AD-AIOS 074 AIR FORCE INST OF TECH WRIGHT-PATTERSON AFS ON SCHOOL--ETc FIG 15/5MULTIPLE MODEL FORECASTING AS AN ALTERNATIVE TO THE STANDARD BA--ETC(U)JUN 81 V A ABRUZZES(. 6 J BOROWSKY

UNCLASSIFIED AFIT-LS!R-23-81 NL

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lommml mm mm mm mMENEi hhhhhhhhl11hhhhhhh

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121

ELECT[-CUNITED STATES AIR FORCE ELC- r 6 98

AIR UNIVERSITY

AIR FORCE INSTITUTE OF TECHNOLOGY AWright-Patteron Air Force Ses*,Ohi.

810 6 192

MULTIPLE LIODEL JORECASTING AS ANI.- ALTERNATIVE TO THEA TANDAIRD

BASE SUPPLY J§YSTEM (DO02A)FOR&CASTIN TECHNIQUE,*-

Vincent A. /Abruzzese, Captain, USAFGeorge 3.A/orowsky, Captain, USAF

- ISSR-Z3-81; 7-

) -czeon aproved/

t.,7, i xe po e

The contents of the document are technically accur~ate, andno sensitive items, detrimental ideas, or deleteriousinformation are contained therein. Furthermore, the viewsexpressed in the document axe those of the author(s) and donot necessarily reflect the views of the School of Systemsand Logistics, the Air University, the Air Training Command,the United States Air Force, or the Department of Defense.

AFIT Control Number LSSR 23-81f

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MULTIPLE MODEL FORECASTING AS ANALTERNATIVE TO THE STANDARD BASE SUPPLY Master' a ThesisSYSTEM. (DOO2A) FORECASTING3 TECINIQUE 6. PERFORMING OIG. REPORT NUMBER

7. AUTNORt'.) 8. CONTRACT OR GRANTr NUMBER(&)

Vincent A, Abruzzese, Captain, USAFGeorge 1. Borowakyo Captain. USAF

9. PERFORMING ORGANIZATION NAME AND ADDRESS AO ROGRAM ELEMENT RJC.TS

School of Systems and Logistics .C sWR NT"M1"

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Forecasting: SBSS Forecasting; Multiple Model ForecastingiRetail Forecastingi Forecasting Methods

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Thesis Chairman. John Re Folkesong Jr.. Majors. USAF

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--The purpose of this thesis was to test multiple model forecastingas an alternative to the Standard Base Supply System (DOO2A)forecasting technique. Actual data were used from Dover AFB,Delaware. The methods used in the multiple model technique weresingle exponential smoothing, double-exponential smoothing, adap-tive exponential smoothing, four-tem moving average and eight-term moving average. Results of each technique were compared interms of mean absolute deviation, bias, and mean absolute per-centage error. The results indicated that the multiple modelforecasting technique vas not optimal when used with the StandardBase Supply System. Recommendations were made based on theanalysis.

UNCLASSIFIESCURITY CLAIPICAO15 OF ' AGIECIMO 0.w. go.

LSSR 23-81

MULTIPLE MODEL FORECASTING AS AN ALTERNATIVE

TO THE STANDARD BASE SUPPLY SYSTEM (DO02A)

FORECASTING TECHNIQUE

A Thesis

Presented to the Faculty of the School of Systems and Logistics

of the Air Force Institute of Technology

Air University

In Partial Fulfillment of the Requirements for the

Degree of Master of Science in Logistics Management

By

Vincent A. Abruzzese, BS George J. Borowsky, BSCaptain, USAF Captain, USAF

June 1981

Approved for public releasesdistribution unlimited

. ...... ..

7

This thesis, written by

Captain Vincent A. Abruzzese

and

Captain George J. Borowsky

has been accepted by the undersigned on behalf of thefaculty of the School of Systems and Logistics in partialfulfillment of the requirements for the degree of

MASTER OF SCIENCE IN LOGISTICS MANAGEMENTDATEs 17 June 1981

iiH

K -. - --=': I I

ACKNOWLEDGMENTS

We would like to thank the Air Force Logistics

Management Center for sponsorship of this thesis. In par-

ticular, Majors Richard Lombardi and Kenneth Faulhaber for

their assistance in providing the data used in this

research.

We would like to extend a special thanks to First

Lieutenants Beverly Dale and Carl Lizza, AFIT/ACD, for

providing their technical assistance in overcoming computer

problems encountered during critical phases of this

research.

Special recognition and appreciation is due to

Major John Folkeson, our thesis advisor, whose guidance,

suggestions, and assistance materially aided in the comple-

tion of this thesis.

Lastly, Captain George Borowsky offers his love and

gratitude to Joan, his wife and friend, for her unceasing

patience, understanding and support throughout the school

year,

iii

TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS . . . .. .. .. .. . . .. . . . i

LIST OF TABLES . . . o . .. . o o o . o . o o . . vii

Chapter

1. INTRODUCTION . . . . . . . . . . . . . . .

Standard Base Supply System . .. . .. 1

Inventory. . . . . . . . . . . . . . . 2

Inventory Control. . . . . . . . . . . 3Forecasting. ............... 0 4

Standard Base Supply Forecasting System. 5

Problem Statement..... .. .... 10

Research Objectives. . . . , . , . * * 10

Research Justification .. . . . . . . . 11

Scope, . . . .o o * o s . . .o o a I * s1

2. LITERATURE REVIEW ............. 12

Background # . o. . ... w.... 12

Multiple Model Forecasting Method. . . . 12

Focus Forecasting . . . . . . o .& . . 13

Garland and Mitchell . . .. .. .. .. 14

Christensen and Schroeder. o * o a . * 15

Brantley and Loreman . .... o w . . 16

Fischer and Gibson. . . . , .. . .. 16

Patterson. .9. . . e o • . . * . o s * . 17

iv

F- .. .. . . . . . . . . .

Chapter Page

Conclusion ...... ......... 18

Research Questions ............ 18

Hypothesis. .... . ...... .... 18

3. METHODOLOGY ....... . ........ 19

Introduction . . . . . . . . . . . . . . 19

Model Selection ...... ...... 19

Moving Average, . . . . . . . . . .. .. 20

Single Exponential Smoothing. .e. . . . . 21

Double Exponential Smoothing, .e. . . . . 22

Adaptive Exponential Smoothing, .e. . . . 23

Multiple Model Forecasting . ...... 24

Accuracy of Forecasting Models. . .6. . . 25

Mean Absolute Percentage Error. .. . . . 26

Mean Absolute Deviation . . . . . . . . . 27

Conclusion*u i ............. 28

4. DATA COLLECTION AND ANALYSIS. . . . . .. 29

Introduction ............... 29

Data Collection ... . . . . . , 0 . . 29

Summary . a . .9. . . . . . . . . . s. . 32

Computer Output .... , o ... . , . 0. 32

Data Base Comparison. . . .. . . . . . 33

Data Analysis ....... . . .... 35

Conclusion . . .... . . . . . . . . . 37

5* CONCLUSIONS AND RECOMMENDATIONS o . o . . . 38

Introduction. .0. . . .0 . . . . . . . . . 38

v

Chapter Page

Conclusions, 38

Recommendations....... 41

APPENDICES . e * a a v a * 43

A. DATA RETRIEVAL PROGRAM. 5s e.. 44

B. SELECTION PROGRAM FOR RANKING BY DEMANDAND FREQUENCY . . . . . . . . . . . . . . . 46

C. PROGRAM FOR DATA ANALYSIS. ....... . . 49

D.* PROGRAM TO COMPUTE FORECASTS AND PERFORMCOMPARATIVE ANALY SI.. .. .. . . .. 52

E. COMPUTED FORECASTS AND ANALYSIS. a . . . . . 61

SELECTED BIBLIOPHP.. . ... .. . .. . . .. 86

A. REFERENCES CITED # * a @ & * * o * e # a @ a 87

B.* RELATED SOURCES. . . . . . . . . . . . . 89

viI

LIST OF TABLE.

Table Page

1. Profile of Preliminary Data. o . . . . . . . . 30

2. Profile of Stock Classes Selected forAnalysis . * . o , . * * @ e @ & 9 a * * @ 31

3. 957 Confidence Interval for Data BaseComparison . . . . . . . . . 0 0 0 0 a 35

4. Results of Computer Analysis . . . . . . . . . 36

5. Inventory Characteristics ..... . . . . . . 41

vii

Chapter 1

INTRODUCTION

Standard Base Supply System

The Standard Base Supply System (SBSS) is an auto-

mated inventory accounting and control system designed to

provide timely support to base level activities. The system

uses the UNIVAC 1050-I computer for storage and maintenance

of records and for the generation of management reports.

The system as a whole consists of both manual components and

interfacing computer programs. The system consists of four

major functional processes--item accounting, accounting and

finance, file maintenance, and management reporting (24,1-2).

When using the UNIVAC 1050-I on-line computer system, all

records affected by a given transaction are updated at the

time of transaction input. The system provides remote

devices in work centers on base to insure timely communica-

tions between man and machine (24,1-5).

The SBSS was designed to help speed the flow of

materials from many sources to the base user organizations.

The SBSS inventory is stocked by material from Air Force

depots, the General Services Administration (GSA), Defense

Supply Agency (DSA) and through local procurement (191).

The SBSS is driven by user demand actions.

I

L

The SBSS automatically provides outputs to other

management systems. Those outputs, such as requisitions,

go to wholesale suppliers such as Air Force Logistics Com-

mand (AFLC) and the Defense Logistics Agency (DLA). The

SBSS imposes, Air Force wide, standard organization, pro-

grams and procedures. The organization is designed for ease

of customer support and efficiency of internal operation

(23#1-6). The entire SBSS is an extension of the basic

supply requirements to order, receive, store, and issue

property.

Inventory

Inventories are used throughout the world in many

organizations, both civilian and military. Inventories can

be classified in many ways. The following classification

is one convenient ways

I. Production inventorieso raw materials, partsand components which enter the organization's product orservice in the production/transformation processes.These may be either special items manufactured to userspecifications or standard items purchased "off theshelf."

2. MRO inventorieso maintenance, repair and oper-ating supplies consumed in the production/transformationprocesses but which do not become part of the product orservice.

3. In-process Inventories a semifinished productsfound at various stages in the production operation.

4. Finished-goods inventories a oipleted productsready for shipment and/or use 14a l89J.

Regardless of their classification, inventories

serve the primary purpose of decoupling successive stages

in the production-distribution-consumption chain (13a 1).

2

L- -

Inventories allow production decisions and/or supplier

demand decisions to be made independent of supplier procure-

ment decisions where demand is independent or near independ-

ent,

Inventory Control

Inventory control is a vital element in the manage-

ment of system resources. Development of analytical tech-

niques and computer capability have combined to transform

inventory control into a critical function requiring profes-

sional managerial skills (l4sl87).

The significance of the Inventory control function

is clearly demonstrated by the level of resources involved.

Studies have shown that a commercial firm's inventory com-

monly constitutes anywhere from 15 to 25 percent of its total

invested capital (141l87), In its everyday operations, in-

ventory control is often a computerized operation within a

carefully defined and controlled structural framework

(14s225). Sound management in the area of inventory control

is vital. Management must try to balance the various risks

of low inventory with its associated risk of stock out,

production halts, back orders; and high inventory with its

risk of high carrying cost and increased risk of obsoles-

cence (23142). To achieve this management objective a

forecast of future demand must be made. This forecast Is

based on uncertain economic ,yla customer demands and

3

advances in technology. In light of this uncertain environ-

ment, inventory control must answer how much to order and

when to order it (1312).

Generally speaking, three basic systems have been

employed in controlling inventories . (1) the cyclical order-

ing system, (2) fixed order quantity system, and (3) mate-

rial requirements planning system (141l94). The first sys-

tem is a time-based system involving scheduled periodic

reviews of the stock level of all inventory items. The sec-

ond type-- the fixed order quantity system--is based on the

order quantity factor rather than on a time factor. The

material requirements planning system concept provides a

way of looking at the management of production inventories

in a dependent demand environment (141l94). Regardless of

the system used, management must have an accurate assessment

of what will happen in the future in order to make its deci-

sions (13s2).

Forecas ting

In almost any activity, having perfect knowledge of

the future would be an immense help. Rather than the cer-

tainty of perfect knowledge, the Inventory manager finds

himself in an uncertain environment. He can do little to

change that environment so he seeks management techniques

which will aid in reducing the levels of uncertainty. All

forecasting techniques have in common the basic goal of

4

reducing the uncertainty in one's expectation of the future

(4,1). As Robert L. Sims says, "It should be obvious that

to forecast is to be wrong. Only in the most fortuitous

cases, and these seldom occur, can a forecaster guess the

future exactly C21a1]." Today, the economics of spiraling

prices and austere budgets make reliable estimates, or fore-

casts, especially critical (3,22). Forecasting for and

acquiring spare parts is an important facet of the material

support system. Forecasts are used to develop dependable

systems and to formulate decisions concerning the techno-

logical and economic feasibility of retaining a system in

use (11.15). The exponential acceleration of spares cost

provides a compelling reason for basing requirements compu-

tation upon the best available forecasting methodology

(3,22).

Standard Base SuDDily Forecasting System

The Air Force Logistics Command (AFLC), throughout

its Air Logistics Centers (ALCs) or depots, buys and dis-

tributes centrally procured items of supply used on mis-

siles, aircraft, and other equipment. Each depot buys and

stocks items in specific federal supply classes (FSCs) and

serves as the primary source of supply for Air Force bases

and other activities (24.11-1).

The SBSS is driven by user demand actions. When a

base needs an item a requisition is submitted to SBSS. If

the item needed is not currently in stock, a request for

5

that item is placed on order. The request may be filled

through the normal operating cycle. In some instances, spe-

cial orders may be needed. Orders for resupply of the SBSS

are logged as due-ins and are maintained until the material

is received (19,1).

Repair parts and supplies with expendability,

repairability, recoverability category (ERRC) designator

XB3 will be stocked, using a variable economic order quan-

tity (EOQ) stockage concept. An XB3 item is an expendable

item, i.e. an item consumed in use or incorporated into

another assembly. The EOQ model is applicable when the

quantity of items ordered arrives in the inventory at one

point in time and when the demand for the item has a con-

stant, or nearly constant, ratel and the cost of the item

is relatively low (2s497). The SBSS requirements determina-

tion may be divided into the range model and a depth model.

The range model refers to the procedure used to determine

if an item is to be stocked at the base level. The depth

model is used if the item is to be stocked to determine how

much to order and when to order it. The depth model is based

on the classic EOQ formulas

EOQ - 2DA/IP(1.1)

where, D - annual demand rateA - cost per order (currently used figure, $4.54)I - annual inventory carrying rate (currently used

figure, 26 percent)P - item unit price (19s2)

6

-I , - - . . . ----------'---|--.------

This formula balances the cost of ordering with the cost of

holding inventory. The derived order quantity will minimize

these total variable costs (19j2).

The Air Force application of the EOQ concept pro-

duces a variable requisition objective by determining the

EOQ in consideration of the number of demands, daily demand

rates, and a stockage priority code. The purpose of the

variable EOQ stockage concept is to prevent the premature

stockage of items based on erratic or indefinite demand pat-

terns (24,11-2). The basic EOQ model has been enhanced to

better meet the variable stockage objectives (VSO) of the

SBSS:

EOQvso = / 2.DDR.VSO.A/(I.P) (1.2)

where, A = cost per order ($4.54)I = annual inventory carrying rate (26 percent)P = item unit price

DDR = daily demand rateVSO = number of days in the EOQ computation (193)

Another important concept incorporated into the

SBSS is that base supply levels are managed on a reorder

point basis. That is, each time the stock position of an

item reaches or falls below the established reorder level,

some type of supply action must be taken to bring stocks

up to quantities authorized (24,11-2). The reorder point

is a combination of the order and shipping time quantity

(OSTQ) and the safety level quantity (SLQ). The OSTQ is

7

that quantity required by a base to permit uninterrupted

replacement from the external supply source. The OSTQ is

given bys

OSTQ = DDR.OST (1.3)

where, DDR = daily demand rateOST = average order and shiptime in days based on

the item source and priority (19135

The safety level quantity is a variable quantity, in units,

computed to provide protection from stockouts during the

reordering process. The SLQ is given by,

SLQ = C r/3.0STQ (1.4)

where, C = the safety factor (typically set to 1, whichimplies an 84 percent service effectiveness,given the assumption of normally distributeddemands)

3 = lead time demand variance/mean ratioOSTQ = order and shiptime quantity (193)

The reorder point (RP) is given by,

RP = OSTQ + SLQ (193) (1.5)

The maximum desired inventory position is called the requi-

sition objective (RO),

RO= INT (EOQvso + CSTQ + SLQ + 0.999) (1.6)

where, INT = integer result of the following computationEOQvso = enhanced EOQ model

OSTQ = order and shiptime quantitySLQ - safety level quantity

0.999 - factor added to the EOQ level to adjust tothe next highest unit (19,4)

8

It can be seen that each of the three variables in the

requisition objective computation are a function of the

daily demand rate. The daily demand rate is the forecast

measurement for the SBSS. If inaccurate estimates for DDR

are made, errors may result (193).

When an item is ordered the daily demand rate is

revised. The SBSS maintains status on the cumulative recur-

ring demand (CRD) and the date of first demand (DOFD). Each

time an item is ordered, the number of units ordered is

added to the CRD. The revised DDR is then

DDR = CRD/max (180, Current Date - DOFD) (1.7)

The minimum of 180 days usage is assumed so as not to over-

stock items that have been recently added to the stockage

list (193). The number of demands for each ERRC code XB3

item will be recorded in six-month increments up to a total

of three increments or 18 monthsl i.e., the current and two

past six-month increments. When 18 months' demands have

been accumulated, the oldest six-month increment will be

dropped and a new six months' accumulation will begin, The

criteria for establishing demand levels for EOQ items (ERRC

code XB3) will vary dependent upon the stockage priority

code, but will not be less than three demands per year

(24&11-3).

9

L I

Problem Statement

The literature search has shown that a significant

error variance exists in the forecasting method employed In

the Standard Base Supply System when compared to the actual

demand experienced. The current forecasting system used by

the SBSS is a combination of exponential smoothing and mov-

Ing averages. The literature suggests that this technique

may not provide the best estimate of future demand.

A critical measurement used in SBSS is forecasted

demand. A forecasting approach which reduces forecast error

has potential impact beyond its effect upon economic order

quantity (EOQ) determination. Accurate demand data in the

context of the SBSS affect average Inventory levels and

holding costs, and improve order and shipping time (lead-

time), thereby impacting safety stock levels and premium

transportation requirements for priority back orders.

This thesis explores whether a multiple model fore-

casting technique can improve demand forecasts.

Research Ob jectives

The objectives of this thesis area

1. Evaluate the multiple model forecasting tech-

nique as an alternative to the Standard Base Supply System

forecasting technique.

2. Determine which forecasting approach will pro-

vide the most accurate estimate of future usage.

10

3. Determine the effectiveness of implementing the

proposed system.

4. Recommend actions based upon the results

obtained.

Research Justification

This thesis applies the research of Mitchell and

Garland at the wholesale level of demand to retail level

forecasting. Those authors used simulated and limited actual

data to conclude that the multiple model forecasting tech-

niques actually forecasted more accurately than the single

method currently used in the Air Force's wholesale level

D062 system (!3:42). This thesis had the sponsorship of the

Air Force Logistics Management Center (AFMIC), Gunter Air

Force Station, in a continued effort to improve present

inventory control methods.

Scone

This thesis will utilize a research data base main-

tained by AFLU!C and containing two and a half years of data

from Dover Air Force Base, Delaware. The data base contains

approximately 15,000 line items (National Stock Numbers).

The data were tested using several different forecasting

techniques. The results were compared to results obtained

by previous research on the SBSS.

112

Chapter 2

LITERATURE REVIEW

B ackground

Major Richard Lombardi of the Stocking Policies

Division, Air Force Logistics Management Center, summarized

the current dilemma of logisticians faced with forecasting

requirements to meet mission demandsa

The Standard Base Supply System (SBSS) demand fore-casting is an unorthodox prediction scheme which maylead to suboptimal forecasting. This is attributed tothe manner in which the daily demand rate (DDR) is up-dated by six month adJ ustments in the SBSS cumulatedrecurring lemand ,CRD and the date of first demand(DOFD) fields. The net effect of those adjustments isto convert the forecasting to a form of exponentialsmoothing in which the value of the smoothing constantwill vary depending upon date of demands. This varia-tion may, depending upon when demands are experienced,provide more weight to past demands at the expense ofcurrent demands, thus dampening the influence of cur-rent requirements [15].

Multiple Model Forecasting Method

In order to choose an effective forecasting system,

the forecaster must decide upon a model which is most appro-

priate given the conditions that exist at the time of the

forecast. A variety of forecasting models are available

from which the forecaster can choose. The selection of a

forecasting method depends on many factors. the context of

the forecast, i.e., the nature of the decision environment

12

L_.w . L.

at the time of the forecast, the relevance and availability

of historical data, the desired accuracy of the forecast,

and the time period to be covered (i3ali). Due to these

factors, certain types of forecasting techniques are better

suited to a particular demand pattern than others. Since

In practice we are seldom faced with a pure "classical"

demand pattern, the forecaster should consider several

methods for forecasting a single demand pattern before

selecting the model best suited to the actual demand pat-

tern,

The multiple model forecasting method used in this

thesis research incorporates forecasting techniques recom-

mended by a variety of experts. These techniques are moving

average, single exponential smoothing, double exponential

smoothing, and adaptive exponential smnoothing. The computer

was programmed with these simple forecasting strategies.

Through the process of simulation, the computer will select

the one best strateg) to forecast an item at a given moment

in time. Whichever strategy best projected the most recent

completed period is the one the computer uses to project

the future (2203).

Focus Forecastingz

A new approach to inventory control using the con-

cept of declining computer costs per computation Is advo-

cated by Bernard T. Smith in his book, Focus Forecastings

13

Computer Techniques for Inventory Control (22). Focus fore-

casting as implemented by Smith used a series of simple

forecasting approaches. It uses the powerful computation

simulation ability of the computer to pick the one forecast-

Ing strategy that will work best f or the one Item for the

next period (22sxii). Focus forecasting goes through all

the computations every time it forecasts a demand.

Several parallel research efforts have been accom-

plished using various forecasting techniques at the wholesale

level on the AFLC D062 inventory control system for expend-

able items and the AFLC D041 reparable asset management sys-

tem. A summary of these theses follows.

Garland and Mitchell

The purpose of their study was to determine if a

multiple model forecasting technique could forecast demand

more accurately than the model currently used in the Air

Force Logistics Command D062 system for expendable items.

Simulated and actual data were used to check the results.

The methods utilized In the multiple model technique were

an eight-quarter moving average, a four-quarter moving aver-

age, exponential smoothing, adaptive smoothing, a least

squares fit and a ratio of change between years method.

Results were compared in terms of mean absolute deviation

adjusted to show percentage change in accuracy compared to

the D062. The statistical test used for comparison was the

14

t-test for matched pairs. This test indicated approximately

a 17 percent improvement in accuracy using either simulated

or real historical data.

Christensen and Schroeder

This research effort compared the D041 Single Moving

Average forecasting method used to forecast reparable gen-

erations of recoverable items with the Box and Jenkins' time

series analysis forecasting methods. Five artificially gen-

erated stochastic processes were used to model the possible

reparable generations observed in practice: (1) a Poisson

process with a constant mean, (2) a Poisson process with a

decreasing mean, (3) a Poisson process with an alternating

linear mean, and (4) a process whose values are the sine

function of the output of a Poisson process. The research

concluded that the D041 forecasting method made unbiased

forecasts for the Poisson process with a constant mean and

the sine function, but made biased forecasts for the other

three processes. Time series analysis forecasting methods

were only used to make forecasts for the processes that

were found to be biased using the D041 forecasting method.

Time series analysis forecasting methods made unbiased fore-

casts for the processes whose means were linearly increasing,

linearly decreasing, and alternating linearly.

Brantley and Loreman

This research effort examined the forecasting tech-

nique used in the Air Force Logistics Command D041 reparable

asset management system. It was hypothesized that the mean

of the absolute values of the D041 forecast error in prac-

tice was equal to zero. This hypothesis could not be

rejected. It was further hypothesized that another time

series forecasting technique (exponential smoothing) would

also yield an error distribution with a mean of zero. This

hypothesis could not be rejected either; moreover, the vari-

ances for the exponential smoothing forecast error distribu-

tions were less than the D041 forecast error distributions

for all four lead times examined (one, tvo, three and four

quarters).

Fischer and Gibson

This thesis effort examined the application of

exponential smoothing to forecast demand for economic order

quantity items.* The research team stated that management of

EOQ items required the use of a demand forecasting technique

to estimate future demand for the purpose of establishing

stock levels. The study compared the effectiveness of four

forecasting models that could be used at base level. The

moving averages method and single, double and triple expo-

nential smoothing were evaluated using 22 months of demand

history for a random sample of 34 EOQ items stocked at a

16

base consolidated supply activity. Four statistical error

measures were used to compare the accuracy of the forecasts

generated by the models for the items. The study concludes

that the methods were not significantly different In fore-

casting EOQ items in terms of accuracy, stability and bias.

The study team recommended a reporting system be considered

,--at would permit the study of the application simultaneously

of various forecasting techniques to the management of an

item and the factors affecting item demand patterns.

Patters on

The purpose of this research was to look into alter-

nate approaches to forecasting demand for expendable Items

in the SBSS. The forecasting models studied were single,

double and adaptive exponential smoothing. Sample Items

were selected from the actual demand records from Dover AFB.

An analysis of the various models was performed by means of

a computer program written for each model. The forecasting

models were compared on the basis of forecast error as meas-

ured by the mean absolute deviation (MAD). The forecast

error for the model currently used by the SBSS was also

measured. The research study concluded that the single

exponential smoothing method, using small smoothing con-

stants, produced the lowest error rate.

17

Conclusion

The literature search has revealed that the current

forecasting system used by the SBSS may not provide the

best estimate of future demand. Additionally, the literature

search has shown the SBSS forecasting method exhibits a sig-

nificant error variance when compared to actual demand.

These facts lead to several research questions which this

research effort will explore.

Research Questions

1. Is there a significant error variance in the

multiple model forecasting technique when compared to pre-

vious research?

2. Which of the forecasting techniques selected

for this study exhibits the smallest error variance, i.e.,

which technique most accurately forecasts demand?t

Hypothesis

The multiple model forecasting technique performs

as well as, or better than, single model techniques to which

It is compared.

18

Chapter 3

METHODOLOGY

Introduction

The methodology used in this research effort

requires data to be gathered and then analyzed using multi-

ple model forecasting techniques. The results obtained from

the multiple model forecasting technique will be compared

to the results of techniques used in previous research.

Using this procedure recommendations on the performance of

the multiple model forecasting technique can be made.

Model Selection

The current Standard Base Supply System (SBsS) is a

mixture of moving averages and exponential smoothing. Itf

is a moving average since the Daily Demand Rate (DDR) is a

quotient of cumulative demands over time divided by the

length of time for which these demands are accumulated (see

equation 1.7). It includes exponential smoothing by the

way updates to Cumulative Recurring Demand (CR1)) and Date

of First Demand (DOFD) are performed (IM:). It is not

apparent# however, that the current SBSS approach provides

the best estimate of future demand. An approach to fore-

casting which reduces forecast error should provide a more

accurate estimate of future demand. The techniques

19

T

considered in this thesis are moving average, single expo-

nential smoothing, double exponential smoothing, adaptive

exponential smoothing, and multiple model forecasting.

Moving Average

When demand for an item does not have a rapid growth

or seasonal characteristics, a moving average can be useful

for forecasting. The moving average model would be expected

to perform well in normal constant demand situations. This

method assumes that the data generating process constitutes

a time seriess

Ft + D e (3.1)

where, Ft W forecasted demand for period t

5 = average demand over timee = random error variable with a mean of zero

as constant variance over time (20s108)

The moving average technique may be described ass

FI M Dt + DtI -2 + "'' + D-nl (3.2)

N

t-l*l

i-t

where, F .t1 - forecast for the next period, t+1t-n+1E Di actual demand at time t, t-l, t-2 ... t-nl

i'tN - the number of observations used in the

coverage

20

li -

The effect of moving average forecasting depends on

the number of observations used in the coverage (N). If N

is large, the equal weighting given to each period is small,

and random fluctuations have little effect on the forecast.

If N is small, the model is more sensitive to changes in

demand (12,17).

Single Exponential Smoothing

In using exponential smoothing, three pieces of data

are neededa the most recent forecast, the actual demand

that occurred for that forecasted period, and a smoothing

constant (W). The equation for a single exponential smooth-

ing forecast iso

F -t+ Ft + Of(D t - Ft) (3.3)

where, F ,,1 - the exponentially smoothed forecast forperiod t+l

Ft - the exponentially smoothed forecast for theprior period t

Dt - the actual demand in the prior period tCa - the desired response rate, or smoothing

constant (13s58)

This equation states that the new forecast is equal to the

old forecast plus an adjustment proportional to the differ-

ence between the previous forecast and the actual experience.

The closer C is to 1, the more the new forecast will incor-

porate an adjustment for the error in the upcoming forecast.

The closer C is to 0, the less sensitive the new forecast

will be to the error in the prior forecast (1358).

21

,II I--

7

Double Exvonential Smoothing

Double exponential smoothing is an extension of

single exponential smoothing. It is usually applied to

items that exhibit a trend pattern. Both single and double

smoothed values lag actual data when a trend exists, the

difference between single and double smoothed values can be

added to the single smoothed values and thereby adjust for

trend (19.11). The single exponential model, equation (3.3),

can be rewritten as:

S t - St-1 * CJ(D t - St-I) (3.4)

where, Si - exponentially smoothed demand in period i.

The apparent trend component of the error factor of our

forecast iss

T; = St - St-l (3.5)

This trend component can also be smoothed or averaged over

time using:

Tt W Tt. + ((T - Tti) (3.6)

The double exponentially smoothed forecast or the smoothed

average forecast including the trend component is the simple

smoothed average plus the smoothed trend component as cor-

rected for lag in Tt by the term (1-ae)/a:s

F t+1 S t + 1-Tt (3.7)

22

S- _-T77

In order to use this approach only three data values

and a smoothing constant are required, Use of this model

should be based on assumptions about the demand pattern.

If the time series has a trending average demand rate, the

double exponential smoothing model produces an accurate

estimate of demand (12.19).

Adaptive ExDonential Smoothing

The adaptive smoothing techniques adjust at over

time based on the size of the forecasting error. The adap-

tive model utilized here is the same as in single exponen-

tial smoothing with one exception. The value for ay is

derived from the equations

01 Ett11 M t (3.8)

where, Et O l(et) + (l-f3)E t 1M t al 7Iti + (l.()mt-1e t D Dt F t

to smoothing constant

and j denotes absolute values (16s54).

The characteristic of not specifying a value for U

is attractive when thousands of items require forecasting.

Also, this method can change the value of O when changes

in the pattern of the data have made the initial C value

no longer appropriate (16s53).

23

a a l I I ll i

Multiple Model Forecastin

The model that most accurately forecasts demand will

be selected from all models considered. In order to do

this, each demand history will be broken into three periodsa

a base (or start-up) period, a test period, and a prediction

period.

The base (or start-up) period is the historical data

base required for each model, The length of the base period

varies from model to model.

After the forecasting start point is established,

each model forecasts demand for a given test period. The

forecasts are compared to actual demand for the test period.

The model with the smallest variation from the actual demand

is selected to forecast demand for the next prediction

period.

This is a recurring process in that the forecasting

horizon defines a new prediction periodl the past prediction

period becomes the current test period; the past test period

joins the base period data base; and older data are dropped

from the base period (13.1).

The multiple model method employed in this research

is shown in Appendix Dg subroutine "Multi.* The actual

demand for the four previous forecasting periods is added

and stored as a new variable. The values forecasted for

these same four periods by each technique are added and this

total is subtracted from the total for the actual demand.

24

This process is repeated for each forecasting technique.

The technique which displays the lowest variance from the

actual demand is selected by the multiple model technique

as the technique it will use to forecast demand for the

next period.

Accuracy of Forecasting Models

Demand for an item is generated through the inter-

action of a number of factors. This interaction is extremely

complex. Due to this complexity, all forecasts will contain

some error,

In many forecasting situations accuracy Is treated

as the main criterion for selecting a forecasting method.

In spite of this fact, little systematic work has been done

to develop a framework for measuring and evaluating accuracy-

related issues. One of the difficulties in dealing w.th the

criterion of accuracy in forecasting situations is the

absence of a single universally accepted measure of accuracy

(16s569). When discussing forecast errors it is appropriate

to distinguish between sources of error and the measurement

of error.

Sources of error can be classified as either bias

or random. Bias error. occur when a consistent "mistake"

is made. Random errors can be defined as those that can~not

be explained by the forecast model employed.

25

Several of the common terms used to measure the

degree of error are mean absolute percentage error and mean

absolute deviation. Additionally, measures of bias may be

used to indicate the amount of any positive or negative bias

in the forecast (9s241).

Mean Absolute Percentap-e Error

One approach used to detect forecast error is to

take the absolute value of each individual percentage error

to obtain the mean absolute percentage error (NAPE).

Percentage error is a relative measure of accuracy

and is defined ass

PEt = D (100) (3.9)

where, PEt - percentage error for any time period tDt - actual value for time period t

Ft = forecast value for time period t (16o570)

The equation for computing the MAPE over N time

periods is given by:

Z PEi

MAPE = il (3.10)N

where, NAPE - mean absolute percentage errorPEi - percentage error for a time period (151570)

However, the MAPE itself does not always give a good

basis of comparison as to the gains in accuracy made by

26

applying a specific forecasting method. MAPE indicates how

well the forecasting model fits the data. In this way, it

aids in evaluating how accurate the model Is (16s568).

Mean Absolute Deviation

The most straightforward measure of error is mean

absolute deviation (MAD). It is computed using the differ-

ences between the actual demand and the forecasted demand

without regard to sign. Since it is the mean devidtion, the

sum of the absolute deviations is divided by the number of

data points. Stated in equation forms

n

MD t-. (3.11)

N

where, Dt - actual demand for period tFt - forecasted demand for period tN - total number of periods

and I denotes the absolute value (9&242).

The mean absolute deviation ignores whether the forecast is

greater or less than actual demand and simply measures the

magnitude of difference.

Bias

Bias indicates the directional tendency of forecast

errors. If the forecasting technique used consistently over-

estimates actual demand, bias will be positivel consistently

27

U-.

underestimating actual demands Will cause the bias to benegative. Bias is defined ass

Z (Ft - D diBias = -1'(3.12)

Nwhere, Ft =forecasted demand for period t

Dt =actual demand for period tN - total number of periods (10331)

Conclusion

All three techniques described here are used toevaluate multiple model forecasting. The measures of errorin the forecasting techniques are used to determine whichforecasting method will provide the most accurate estimateof demand. By using the forecasting technique which is themost accurate, the error variance in the Standard Base SupplySystem can hopefully be reduced,

28

Chapter 4

DATA COLLECTION AND ANALYSIS

Introduction

The purpose of this chapter Is to identify the

source of data used in the analysis and describe the selec-

tion procedure used to obtain a sample of 279 National

Stock Numbers (NSNs). Additionally, this chapter will pre-

sent an analysis of that data.

Data Collection

As mentioned in Chapter 1, this research had the

sponsorship of the Air Force Logistics Management Center

(AFLMC), Gunter AFS, Alabama. Two computer tapes were pro-

vided which contained Standard Base Supply System data from

Dover AFB, Delaware, for a two and one-half year period

froan October 1976 to March 1979. One tape contained item

record data for 33 stock classes, ranging from the 1005 to

the 5315 stock class. The total number of stock classes was

115 containing a total of 10,607 individual National Stock

Numbers. The remaining tape contained transaction history

data for these same NSNs. A Fortran program (Appendix A)

was developed which aggregated these records by stock class;

total items in each class; and total recurring demands.

29

The next step was selecting the stock classes to be

used in the actual analysis. A previous study by Patterson

(19) testing alternative forecasting techniques for the

Standard Base Supply System (SBSS) used stock classes 28, 47,

59, and 66. It was the researchers' Intention to select a

sampling of these same classes In order to make a comparative

analysis of results. However, since the data only included

through the 53 class, two additional alternative stock

classes were chosen. A Fortran program (Appendix B) was

used to prioritize the data into groups of high activity

(frequency of demand) and quantity demanded. With this

information, the authors were able to identify the 51 and

53 stock classes as having characteristics that would lend

themselves to alternative forecasting methods and, partic-

ularly, to the multiple model method. Table I shows a cap-

sulized summary of the activity and demands for the four

stock classes selected.

Table I

Profile of Preliminary Data

TotalStock Class Total NSN's Recurring Demands

28 386 18,196

47 1313 84.939

51 2407 126,571

53 2331 842,654

30

Due to the large frequency and quantity of demand

data and the limited computer resources, a sampling of this

population was taken. Recurring demands were tabulated from

the transaction history tape (see Fortran program in

Appendix C) and aggregated into 130 weeks or data points for

each selected item.

Prior to the selection of the final sample, the data

were scanned for any obvious outliers. As in Patterson' s

research, one stock number (47 stock class) had 6,160 units

requested in one period and zero demands for the remaining

129 periods. This item was dropped from the sample. A 28

stock class item was also discarded because data were found

to be available only for the first one and one-half years of

the survey period.

Table 2 is a summary of the final stock classes

used in testing the alternative forecasting methods.

Table 2

Profile of Stock Classes Selected for Analysis

Total

Stock Class Total NSN's Recurring Demands

28 99 89137

47 99 14,131

51 31 21v659

53 50 234,689

31

In summary, the data used for the actual analysis

consisted of centrally procured items identified by the

Expendability, Repairability, Recoverability Category (ERRC)

of XB3. A total sample of 279 line items was selected

based on high activity and a relatively high frequency of

reorder periods. An inherent bias in the data collection

was the researchers' attempt to identify those stock numbers

which exhibited characteristics which would accommodate the

time series forecasting techniques to be exercised.

This research addressed the applicability of multi-

ple model forecasting as an alternative to the. standard base

supply forecasting system. In order to test this hypothesis,

the data collected by the methods described were processed

by use of a Fortran IV computer program (see Appendix D).

Computer Output

For each stock number in each stock class, the

actual units demanded, the units forecasted by each fore-

casting technique used, and the units forecasted by the mul-

tiple model forecasting technique were shown on the output

(see Appendix E), The mean absolute deviation (MAD) com-

paring the forecasted demand and the actual demand was com-

puted (see equation 3.11). Additionally, a bias (equation

3.12) and mean absolute percentage error (NAPE, equation

3.10) were computed. These values were necessary to complete

32

the statistical tests required to determine the accuracy of

the various forecasting methods.

Data Base Comparison

In order to attain the objective of evaluating the

multiple model forecasting method, it is necessary to show

that a similar data base exists with which to compare our

results. In his research, Patterson obtained a mean abso-

lute deviation for single and double exponential smoothing,

using an alpha of .2, among others (1909). A comparison of

the means for these two forecasting techniques will test the

data base used to see if it is essentially the same as that

used by Patterson in his research. The precise stock numbers

used by Patterson were unknown to us,

To test this assumption* 95 percent confidence inter-

vals were computed, It is necessary to calculate a value for

the standard deviation for Patterson's research, since none

was given. When forecast errors are normally distributed,

the MAD is related to the standard deviation bys

I Standard Deviation 7 x MAD (4.1)

where, 7r - 3.1416

or conversely,

1 MAD - 0.8 Standard Deviation (9o242) (4.2)

33

The central limit theorem tells us that for almost all popu-

lations the sampling distribution of the sample mean is

approximately normal when the sample size is sufficiently

large (181202). Since the sample size used by Patterson is

large (200), normality can be assumed, and a value can be

calculated for the standard deviation.

Using this value for the standard deviation of both

samples, a 95 percent confidence interval was constructed.

To construct a confidence interval, an unbiased estimator of

the difference in the two sample means is required. This

estimator is denoted by Di

B = Y - 1 (4.3)

where, Y - mean of observations from sample 2X mean of observations from sample 1 (18312)

Additionally, an unbiased estimator for the standard devia-

tion of D is requireds

S2(D) S $(Y) + S(X (4.4)

where, S2 (Y) - 22

n

s 2 () S 1 2 (18,3.6)n

The formula for calculating the two-sided confidence inter-

val iss

L = - a(l-a/2)s( ) (4.5)U + a(1-O/2)s(I;) (18,316)

34

The results of the confidence interval calculations

are shown in Table 3:

Table 3

95% Confidence Interval for Data Base Comparison

Lower Mean Upper

Model Limit MAD Limit

Stock Class 28

Single Exponential .6282 2.11 2.5918

Double Exponential .8670 2.36 2.8931

Stock Class 47

Single Exponential .5062 2.06 2.2938

Double Exponential .2405 2.47 2.6396

Since the means fell within the limits# we have concluded

that for practical purposes our data base and that used by

Patterson were essentially the same.

Data-Analysis

The results of the computer analysis of the data

are shown in Table 4. In three of the four stock classes,

on the average, single exponential smoothing consistently

displayed the lowest mean absolute deviation, This is con-

trary to what was expected. The data were selected from

the various stock classes based on large amounts of demand

occurring in the most time periods. Essentially the *deck

35

pi L

Table 4

Results of Computer Analysis

Mean MAD Mean Bias Mean MAPE

Stock Class 28

Single Exponential 2.1115 - .6691 88.7535Double Exponential 2.3659 - .3165 114.7806Adaptive Exponential 2.9618 .5948 178.40094-Term 2.3750 - .2396 117.14078-Term 2.2967 - .3491 111.1047Multiple Model 2.7200 - .2081 152.5846

Stock Class 47

Single Exponential 2.0682 - 1.0852 213.0647Double Exponential 2.4756 - .1933 278.1608Adaptive Exponential 3.8648 1.3457 388.11054-Term 2.5769 - .2905 265.93128-Term 2.3863 - .4338 251.1996Multiple Model 2.8990 .6206 328.0684

Stock Class 51

Single Exponential 13.6679 - 1.6520 615.5107Double Exponential 14.8354 .8196 781.0071Adaptive Exponential 18.1501 3.8259 1081.69324-Term 14.4877 - .3390 710.09438-Term 13.9992 - .6066 677.3004Multiple Model 16.1558 '1.8196 894.6500

Stock Class 53Single Exponential 98.2697 - 3.9447 4023.2286Double Exponential 107.5422 14.2225 5036.5975Adaptive Exponential 114.3334 15.5944 5373.49774-Term 103.0422 - 1.0954 4245.18738-Term 97.7790 - 2.0539 4073.0743Multiple Model 107.2436 8.0751 4762.1244

36

.. . ... . . - - r

L!

was stacked" In favor of the time series techniques. The

multiple model technique did not produce the most accurate

estimate of demand, nor did it even tie with the most accu-

rate method. In the case of the 51 and 53 stock classes,

the MAD for all techniques considered rises considerably.

This indicates the problems encountered in using time series

analysis on data that are highly erratic and sparse (many

zero entires). The MAPE reflects this highly erratic

nature. The relatively large values for the MAPEs indicate

abrupt changes in the demands in the data (see Appendix E).

There are numerous periods in which zero demand is Incurred

and suddenly a large change in demand occurs and abruptly

drops off to zero again.

Conclusion

Through the use of confidence intervals it was shown

that the data base used in this research was essentially the

same as that used by Patterson in his previous research. The

Fortran IV program produced results that indicated single

exponential, and not multiple model forecasting, was the

most accurate of the techniques considered. The implica-

tions and conclusions which have been drawn from this will

be further discussed in the next chapter.

37

Chapter 5

CONCLUS IONS AND RECOM'MENDATION'S

Introduction

This research was directed at exploring the hypoth-

esis: the multiple model forecasting technique performs as

well as, or better than, single model techniques to which

it is compared. The research addressing this hypothesis led

to several conclusions, which can be associated with the

four objectives of this thesis.

Conclusions

The first objective of this research was to evaluate

the multiple model forecasting technique as an alternative

to the Standard Base Supply System forecasting technique,

Closely related to this was the second objective, to deter-

mine which forecasting approach will provide the most accu-

rate estimate of future demand.

The multiple model forecasting technique and the

additional techniques were processed by the use of the For-

tran IV program referred to in Chapter 4. Table 4 in Chap-

ter 4 reflects the results of the data analysis, As can be

seen, multiple model forecasting did not produce the most

accurate estimate of demand. Based on the mean MAD computed

after the computer analysis was completed, multiple model

38

consistently ranked next to last in accuracy. On three out

of the four stock classes, single exponential smoothing was

ranked as the most accurate. On the fourth class, stock

class 53, single exponential smoothing was the second most

accurate method, following closely behind 8-term moving

average.

The bias is an indicator of the directional tendency

of the forecast errors for each forecasting technique. In a

perfect forecasting model the bias would be expected to be

zero, i.e., the random errors due to overforecasting would

be offset by random errors due to underforecasting. Again,

referring to Table 4, in three out of the four stock classes

analyzed, multiple model forecasting consistently on the

average overforecasts the demand. The implications of

overforecasting demand come into play when the holding cost

of an item is considered. Holding cost is important to any

manager concerned with any form of inventory. Holding cost,

along with order costs and demand rates, makes up the eco-

nomic order quantity (EOQ). The multiple model forecasting

technique used in this research would cause the holding cost

to rise, if only slightly, due to its consistent over-

estimating of demand and subsequent over-stocking of inven-

tory. Single exponential smoothing, as used in this

research, consistently under-estimates demand and therefore

again becomes a more acceptable forecasting technique when

compared to others, including multiple model.

39

- -U----- ~ -~-- ,-~- -~

Finally, the mean absolute percentage error (MAPE)

of the multiple model technique consistently ranks as the

next to least accurate. The MAPE indicates how well the

technique in question fits the data. Therefore, the multi-

ple model forecasting used in this research does not fit

the data as well as other methods. Single exponential

smoothing fits the data best, i.e., it consistently exhib-

ited the lowest NAPE. The high NAPEs encountered in this

research indicate the highly erratic nature of the SBSS.

An example of the erratic nature of the demand data is shown

in Appendix E. Additionally, it can be seen that, as a gen-

eral rule, trend is not apparent in SBSS items. Therefore,

methods of forecasting that did adjust for trend did not

reduce the forecast error. When an abrupt change occurred

in the data, both double and adaptive exponential smoothing

reacted to the change as if it were a trend. However, the

data usually abruptly returned to zero and a trend did not

develop. As a result, these forecasting methods were not

among the most accurate of the methods tested.

The third objective of this research was to deter-

mine the effectiveness of implementing the proposed system.

In order to demonstrate a significant cost savings to the

Air Force, there must be a significant increase in fore-

casting accuracy. The results indicate that the multiple

model forecasting technique used here would not support

this significant increase in forecasting accuracy.

40

Therefore, any cost savings attributable to implementing the

multiple model forecasting technique are in doubt. It also

becomes apparent that the time series forecasting models

used in this research did not yield any significant Improve-

ment in the forecasting of demand for SBSS items,

The final objective of this research was to recomn-

mend actions based upon the results obtained. The following

section will address this objective.

Recommrendati ons

-Implied throughout this study is the fact that

inventory models are used to assist managers in determining

when items should be ordered and how large the order should

be so as to minimize variable costs and insure that adequate

stockage is on-hand to meet mission requirements. Using the

EOQ model as a depth model, however, has two inherent

assumptions, ise., the demand activity remains relatively

continuous and the items are relatively low in cost. Refer-

ring to Table 5, we note that this model was intended for

use under the conditions which are present in Quadrant I.

Table 5

Inventory Characteristics

Inventory Item CostHI LO

HI IItem

Dead LO III IV

41

Quadrant I exhibits the ideal conditions for ECQ, i.e., a

high frequency of demand with continuous demand behavior.

Scarcity of resources and other fiscal environmental factors

have made the conditions within Quadrant 11 not at all un-

common. Average item costs have been Increasing signifi-

cantly In recent years. The EOQ model, while not optimal,

can handle these conditions fairly well as long as the

demand patterns remain relatively continuous. In addition

to costs, technology factors have increased reliability on

many items resulting in lower demand frequency. This has

the effect of moving many items into Quadrant III and IV.

An example would be vacuum tubes which are now replaced by

solid state technology resulting in a higher Mean Time Be-

tween Failure. Quadrant III and IV contain characteristics

of low demand for both low and high value items. The math-

ematical assumptions inherent within the EOQ model were not

meant to address the conditions of low demand, especially

the sparse lumpy conditions found frequently in the SBSS

data. Examples of this demand data are found in Appendix E,

We conclude that the EOQ model is an inappropriate

depth model for items characterized by erratic and sparse

demand patterns.* Our recommendation is to divert further

efforts fro improving SBSS forecasting techniques to direct-

ing research efforts in a search for alternative decision

models which will be more appropriate for the SBSS depth of

stockage decision. 4

APPEND ICES

43

APPENDIX A

DATA RETRIEVAL PROGRAMf

'44

103 CHARACTER STCLASS*4.CLHOLD*4.STNUMB*15,SNHOLDI5S'203 INTEGER CLASSCNTTOTCNT.RDCNT.RD60# READ(20,100,ENDS900)STCLASS,STNUMB,RD70#100 FORMAT(T5,A4,T5.A15.T116,16)80# TOTCHTaI903 CLASSCNT=1100# CLHOLD=STCLASS1103 SNHOLD-STNUMB120# RDCNT=RD1303 ITEMCNT=1140N URITE(6.125)150#125 FORMAT("ISTOCK CLASS TOTAL ITEMS TOTAL RECURRING DEMAND")1601 DO 500 K:1,11000170# READ(20,100,END=900)STrLASS,STNUMB,RD1903 TOTCNT=TOTCNT,12203 IF(STNIJNB.GE.SNNOLD'GO TO 150230# PRINT,- ST NUMBERS OUT OF SEO:REC# ".TOTCNT2401 STOP2503150 SNHOLD=STNUMD260# lF(STCLASS.EO.CLHOLD)GO TO 200330# CLASSCNT=CLASSCNT~l3403 URITE(6.1010)CLNOLD,ITEMCNTRDCNT3503 CLNOLDuSTLLASS3601 RDCNT203703 ITEMCNTzO3803200 RDCNT=RDCNT+RD3903 I'(EMCNT=ITEMCNr,14003500 CONTINUE4100900 IRITE(6,1010OCLHOLDITEMCNT,RDCNT4201 URITE(6.950)CLASSCNT4303950 FORMAT(/" TOTAL NUMBER OF STOCK CLASSES a ,16)4400 URITE(6,1000)TOTCNT45031000 FORMAT(" TOTAL NUMBER OF RECORDS =".16)46031010 FORMAT/2X,A4,T1,I9,T33,I11)4701 STOP480# END

45

L-

APPENDIX B

SELECTION PROGRAM FOR RANKING BYDEMAND AND FREQUENCY

46

LIST GE09

10 INTEGER SC,TD,IARRAY(131)20 CHARACTER*l5 SN,HOLDSN30 IFLAG=040 HOLDSN=*123456789123456"50 50 READ(40,100.END=500)SC.SNIDATE.IDEIAND60 100 FORMAT(T1,12.T1.AI5,T67,I4,T79,IA)70 IF(SC.GE.53)GO TO 20090 60 TO 50100 200 IF(SN.ME.IIOLDSM)60 TO 300110 CALL TALLY(SN,IDATE,IARRAY,IDEMAND,ITOT)120 60 TO 50130 300 IF(IFLAG.EO.0)GO TO 350140 DO 400 X=1,131150 IDUCKE7S=IBUCKETS+IARRAY (K)160 400 CONTINUE170 IDUCKETS=IBUCXETS.100000180 ITOT=ITOT+1000000000190 URITE(50,425)HOLDSN,IBUCKETS,ITOT200 425 FORMAT(lX,A15,1X,I4,1X,18)205 350 IF(SC.GT.53)GO TO 500210 IFLAGSI220 HOLDSN=SN225 IBUCKETS=0230 ITOT=0240 DO 450 J=1.131

250 IARRAY(J)=0260 450 CONTINUE270 CALL TALLY(SN,IDATE,IARRAY,IDENAND,ITOT)280 G0 TO 50320 500 URITE(6,530)330 550 FORMAT(* END OF SN PROGRAM")

340 STOP350 END360 SUBROUTINE TALLY(SN.IDATE,IARRAY,IDENAND,ITOT)370 CHARACTER SN*15

380 INTEGER IARRAY(131)390 IF(IDATE.GE.6276.AND.IDATE.LE.9091)G0 TO 600400 URITE(6,575)SN,IDATE

47

410 573 FORIIAT( DATE OUT OF BOUNDS= M.AI5,5X,14)420 RETURN430 600 CONTINUE440 IF(IDATE.GE.462?6.AND.IDATE.LE.6366)ISJD=(IDATE-6269)/7450 IF(IDATE.GE.7001 .AND.IDATE.LE.7365)ISUD=(IDATE-6994)/7+13460 IF(IDATE.GE.aO0l .AND.IDATE.LE.8365j)ISUD=(IDATE-7993)/7*65470 IF(IDATE.6E.900l .AND.IDATE.LE.9091)ISUB=(IDATE-8992)/74117490 IARRAY(ISUB)=1490 ITOT=ITOTIDENAND500 RETURN510 END

LIST SORT-l8

0099$#N0RM1,J0100S:IDEN7:UPllA,AFXT ACDS I'T MAIER0120S:6NAP:NDECK0130:600SN:NOMAP0140:SORT:INOUT, ,5O150:FIELD: (Cl6,C5,C9)0160 SEQ : (D2 * , Al)0170:FILCB:INOUT.**,20180:END

0190$:EXECUTE0200$:LINITS: 100210$:PRMFL:SA.S.DOBF/DAIAI-470220$:PRtIFL:SZ.U,S.BOBF/DATA1-D

0230$:F!LE:Sl,X1R.10R0240$:FILE:S2,X2R,1OR0250f:FILE:SJ,X3R, IOR0260$:ENDJOB

LIST SORT-11D

009911N0RM1, J0O0S:IDENT:UP1I86,AFI7 ACDS LT MIAIER0120S:GtIAP:NDECK0130:600SM:NCNAP0140:SGRI:INOUT,,50150tFIELD: (CI6,C5,C9)0160iSEO: (D3,D2.AI)0170:FILCB:INOUT.**,20180 sEND01905SEXECUTE020O5:LIMITS:100210$:PRNFL:SA.R,SDODF/DATA1 -470220sPRHIFL:SZ.U,S,BOBF/DATAl -D0230W:ILE:Sl .XR.IOR0240$:FILE:S2,X2R. IOR0250$:FILE:S3.X3R,1OR02605 :ENDJOB

48

APPENDIX C

PROGRAM FOR DATA ANALYSIS

49

LIST NOVEIT

10 CHARACTER*15 SNI,SN220 INTEGER BUKETI(130).BUKET2(130),DUKET3(130)30 5 READCIO,10,END=500)SN1,(BUKET1CK),K=1,130)40 READ(20.10,END=600)SN2,(DtJKET2(J),J=1,130)50 10 FORIATAI5,5(/2615))60 IF(SNI.NE.SN2)6O TO 70070 DO 30 L=1.13080 BUKET3(L)zDUKET1 (L)4BUKET2(L)90 30 CONTINUE100 URITE(30.50)SN1,(BUKET3(I),I=1,130)110 50 FORMAT(A15,12I5,7(/1515)/13I5)120 GO TO 5130 500 URITE(6,330)140 550 FORMAT( END OF FILE-I*)150 READ(20.10,END=575)160 URITE(6,590)SN2170 590 FORM$ATW EOF-1,BUT INFO STILL ON FILE-2.SN2=*,AI5)190 STOP190 575 URITE(6,595)200 595 FORMAT(" EOF ON BOTH FILES, ALL Ok")210 STOP220 600 URITE(6,660)SN1230 660 FORMAT(" UNEXPECTED EOF-2.SN1=",A15)240 STOP244 700 URITE(6,750)SNI.SN2246 750 FORMATV' UNMIATCHED SN'Smo.A15,2X,AI5)249 STOP250 END

410 IARRAY(ISUB).IARRAYCISUB).IDEMAND420 IF(IARRAYCISUB).GT.99999)URITE(6,700)SN430 700 FORMAT( *IDEMAND HAS EXCEEDED 99999, SN=",A15)440 RETURN450 END460 SUBROUTINE INIT(IFOUND, IARRAY)470 INTEGER IARRAY(130)480 DO 800 J-1.130490 IARRAY(J)20500 800 CONTINUE510 IFOUND20520 RETURN530 END

50

10 INTEGER IARRAY(130?20 CHARAC7ER*15 SN.HOLDSN30 CALL INIT(1FOUND,IARRAY)40 READ(30. 10.END=50O)HOLDSM50 10 FORNAICAlS)60 50 READ(40,100,END=499)SN,IDATE,IDENAND70 100 FORIIAT(Tl,AIS,T67,I4,T79,I6)80 20 IF(SN.NE.HOLDSN)G0 TO 15090 IFOUNDul100 CALL TALLY(SN,IDATE.IDEMAND,IARRAY)110 GO TO 50120 150 IF(IFOUND.EQ.1)GO TO 300130 IF(SN.GT.HOLDSN)GO TO 200140 GO TO 50150 200 URITE(6.250)HOLIISN160 250 FORMIAT(" THIS SN NOT ON THIS5 TAPE=",AIS)170 60 TO 450180 300 UR17E(50,400)HOLDSN.(IARRAY(I),1z1,130)190 400 FORNAT(A15,5C/2615))200 CALL INIT(IFOUND,IARRAY)210 450 READ(30,?0,ENDx50Q)HOLDSN220 GO TO 20230 499 URITE(6,9F'9)HOLDSN240 999 FORMAT' END OF TAPE=",A15)250 500 URITE(6,550)260 550 FORMAT(" END OF SN PROGRAM"M)270 STOP280 END290 SUBROUTINE TALLY(SNIDATE,IDEMAND,IARRAY)300 CHARACTER SN*15310 INTEGER IARRA'1(130)320 IF(IDATE.GE.6276.AND.IDATE.LE.9089)GO TO 600330 URITE(6,575)SN,IDATE,IDEMAND340 575 FORMAT("M DATE OUT OF BOUNDS- ",A15.5X,14.5X,I5)350 RETURN360 600 CONTINUE370 IF(IDATE.GE.6276.AND.IDATE.LE.6366)SU=IDATE-6269)'7380 IF(IDATE.GE.7001.AND.IDATE.LE.7365)ISUBu(IDATE-6994)/7+13390 IF(IDATE.GE.8001.AND.IDATE.LE.8365)ISUBu(IDATE-7993)/7+65400 IF(IDATE.GE.9001 .AND.IDATE.LE.9089)ISUBs(IDATE-8992)/741 17

51

APPENDIX D

PROGRAM TO COMPUTE FORECASTS AND PERFORMCOMPARATIVE ANALYS IS

52

1114C STAR PROGRAM COMPUTES FORECASTS USING MULTIPL.E TECHNIQUES1214c AND PERFORMS BASIC COMPARATYE ANALYTSIS

146a PROGZAM SIAR(INPUTOUTPUTTAPEII:INPUTIAPE&:OUTPUT)1312 COMMON NSN(2htNAT(159),IFSE151,ilFE(15g),I1#= 1IFAE(I5f9bIFMA4(I59hvIFMA8(159)tI79: lMS(1363 vIMM(I511ltISEQ(35ff)189:- READ(If9ft9) I1904961 FORMAT(14)

211- DO 999 J:1,25221: READ(I199I)ISEQ(I),NSNc1),N5 O(Z),Z306: I(NDAT(12) ,12:1,12) ,ISEg(I+1) ,(NOAT

260-: 112:43,57) ,ISEQ(I+4W NDAT(IZ)tZ76: 112:58,7Z) ,ISEG(145) .(NDAT (12),

3oo-: 112:13,17)ISEQ(I,)(NDATIZ),

^)29:996 FORMAT(14,1IA19,A5,1215,7U114,15151,/14,13I1336= J5:L.8'a49: 00 195 J1:L,.JS3535: IF(ISEQ(J1).NE.JI) GO TO 898360=1#5 CONTINUE376m CALL SINCE3812 CALL DOUBEX3969: CALL ADAPEX40ff: CALL MOY4416: CALL NOYS429: CALL MULTI439: CAL ERROR44f: L:L+9430: imL469:499 CONTINUE471m STOP48949q8 PRINT 97SPISEQ(JI-1)4904975 FORMTC51PI,2KARD OUT OF SEQUENCE14IiI4)501: STOP5118 END

53

53fC SUBROUTINE SINCEI COMPUTES SINGLE EXPONENTIAL FORECAST540--C VALUES

54 SUBROUTINE SINGEX579: COMMON NSN(2hUDAT(151),IFSEISII vIFDE(159).589: IIFAE(151),IFMA4CI5h)IFA(15),5902 lNS(139)vIMM(I19v ISEQC35fl)-499: IFSE(1):-NDAT(1)619: 00 299 1:1,129629z FSE:IFSE(I)+C.Z#(NDAT(I)-IFSE(I)))630- IFSE(I+1A:IFIX(FSE)6492ff CONTINUE6509: RETURN669:- END67laC

6912C SUBROUTINE DOUBEK COMPUTES DOUBLE EXPONENTIAL FORECAST700%C VALUES

730: SUBROUTINE DOUBEX740% COMMON NSN(ZhtNDAT(15I) ,IFSE(151) tIFDE(150It75f: IIFAE(159) PIFNA4(15#)pIFMA8(150)t760t lMS(13l) ,IMM(15I) iISEQ(35#@)771a IFDEt1~mNOAT(1)

796a. STC:9.9

out: DO3H9 I:2v1298169: ATCzIFSE(I).IFSE(I-1)829: STCzSTC+ .2* (ATC-STC))639x: IF(STC.LT.9.) STC20.984#aC 5:11.2859. FDE*IFSE(I) 4(5#STC)869: IFDE(IU:IFIICFDE)879.3ff CONTINUEMr9 RETURN

899m END

54

929:-C SUBROUTINE ADAPEX COMPUTES ADAPTIVE EXPONENTIAL FORECAST930-:C VALUES940--C

940: SUBROUTINE ADAPEX971-: COMMON NSN(Z)bNDAT(151),IFSEC1SIJ ,IFDE(I51),980-- IIFAE(15SIbIFNA4(1Sl),IFM8(1501,991: IMS(I3f1 ,IM(156) ISEQ(35f11

Ifff: IFAE (1) *NDAT (1)III$= ERTxI.l1621:m ENRT--I.I11301: DO 411 1:1,129

16562 IM(ET.EQ.O.) GO TO 3761610: CO TO 380113371 ALPHA.I1680: ERT4l.I1090Z EMRT:I.l11t"= GO TO 3911111:380 ERT=(.Z*IET)+(.S#ERT)11t'3: IET=IADS(IET)1136:- ENRT(.2*IET)+(.4ENRT)1140= ALPHA=ABS(ERTIEMRT)1150:390 FAEzIFAE(I),(ALPHAIINAT(I)-IFAE(I)))1169: IFAECI11:IFIXCFAE)1170:409 CONTINUE1180: RETURN1190: END120#4C

1229zC SUBROUTINE HOV4 COMPUTES 4 TERN MOVING AVERAGE12364C FORECAST VALUES1241-C

1260: SUBROUTINE MOV41270= COMMON NSNL2bNDATCI59),IFSE(150)pIFDE(151),1290: IIFAE(1591,IFNA4CI5I),IFMA8(150),1290: INS (130) tIMI(15f) iISEG (3561130z: DO 490 11:1,4131#2490 IFNA4(Il)2NDAT(I1)1329: IFNA4C1)NDAT(4)1333: DO 5H8 I4,129134fx FN4:NDAT(I).NDATCI-1).NDATUI-21.NDATCI-3))!41350s IFNA4(1.1):JFII(FM4)136#:568 CONTINUE1373: RETURN130: END

55

1419=C SUBROUTINE MOVO COMPUTES 8 TERM MOVING AYERACE14Z1:C FORECAST VALUES1431--C

1459:- SUBROUTINE NOVO14649: COMMON NSN(2) ,NDATC15I) ,IFSE(15#) ,IFDE(15I(,1479: IIFAE(153) ,IFMA4(150),IFMAS(15S1b1489: 1MS(130)PIRMM153IISEO3500)1499:- DO 599 11214815U=590 IFMA8(I1)zNDATCI1)1510: IFMA8(I):-NDATCS)1539: 00 699 I-4P1291536: FMAS: (NDA7 ( I)NDAT (1-1)+NDATII-Z).NDATCI-3( +15409: INDAT(I-4)4NDAT(1-5)4NDAT(I-6)4NDAT(I-7))/S

156#--6N CONTINUE1573: RETURN15892 END

160#=C SUBROUTINE MULTI COMPUTES MULITPLE MODEL161@=C FORECAST VALUES

164#= SUBROUTINE MULTI165#9: COMMON NSN(2),NDATCI59bvIFSE(15I),IFBE(153)i

1671m 1MS(1393 ,IMM(1) tISEG (3599)1689: DO 699 11:1,91699:691 MS(I1):I1706z D0 729 1:9,12917169: NVAR9:NDAT(I)+NDAT(1-1)4NDAT(I.2)+NDAT(I-31723:- NVAR1I--NYARI-(IFSEI1)+IFSE(1-1)+IFSE(1-2),17369: IIFSE(I-3)))1746c NVARIzIA3S(NVARI)1759k NYAR2zIA8s(NVAR3-(IFDE(I)+IFDE(I-1),IFDE(I-2)41760: IIFUE(I-31))

1789x 1IFAE(I-3))1791: NVMR4:IA3S(NYR-(IFA4()IFA4(1-1).IFA4(1-2I,lofts IIFMA4(1-3)))16112 NVAR5:-IABS(NVAR9.(IFMA8(I)+IFMA8(I-1),1829:. lIFNA8(I-2)4IFHAO(I-3)))

56

1840: NYAR-UVARI1856P IFINVARZ.LI.NYAR) GO TO 76518614101 IF(NVAR3.LT.NYARI GO TO 761871=76Z IF(NYAR4.LT.NVAR) GO TO 7671880:793 IF(NYAR5.LT.NVAR) 00 TO 761890: CO TO 710190#4705 N:?1919:- NVAR:NYAR21920: CC TO 7011936=766 NQ:1941: NYAR:NYAR31956:- CO TO 7921961476 Nz41970: NYAR=NVAR41989: CO TO 7631996:768 ":529#=711 NS(I)%M2016: IF(PS(1).EQ.1) IMMII,1)zIFSE(141)2626: IF(NS(I).EQ.Z) INNM(1+1):-IFDE(141)2631= IF(MS(I).EQ.3) IMH(I+1)zIFAE(1+1)Z64#: IF(MS(I).EQ.4) IPM(1+1)=IFNA4(I11

26664726 CONTINUEZ 671-- RETURNZ#80-- END

210#=C SUBROUTINE ERROR MEASURES THE DECREE OF ERROR AND BIAS INz1l6:C THE FORECASTS

2136: SUBROUTINE ERROR2146:- COMMON NSN(2) ,NDAT(15),IFSE(IS9),IFDE(15612156: IIFAE(t59) tIFMA4(159) ,IFNAS(150)92166: 1MS113)Pu1M(15)tISEQ(35#tlLI76 DIMENSION ICTR(139)216:2 SEMADs6.1219#2 DEMAD:6.#2206:- AMADs#.6221#2 A4804:.12226: ABNADZ#.#2239:- SEREs0.92249s DEREa6.#2256: AEREzlf.2266: A4REz6.6Z276w ASRE#.#2268: SEPE21.122W: DEPE2#.§2368 AEPEt#.92316: W4E&#.62326P AOE:0.I2339' Fl~t#. I23412 FREr#.#

ZmX Fs#.l57

365:a D 8ffO 1-13,1312379s ERR - NDAIM-IFSE(1Z380: SE A4S (ERR i+SENAD2396t SEREtERR+SERE24ff: IF(ERR.EQ.6.) GO 7O 75Z241#: IF(NDT().EQ.1.) C0 TO 7512429: SEPE:- (ASS (ERR/NDAT(1) I'U.)+SEPE2430= CO TO 7522440-:751 SEPE-lABS(ERR/1).1NjSEPE2450:75Z ERR:-NDAT(1)-IFDE(1)246#: DEIIAAS (ERR) 4DENAD24712 DERE:-ERR+OERE2480= IF(ERR.EQ.$.3 GO TO 7542491: IF(NDAT(I).EG.§.) GO TO 753Z5f0= OEPE(ASERR/NDT(1)D,19g. )+DEPE25105: GO TO 7542529#753 DEPE: (ABS (ERR/1)elffj.DEPE25312:754 ERRaNDAT(I)-IFAE(I)2549: AEAD=ABS (ERR) 4AERAD25560: AERE:-ERR.AERE25609- IF(ERR.EQ.0.) GO TO 7562570: IF(NDAT(I).E9.) CO TO 7552580= AEPE: (ADS (ERR/NOATCI) )#l9. ).AEPE25919: GO TO 75626##=715 AEPE(AS(ERR/),1ff.),E2610:756 £R:NDAT(1)-IFMA4(I)z~29z A4MD:AS(ERR14oft2 639: -- A4RE:-ERRtA4tE26W: IFERR...) CO TO 7582659: IF(MDAT(I).E0.I.) CO TO 7572W:Z A4PEz(ABS(ERR/DATC))419l.),A4PE2670= CO TO 759Z686--757 A4PEz(ABS(ERR/1)#lNj+4PE2699:758 ERRMDAT(DIFM8(DI27ff: AOIAD:ADS (ERR) +ASfAD2719: AGREzERR+ASRE2729: IF(ERR.EQ.0.) CO TO 7662736k !F(WDAT.E.I.) GO TO 7592740: ASPE:(AIS(ERR/NDAT())#199.).A6PE2759' GO TO 7492769:759 A8PE(AlSlEfRR/D.1ff.).ASPE

28ff IF(ERRA.Q..) CO TO 76528119 IFWDAT(I).1g CO TO 761MAX9 FPE-(ABIERR/DAT()).1ff.)VPE

2849:761 FPEalAlSERR)lD s.),FPE2865 CONT IE2859:76 CONTINUE

58

97: SERAD:SEYA/118.2W:- SERE-m(SEREIII8j,(.l.,)28969: SEPE:SEPEII19*2999: DERAD:DMD,18.2911:- DERE--(DERE/11.,(12929 DEPE2DEPE/118.2931: AEMADsAEMD/118.Z940: AEREz(AERE/118.).(-j*9)2959:- AEPEcAEPE,118.2960= A4)ID944MO/118.2179= A4RE:CA4RE/118gj,(-j*g)2980,- A4PE:A4E, 11.2990= A8HAADII18.3100f: A8RE(ARE/118.)(.@j,301#2 A8PEzA8PE,118.3929: FRAD:F"AMIS1.3639: FREz(FREIII.M8 .0,)31463: FPE:FPE/118.31509c ICTR(1)m13691= DO 861 1--2,1303179:860 1CTR(1)21CTRl1-1,113089:m IRITEC60689 NSNCI),NSN(2)3996#99 FORMATURIII 15IMM1S4: ZA1#)3199= 13--l3110m 14--153120= UZI1313 6C DO 879 12:1,831409: IF(II.EB.4) 0O TO 8653159: Go To 8613169:865 WRITE(6,912)31790912 FoRmAT.(l l)3189: 11:1l31909:861 MRITE(6,M1D(CTRMt),:13,14)32U-:911 FORNAT (//I 8H#e#EE#n,41,13, 14171321#: VRITE(6,9z (lATh) p1:13tl4)32Z2992 FORMAT(l51,6NMCTUA.,41,l5t14h

7)3230: IRITEC6,913;(IFSE(I),1:13,14,3240903 FORNTUATI -SINCEI,1 4I7132.5#. VRITE(6,Y9f4)(IFDEI),II

3 4)3260--904 FORNAT(/53,8H2.DOUILEi,5,51417)3271z URITE(6,995) (IFAEI!).1:3,4)320#'M9 FO(MTI53,MH-AWTP,31, S, 1417)32W RT?19INV 111t4330#2996 FORNATC/5I74.4TE~M,31,I 1417)3W7J99 FORNTuSI,7H5-8ER,,3loIs,

141 7)3339 VRITE(6v"8) (IS(1),1z13, 14)3M41998 FORMAT(5I,6gMO,41,zstl4xl,3359' NITE(6,919) (INNII) iI'3,l4)3369:999 FRT(/5 &I,8uNG00, 15I,1417)3379: 134[3+153381a 1414+153399a I1aII+iRUM947 CONTINUE

59

411: VRITEC4,9l1) (ICTRII) ,1:13913l)

34Z9: WRITEt6091)343 II1 FORNAT(1H49II,3lf~lAD9I4H31AS~l,4HlAPE)3449: IRITE(6&9921 CNOT(1)tI'[3t 136)

3459s VRITEC6tW3)(IFSE(l),lzI3t13I

3469: MRITE(bP911) SEMADSEREPSEPE34714911 FORMAT(IN4,841,3V11.4)

3499: VRITE(6,911) DEMADDEREOEPE3599:- WRITE(6t9f5)(IFAE(1)f.13.!39)3519: MR1TE(6p9l1) AEMADAEREvAEPE35z9: lRITE(6t9f6) (IFNA4(1) g113,13l)3539:- VR1TE(6t911) A4NADtA4RE,A4PE'3541s VR1TE(697)(FA8WI~o 3tl3lJ3559S VRITE(6'9111 M8ADvA8RErASPE3549: mRITEj6p998) (NSIhl:13, 139)3571: VRITE(6t9f9) (IM 1143,1

3h1

3589: URITE(6v911) FIMOPFREtFPE3593P RETURN36ff: END

60

APPENDIX E

COMPUTED FORECASTS AND ANALYS ISf

61

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M a M U a a N .4 m of CD. a . a .4 .4 pe 4 2 a m .4 .4 .4 4 .4

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ara

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SELECTED BIBLIOGRAPHY

86

A. REFERENCES CITED

1. Adam, Everett E., Jr.# and Ronald J. Ebert. Productionand Operations Manaements Concepts. Models. andBe . Englewood Cliffs t Prentice-Hall, Inc.,

2. Anderson, David R., Dennis J. Sweeney, and Thomas A.

Williams. An Introduction to Manemen SciencesOuantitative Approaches to Decision Making. NewYorks West Publishing Company, 1979.

3. Belden, Colonel David L., and Ernest G. Cammack."National Security Managements Procurement."Unpublished research report, unnumbered, IndustrialCollege of the Armed Forces, Washington, D.C., 1973.

4. Benton, William K. Forecastin6 for Management. ReadingsAddison-Wesley Publishing Company, 1972.

5. Box, George E. P., and Gwilym M. Jenkins. Time SeriesAnalysis Forecastina and Control. San FranciscooHolden-Day, Inc., 1976.

6. Brantley, Captain Jim S., USAF, and Captain Donald E.Loreman, USAF. "A Comparative Analysis of the D041Single Moving Average and Other Time Series Analy-sis Forecasting Techniques." Unpublished master'sthesis. ISSR7-77A, AFIT/SL, Wright-Patterson AFBOH, June 1977. AD A044078.

7. Budnick, Frank S., Richard Mojena, and Thomas E. Voll-mann. Princioes of Ooerations Research for Manage-ment Homeoods Richard D. Irwin, Inc., 1917.

8. Buffa, Elwood S., and Jeffrey G. Miller. Production-Invento Systems P IamDnd Control. HomewoodaRichard D. Irwin, Inc.* 19/9.

9. Chase, Richard B., and Nicholas J. Aquilano. Productionand O~rationa ManaLge , Homewooda Richard D.Irwin, Inc., 191/8

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10. Christensen, Captain Bruce R., USAF, and Gene J.Schroeder. "A Comparative Analysis of the D041System and Time Series Analysis Models for Fore-casting Reparable Item Generations." Unpublishedmaster's thesis. SLSR 27-76B, AFIT/SL, Wright-Patterson AFB OH, September 1976. AD A032364.

11. Clark, Charles T., and Lawrence L. Schkade. Statis-tical Methods for Business Decisions. Chicago.South-Western Publishing Company, 1969.

12. Fischer, Major Donald C., USAF, and Captain Paul S.Gibson, USAF. "The Application of ExponentialSmoothing to Forecasting Demand for Economic OrderQuantity Items." Unpublished master's thesis.SLSR-ZI-72A AFIT/SL, Wright-Patterson AFB OH,January 1971. AD 743412.

13. Garland, First Lieutenant Todd R., USAF, and CaptainHenry P. Mitchell, USAF. "Multiple Model DemandForecasting Compared to Air Force Logistics Cam-mand D062 Performance." Unpublished master'sthesis. LSSR 61-80g AFIT/SL Wright-PattersonAFB OH, June 1980. AD A089318.

14. Lee, Lamar, Jr., and Donald W. Dobler. Purchasin andMaterials Manaaement. New Yorks McGraw-Hill BookCompany, 1977.

15. Lombardi, Major Richard. Stockage Policies Division,AFIIC/LGS. Letter, subjects EOQ Excess Computa-tion, to AFIT Students, 7 October 1980.

16. Makridakis, Spyros, and Steven C. Wheelwright. Fore-castipa Methods an Applications. New YorksJohn Wiley and Sons, 1978.

17. Mitchell, Arnold, et al. Handbook of Forecasting Tech-niques. Supplement to IWR Contract Report 75-7,Fort Belvoir VA, August 1977.

18. eter, John, William Wasserman, and G. A. Whitmore.Aoolied Statis ics. Boston Allyn and Bacon@Inc., 1978.

19. Patterson, Wayne J. "A Preliminary Analysis of Alter-native Forecasting Techniques for the Standard BaseSupply System (SBSS)." Unpublished research report,unmbered, Air Force Logistics Management Center,Gunter AFS AL, 1980.

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20. Peterson, Rein, and Edward A. Silver. Decision Systemsfor Inventory Manaaement and Production Planning.New York, John Wiley and Sons, 1979.

21. Sims, Robert L. "Routine Forecasting for InventoryControl." Technical report# SLTR 21-70, AFIT/SL,Wright-Patterson AFB OH, December 1970.

22. Smith, Bernard T. Focus Forecasti l Comuter Tech-nigues for Inventory Control. Bostons CBIPb-

lishing Company, Inc., 1918.

23. Taff, Charles A. Manaaement of Physical Distributionand Trans or tdon. Homewoodo Richard D. Irwin,Tnc., 1978.

24. U.S. Department of the Air Force. USAF Supply Manual.AFM 67-1, Vol. II, Part 2. Washingtons GovernmentPrinting Office, 1979.

B. RELATED SOURCES

Carrillo, Major John, USAF, and Captain Donald G. Peabody,USAF. "An Empirical Analysis of a USAF Economic OrderQuantity Parameter." Unpublished master's thesis.ISSR 36-78B, AFIT/SL, Wright-Patterson AFB OH, September1978. AD A061299.

Cullinane, Thomas P., and Steven Nahmias. "An Analysis ofForecasting Techniques for the Recoverable ConsumptionItem Requirements System (DSD D041)." Unpublishedresearch report, unnumbered, Air Force Office of Sci-entific Research, Washington, D.C., 19 August 1977.

Demmy, Steven W. "Statistical Characteristics of Forecast-ing Techniques for D062 Economic Order Quantity Items."Technical report. TR-79-02, Air Force Business ResearchManagement Center, Wright-Patterson AFB OH, May 1979.

Eichenberger, Captain Joel D., USAF, and Donald F. Norville."Forecasting Depot Overhaul Costs of Tactical MissileGuidance and Control Subsystems." Unpublished master'sthesis. LSSR-9-78A, AFIT/SL, Wright-Patterson AFB OR,June 1978.

Fatianow, Peter R. "Overhaul Factor Forecasting." NationalTechnical Information Service AD-A012491, PhiladelphiaPA, April 1975.

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Gonsalves, Master Sergeant, USAF# and Staff Sergeant Morgan,USAF. System Analysts DOOZA System, HQ AFLC, Wright-Patterson AFB OH. Personal interview. 27 October 1980.

Mitchell, Lieutenant Colonel Charles R., USAF, LieutenantColonel Robert A. Rappold, USAF, and Wayne Bo Faulkner."An Analysis of Air Force Economic Order Quantity TypeInventory Data with an Application to Reorder PointCalculation." Unpublished research report, USAFA TR80-6, Air Force Logistics Management Center, Gunter AFSAL, April 1980.

Orr, Donald. "Demand Forecasts Using Process Models andItem Class Parameterso Application of Ancillary Vari-ables." Unpublished research report, unnumbered USDRCInventory Research Office, Fort Lee VA, April 196.

Ostrofsky, B, "Unit Replacement Models for NASA." Unpub-lished research report, number NAS-3.l, University ofHouston, Houston TX, September 1977.

Rand Corporation. Forec astin Processina Requirements ofStandard USAF Base Level Computer Systems. Rand reportgR-2334-AF, Santa Monica CA, July 1978,

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