curve that extends in both directions to 
infinity. Rarely will it be necessary for the tails of a 
normal distribution to be extended for any great distance 
because the area under the tails which lies farther away 
from the mean 4 or 5 standard deviations is for all intents 
and purposes negligible. In practice, a standard normal 
table can be used to determine the areas under normal 
curves. This table gives the areas beneath different 
portions of the normal curve for the normal distribution 
where the mean is zero and the standard deviation is one. 

In order to convert this information to that which can 
be associated with a random variable x, normally distributed 
with a general mean of m and the standard deviation a, the 

folio wing equation is used: 

z ^ (x-m) 

a 

In order to find the areas under those normal curves 
where the mean is not and the standard deviation is not 1 , 



102 



the value of any x of interest is converted into z and then 
the standard normal distribution table may be used. This 
table's entries are the areas beneath the standard normal 
distribution curve between a and non-negative values of z. 
For determining the probability of z lying between two 
values, take the difference between the area values for both 
the smaller and larger values of z. 

In the field of inventory management, when we apply this 
principle, we have the mean during the procurement lead time 
represented as: 
m-DxL 

The variances of the demand and the lead time which are 
the standard squared are represented: 

aD 2 =1.57(MADD) 2 
aL 2 =1.5 7(MADL) 2 

The variation of demand during lead time can then be 

represented by : 

2 2 2 2 
a =LxaD +D xaL 

and the standard deviation is then the square root of this 
equation . 

If we are interested in the probability that demand 
during lead time is less than or equal to some value, say x, 

we first compute: 

(x-m) 

a. z using equation z=- - 

b. m using equation m=DxL 

2 2 2 2 

c. a using equation a =LxaD +D xaL 



103 



Then we look up the area associated with z in the table 
of the standard normal. This area is the desired 
probability value. 

L. POISSON DISTRIBUTION 

The Poisson distribution is a discrete distribution 
represented by the following formula: 

f(x,A) = ^-Ip- for x= 0, 1, 2, . . . 

with A equal to the product np and in the inventory field 
X= DL. 

When we use Poisson distribution we need only the mean 
of the mean demand (DL) during lead time. 

To compute f(x) for x=l, 2,3,.. ., we use the 
following steps: 

-DL 



for x=0, f(0)=e 



-DL 



for x=l. f(l)=DL-e =f(0)DL 

2 -DL 
for x=2, f(2) = 1 DL >J = f (DLe- DL )= %(D 

for x=3, f(3)= (DL) e " DL = 5tf (2) 

3! 3 



In general, f(x)= — f(x-l) 

x 



Example : 

Suppose that: D=0.5 units per quarter 

L= 6 quarters 
Then: DL=( . 5 ) ( 6 ) =3 . 



104 





1 

2 
3 
4 
5 



f(x) 

e~ 3 = 0.0498 

3/1(0.0498) = 0.1494 

3/2(0.1494) = 0.2240 

3/3(0.2240) = 0.2240 

3/4(0.2240) = 0.1680 

3/4(0.1680) = 0.1008 



£=0 f « 

0.0498 
"0.1992 
0.4232 
0.6472 
0.8152 
0.9160 



105 



VI. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 

A. SUMMARY - 

In the first chapter we described the difficulties that 
the Hellenic Navy faces in its efforts to supply the 
necessary materials wherever and whenever they are needed. 
We also discussed the procedure and the technique used in 
order to accomplish this. 

We then introduced the concept of inventory techniques 
and the costs that are subject to control by our inventory 
technique, such as, holding cost, stockout cost, ordering 
and procurement cost. 

We have had a glance at the history of inventory models' 
development and the efforts made by the United States Navy 
in order to develop models that fulfill specific demands. 

In the second chapter, we developed the meaning of ABC 
Analysis and the manner in which this analysis can be usad 
so that we can accomplish a more effective control of the 
surplus with less cost. 

In chapter three we discussed provisioning of depot 
stock to provide initial backup supply support to a newly 
inducted equipment or weapon system. In this chapter, we 
began with the definition of provisioning and provisioning 
methods and then we introduced the key dates that are 
considered important for provisioning. This was followed by 



106 



a discussion of demand and how to determine initial demand 
forecasts and then the meaning of demand and non-demand 
items was introduced. A model called the Cost Difference 
Formula was then described, determining the range of items 
to buy. Finally, a model for computing the purchase 
quantity for those items to be bought was presented and 
steps for computing the procurement budget were shown. An 
example which illustrated the steps for developing a 
provisioning budget was also presented. 

In chapter four we formalized the concepts of costs that 
were introduced in chapter one, into mathematical inventory 
control models. We discussed the development of the simple 
Economic Order Quantity Model (EOQ) in which we assumed a 
constant and known rate of demand and a constant lead time 
without stockouts. The formula for total annual cost, the 
optimal order quantity Q and the reorder point were derived 
and their use was illustrated by an example. Here, we 
discussed the meaning of continuous and periodic review 
models and when they are applied. Then we introduced the 
Material Requirement Planning (MRP) technique and an example 

was given. Finally, a comparison betwen EOQ and MRP was 
also given. 

In the fifth chapter, we dealt with forecasting lead 
time demand and probability distribution for this demand. 
Two forecasting models, the Moving Average and the 



107 



Exponentially Weighted Average were presented. The moving 
average is a simple model for estimating the mean value of 
demand based on four observed demands. The exponentially 
weighted average is a model that overcomes the disadvantage 
of storing four times of demand information. It forecasts 
based on one time demands and its forecast. The weight can 
be changed if trends are detected. Another model, based on 
the mean absolute deviation (MAD) of forecasting errors was 
suggested for estimating the standard deviation of demand. 

B. CONCLUSIONS 

Total inventory costs can be reduced through the 
implementation of various models for cost optimization. We 
can establish a conscious policy to increase inventory as 
long as the additional expenditure for inventory leads to 
compensating cost reductions in other areas. For example, a 
high inventory level significantly decreases the risk of 
backorder and stockout costs. 

The cost of storage varies depending upon the type of 
inventory. Raw materials invariably require minimal storage 
facilities compared to finished goods which need rather 
sophisticated facilities and may even require temperature 
and humidity control. In the case of the Naval Stores 
Depot, most of the inventory consists of finished items 
requiring careful handling, and, at times, regulated 
temperatures . 



108 



The fixed quantity model for cost minimization has been 
discussed. Customarily, this type of model is used when 
dealing with the more important inventory items. A 
continuous review must be used for these items. Close 
surveillance is expensive and should only be done for the 
more important items. A periodic review model would be to 
review inventories at fixed intervals and order variable 
quantities. That model does not require the close 
monitoring of inventory levels. Such a periodic review 
model is often used for less expensive items. 

C. RECOMMENDATIONS 

The sophisticated inventory control models must start to 
be used and tested in the Hellenic Navy for the inventory 
control. In order to accomplish the above, the folio wing 
procedure is recommended: 

1. There must be specially trained personnel to control 
the supplies. The training of the personnel must be 
oriented to the requirements needed to perform the job 
in order to comprehend and successfully implement the 
sophisticated inventory control models. 

2. An up-to-date, detailed historic data file of all 
materials in inventory must be kept. 

3. Every inventory control model must be tested, 
improvised and implemented in accordance with the 
realistic and pragmatic needs of the Hellenic Navy. 

As long as the model is tested and is proven to be 

acceptable, then, and only then, can it be approved, become 

official, and go into the applications phase. 



109 



In this thesis the models used are not highly- 
sophisticated but they constitute a starting point from 
which to develop more elaborate ones in the future. They 
are the ones that meet the present needs of the Hellenic 
Navy and can be most realistically applied. 



110 



LIST OF REFERENCES 



1. Killeen, L. M., Techniques of Inventory Management , 
American Management Association, 1969. 

2. Hendrick, T.E. and Moore, F.G., Production/Operations 
Management , Richard D. Irwin, Inc., 1985. 

3. Bardi, E.J. and Coyle, The Management of Budiness 
Logistics , West Publishing Co., 1984. 

4. NAV SUP PUB 553, Inventory Management , Department of 
the Na vy . 

5. Noidder, E., Inventory Management , John Wiley and Sons, 
Inc., 1966. 

6. Hardley, G. and Whitin, M., Analysis of Inventory 
Systems , Prentice Hall, 1963. 

7. Lewis, CD., Demand Analysis and Inventory Control , 
Saxon House, 1975. 

8. Blanchard, Benjamin S., Logistics Engineering and 
Management , Richard D. Irwin, Inc., 1985. 

9. Plossl, C.W. and Wight, O.W., Production and Inventory 
Control, Principles and Techniques , Prentice Hall, 
1967. 

10. Turban, Efraim and Meredith, Jack R., Fundamentals of 
Management Science , Business Publications, 1985. 

11. Miller, Irwin and Freund, John E . , Probability and 
Statistics for Engineers , Prentice Hall, 1985. 



Ill 



INITIAL DISTRIBUTION LIST 



1 . Defense Technical Information Center 
Cameron Station 

Alexandria, Virginia 22304-6145 

2. Library, Code 0142 
Naval Postgraduate School 
Monterey, California 93943-5002 

3. Department Chairman, Code 54 
Department of Administrative Sciences 
Naval Postgraduate School 
Monterey, California 93943-5004 

4. Professor John W. Creighton, Codr 54Cf 
Department of Administrative Sciences 
Naval Postgraduate School 

Monterey, California 93943-5004 

5. Professor Roger D. Evered, Code 54Ev 
Department of Administrative Sciences 
Naval Postgraduate School 
Monterey, California 93943-5004 

6. Hellenic Navy Staff 
Stratopedon Papagou 
Athens. Greece 

7. SARRIS, Demos 
Herakliou 35 and Helpidos 
Gala tsi 

Athens, Greece 



No. Copies 
2 



112 



215578 




Sarris 

Basic techniques of 
inventory management 
with possible applica- 
tions to improve the 
existing inventory- 
control of the Helle- 
nic Navy. 



3 W* no 



no: 09 



Thesis 
S1673 
c. I 



215576 

Sarris 

Basic techniques of 
inventory management 
with possible applica- 
tions to Improve the 
existing inventory 
control of the Helle- 
nic Navy. 




Basic techniques of inventory management 




3 2768 000 68789 1 

DUDLEY KNOX LIBRARY