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

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THESIS

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

Demos D. Sarris

December 1985

Thesis Advisor;
Co-Advisor :

John W. Creighton
Roger D. Evered

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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

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iarris , Demos" D.

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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.

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

of the Hellenic Navy

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.

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

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

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

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).

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

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

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]

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]

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

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

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

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

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]

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

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.

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 .

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

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Figure 1 .
Pareto's Law of Maldistribution

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

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]

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

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

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

TABLE 1
ABC ANALYSIS

(1)

Number of
Items

(2)
Item
Code

(3)

Number of

Items per

Year

(4)
Unit Cost

(5)
Usage
Value

4710-00-
2776101

-11-2778703

0.25

-11-2785411

-11-5422909

0.05

-11-5422918

0.1

4720-00-
2889751

0.5

2.5

4730-NT-
AA21753

4730-NT-
AA45761

1200

4730-00-
1720045

4730-00-
1874191

600

.50

300

4730-00-
1892624

0.5

4730-00-
1892628

1000

-11-1899735

120

-11- 1892552

260

0.5

130

-11- 1892583

200

TABLE 2
ABC ANALYSIS

(1)

Number

Items

(2)
Item
Code

(3)

Number

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 %

4710-00-
2776101

1200

6.7

1200

38.5

-11-2778703

1000

2200

-11-2785411

600

300

2500

-11-5422909

200

2700

-11-5422918

260

130

2830

4720-00-
2889751

120

2950

4730-NT-
AA21753

3013

4730- NT-
AA45761

3049

4730-00-
1720045

3077

4730-00-
1874191

3093

99.4

4730-00-
1892624

3101

99.7

4730-00-
1892628

.25

3104

99.8

-11- 1899735

2.5

3106.5

99.9

-11- 1892552

3108.5

99.95

-11- 1892583

.05

1.5

1000

3110

100

c
u

L
A

I
V
E

P
E
R
C

E
N
T

U
S
A
G
E

V
A
L
U
E

100

Items C

100

CUMULATIVE PERCENT OF ITEMS

Figure 3
ABC Analysis - The SO -20 Rule

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

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

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.

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

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

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

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

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

(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

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

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.

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.

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

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.

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

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

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:

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

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

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).

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.

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

Cumulative Program Buildup

Year, 1986

Months

Mo. #

Ik 1/

Dm 2/

1.5

11.5

Year, 1987

Months

Mo. # 11

Ik 1/ 6

Dm 2/ 28

34.5

41.5

48.5

7 25

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

The initial TWAMP for PTB=12 will be:

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

TWAMPi =

PTB TT

157

= 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

(-)

0.35

150

(-)

0.15

(-)

0.05

( + )

0.10

The L value is 5.4 quarters for all items

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-

The Provisioning Budget will be

For item 1
item 2
item 3

22xl50=$3300

31x 10=$ 310

lx 30=$ 30

Total budget

$3,640

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,

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.

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

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 .

A
N
N
U
A
L

S
T

12000

8000 _

6000 _

4000

2000 _

120

160

200

N
N
U
A
L

8000

6000

4000

2000

SIZE OF ORDER QUALITY

Figure 5. Carrying Cost

120

200

SIZE OF ORDER QUALITY

Figure 6. Order or SetuD Cost

Total Costs

N
N
U
A
L

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

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).

Level of Inventory

< — * — ►]

ventory

1/2 Q

TIME

Figure 8. Sawtooth Model

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:

8AA

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. •*

TABLE 3
TOTAL COSTS FOR VARIOUS EOQ AMOUNTS

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

6000

260

2770

3250

6020

300

2400

3750

6150

340

2120

4250

6370

400

1800

5000

6800

500

1440

6250

7690

N
N
U
A
L

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

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

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

Inventory
Level

Recorder
Point

Q \ :

A \

Safety \
Stock

TIME

Figure 10 .
Inventory Model Under Conditions of Uncertainty

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:

'-%,

E. MATERIAL REQUIREMENTSS PLANNING (MRP)

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

H
A
N
D

Requisitioning
Objective (RO)

Review

T'me

Demand

Procure-
ment
Lead
Time

Demand

Safety-
Level

t
A

Figure 11

A Periodic Inventory

Svstem

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

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

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

Level C

B(l

10(3)

C(l)

Level 1

20(1)

D(2)

60(1)

30(2)

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

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

A(l)
LT = 4

Level

B(l)
LT = 3

C (2)
LT= 2

D(l)

LT = 1

E(2)
LT=1

Level 1

Level 2

Figure 13. Typical Product Structure

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

Gross
require-
ments

100

Planned

order

releases

100

Gross
require-
ments

100

Planned

order

releases

100

Gross
require-
ments

200

Planned

order

releases

200

Gross
require-
ments

200

Planned

order

releases

200

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

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

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

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 :

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.

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.

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

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

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

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

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

TABLE 6
HISTORICAL DATA (MOVING AVERAGE)

Year

uarter

Period Number

# of I terns

1982

1
2
3
4

1
2
3

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

5,500

9,500

7,500

15,000

1985

1
2

13
14

13,500
17,500

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

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

t-1

Period t

Period t+1

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

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.

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

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)

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)

Example :

Suppose that: D=0.5 units per quarter

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

104

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

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Department of Administrative Sciences
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Department of Administrative Sciences
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Basic techniques of
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control of the Helle-
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Basic techniques of
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with possible applica-
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existing inventory
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Basic techniques of inventory management

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