A SIMULATED SALES
FORECASTING MODEL:
A BUILD-UP APPROACH

, Thesis for the Degree of Ph. D.

MICHIGAN STATE UNIVERSITY

FRED WILLIAM MORGAN, JR..
1972

 

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thesis entitled

A SIMULATED SALES FORECASTING MODEL: A BUILD-UP APPROACH

presented by

Fred William Morgan, Jr.

has been accepted towards fulfillment
of the requirements for

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ABSTRACT

A SIMULATED SALES FORECASTING MODEL:
A BUILD-UP APPROACH

BY
Fred William Morgan, Jr.

Business firms have long been frustrated in their
attempts to evaluate their forecasting capabilities prior
to anticipated sales becoming actual sales. This disserta-
tion is a presentation of a way to deal with this measure-
ment problem. This is accomplished by devising both a
forecasting archetype and an approach for tailoring the
forecasting model to meet specific needs.

Three traditional bases for categorizing fore-
casting models are:

l. The length of the forecasting period

2. The level of the forecast

3. The technique utilized.

Forecasting periods shorter than one year can be arbitrarily

defined as short-term, while periods lengthier than one

 

 

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year are long-
could be the
the firm are 1:
region levels.
mathematical c
Playing a vita

The ob
imPlement a mo
sions of predi
“ique. Each 0
rThe PrediCtion
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forecasts are

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Fred William Morgan, Jr.
year are long-term in nature. The level of the forecast
could be the economy, the industry, or the firm. Within
the firm are product, product group, region, and product-
region levels. Techniques can be described as either
mathematical or nonmathematical with managerial judgment
playing a vital role in either case.

The objective of this research is to build and to
implement a model with flexibility along the three dimen-
sions of prediction interval, level of detail, and tech-
nique. Each of these dimensions was studied thoroughly.
The prediction interval and level of detail were treated
as aspects of the planning horizon for forecasting. Since
forecasts are critical inputs to the planning process, the
planning horizon influences both of these dimensions.
Long-term planning requires aggregate forecasts for lengthier
time periods. Short-term forecasts are more detailed and
cover smaller time intervals. The emphasis of this study
was arbitrarily placed on a short—term (one year) time Span.

To aid in the selection of the appr0priate fore-
casting technique. a set of guidelines was deve10ped. This
set includes the following: (1) cost, (2) level of detail,
(3) accuracy, (4) turning points, (5) market factors,

(6) input requirements, (7) planning horizon, (8) timing,

 

 

 

 

(9) rigor, and
compared usin!
Sever
III factor lis
force composit
age, (6) eXpor
and (8I regreg
of these tech

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Fred William Morgan, Jr.
(9) rigor, and (10) clarity. Prospective techniques can be
compared using these criteria.

Several techniques were explored, including
(1) factor listing, (2) jury of executive Opinion, (3) sales
force composite, (4) users' expectations, (5) moving aver-
age, (6) exponential smoothing, (7) time series analysis,
and (8) regression and correlation analysis. A comparison
of these techniques with respect to the set of guidelines
revealed that exponential smoothing was the most appr0priate
short-term forecasting method.

The need for a flexible forecasting model was dis-
covered as a result of a research project at the Graduate
School of Business at Michigan State University to deve10p
a viable long-range planning model for physical distribu—
tion systems. The model, referred to as the Long-Range
Environmental Planning Simulator (LREPS), includes (1) the
basic components of the physical distribution system, (2) a
strategic planning horizon, and (3) the sequential decision
prdblem. The model is modular in nature and, since its
initial uses, has been extended to cover broader classes
of manufacturing firm and public sector planning.

LREPS provides the framework for the forecasting

model and a way to validate the forecasting model's

Fred William Morgan, Jr.
capability under controlled conditions. Several hypothe-
sized actual sales patterns, each the result of different
marketing plans and environmental conditions, can be simu—
lated with LREPS. Based on physical distribution costs
and forecasting accuracy, management can determine the
most appr0priate forecasting technique, prediction interval,
and level of detail needed to anticipate these sales pat-
terns. Assuming given external conditions, management can
ad0pt a market plan and know which forecasting system is
most useful.

The research objective, the construction and imple-
mentation of a flexible short—term forecasting model for
use in conjunction with LREPS, has been achieved. An indus-
trial sponsor supplied sample data for the develOpment of a
specific model.

Five values for the exponential smoothing constant
(0.01, 0.05, 0.10, 0.30, 0.50) and for the prediction
interval (1 Wk., 2 wks., 1 mo., 2 mos., 3 mos.) were
examined. Each of these two variables was associated with
variable physical distribution costs through regression
analysis. The t statistic revealed several statistically
significant correlations. Alternative levels of detail

were compared using the F statistic. Based on statistical

Fred William Morgan, Jr.
evidence, the following recommendations were made:

1. Smoothing constant values in the 0.01 to
0.10 range are apprOpriate.

2. Prediction intervals from one to two weeks
are apprOpriate.

3. Product forecasts are as accurate as product-
region forecasts.

The relationship between forecasting accuracy (an
index composed of the relative forecasting variance and
Theil's inequality coefficient) and variable physical dis-
tribution cost was measured using Spearman's rank correla-
tion coefficient. A statistically significant direct rela-
tionship was observed.

LREPS provides several measures of system service
achievement, one of which is the percent of case units
backordered. Percent backorders was regressed against
variable physical distribution cost. The relationship was
an inverse one and was significant at the .01 level, based
on the t statistic. Since service and percent backorders
are inversely related, service and cost proved to be
directly related.

The computer experimentation provides a general
way to adapt this build-up forecasting model for use by

any firm selling products in different market segments.

Fred William Morgan, Jr.
The forecasting technique, the prediction interval, and the
level of detail should be manipulated to Optimize the
firm's objective. The LREPS model facilitates this manipu-
lation by allowing the firm to input alternative simulated

actual sales for testing different forecasting models.

A SIMULATED SALES FORECASTING MODEL:
A BUILD-UP APPROACH

BY

Fred William Morgan, Jr.

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Marketing and Transportation

1972

© Copyright by
FRED WILLIAM MORGAN,

1972

JR.

AC KNOWLEDGMENT S

Several individuals and groups deserve recognition
for their contributions, both direct and indirect, to this
research. The industrial sponsor Of LREPS, Johnson and
Johnson Domestic Operating Company, is gratefully acknowl-
edged. The research team, headed by Dr. Donald J. Bowersox,
faculty advisor, and composed Of several doctoral students,
must be thanked. Team members were Dr. 0. Keith Helferich,
Dr. Edward J. Marien, Dr. V. K. Prasad, Dr. Michael Lawrence,
Dr. Peter Gilmour, and Richard Rogers.

The dissertation committee consisted Of Dr. Donald
J. Bowersox, Dr. Richard J. Lewis, and Dr. Donald A. Taylor,
all Professors Of Marketing and Tran3portation at Michigan
State University, and Dr. 0. Keith Helferich, Systems
Research Incorporated, Lansing, Michigan.

Dr. Bowersox, committee chairman and academic
advisor, has guided me since the outset Of my doctoral pro-
gram. He gave me the Opportunity to participate in the
LREPS project and kept me focused on the research Objectives
Of this dissertation.

Dr. Lewis' knowledge Of forecasting techniques and
Statistical analysis was Of great value in the development

0f the technical aspects Of this research. His constant

iii

encouragement enabled me to persevere to the end.

Dr. Taylor, as department chairman, has been a
steadying influence throughout my academic career. This
is in addition tO his valuable comments and suggestions
regarding this work.

Dr. Helferich spent many hours explaining the in-
tricacies Of the LREPS model and infOrming me Of the latest
model SOphistications. His suggestions led to many improve-
ments in the forecasting model.

Additional support in the form Of computer time and
guidance was provided by Systems Research Incorporated.
Without this assistance this study would have been extended
by several months and hundreds Of dollars.

TO Gerald Brown, who provided the computer program-
ming expertise for this research, I am indebted. His good
humor as I continually changed by programming requirements
should not be unrecognized.

The professional typing assistance provided by
Mrs. JO McKenzie is greatly appreciated. She remained
patient despite my missed deadlines.

Finally, I wish to thank my wife, Karen, and son,
Todd, for their patience and support throughout the duration

Of this research and my doctoral program.

iv

TABLE OF CONTENTS

ACMOM‘EDGMENT S O O O O O O O O O O O O O O O 0

LIST OF TAfiES O O O O O O O O O O O O O O O 0

LIST OF F IGURES O O O O O O O O O O O O O O O 0

Chapter

I.

II.

III.

IMRODUCTION . O O O O C O O O O O O 0

Statement Of Purpose. . .
Situation Analysis. . . .
Research Problem. . . . .
Organization Of Thesis. .

OVERVIEW OF SALES FORECASTING . . . .

Introduction. . . . . . . . . . .
Planning HOrizon for Forecasting.
Uses for Sales Forecasts. . . . .
Criteria for Technique Selection.
Summary . . . . . . . . . . . . .

SALES FORECASTING TECHNIQUES. . . . .

Introduction. . . . . . . . . . . .
Presentation Of Techniques. . . . .
Comparison Of Sales Forecasting
Techniques . . . . . . . . . . . .
Selection of Forecasting Technique.
Summary . . . . . . . . . . . . . .

FOMCAS TING ACCUMCY . O O O O O O O 0

Introduction. . . . . . . . . . . .
Statistical Accuracy Evaluation . .
Nonmathematical Accuracy Evaluation
Accuracy Evaluation by Objectives .
Summary . . . . . . . . . . . . . .

Page
iii

vii

ix

10
14

17

17
19
31
36
46

50

50
50

85
91

98

98
100
107
111
112

Chapter

V.

VI.

VII.

VIII.

RESEARCHIMETHODOLOGY. . . . . . . . . .

Introduction. . . . . . . . . . . . .
The General Model . . . . . .
Researchable Questions and Hypotheses
Research Sequence . . . . . . . . . .

DEVELOPMENT OF THE DETAILED
FORECASTING MODEL. . . . . . . . . . .

Introduction. . . . . . . . . . . .
Smoothing Constant and Prediction

Interval Experimentation . . . .
Level of Detail Experimentation .
Cost-Accuracy Considerations. . .
Summary . . . . . . . . . . . . .

PHYSICAL DISTRIBUTION COST-SERVICE TRADEOFF

Introduction. . . . . . .
Traditional Propositions.
Experimental Results. . .
.Summary . . . . . . . . .

SIMULATED SALES FORECASTING: FINDINGS
AND IMPLICATIONS . . . . . . . . . . .

Introduction. . . . . . . . . . . . .
Summary Of Experimental Results . . .
A General Approach to Short-

Run Forecasting. . . . . . . . . . .
Extensions to Long-Range Forecasting.
Implications for Future Research. . .

BIBL IOGRAPHY O O O O O O O O O O O O O O O O 0

vi

Page
115

115
116
117
122

125
125
126
141
150
154
156
156
157
159
166
168

168
169

174
183
187

199

LIST OF TABLES

Table Page
2.1 Shortest Time Breakdown Used for
Sales Forecasts . . . . . . . . . . . . . . 21
2.2 Frequency Of Sales Forecast Preparation . . . 22
2.3 Frequency Of Sales Forecast Revision. . . . . 23
2.4 Longest Period Ahead for Which Forecasts
Are Regularly Prepared. . . . . . . . . . . 24
3.1 Comparison Of Sales Forecasting Techniques. . 86
6.1 Combinations of Smoothing Constant and

Prediction Interval Values. . . . . . . . . 129

6.2 Physical Distribution Cost as a Function
of Smoothing Constant . . . . . . . . . . . 130

6.3 Physical Distribution Cost as a Function
of Prediction Interval. . . . . . . . . . . 131

6.4 Regression of Physical Distribution
Costs (Y) on Smoothing Constant
Values (X) with Prediction
Interval Fixed. . . . . . . . . . . . . . . 134

6.5 Regression of Physical Distribution
Costs (Y) on Prediction Interval
Values (X) with Smoothing
Constant Fixed. . . . . . . . . . . . . . . 137

6.6 The "Best" Build-Up Function. . . . . . . . . 142
6.7 Summary Of Product-DU F Tests . . . . . . . . 145
6.8 Summary of DU F Tests . . . . . . . . . . . . 146
6.9 Summary Of Build-Up Breakdown Comparison. . . 149
6.10 Indexes of Forecasting Accuracy . . . . . . . 152

vii

Table

7.1

Physical Distribution Cost-Service
values 0 O O O O O O O O O O O O O O O O O O 164

Cost-Service Regression . . . . . . . . . . . 165

Comparison Of Strategic and
Tactical Planning . . . . . . . . . . . . . 184

viii

LIST OF F IGURES

Figure Page
1.1 Stages Of the Physical Distribution

Network 0 O O O O O O O O O O I O O O O O O 5

1.2 Physical Distribution Systems Concept . . . . 8

ix

CHAPTER I

INTRODUCTION

Statement Of Purpose

 

The determination Of sales volumes for future time
is mandatory for assessing a company's prosPects. The
sales forecast is the core Of management's planning effort.
However, even firms with the most SOphisticated forecasting
systems cannot evaluate their forecasting capabilities un-
til anticipated sales become actual sales. The overall
purpose Of this research is tO develOp a way to deal with
this measurement problem. This is accomplished by devising
both a forecasting archetype and an approach for tailoring
the forecasting model to meet specific needs.

Three traditional bases for categorizing forecast-
ing models are:

l. The length Of the forecasting period

2. The level Of the forecast

3. The technique utilized.

Forecasting periods shorter than one year can be arbitrarily

defined as short-term, while periods lengthier than one

1

year are long—term in nature. The level Of the forecast
could be the economy, the industry, or the firm. Within
the firm are product, product group, region, and product-
region levels. Techniques can be described as either
mathematical or nonmathematical with managerial judgment
playing a vital role in either case.)

TO set the stage for the prOpositions which follow,
a definition Of a sales forecast is needed. The following

definition that the American Marketing Association pre-

scribes is used:1

Sales Forecast--An estimate Of sales in dollars
or physical units for a specified future period
under a prOpOsed marketing plan or program and
under an assumed set Of economic and other forces
outside the unit for which the forecast is made.
The forecast may be for a specified item Of mer-
chandise or for an entire line.

Comment--Two sets Of factors are involved in making
a Sales Forecast: (1) those forces outside the
control Of the firm for which the forecast is

made that are likely to influence its sales,

and (2) changes in the marketing methods or prac-
tices Of the firm that are likely tO affect its
sales.

In the course Of planning future activities,
the management of a given firm may make several
forecasts, each consisting Of an estimate Of
probable sales if a given marketing plan is
adOpted or a given set Of outside forces prevails.
The estimated effects that several marketing plans
may have on Sales and Profits may be compared in
the process Of arriving at that marketing program
which will, in the Opinion Of the Officials Of the
company, be best designed tO promote its welfare.

The following comments about the usefulness Of

3
forecasting provide an alternative viewpoint:2

Once established, the sales forecase becomes
the basis for marketing and other plans in the
company, with the volume Of sales forecast, in a
sense, as a built-in goal. As a chemical company
executive puts it, "When sales are forecast at
a certain level, the entire Operation—-production,
marketing support, sales manpower, etc.--is geared
to that level Of activity." This leads some tO
argue that the forecast is to a considerable ex—
tent self-fulfilling, sO that any later comparison
Of actual sales with the forecast value may be a
better gauge Of marketing accomplishment than Of
forecasting accuracy.

The spOkesman for a large Office equipment
company feels strongly about this point. "I do
not consider what we do 'forecasting,'" he
asserts. "We are setting targets, self-fulfilling
prophecies. One only forecasts events over which
he has no control. This distinction needs far
more emphasis than it is typically given."

The American Marketing Association's definition
provides considerable direction for this research. First,
several forecasts, each resulting from a different set Of
environmental conditions and marketing plans, should be
prepared. Next, the forecasting period should be specified
because different length periods are possible. Finally,
the forecast could be made for an individual product or for
the entire product line.

The executives' comments imply that a gauge for com-
paring forecasts with actual sales helps to evaluate fore-

casting accuracy and to measure marketing effectiveness.

4

Situation Analysis

 

Computer simulation can incorporate the desired
forecasting model features into a single comprehensive
model. Simulation permits a more realistic and complex
model for solving business problems than those possible
through the application Of analytical techniques. '

While a generalized simulation Of the firm is not
yet available, the physical distribution system has been
modeled successfully. The integrated physical distribution
network has been conceptualized as consisting Of fixed
facilities, transportation capability, inventory alloca-
tions, communication, and unitization.

An overview Of the typical physical distribution
system appears in Figure 1.1. There are three stages Of
activities: (1) the Manufacturing Control Center (MCC)
stage at which products are produced and inventoried at the
Replenishment Center (RC), (2) the Distribution Center (DC)
stage at which products are located adjacent tO the market—
place, and (3) the customer demand stage, identified in
Figure 1.1 as the Demand Unit (DU) stage. Demand units
consist Of the geographic customer groupings because the
inclusion Of individual customers as DU's is prohibitively

costly and time-consuming. For this application DU's are

defined as ZIP Sectional Centers, although counties,

FIGURE 1.11

STAGES OF THE PHYSICAL DISTRIBUTION NETWORK

 

STAGE 1:

Hanufacturin
Control
Centers
and
Replenish-
ment
Centers

STAGE 2:

Distri-
bution
Centers

STAGE 3:

Demand
Units

 

 

 

PD REGION

 

PD REGION

 

 

 

 

 

 

——INFORMATION FLOW PRODUCT FLOW

REGION...THE REGION IS DEFINED BY THE ASSIGNMENT OF RDCS AND DUS T0
AIPDC.

CC......EACH MANUFACTURING CENTER PRODUCES A PARTIAL LINE.

RC.......REPLENISHMENT CENTERS STOCK ONLY PRODUCTS MANUFACTURED AT
COINCIDENT MCC.

RDC. . . . . .REDDTE DISTRIBUTION CENTER, FULL OR PARTIAL LINE.

PDC......PRIMARY DISTRIBUTION CENTER, EACH PDC IS FULL LINE AND SUPPLIES

ALL PRODUCTS TO DUS ASSIGNED TO THE PDC REGION; PRODUCT CATE-

GORIES NOT STOCKED AT THE PARTIAL LINE RDCS IN THE REGION ARE

ALSO SHIPPED BY THE PDC.

DU.......THE DEMAND UNIT CONSISTS OF ZIP SECTIONAL CENTER(S).

 

 

 

1

D. J. Bowersox, et al., Dynamic Simulation of Physical Distribu—
tion Systems, Monograph (East Lansing, Michigan: Division Of Research,

Michigan State University, Forthcoming).

6
Standard MetrOpolitan Statistical Areas, Economic Trading
Areas, and REA modified grid blocks were also given con-
sideration.6

The distribution center stage includes four levels:
(1) Primary Distribution Centers (PDC), which handle a full
line Of products and have the potential to serve all the
DU's in a defined region Of the total market area; (2) Re-
mote Distribution Centers—Full Line (RDC-F), which handle
all products; (3) Remote Distribution Centers—Partial Line
(RDC-P), which handle only a portion Of the product line;
and (4) Consolidated Shipping Points (CSP), RDC-P's Which
handle no products, but function as points at which the
demand Of several DU's is agglomerated and served by a PDC.
PDC's are capable of serving the same DU's served by
RDC-P's; however, PDC's cannot serve the DU's served by
RDC-F's.

A computerized model, encompassing all Of the
aforementioned components and activities, has been
developed.7'8 This model is entitled Long-Range Environ-
mental Planning Simulator (LREPS). It is capable of simu—
lating changes in the firm's physical distribution system,
such as the addition Of distribution centers or the re-
arrangement Of communication linkages.

The conceptual model can be most easily understood

7
by examining Figure 1.2, which illustrates the major model
components. The Demand and Environment Subsystem (D&E)
focuses on testing for changes in the customer and product
mix and in order characteristics. The D&E also provides
the sales level and the basis for allocating sales among
DU's. The Operations Subsystem (OPS) processes orders
through the major physical distribution activities. The
Measurement Subsystem (MEAS) develOps the criteria for
evaluating alternative distribution system configurations.
The Monitor and Control Subsystem (Mac) is the model super-
visor and the controller section Of LREPS in which feedback
from past activities can dynamically affect current policy
decisions. Exogenous data are inputted through the Support-
ing Data Subsystem which audits, reduces, and formats infor-
mation into usable terms. Finally, model output is con-
verted into managerial reports by the Report Generator
Subsystem.

Figure 1.2 reveals the importance Of the sales
pattern as a critical input to LREPS. One Of the unique
features Of LREPS is the treatment Of sales volumes and
patterns. Several activities carried out within the Sup-
porting Data Subsystem relate tO the preparation Of sales

data.

The first step is a detailed analysis Of sales

 

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9
invoices. All invoices for several years can be analyzed,
but statistical sampling can significantly reduce this
number. Sample invoices are arrayed in matrix form. In-
voices are randomly selected from the matrix, and each line
entry on the invoices is compared with the list Of tracked
products (those included in LREPS as being representative
Of the entire product line). If the line entry matches a
tracked product, then it is included as a line entry on a
simulated invoice. The entry consists Of product order
dollars, weight, cube, and cases. Order summaries, in-
cluding total order dollars, weight, cube, cases, and lines,
are accumulated for all products. The simulated invoices
representing the tracked products and customer types com-
prise the Order File Generator, from which orders are
selected tO fill simulated demand requirements.

Multiple customer types with different order char-
acteristics (e.g., different average order dollars, weight,
etc.) can be simulated. New customers with hypothetical
order characteristics are also permitted. New products can
ibe modeled by assuming values for the average and standard
deviation Of cases per order and dollars, weight, and cube
per case. The distribution Of lines per order can also
be varied.

LREPS requires a data stream representing simulated

10
actual daily sales. The pattern is arbitrary. It can be
a simple linear trend, an oscillating function, or even a
random function. Daily sales are allocated tO 390 domestic
DU's (derived from ZIP Codes) based on weighted indexes.
The indexes are constructed by correlating regional sales
with one or more independent variables. For example, if
lpopulation were the only independent variable selected,
then each index would be the ratio Of the DU's pOpulation
to the total U.S. pOpulation.

Orders are randomly selected from the Order File
Generator until their total sales equals simulated actual
daily sales. Detailed records are maintained for the
tracked products for inventory control and system costing
purposes. The results for the tracked products are extra-

polated tO represent the entire product line.

Research Problem
A specific research problem can now be formulated.
The LREPS model facilitates the inputting Of many sales
patterns, each representing the effects Of a different com-
bination Of marketing and environmental factors. The use Of
several forecasting levels is possible with LREPS, the most
detailed being the product-DU level. since one day is the

smallest discrete event processed within LREPS, one week

 

 

has been arhi
val; however,
forecasting t
or regions.

easily be inc

 

Of a forecast
the LREPS str
The c
implement a n
Sim 0f fore
utilizing the
Order File 3,
detailed I20 .
EmPhasis is
the Span.
LREE
medal and a

hint}! up

11
has been arbitrarily defined as the shortest forecast inter-
val; however, any longer interval is permissible. Different
forecasting techniques can be applied tO different products
or regions. Finally, accuracy measurement formulae can
easily be incorporated into LREPS. Every desirable feature
Of a forecasting model noted earlier can be handled within
the LREPS structure.

The Objective Of this research is tO build and tO
implement a model with flexibility along the three dimen-
sions Of forecasting technique, time interval, and detail,
utilizing the unique allocative capability Of the LREPS
Order File Generator. The result is a build-up (from
detailed tO aggregate levels) forecasting mechanism.
Emphasis is arbitrarily placed on a short-term (one year)
time span.

LREPS provides the framework for the forecasting
model and a way to validate the forecasting model's capa-
bility under controlled conditions. Several hypothesized
actual sales patterns, each the result Of different market-
ing plans and environmental conditions, can be simulated
with the LREPS Order File Generator. Based on physical
distribution costs and forecasting accuracy, management can
determine the most appropriate forecasting technique, pre-

diction interval, and level Of detail needed to anticipate

 

these sales 3

 

management cs
casting syste

To ac
have been ca:
sions of the
iled forecas:
initial portj
for later co:

fOrlnulatedz

l. I-

77;

 

12
these sales patterns. Assuming given external conditions,
management can adOpt a marketing plan and know Which fore—
casting system is most useful.

TO accomplish this Objective, two research phases
have been carried out. In the first phase the three dimen-
sions Of the forecasting model are studied, and a general-
ized forecasting mechanism is constructed. TO guide the
initial portion Of this research and to lay a foundation
for later computer experimentation, these questions were
formulated:

1. What are the criteria for selecting the most
useful forecasting system? How should a short-
term (one year) forecasting mechanism be chosen?
Although each firm is in a somewhat unique situ-
ation, perhaps certain guidelines could
prove to be universally applicable.

2. What is the current "state Of the art" Of
forecasting? What techniques are presently
available for use in predicting sales volumes?
Will the shortened time period (one year) de-
crease the number Of alternatives?

3. What are the criteria for evaluating forecast-
ing accuracy?

The second research phase is an example Of an

13
application Of the generalized forecasting model, used in
conjunction with LREPS. Computer experimentation is used
to determine levels for the smoothing constant (parameter
Of the simple exponential smoothing model, the chosen fore-
casting technique), the time interval, and the level Of
forecasting detail. The effects on physical distribution
costs and forecasting accuracy Of varying these three
dimensions are subjected tO statistical analyses.

Both smoothing constant values and prediction inter-
val values can be associated with physical distribution
costs and forecasting accuracy by using regression and cor-
relation analysis. The t statistic is used to test for
significance Of the relationships. The appropriate level
Of detail can be determined by comparing forecasting vari-
ances for alternative levels through the use Of the F test.
By specifying design constraints (e.g., minimized physical
distribution costs or forecasting accuracy), management
specifies the levels Of the dimensions Of the forecasting
model.

Additional experimentation associating physical
distribution costs and service is presented to illustrate
a specific use for the detailed, short-term forecasting

model.

14
Organization Of Thesis

This dissertation consists Of eight chapters.
After the introductory chapter, Chapter II provides an
overview Of sales forecasting. The planning horizon
covered by the forecast is discussed, as are the many uses
for sales forecasts. A set Of guidelines to aid in the
selection Of the forecasting technique is presented.

Chapter III details the various forecasting tech-
niques along with a comparison Of these alternatives. A
forecasting technique to be used in conjunction with LREPS
is chosen, using the selection criteria develOped in the
previous chapter.

Measures Of forecasting accuracy are explored in
Chapter IV. Both quantitative and qualitative approaches
are dealt with in detail. In addition, an evaluative
process is covered which differs somewhat from conventional
statistical error analysis.

Chapter V delineates the research methodology
followed in the computer experimentation. The research
hypotheses are devised in testable form.

The first set Of computer experiments is described
in Chapter VI. At this stage the predictive equations,
the build-up function, and the prediction interval are

studied. The final version Of the applied, short-term

 

forecasting
The
cost and ser

in Chapter V

 

the traditio:
Fina
findings to
Sales foreca
cam“? are

15
fOrecasting model is presented.

The second group Of experiments, those relating the
cost and service Of physical distribution, are presented
in Chapter VII. A comparison Of experimental results with
the traditional concept is Offered.

Finally, Chapter VIII summarizes the previous
findings to suggest a generalized approach to simulated
sales forecasting. The implications for longer—term fore-
casting are discussed. Areas for future study which have

been uncovered by this work are also outlined.

 

 

lam
Terms (Chicag
p. 22.

 

25L“

hperiences i
The National

3P. I
11°.“ (unpubl:
University, ;

4
For

in the analys
DeVelo ment c
Ph Sical Dist
mica) Mode]

5D

6Hel:

16

CHAPTER I--FOOTNOTES

1Marketing Definitions: A Glossary Of Marketing
Terms (Chicago: The American Marketing Association, 1960),

p. 22.

2Sales Forecasting Practices: An Appraisal,
Experiences in Marketing Management, NO. 25 (New York:
The National Industrial Conference Board, 1970), p. 34.

3P. Gilmour, Development of a Dynamic Simulation
Model for Planning Physical Distribution Systems: Valida—
tion (unpublished doctoral dissertation, Michigan State

University, 1971).

4For a discussion Of the usefulness Of simulation
in the analysis of business problems, see 0. K. Helferich,
.pgvelopment Of a Dynamic Simulation Model for Plannipg
Physical Distribution Systems: Formulation of the Mathe-
matical Model (unpublished doctoral dissertation, Michigan

State University, 1970).

5D. J. Bowersox, E. W. Smykay, and B. J. LaLonde,
Physical Distribution Management (New York: The Macmillan
Company, 1968), Ch. 5.

6Helferich, pp. 112-121.

7Helferich.

8E. J. Marien, Development Of a Dynamic Simulation
Model for Planning Physicalgpistribution Systems: Formu-
lation of the Computer Model (unpublished doctoral disserta-
tion, Michigan State university, 1970).

CHAPTER II
OVERVIEW OF SALES FORECASTING

Introduction

As firms continue to adOpt and tO practice the
marketing concept, anticipation Of the future becomes
critical. Prompt reaction to diagnosed needs indicates
that the marketing concept has been implemented. The
diagnosis, or the anticipation, provides the information
base upon which marketing plans are constructed.

Many companies formalize this anticipatory process
and call it "planning." The planning process includes
Objectives and strategies, policies, and detailed plans
designed to achieve these Objectives. Further, planning
is Operationalized through an organization which implements
decisions and reviews performance to set the stage for
another planning cycle.1

A primary component Of planning is the sales fore—
cast. The sales forecast is a vital link in the circuitous
forecast-marketing activity-results (sales)-forecast, etc.
relationship. Without the forecast, levels Of marketing

17

18
activity cannot be meaningfully determined. Conversely,
not knowing the sales that result from a given level Of
marketing effort, the marketer can't develOp a sound fore-
cast. This circular process can "explode" by compounding
the inaccurate forecast, or it can be "fine-tuned" by dis-
covering the nature Of the marketing-output relationship.

It is apparent that the Objective Of sales fore-
casting is tO reduce the uncertainty which enshrouds man-
agement decision making.2 The amounts Of product sales in
the different market segments Obviously cannot be known
exactly. The purpose Of sales forecasting is to reduce
the range within which sales will lie. SO sales forecast-
ing deals with probabilities, averages, variations, and
confidence intervals.

An important aspect Of any probabilistic process,
such as sales forecasting, is the error Of the estimate.
(See Chapter IV for a detailed discussion Of error
analysis.) Anytime the future is evaluated, a certain
amount Of error is bound to be present under nondetermin-
istic conditions. Error can arise from two different
sources, depending on which is utilized: extrapolating
historic data and estimating future business conditions.
These are the two types Of limiting approaches tO fore-

casting. Using only historic data, Or intrinsic factors,

 

 

I re toreca
and condiI
tions can
into acco
tionships
I N
ness of t
Order to '
th<°---fact,
I Wide man
PEI‘iod.
smoothlY

19

the forecaster assumes a continuation Of past relationships
and conditions. On the other hand, new variables and func-
tions can be developed from extrinsic factors which take
into account a supposed restructuring Of traditional rela-
tionships.3

NO matter which perspective is adOpted, the timeli-
ness Of the forecast is an important consideration. In
order to be a forecast, the estimate must be made before-
the-fact. The estimate must be available soon enough to
guide management as it develOps plans for the forecasted

period. As a result, the feedback mechanism must Operate

smoothly and precisely. Data must be available for analysis

as soon as they become "history."

Planning Horizon for Forecasting

The forecasted planning horizon can be studied

from two standpoints. First, it can be viewed from strictly

a time-oriented perspective. Over how long a period is the

firm forecasting? Is it a month, a year, or several years?4

The other viewpoint refers to the scOpe or level Of the
forecast. Is the forecast made at the product, firm,

industry, or even the national level?

 

Forecastin

 

The
first. Ther:
investigatio
data are pre
preparation

subset is th

 

 

 

 

term forecas

A re
m0“ Popular
lights the r
The rInge 01
week. month‘

As 1
cast prePar.
for which f.
data On fre:
revised betr
supported b}

ASE

short‘terrn I

I

2
.4 ”Maria

20
Forecasting Frequengy

The frequency Of the sales forecast is examined
first. There are actually three subsets to this area Of
investigation. The specific time period for which forecast
data are prepared is one area. Next is the frequency Of
preparation and revision Of forecast data. The remaining
subset is the longer-term period for which these shorter-
term forecasts are collected.

A recent survey Of 161 companies revealed that the
most pOpular forecast period is one month. Table 2.1 high-
lights the responses collected from the reporting companies.
The range of time periods which were mentioned includes day,
week, month, quarter, half-year, and year.

As might be expected, the frequency Of sales fore-
cast preparations varies considerably from the time period
for which forecasts are compiled. Table 2.2 presents the
data on frequency Of preparation. Forecasts are, however,
revised between major preparations. This contention is
supported by comparing Tables 2.2 and 2.3.

As noted in Chapter I, this research is aimed at
short-term (one year and less) estimations; however, to
complete this phase Of the analysis, the length Of the
longer-term forecasting period should be presented. Table

2.4 summarizes the answers provided by the surveyed firms.

‘ t

21

TABLE 2.l.--Shortest Time Breakdown Used for Sales Forecasts1

 

 

 

 

2
Percentage of Forecasts
Time Period All Manufacturing Service
Breakdown

Companies Companies Companies

Reporting Reporting Reporting
Month 52% 552 43%
Quarter 21 23 13
Year 22 17 40
Other3 5 5 4

Total 100% 1002 1002

 

Note: Based on information from 161 reporting companies-~132
manufacturers and 29 service firms (insurance, banking, transporta-
tion, utilities).

lSales Forecasting Practices: An Appraisal, Experiences in
Marketing Management, No. 25 (New York: The National Industrial
Conference Board, 1970), p. 23.

2Percentages are for forecasts made at all levels of product
detail.

3Includes day, week, half—year.

"37;. m2". 1"

22

TABLE 2.2.--Frequency of Sales Forecast Preparation1

 

 

Percentage of Forecasts2

 

Time Period

 

A11 Manufacturing Service
Breakdown

Companies Companies Companies

Reporting Reporting Reporting
Annually 58% 532 76%
Semiannually 4 3 ll
Quarterly 20 22 9
Monthly 14 17 2
Other3 4 5 2
Total 100% 100% 1002

 

Note: Based on information from 161 reporting companies--132
manufacturers and 29 service firms (insurance, banking, transporta-
tion, utilities).

lSales Forecastigg Practices: An Appraisal, Experiences in
Marketing Management, NO. 25 (New York: The National Industrial
Conference Board, 1970), p. 21.

2Percentages are for forecasts made at all levels of product
detail.

3Includes "as needed,” bimonthly, weekly, seasonally, biennially,
and irregularly.

23

TABLE 2.3.—-Frequency of Sales Forecast Revision1

 

 

2
Percentage of Forecasts

 

 

Time Period All Manufacturing Service
Breakdown Companies Companies Companies
Reporting Reporting Reporting
Monthly 24% 28% 0%
Quarterly 29 30 28
Semiannually 12 12 12 I
Annually 20 16 42
As needed 7 6 10
cam-3:3 __§ ___8 __§
Total 100% 100% 1002

 

Note: Based on information from 161 reporting companies--132
manufacturers and 29 service firms (insurance, banking, transporta-
tion, utilities).

1Sales Forecastipg Practices: An Appraisal, Experience in
IMarketing Management, NO. 25 (New York: The National Industrial
Conference Board, 1970), p. 22.

2Percentages are for forecasts made at all levels of product
detail.

3Includes daily, weekly, bimonthly, and a few irregularly timed
revisions.

24

TABLE 2.4.-—Longest Period Ahead for Which
Forecasts Are Regularly Prepared

 

 

Percentage of Forecasts2

 

 

Longest Period All Manufacturing All Service
Companies Reporting Companies Reporting
Less than one year 12% 4%
One year 36 35
Between one and five years 19 11
Five years 28 33
Over five years 5 17
Other3 __-_a __0
Total 100% 100%

 

Note: Based on information from 161 reporting companies--132
manufacturers and 29 service firms (insurance, banking, transporta-
tion, utilities).

1Sales Forecasting Practices: An Appraisal, Experiences in
Marketing Management, No. 25 (New York: The National Industrial
Conference Board, 1970), p. 24.

2Percentages are for forecasts made at all levels of product
detail.

3Includes irregular intervals (e.g., "life of product"); "skip"
intervals (e.g., "next three years and the fifth"); and other
indeterminate periods (e.g., "through the next season").

8Less than 1%.

‘l‘ -E7Illh‘l|

25

The previous data indicate that the prediction
period, revision frequency, and overall planning range vary
considerably. Because Of this variation, forecasts are
generally classified as short-term (Operating) or long—term
(planning) in nature. The dividing line between these two
extremes is not a sharply defined one. Often this margin
is defined as the area Of intermediate forecasts. A long-
term forecast for one firm may be a short-term estimate
for some other company, depending on several conditions
which are discussed later.

Operating forecasts guide the company in its day-to-
day or week-tO-week functioning. Of particular relevance
to this research are the effects Of forecasts on inventories,
distribution service capabilities, and distribution costs.
Considerable detail is required for these Operating fore-
casts tO be useful. For example, product forecasts, or at
least product group forecasts, would be necessary to main-
tain the inventory control system. I

Long-range forecasts emphasize general tendencies
.in.the sales pattern. These estimates are used as overall
gpuides for the establishment Of policy and the direction Of
corporate effort. Capital investment might be based on
long-range sales expectations. The level Of detail isn't

necessarily as demanding for long-term forecasts. The

26
general purpose Of these estimates doesn't require a
product-territory breakdown.

A convenient scheme for classifying forecasts could
be based on a period Of one year. If the sc0pe Of the
forecast is one year or less, it could be defined as short-
term in nature. If the forecast is for several years, it
is a long-range estimate. TO hedge slightly would be tO
define the range for intermediate forecasting as going from
one to three years. The classificatory criterion is
strictly arbitrary.

One rule to aid in the selection Of the prediction
interval has been Outlined: the purpose Of the forecast
(Operating vs. planning). A general set Of guidelines can
be suggested:5'6'7'8

1. Purpose Of the forecast

2. Degree Of accuracy desired

3. Characteristics of the time series

4. Availability Of forecasting techniques

5. Fiscal year Of firm.

The first guideline has already been covered in
sufficient detail. The desired degree Of accuracy refers
to a general relationship between the length Of the fore-
cast period and the accuracy Of the forecast. An accepted

belief is that accuracy decreases as the time interval

27
increases. This seems to be reasonable because the distant
future is usually more unclear than the near future. The
validity Of this hypothesized relationship is explored
during the experimental phases Of the research.

Equally important as the level Of accuracy are the
basic characteristics Of the time series. In other words,
what is the expected volatility Of sales over future time
paths? A pattern indicating a smooth, regular change over
time between periods Of high and low sales may allow a
relatively lengthy prediction period. Conversely, an
erratic pattern may necessitate a shorter interval. Many
factors could affect the regularity Of sales. These in-
clude the nature Of the product, geographic location of the
market, and the rate Of innovation, to name only three.

The availability Of forecasting techniques is a
"state Of the art" limitation. As technology, primarily
computers, advances, problems Of data storage and manipula-
tion are being overcome to a substantial degree. Excepting
long-term trend analysis, long-range forecasting isn't
reliable because Of the limitations Of current forecasting
techniques.9 Numerous authors have reported attempts to
forecast the business cycle with varying degrees Of
success.10'll'12 Until executives understand the inherent

relationships Of the business cycle, long-range forecasting

IF- 51ml

28

will remain underdeveloped; furthermore, prediction intervals
will necessarily remain short.

Finally, the corporate fiscal year imposes restric-
tions on the forecasting interval. Financial statements,
tax returns, and budgets are generally prepared to conform
to the fiscal time period. Since forecasting is such an
integral part Of budgeting, it is logical that the forecast

13'14 Perhaps periods

would parallel the fiscal year.
shorter than the fiscal period might be forecasted, but
these forecasts could be aggregated to yield the forecast

for the fiscal year.

Forecasting Level

The different levels Of forecasting are typically
classified as the economy, the industry, and the firm.
‘Within the firm it is possible to reach an even more de-
tailed level, such as by product, by geographic region
(based on sales territories, supply locations, or some grid
system) or by customer type. As firms become larger and
look for new markets, perhaps the economy level will become
a subset Of a global forecast.

The implication Of this treatment Of forecasting
levels is, so far, that proper forecasting technique en-

'tails a general-to-specific direction. In other words, the

I" -:"_a-|_AIO'1

29
first forecast should be a general economic analysis, per-
haps with an estimate of gross national product or dispos-
able personal income. Knowing the forecast for general
business conditions and the relative importance Of the in—
dustry to the economy, a firm can develOp the industry
forecast. This is the "pot" for which competitors in an
industry vie. Relative marketing effort determines what
percentage Of industry sales a given company captures.
Beyond this, the marketing effort for a given product in
a certain geographic area determines that product's sales
in the area.

It is the contention here that the build-up approach
is just as reasonable and logical an approach tO forecast-
ing as the aforementioned breakdown method. The build-up
technique is essentially the Opposite Of the breakdown
approach. Instead Of going from general-to—specific, the
lnaild-up method emphasizes a reverse flow. The overall
forecast is the result of consolidating many smaller, more
detailed ones.

Several reasons can be suggested in support Of the
tnrild-up approach. They are as follows:

1. The computer has significantly reduced the

data storage and computational barriers tO
build-up forecasting.

2. Geographic segments may differ substantially

30

in terms Of buying behavior.

3. Different products may exhibit dissimilar
sales patterns over time.

4. Relative marketing effort may have a

greater impact on sales than general
business conditions.

As noted in Chapter I, the electronic computer is
characterized by processing speed and data storage capacity.
The nature Of build-up forecasting calls for a large data
bank. For example, a geographic-product class reference
system, such as the one in LREPS, requires input data for
each forecasting cell. In addition, predictive equations
and parameters must be built for each cell, although certain
cells may utilize the same equations. The critical role Of
the computer becomes evident. Without the data storage
capacity the essential inputs could not be organized, and
without the computing speed the forecasts would be prohibi-
tively expensive and untimely.

For many reasons people in different parts Of the
country may react in unique ways to the firm's marketing
effort. For this research the reasons aren't as important
as providing a mechanism.which allows the inclusion of con-
trasting behavior. If these segments weren't analyzed
separately, the overall forecast might be reasonable;

however, offsetting errors might hide the individual

.‘..a “J'Kl’

 

 

mistakes

can exh
formula
product
managen

Virtual

approac
market;
variab.
times A

affect

31
mistakes at the detailed level.

As with geographic variance, individual products
can exhibit greatly differing sales patterns. A prediction
formula for each product may be in order. Accuracy at the
product level is especially important in terms Of inventory
management. Offsetting errors by product could result in a
virtually ineffective system Of inventory controls.

Perhaps the foremost reason for using the build-up
approach is that it deals directly with the effect Of the
marketing plan. The breakdown method treats the marketing
variables after considering general economic factors. Often
times the firm in question may be only insignificantly
affected by the level Of national prosperity. In such
cases, relative marketing effort may hold the key to sales
volume. The build-up approach facilitates such an analysis

by beginning with a detailed, segment-by-segment forecast.

Uses for Sales Forecasts
Earlier the distinction between long- and short-
term forecasting was described, as was the purpose Of these
projections. The value tO tOp management Of sales estimates
for distant time periods was noted. The forecast is a fun—
damental input to the long-range planning process, and the

long-range plan provides the framework for short-term

Q

11‘

 

 

 

 

operations
with devei

discussed

uses for
tion char
Sales esI
here is I
other US
many com

include

. 15
Operations.

32

Since this research is primarily concerned

with develOping a short—term forecasting device, the uses

discussed here relate to this time span.

The simplest way tO appreciate the multiplicity Of

uses for forecasts is to examine a typical firm's organiza-

tion chart.

sales estimate as a guide to its Operation.

Nearly every branch or department requires a

The emphasis

here is on marketing's utilization of the forecast, but

other uses are covered for completeness.

A listing of the

many company areas interested in the sales forecast would

include the following:

1.

Production

a. output

b. materials procurement
Engineering

Research

Personnel

Finance

a. budgeting

b. pricing

Marketing

a. promotion

b. pricing

c. sales budgeting

d. sales service

e. distribution--inc1udes inventories,

trans-

portation, communications, unitization,

and facility location.

33
Economies in the production process are attained via
high—volume production runs. Applying the systems concept,
management realizes that minimizing production costs doesn't
necessarily imply maximizing company profits. One means Of
emphasizing this message to production management is through

the sales forecast. Fluctuating seasonal production requires

“I.”

trading Off among production economies, storage costs, and

IT-'“~=
ll

other firm expenses. An important use Of the sales fore-
cast is tO provide production managers with a gauge for
planning and controlling output.16 The forecast becomes
the basis for assigning plant capacity, anticipating work
force needs, and sequencing the delivery and storage Of
supplies and input materials.

A common use for the sales forecast by the engineer-
ing department would be in the scheduling Of machinery re-
pair and plant maintenance.17 The sales forecast guides
the production schedule which, in turn, can be used by
engineering to arrange upkeep work during minimal production
periods.

Anticipating the sales volume Of a new product is
a most difficult and critical undertaking, yet too Often
this is not done. A textbOOk application Of the marketing
concept would entail discerning an unsatisfied need as the

first step in new product planning. But if the technical

34
staff develops the product in the laboratory, independent
of market needs, the sales forecast might be overloOked.
This should not be the case. Regardless Of the source Of
the innovation or its "newness," the sales forecast Offers
a rational assessment Of potential.

The very nature Of the personnel function implies
a need for estimates Of future sales. Determining the size
Of the work force, especially that prOportion classified as
a variable productive force, is dependent upon the volume
of output. Again the sales forecast is a vital information
requirement.

Another area inherently affected by the sales fore-
cast is finance. Preparing corporate budgets and, with the
help Of department personnel, the departmental budgets,
financial executives must know the anticipated sales
volumes. A considerable amount Of detailed forecasting
is required to generate adequate budgets, especially for
individual products or product groups. Long-term financial
planning utilizes forecasts also, but this area is outside
the limits Of this research.

Marketing relies on correct forecasts as much as,
if not more than, any other department. Often times prO-
motional expenditures are planned on the basis Of revenues.

(The validity Of this allocative sequence is not questioned

I“

35

.ere.) Marketing and finance collaborate to set selling
rices. The price is a function of market conditions and
tandard costs, to list only the two most important factors.
.n estimate of volume is necessary to determine cost levels
,nd to validate market conditions. This is a circular
Irocess since sales depend on price and vice versa.

The sales manager needs the forecast to set terri-
Orial and product sales quotas and targets. The expected
’Olume in each territory helps the manager allocate personnel
In an equitable basis. Regional estimates aid in the estab-
.ishment Of service branches by benchmarking the areas of
Ioncentrated sales effort.

Distribution is another marketing area for which
,he sales forecast is an essential input. The impact of
.he forecast on inventories is readily observable from the
Itandard formula for the economical order quantity. If
Inly a constant cost of ordering (A) and annual carrying
:harge (i) are assumed, then the order quantity which

rinimizes cost is
AS

Y: ._.,__
1.

here 8 is annual sales units. Adding more cost elements
omplicates the formula, but the same cost minimization
Iroblem remains. The prOblem seems simple enough. Yet an

.naccurate estimate for S makes the entire Operation

_‘ {I ‘ ”3779‘”!

 

36
superfluous. Without an accurate estimate for sales, the
analysis reduces to a test of mathematical dexterity.

The other elements of the distribution system are
influenced by the sales forecast more on a joint basis,
rather than individually. This is a manifestation of the
systems concept. An accurate forecast can reduce the num-

ber and size of inventories in the distribution system.

1 N cam—L‘A 1

The number of inventories is synonymous with facility

Iii

locations. Facility location points can be reduced to the
level where total distribution costs, also including trans-
portation, communications, and unitization, are minimized.
Without precise forecasts transportation and communications
costs may be lowered because of the many, large inventory
placements. The overall effect may be to incur nonoPtimum
system costs, due primarily to exorbitant inventory cost.
Forecasting accuracy allows management to minimize the sum
of all costs with a greater degree of confidence in the

results.

Criteria for Technique Selection
Several points have been covered which can be listed
.in a set of criteria for guiding the selection of a sales
.forecasting mechanism. Other considerations have not yet

been covered explicitly, but they merit inclusion in the

37
ist which follows:18'19

1. Cost

2. Level of detail

3. Accuracy

4. Turning points

5. Market factors

6. Inputs i:

7. Planning horizon

8. Timing

9. Rigor

10. Clarity.

There is the temptation to beg the issue by
Ieclaring that all companies are different and so to con-
:lude that this list is not useful. On the contrary, these
en factors are independent of the firm being analyzed.
very company should be able to appraise itself with
espect to each factor. Contradictory Objectives may be

lluminated by such an analysis; nevertheless, these

riteria help to focus on feasible forecasting methods.

Cost is the expense associated with the functioning
f the sales forecasting mechanism. This category includes

he computer or clerical cost to Operate the model, the

38
cost to gather and format the data, and the cost to analyze
and to prepare reports. By now the interdependence of these
criteria should be apparent. Detail and accuracy, for ex—
ample, are attained at a specific cost. Changing either of
these will result in a different cost. Management must
decide if the given forecast is the best for a reasonable
cost level. If not, either the forecasting method can be
changed, or the present approach can be analyzed for poten-

tial improvement.

Level of Detail

The level of detail refers to the intrafirm fore-
casting level. Is a forecast going to be developed for
each product in each sales region? Or will a selected
sample of products be tracked over time, as in the initial
LREPS model? The importance of detail for Operating fore-
casts has already been pointed out. Of course, if every
;product is forecast for each tiny geographical segment,
accuracy is lost. There seems to be a level of detail
beyond which sales volume is so small and erratic that

:forecasting accuracy is decreased.

Ac cur agy

Accuracy is an after-the-fact concept. Certain

forecasting techniques may logically seem to be more useful

39
in a given situation, but only by comparing performance
with estimates can the forecast be evaluated. Management
must continually monitor the forecasting mechanism for
accuracy readings. (See Chapter IV for suggested accuracy
measurement approaches.) Standards and tolerances can be
set, based on managerial experience and judgment. If the
forecasted data don't satisfy these conditions, a review
is in order to pinpoint the causes. Diminished levels of
accuracy can be blamed on erroneous assessments about
certain of the other selection criteria. For example, the
geographic grid system may define too many small regions

with very little sales activity.

Turning Points

Foreseeing turning points could be considered as
yet another form of accuracy measurement. However, it can
be argued that most forecasting techniques are reasonably
precise from a statistical viewpoint. The real test of
the tool is whether or not it predicts turning points in
the time path of sales.20 This is particularly important
for long-term forecasting. On a shorter time span, adjust-
rnents can be made for directional changes in sales patterns.
For lengthy forecasts a shift in direction after a few

Inonths renders useless the remainder of the analysis based

 

 

on the it

correctlj

Market F

have an
techniqr
sity of
Channel,

QEOgrapI

40
In the forecast. The prOportion of turning points estimated

zorrectly can be compared with a standard or accepted value.

Iarket Factors

A number of market factors can be proffered which
rave an impact on the selection of a sales forecasting
:echnique. The most important of these are (l) the diver-
sity of the product line, (2) the number of marketing
:hannels, (3) the degree of product "newness," and (4) the
geographic market size.

Companies which have been acquiring subsidiaries
>r have been exPanding into new markets have broad, and
>ftentimes unrelated, product lines. Unlike products are
>ften affected by different factors, so the forecasting
system must be more complex to deal with this divergence.
Iome products may be relatively easy to forecast, while
>thers require a detailed technical analysis. The more
liverse the company's product offerings, the more complex
rnd burdensome the forecasting mechanism becomes.

The length, as well as the type, of the marketing
:hannel influences the choice of the forecasting scheme.
fhe company selling directly to the final consumer has only
.ts own and its competitors' marketing strategies to assess.

is the channels become lengthier, the marketing strategies

50". A.—‘.‘1

 

 

 

of the
cast.

types I
under a
retail
the as
the sa

Produc

produc
manY 5
theme:
Prod“,
0f tn.
techm

41
of the intermediaries have a greater impact on the fore-
cast. Also, the same product may be sold through different
types of channels. For example, appliances may be sold
under a firm's private label as well as through national
retailers. Although the physical products are identical,
the assumption that the same factors affect sales or that
the same forecasting techniques are applicable for both
products may be invalid.

An obvious prOblem in estimating the sales of a new
product is the absence of historical data. Today, however,
many so-called new items are merely variations on Old
themes or designs. Forecasts for these Older or similar
products can be modified to reflect the supposed advantages
Of the new product. A truly new development, such as a
technological innovation, is a project for the marketing
research department.21

If a firm sells certain products nationally and
others regionally, then a regional approach to developing
estimates seems reasonable. A product's sales may be
affected by different factors in different parts of the

country, again suggesting localized forecasting.

 

 

Input Rec

ware. D
requirem
can be f
or the 5
t0 reCOg
is neede
ing tech
maniPula
interpre.
f0recast.
deviceS :
the tem.

p r°°esse

tl’pes is

gory may

42
Input Requirements

Inputs are of three types: data, human, and hard-
ware. Data input refers to the "numbers," or informational
requirements, of the forecasting model. The human category
can be further broken down based on the task to be performed
or the skills brought to bear on the problem. The ability
to recognize and to choose among data source alternatives 3
is needed, and mastery of the intricacies of the forecast— L
ing techniques is also important. Someone must perform the
manipulative task of formatting the input data. Finally,
interpretive skills are basic to prOper utilization of the
forecasted results. The last category, hardware, refers to
devices such as computers which replace humans to perform
the tedious, repetitive, and time-consuming computational
processes.

It is difficult to say which of the three input
types is the most important. A weakness in any one cate-
gory may result in an unreliable forecast. Data are avail-
able from many locations. A firm with a good record-keeping
system can rely on this internal source for much historical
data. Statistical sampling can reduce considerably the
data bank required to Operate the forecasting mechanism.

At the same time, data can be collected by a direct research

program or by dealing with research agencies or public

1 sources 0
analysis I
’ into the

even be 1

 

casting

Broad 1e

 

availab
teChnic

lOWer ]

 

 

POrate
“Seful

inCree

43
sources of information, such as the government. A joint
analysis of intra- and extrafirm data could provide insight
into the future of sales patterns. Data associations might
even be recognized which lead to correlation analysis.
The human element is an integral part of the fore-
casting process. A wide spectrum of know-how is required.

Broad level guidance for choosing the model based on data

‘3“ “*r-c-cr‘fi

availability is a must. This suggests a combination of
technical competence and managerial judgment. At a slightly
lower level, at least in terms of decision-making, is the
capacity to extract the needed data from the massive cor-
porate and public banks of information and to format it
usefully. This is especially important in view of the
increased reliance on electronic data processing equipment.
Ultimately, the forecast must be used; a forecast
is not a goal in itself. The many uses for sales forecasts
already mentioned in this chapter are evidence of this.
.Management at several levels will have access to the fore-
casted results. They should be aware of the weaknesses in
the other factors, the data and the technique used. They
should be told the degree of confidence which can be placed

in the forecast.

44

Planning Horizon

The planning horizon has been detailed very
thoroughly previously. Long-term or planning forecasts
dictate gross forecasting approaches which sum but don't
report explicitly all geographic and product estimates.
Conversely, short-term or operating forecasts suggest this
detailed reporting.

The specific forecast interval, such as a week or
a month, affects the selection of the technique, as does
the frequency of preparation of forecasts. 0ft-repeated,
short-term forecasts necessitate a model which is inexpen-
sive to use. This implies a relatively small data base and
an algorithm which iterates quickly. Forecasts for a year
or more can be more sophisticated in terms of formulae and

data needs if they aren't generated frequently.

Timing

No forecast, regardless of its precision or detail,
is useful unless it is available on a timely basis-~that
is, available for use when needed. The speed with which a
forecast can be generated, given the input, should be as
fast as is economically feasible. Computers have resolved
this problem considerably; however, less SOphisticated or

smaller firms may rely on mechanical or manual calculation.

 

 

 

For the:

such as
timing

he in;
series.

cast t}

Ri or

Casting
E’valua.
it is ;
ShOuld
managex
unbias.

by Cap

45
For these companies speed is very much a consideration.

If new input data are necessary for each forecast,
such as with correlation and regression analysis, the
timing of the availability of this information is critical.
The input series should precede or "lead" the forecasted
series. This enables the firm to use current data to fore-

cast the future.

311.919.;

Rigor refers to both the objectivity of the fore-
casting model and its technical assumptions. Subjective
evaluation of the forecast is certainly permissible, but
it is reserved for the users of the forecast. The model
should not be designed to yield forecasts which match
management's preconceived notions. The model should be an
unbiased manifestation of fact, professionally constructed
by capable personnel.

All of the quantitative forecasting methods are
based on certain inherent assumptions, not always explicitly
mentioned. Any forecasting method is weakened if it does
not satisfy these assumptions about the data, sales pat—
terns, etc. The more powerful methods have more rigorous
sets of assumptions, but they yield more reliable output if

these assumptions are met. Forecasting is analogous to

 

 

statisti
searcher
requireu

searcher

Clarity

46
statistical testing. Nonparametric tests allow the re-
searcher to test hypotheses. If the data conform to the
requirements of certain parametric tests, then the res

searcher has more powerful tools at his disposal.

Clarity

This final guidelines draws on nearly all of the
preceding criteria for its substance. A useful forecast
must be understandable in terms of the technique used, the
weaknesses of the forecast, the physical presentation of
the data, and the preforecast research and analysis. A
manager who merely receives a host of numbers referring to
products and regions and time periods is in no position to
make use of this data. On the other hand, every manager
needn't be well versed in all of the technical facets of
forecasting. For the manager perhaps physical layout is
the most important factor. HOpefully, among the team mem-
bers required to complete the forecasting process from
start to finish will be peOple capable of answering any

questions that management might ask.

Summary

This chapter has introduced the broad considera-
tions of sales forecasting. The role of sales forecasting

as a key element of the planning process should be evident.

 

 

Beth 10:
The lens
concern
period I

period

serve t
mates .

0f the

0r eva]

factors

startir
of the
is p]
import;

47
Both long- and short-range planning utilize the forecast.
The length of the planning horizon is, therefore, a major
concern of the firm. The impact of this variable planning
period on sales forecasting is manifested in terms of the
period length and detail of the forecast.

The several examples of the uses for forecasts
serve to illustrate the company-wide value of these esti-
mates. Virtually every department in the firm can make use
of the sales forecast.

Finally, another perspective, that of a firm about
to select a forecasting mechanism or evaluate the present
one, suggests a set of guidelines to aid in the selection
or evaluation. This universal list represents the major
factors that a firm should consider.

With this overview of sales forecasting as a common
starting point, a detailed discussion about and comparison
of the various techniques for forecasting is meaningful.
This presentation is found in Chapter III. Further, the
importance of forecasting accuracy can now be better under-
stood. Methods of error analysis are discussed in Chapter

IV.

..___,__m.__.1

 

 

 

 

48

CHAPTER II--FOOTNOTES

1G. A. Steiner, Top Management Planning_(New York:

The Macmillan Company, 1969), p. 7.

 

2L. G. Erickson and R. J. Lewis, forthcoming pub-
lication (New YOrk: McGraw—Hill, Inc., 1972), ch. 7.

3Management Qperating System: Forecasting,
Materials Planning and Inventory Management--Genera1 (White
Plains, N.Y.: International Business Machines Corporation),
p. 1.

4For an excellent treatment of the temporal dimen-
sion of planning see Steiner, same reference as footnote 1,
pp. 21-25.

5Erickson and Lewis, ch. 7.

6ForecastingSales, Studies in Business Policy,
No. 106 (New York: The National Industrial Conference

7W. J. Stanton and R. H. Buskirk, Management of
the Sales Force (Homewood, Illinois: Richard D. Irwin,
Inc., 1964) 1 pp. 549-551.

8F. E. Hummel, Market and Sales Potentials (New
York: The Ronald Press Company, 1961), ch. 11.

 

9
Forecasting Sales, p. 9.

 

1OJ. Dean, Managerial Economics (Englewood Cliffs,
New Jersey: Prentice-Hall, Inc., 1951), ch. 4.

11D. H. McKinley, M. G. Lee, and H. Duffy,
Forecasting Business Conditions (The American Bankers
Association, 1965), ch. 4.

12R. Fels and C. E. Hinshaw, Forecasting and
Recognizing Business Cycle Turning Points (New York:
National Bureau of Economic Research, 1968), pp. 7-11.

 

 

13W. Lazer, "Sales Forecasting: Key to Integrated
Management," Business Horizons (Fall, 1959), p. 64.

7..-,

 

Individual Business Enterprise
University Microfilms, 1967), pp. 41-49.

49

14Erickson and Lewis, ch. 7.

15Steiner, pp. 211-212.

16Forecasting Sales, p. 4.

l

 

7Ibid., p. 5.
l81bid.. pp. 100-103.

19B. R. Copeland, Sales Forecasting for the

 

20Erickson and Lewis, ch. 7.

21Forecasting Sales, p. 103.

 

(Ann Arbor, Michigan:

“Hf-77““)

 

 

 

Par:

f0“

tec}

CHAPTER III

SALES FORECASTING TECHNIQUES

Introduction

 

u . Anni!“ "

This chapter presents an analysis of the various
Ways 0 both mathematical and nonmathematical, to forecast
sales. The techniques covered are those that have been
sYStemetized through usage. Individual guessing based on
hunches, for example, is not included. Only those methods
Which can be reduced to a series of logical steps are dis-
cussed. The advantages and disadvantages of each technique
are also presented. Next, the various techniques are com-
pared with each other. The objective is to select the most

appropriate technique for use in later experimentation.

Presentation of Techniques
Although considerable space is allotted to sales
forecasting in most marketing texts, the basic forecasting
techniques have not changed significantly in recent years.
A“ c><.‘.<:asional new application is mentioned, and perhaps

small technical dimensions are added from time to time.

50

How

 

No:

 

 

 

 

ti!

1'10“

The

de

ef

ar.

51
However, the methods remain virtually unchanged.

Two general approaches to sales forecasting are
popular. These are the build—up and the breakdown
approaches. The build-up approach is characterized by
qualitative or nonmathematical estimating, while the break-

down approach can be either qualitative or quantitative.

Nonmathematical Forecasting

Four nonmathematical techniques are common:

1. Factor listing

2. Jury of executive Opinion

3. Sales force composite

4. Users' expectations.

The overall approach in each instance is qualita-
tive; however, this is not to say that these approaches are
not structured. For example, in the sales force composite
method each salesman may contribute his estimate based on a
very'thorough analysis.

Factor:§isting.--The factor listing approach is the
Simplest of the qualitative approaches. It involves the
develOpment of a list of factors or events which have an
ef-"fect on sales. Those factors which would increase sales
are, denoted accordingly, as are those lowering sales. Then

the list is evaluated in one or both of two ways. First.

52
the number of positive factors is compared with the number
of negative ones. If there are more positive factors, then
sales are expected to increase in the future. As might be
suspected by now, a majority of negative factors would lead
to a forecasted decline.

The second possibility is to assign weights, as well

as a positive or negative sign, to each factor. A weighted

' .- __r_.

total can then be computed by multiplying weights and signs a,
and summing the results. Again, a positive score suggests
a sales increase, while a negative total foretells a
decline. The relative change expected might be available
from the magnitude of the total score.

Obviously this technique, though structured, is
unsophisticated.1 It relies on the compilation of a
thorough list of factors. Without such a list the approach
is trivial. Considerable expertise on the part of the com-
piler of the list is required. In addition, the arbitrary
assignment of weights under the second scoring possibility
is subject to criticism. Simply by manipulating the
weighting values, management can change both the sign and
magnitude of the total score.

Jury of Executive Opinion.-—This approach to sales

 

forecasting has been practiced for many years by companies.

30 in spite of its simplicity, it's one of the oldest

“'|

53
techniques available and in use.2 It involves a combining
or grouping of the estimates supplied by a cross-section of
a company's executives. One writer has glamorized the pro-
cess by subdividing it into the following three variations:3
1. An originating committee approach

2. A reviewing committee approach

3. A presidential survey approach.
The originating committee compiles the tentative 1
forecast, as well as revised and final versions. If the
committee also happens to be the budget committee, it can
grant final approval of the sales forecast as the sales
budget.
A reviewing committee does not prepare the initial
forecast. Instead, this first draft is submitted to the
reviewing committee for examination and revision. Ulti-
mately, the reviewing committee approves a final forecast
and submits it to the person or persons who have the
authority to approve the forecast as the budget. It is
possible that this authority is vested in the reviewing
committee itself: hence, no further evaluation is necessary.
The presidential survey is similar to the originating
Committee approach in that several executives develop and
SUbndt.forecasts. The executives don't meet as a group.

The fbrecasts are reviewed by the chief operating officer,

 

 

W?

In

54
who eventually develOps the finalized forecast. In this
way the estimates of those the president considers to be
the most pragmatic can be weighted more heavily; however,
this technique stifles group discussion and relies on the
skills of the president, who may not be the most qualified
forecaster in the firm.

The jury of executive Opinion method offers several
advantages and disadvantages.4'5'6'7'8 First, on the plus
side, the approach can be implemented quickly. By specify-
ing regular due dates for the projections, the committee or
the president can routinize the process. Second, detailed
or complex statistics may not be mandatory. Executives may
rely on their many years of experience to develOp their
forecasts. Next, balance is achieved by drawing on many
different departments throughout the company. Production,
finance, marketing, and others may all be invited to par-
ticipate, resulting in forecasts as seen from several van-
tage points.

Another benefit of the jury method is that it is
"data free." That is, the jury approach doesn't require a
data bank beyond that which is stored in the executives'
memories. This method might be especially valuable for new
firms, new products, or new markets for existing products.

Finally, this technique supposedly synthesizes the most

cu
th

h
re
ch
ex
f0
be
th
SD
is
hi
ca
fa
th
an:
80;
we,

 

 

 

55
current information available. Alert managers are aware of
the latest happenings within their departments, and marketers
should be cognizant of market trends. The result should be
an up-to-date, relevant forecast.
Considerable negative criticism has been aimed at

the jury method of forecasting. The most obvious one is

SJ.

that personal biases and Opinions are given considerable

If. ._a

recognition. Guesswork, rather than fact—finding, may
characterize this scheme. It has been suggested that many
executives are in no position to assay potential market per-
formance. Second, should highly paid and skilled executives
be bothered with develOping these estimates, particularly
the Operating forecasts? Couldn't their time be better
spent on Other tasks?

Another disadvantage is that the ultimate forecast
is an average. The accuracy of an average of Opinions is
highly suspect. Fourth, since it is an average, the fore-
cast cannot be traced to any one individual. Responsibility
for the projections is dispersed throughout the firm. If
there is a disparity between actual and forecasted sales,
anyone can ease the pressure placed on him by simply blaming
8Omeone else.

Fifth, to get any kind of local, product line, or

wee'klyforecast is nearly impossible. This would occupy

56
an inordinate prOportion of the executives' time. Manage-
ment must settle for aggregate forecasts. Lastly, the
inertia of committees may slow down the forecasting process.
Several confident men in positions of power, each with a
different Opinion, provide the fodder for controversy and
indecision.

Sales Force Composite.--The sales force composite
method involves gathering data from either salesmen or
sales managers. The former approach has been described as
a "grass-roots" one because it represents the forecasts of

9

the men closest to the markets. Each salesman is asked to

10

estimate future sales within his territory. Often esti-

mates are submitted for each product for which the salesman
is responsible.
The National Industrial Conference Board, in a
recent summary, cited many advantages of the sales force
11

composite method:

1. Uses specialized knowledge of men closest to
the market.

2. Places responsibility for the forecast in the
hands Of those who must produce the results.

3. Gives sales force greater confidence in
quotas develOped from these forecasts.

4. Tends to give results greater stability because
of the magnitude of the sample.

5. Lends itself to the easy develOpment of product,
territory, customer, or salesmen breakdowns.

S7

The same source, however, also notes a number of

disadvantages. These are as follows:12

1. Salesmen are poor estimators, often being
either more Optimistic or more pessimistic
than conditions warrant.

2. If estimates are used as a basis for setting
quotas, salesmen are inclined to understate
the demand in order to make the goal easier
to achieve.

3. Salesmen are often unaware of the broad
economic patterns shaping future sales and
are thus incapable of forecasting trends for
extended periods.

4. Since sales forecasting is a subsidiary func—
tion of the sales force, sufficient time may

not be made available for it.

5. Requires an extensive expenditure of time by
executives and sales force.

6. Elaborate schemes are sometimes necessary to
keep estimates realistic and free from.bias.

By bypassing the salesmen and utilizing the special-
ized knowledge of the sales managers, a company can overcome
many of the aforementioned shortcomings. These managers
view the need for adequate and realistic sales forecasts
from a management perspective. They realize the need for
constant monitoring and updating of the forecast. Consider-
able time should be saved by freeing salesmen from the fore-
casting tasks for which they are likely ill-equipped.13 A
serious drawback of basing the forecast on sales manage-

ment's estimates is the loss of the localized knowledge of

‘37:“!

‘f' *7

58
the salesmen: however, managers might consult with their
salesmen prior to formulating the forecast.

Users' Expectations.--Advocates of the users' expec-

 

tations method prOpose that actual and potential customers
are the best sources of information upon which to base an
estimate. Of course, anytime a survey or questionnaire is
used, problems of accurate representation of the pOpulation
are encountered. Anticipating a poor rate of response,
forecasters might poll an extremely large sample. If the
population is small, it might be enumerated completely and
researched.

As was the case earlier, arguments can be made by
those favoring and those opposing this approach to fore—
casting.l4'15 First, the users' expectations method is
based on information Obtained directly from the users who,
taken together, make up the firm's market. Second, the
company can learn, maybe only subjectively, the thoughts
underlying the intentions of buyers. Next, indirect
sources, middlemen, are eliminated by going to the cus-
tomer. The level of detail is under the control of the
forecaster. Fourth, new product sales or new markets can
be estimated when other methods are inapplicable.

Also, the notion of a survey seems logical because

buyers are worthy of consideration. Other methods overlook

th;
buj
kn:
Wht
a1

ch

 

no

is

no

to

SE

OF.

 

 

"P

 

59

this basic fact. Industrial buyers often plan ahead and
buy periodically. Perhaps this personal contact will make
known facts not discernable from other approaches, such as
when a buyer plans to shift to another supplier. Last of
all, the users' expectations method can serve as a cross-
check on the results of another way of forecasting.

Objections to this approach have been raised. As
noted, diverse markets with many products and users do not
lend themselves, except at the expenditure of much time and
money, to a survey approach. The reliability of users has
to be considered. Uninformed or uncOOperative buyers can
seriously hamper the research. Third, any forecast based
on expectations is a function of those expectations. If
for some reason buyers' expectations are altered, the old
forecast would be immediately outdated.

I A survey approach is necessarily time-consuming.
Pretesting of the questionnaire is almost mandatory. Con-
siderable manpower is required to contact personally each
respondent in the sample. The alternative is to rely on
the lower return rate of voluntarily completed mail surveys.
If there are any middlemen, they can exert considerable in-
fluence on the buying practices of purchasers. These
intermediaries should be polled in a separate interview for

completeness .

 

 

60
This concludes the study of the nonmathematical
approaches to sales forecasting. These judgmental approaches
may not be appealing to the trained statistician; neverthe-
less, they provide the means for the less technically

trained forecaster to complete his assigned task.

Mathematical Forecasting

The mathematical techniques for forecasting which
are covered here are the following:

1. Moving average

2. Exponential smoothing

3. Time series analysis

4. Regression and correlation analysis.

For each of the above quantitative approaches, a
specific numeric or logical decision rule or process is
executed to generate the forecasted value. There is nothing
inherently superior about a quantitative technique as com-
pared tO a qualitative one, despite the aura of infalli-
bility which seems to surround the former.

Moving Average.--Again, the starting point is the

 

simplest of the alternatives. The term "moving average"
is precisely definitive of the nature of this technique.
The forecast is calculated by averaging sales for the most

recent n time periods. As the data for another period

 

;‘1 ‘1...

 

 

be

th

si

de

61
become available, the average is recalculated, again for
the last n periods. SO the moving average technique con-
sists of adding to the total the latest period's data and
deleting the data from n+1 periods in the past. This total
is then divided by n to achieve the forecasted value.

If t denotes the most recent time period and S(t)
represents sales in period t, then the current moving aver-
age value is MA(t). Expressed symbolically, this relation-
ship is

MA(t) = S(t) + S(t-l) + + S(t-n+1)
n

where n is the number of time periods.

Obviously the moving average value is easy to com-
pute, especially once the initial value is obtained. The
mechanics of the process can easily be programmed for use

16 Also, the technique is easily

on an electronic computer.
understood, so the problem of training personnel in its use
is a minimal one.

Unfortunately, there are several limitations which
cannot be overlooked. An inherent assumption of the moving
eaverage method is that the future will be, for the most part,
‘an.unweighted and lagged extension of the past. If this

‘trend can be validated for a given product, then perhaps

the moving average approach is an adequate one: otherwise,

62
it's use ought to be discontinued.

Related to this first shortcoming is the unrespon-
siveness or sluggishness of the technique. For large values
of n, current sales data make up only a small proportion of
the total before averaging. Thus, if there is a radical and
penmanent shift in the direction of the sales pattern, the
moving average won't reflect this until the preshift data
are eliminated from the total. On the other hand, a small
n value will result in a highly responsive, even volatile,
system that overstates one-time fluctuations. The fore-
caster must be familiar with the product in order to choose
wisely the value for n.

The size of the data base required to Operate a
moving average model is also a function of the number of
periods. Extensive records must be maintained for each
product. If n is increased, this data file increases
accordingly.

Finally, because the moving average technique is
a way to measure central tendency of data, the computed
'value is inapprOpriately called a forecast. Instead, any
iiverage is representative of the interval over which it
Vfiis calculated. If the value must be located at some point
‘Within this interval, the midpoint is a much more logical

Point than an endpoint (as is the case with using the

 

 

 

63
average value as a forecast). Theoretically, any moving
average value represents some past time interval and
shouldn't be interpreted as a forecast.

Exponential Smoothing.--Certain of the shortcomings

 

of the moving average method have been eliminated by expo-
nential smoothing, which is really nothing more than a
weighted type of moving average.17 (The derivation which
follows is based on work by Brown.18'19) Exponential
smoothing bases the new estimate of sales on the previous
estimate incremented by some fraction of the amount by
which the old estimate differed from actual sales. Ex-
pressed in equation form, the relationship is

E(t) = E(t-l) + d(D(t-l) - E(t-l))
where E(t) is the estimate for period t, D(t-1)‘ is the actual
demand for period t-l, and @111. If like terms are com—
bined, the equation becomes

E(t) = aD(t-1) + (l-a)E(t-1).
Brown has shown that by substituting consecutive values for
13(t-l), E(t-2), etc., a form of weighted average is derived

VVhere

E(t) = aD(t-l) + d.(l-d)D(t-2) + d(l-a.)2D(t-3) + . . .
+ a.(l-a.)kD(t-k-l) .

Tflme current estimate is a sum of past sales multiplied by

diJfferent weights, which sum to one. The resulting equation

 

 

 

 

rf

rn

64
is
New Average = a(New Demand) +(l-a)(Old Average).
This formula doesn't correct for trend. It is
possible to alter this equation so that corrections for
trend are automatic. An estimate of the present trend
could be
Trend - New Average - Old Average.
Reasoning analogous to that underlying the derivation of
the New Average yields
New Trend - a(Current Trend)-+(l~a)(Old Trend).
SO the estimate for sales is the combination of
trend and average values. The expected sales total is
Expected Sales = New Average + (lle (New Trend).
The analysis can be carried furth:r if needed.
Second and third order formulae which include the trend
(and the acceleration of change, respectively, can be de-
rived.20 The second order approach involves calculating
the New Average as just shown, but calling the result the
New First Average. That is,
New First Average = a(New Demand)4-(l~a)(Old First Average).

ZKJaother average, based on the previous computation is

New Second Average = a(New First Average) +
(l-a)(Old Second Average).

65

The latest forecast is

New Forecast = 2(New First Average) - New Second Average.
The trend value is

New Trend = New First Average - New Second Average.
Last, the final forecast is

New Final Forecast = New Forecast + New Trend.

Third order analysis requires that a new Third

Average be computed so that the acceleration factor can be
derived. The final forecast includes, then, the New Fore—
cast, the New Trend (rate of change in forecast), and the
New Acceleration (rate of change of rate of change in fore-
cast). Both second and third order models are very sensi-

21

tive to shifting sales. Further corrections are possible

to adjust for seasonality patterns in the data.22
A final variation of exponential smoothing is
adaptive smoothing. Here, the value of the smoothing
constant (a) is reviewed regularly, perhaps each time a new
forecast is made. The value for the smoothing constant used
to make the next projection is that value which would have
given the most precise estimate for the last forecast period.
In other words, alternative a values are used to project
last period's sales. These several projections are compared

with.last period's actual sales. The smoothing constant

Value yielding the projection closest to actual sales is

66
used to generate the next forecast.

EXponential smoothing is, because of its origin,
more complicated than the moving average technique. This
complexity can hinder the adoption of exponential smoothing
as a method of forecasting. Lack of understanding may cause
firms to select another, less SOphisticated approach.
SOphistication isn't inherently good, but to rule out a
technique because of its complexity is unfortunate.

A serious disadvantage is the distortion over time
in amplitude of the smoothed sales flow. The distortion
depends on the nature of the input, the order of the
smoothing model, and the prOportion of disturbance or

"noise" in the input information.23'24

A random input,

such as sales being twice the volume in a certain period

as compared with any other period, would cause the fore-

casting model to overestimate for the next period. Then,

the anticipation of a continued decline because of a return

to previous sales levels would cause the subsequent period's

sales estimate to be decreased. This distorted value would

gradually be "washed out" of the system. The predictive

pattern would be that of a dampened oscillation over time.
Several positive attributes can, however, be

mentioned. After the model has cycled one time, the only

data which must be saved are the most recent prior values

 

 

 

 

L...

U!

E!

In

67

of the trend and the average (or the previous average and
the most recent demand if the non—trend-adjusted version is
used). Data storage requirements are practically nonexist-
ent. Further, the computation is simple. Last of all,
exponential smoothing is very apprOpriate for short-
interval forecasting because in such cases causality or
association can't be handled in a practical way.

Time Series Analysis.--A time series is a group or
set of statistical observations arranged in chronological

order.25

There may or may not be a relationship between
or among the values of the series. If such a relationship
doesn't exist, successive values are said to be independent.
Obviously, this study is not concerned with independent time
series because they cannot be forecasted. Dependency is
exhibited if successive values can be estimated based on
previous values.

The standard time series model is composed of four
components. These are:
l. Secular trend
2. Cyclical movements
3. Seasonal patterns
4. Irregular fluctuations.

Secular trend is described as the underlying general

tendency of the time series. It is a long-term concept,

68
encompassing ten or more years for adequate description.
By definition secular trend is a stable phenomenon, mani—
festing itself in the form of a smooth line if plotted
graphically.

Representation of the secular trend can be achieved
by a variety of approaches. The simplest is merely to plot
the data on a graph and visually fit a line to estimate
trend. This is a very quick method, but it is dependent
upon the bias of the drawer. Any two peOple are likely to
develOp different lines; hence, there are no criteria for
fitting the line.

Another possibility is to divide the data into two
equal time intervals. Then the average value for each of
the two intervals is computed. These averages are plotted
at the midpoints of the two intervals and are connected
with a straight line. By finding the arithmetic difference
between the two mean values and dividing this by the number
of time periods, the slope of the line can be determined.
The origin of the line can be arbitrarily set anyplace on
the time scale by moving away from either of the means.
This technique isn't biased like the free-hand method, but
it is still very crude. Only straight lines can be gen-
erated, a very real weakness.

Last,a line can be fitted to a set of data on the

69

basis of one of several statistical criteria. Perhaps the
sum of the absolute differences between actual and computed
(using the trend line) values could be minimized. A rather
common approach is to minimize the standard error of the
estimate. This leads directly to the "least-squares"
method of line-fitting. Here, the sum of the squares of
the differences between corresponding actual and computed
(using the trend line) values is minimized. This means that

E(Y‘Yt)2 is a minimum
where Y represents the actual values and Yt refers to the
corresponding computed trend values. An additional
prOperty of the least-squares method is that the sum of
the differences between actual and computed values is zero.
In other words,

s(Y-Yt) = 0.

Calculus can be applied to assure that these two
restrictions are enforced. If a rectilinear relationship
is assumed, the trend equation is of the form Yt = a + bx,
where Yt is the forecasted (dependent) variable and x is
the time (independent) variable. values for a and b must
be chosen such that the aforementioned conditions hold.
Thus, the deviations which are to be minimized are functions

of a and b. So

2

f(a.b> = ew-Yt) .

70
Since Yt - a + bx, this relationship can be substi-
tuted into the above equation. Thus,
f(a,b) = e(Y - a — bx)2.
To minimize f(a,b), compute partial derivatives with

respect to a and b and set them equal to zero. Hence,

afgalb)

3a

af§a,b)
ab

(-2)€(Y - a - bx) = O and

(—2X)e(Y - a - bx) = 0.

These two equations can be solved to get the so-

called "normal equations"

EY na + bex

EXY asX + bEXZ.
Because of arbitrary coding of the time (x) vari-
able, the ex term drOps from each equation because it equals

zero. The remaining relationships are easily solvable for

a and b

eY na a = eY/n

hex2 b e:XY/eX2 .

eXY
Curvilinear trend lines can be derived simply by
assuming any of several possible curved relationships be-
tween x and Y and repeating the preceding minimization
steps.
The least-squares and similar approaches seem to be

‘Ehe most useful of the trend-fitting techniques. Least-

71
squares satisfies a specific set of criteria: it is unbiased
and consistent. Further, it can be used to develOp both
straight- and curved-line relationships.

Cyclical movements refer to activities of the busi-
ness cycle which occur over two to ten or more years. These
recurring cycles are generally measured by estimating the
interval between consecutive like turning points (e.g., from
peak to peak). Length and amplitude of the cycle vary from
product to product. The absence of a constant period and
amplitude for a given product makes prediction even more
difficult.

The combination of interproduct variation and intra-
product inconsistency results, as would be expected, in no
highly accurate method for forecasting this particular part
of the time series model. The standard approach is to
describe the trend and seasonal factors and to combine the
cyclical and irregular factors as a residual.26 In par-
ticular cases the develOpment of basic trigonometric func-
tions to mirror the cyclic element might be feasible if
consecutive periods are nearly the same and the amplitude
variation is minimal. Fourier series analysis might also
1be attempted under such circumstances.

Seasonal patterns reflect the variations which

occur regularly and complete a cycle each year. Such

72
factors as weather, customs, and religion are usually
considered to be the major causes of seasonality. Higher
sales during the days before Christmas exemplifies the
impact of the seasonal element.

Numerous approaches for depicting seasonal patterns
have been develOped. Among these methods are (1) general
average, (2) link—relative, and (3) ratio-to-trend.28 The
general average technique involves fewer computations and
is probably the easiest to understand. Historic data for
several periods are tabled. Then average sales values for
each quarter (or month) are computed, and average quarterly
(monthly) sales for the entire time (the "general average")
is calculated. Indexes are derived by dividing the four
(twelve) quarterly (monthly) averages by the general aver-
age. These indexes must sum to 400 (1200) to be adjusted
for trend.

The link-relative method formulates the indexes
into a chained or linked sequence by basing each index on
the previous one. Again the data are arranged in table
format by year. Indexes are computed by dividing quarterly
(monthly) sales by sales for the immediately preceding
period. In this way the indexes are linked together. The
average index for each period is determined. Since the

original data contain a trend factor, this can be removed

73
by assuming a rectilinear relationship and adjusting the
average indexes. As always, quarterly (monthly) indexes
should be adjusted so that they sum to 400 (1200).

The last main approach to develOping seasonal in-
dexes, ratio-to-trend, is the most complex. The initial
step is to devise a trend line to represent the historic
data. A least—squares approach would be acceptable, as
would a four-quarter (twelve-month) or longer moving aver-
age because a long—term average eliminates seasonal fluctua-
tions. Ratios of actual sales to trend values are calcu-
lated and tabled by year. Then average quarterly or monthly
indexes can be computed and adjusted to sum prOperly.

Certainly these means of isolating the seasonal
element differ in usefulness. The ratio-to—trend approach
involves more computation, yet it will permit curvilinear
trend assumptions. All the other approaches assume a
rectilinear trend. The link-relative method is the easiest
to use because once an initial trend value is known, all
other seasonal-adjusted estimates for a given year can be
obtained by a simple multiplication. The general average
technique is a simple and "common sense" method for obtain-
ing rough indicators of the seasonal factor.

The fourth and final time series component is

irregular fluctuations. These movements are erratic and

74
unpredictable. They result from such causes as disasters
and windfalls. Because of their very nature, irregular
fluctuations are not able to be forecasted; instead, they
are included as residual variations.

These four time series components are typically
related to each other in either a multiplicative or additive
model. The general form of the multiplicative model is

Y = T x C x S x I
where
Y = actual sales data
T = secular trend
C = cyclical movements
S = seasonal patterns
I = irregular fluctuations.

Y and T are in terms of sales dollars or units.

S, C, and I are ratios (or percentages) which adjust the
‘trend to equal actual sales. An additive model can be used
which has the form

Y = T + C + S + I.
In.this case all components are in terms of dollars or units.

Time series analysis offers several advantages to
hits users.29 It forces forecasters to probe into the com-
INDnent factors which affect sales. By isolating the various

1Influences, management hopefully can develOp a better

75
understanding of products and their sales patterns. Related
to this first advantage is the systemitized approach to
forecasting offered by time series analysis. It is an
organized, step-by-step method which should result in con-
sistent findings when applied by any trained forecaster.

A third reason for adOpting time series analysis is
that considerable detail is possible. Naturally much work
would be necessary to derive initially the equation para-
meters for many products and regions, but then a computer
could perform the forecasting and revisions with ease by
simply iterating through a matrix of equation parameters.

Unfortunately, short—term forecasting using time
series analysis is a bit risky, especially if the data base
used to build the model is formulated in terms of longer
time periods. For example, if quarterly historic data were
used to construct the relationships, monthly or weekly fore-
casts are theoretically possible, but practically unsound.

Regardless of the data, trend and cyclical com-
ponents are multiyear in nature. This violates the earlier
one-year-or-less definition of a short-term period.

The need for considerable historic data has been
alluded to already. In addition, technical know-how for
develOping the projection model from this broad spectrum of

data is vital. In the hands of a novice, time series

76
analysis as a forecasting tool could be a dangerous weapon.

A series shortcoming is the lack of a causal rela-
tionship. Time series analysis assumes a continuation of
prior sales movements. There is no intrinsic relationship
between time and sales volume. Of course, if adequate
research and study suggest a continuation of past patterns,
then time series analysis is quite useful.

Finally, there is a chance that random or irregular
factors present in past data may overshadow relatively the
effects of the predictable time series components. Care
must be taken to isolate the regular factors without being
misled by the unusual fluctuations.

Regression and Correlation Analysis.--Regression

 

analysis and correlation analysis are sometimes mistakenly
defined alike. Actually regression analysis refers to
methods for estimating values of a variable based on infor-
mation about one or more other variables. Correlation
analysis encompasses measurement of the degree or strength
of the association among the several variables.30
Regression analysis can be categorized as either

simple or multiple. Simple regression involves estimating
values for one variable (dependent) based on corresponding

Values for one other variable (independent). Multiple

regression, then, forecasts dependent variable values on

77
the basis of values for two or more independent variables.

No directional causality is implied for dependent
and independent variables. A cause-effect relationship
could, in fact, exist in either direction: however, deter-
mination of causality is not a necessary condition.

A graph or scatter diagram is an advisable first
step in the use of simple regression analysis. The diagram
depicts the general nature of the relationship and aids in
the selection of the mathematical archetype.

As was the case with time series analysis, regres—
sion analysis utilizes a goodness-of-fit criterion in
develOping an equation to represent historic data. The
most widely used rule is, again, to minimize the sum of
the squares of the deviations of actual and computed sales
values (vertical deviations with sales plotted on the
ordinate). The analysis is similar to that described for
time series, except that the x value is no longer restricted
to a time dimension. The units of x may be in terms of any
dimension measurable on an interval scale. Obviously for
multiple regression a scatter diagram is difficult to draw
for two independent variables and impossible for three or
more .

Several assumptions underlie the use of regression

31
analysis for forecasting. They are as follows:

78

l. The regression error must be randomly dis-
tributed with zero expected value.

2. The variance of the regression error must
be the same for all values of x (homo-
scedasticity).

3. Individual forecast errors must be statis-
tically independent of each other (no auto-
correlation3 ).

4. Individual forecast errors must be uncorre-
lated with the independent variable in the
forecast equation.

5. The underlying relationship between Y and x
must be strictly linear if the regression
slope parameters and forecasts based upon
it are to be independent of the distribution
of the X's in the sample.

1\ sixth restriction, applicable in the case of multiple re-
gression, is that multicollinearity should be minimized and,
ideally, equal to zero. It is beyond the sc0pe of this
Paper to explain rigorously the impact of imposing these
Six restrictions. Each condition can be commented on in
terms of its practical importance.

The first assumption has intuitive appeal even for
the nonstatistician. The error in using the regression
Ifcxrmmla (YeYb) to estimate sales should be randomly distri-
1Duted and should sum to zero for a large number of obser-

vations. Otherwise, the so-called error would be predict—

‘allle and could be incorporated into the formula. Only when

the expected value is zero is the equation reliable.

79

Homoscedasticity simply means that the variance of
the regression error is independent of the location within
the relevant range of the predictive equation. For example,
if Y is an increasing function of x, then larger Y values
are associated with larger values of x. Homoscedasticity
implies that the variance of the prediction error is the
same for both large and small values of x. The confidence
interval about the regression line is of constant width for
all X values and is not extreme-value sensitive.

Autocorrelation of forecast errors generally causes
the forecast variance and the variance of the regression
slope parameter to be biased downward. This implies more
information about the regression slope, b, than is actually

33 Autocorrelation should be minimized.

available.
The fourth assumption relates somewhat to the con-
cept of homoscedasticity. Here the regression error is not
permitted to be an increasing or decreasing function of the
independent variable. If there is a relationship between
x and error, the forecast can reflect this association.
This restriction is more important for structural analysis,
for Obtaining unbiased b estimates, than for forecasting.34
Model linearity refers to the regression equation's

coefficients. Adding a cx2 term to the right side of the

standard Y = a + bx equation does not result in a nonlinear

80
function. The variables are still included in linear com-
binations. However, adding an Xc term generates a nonlinear
form. Logarithms provide a means of eliminating nonline-
arity in this second example. If the underlying relation-
ship between Y and X is curvilinear, the distribution of
the independent variable must be controlled to ensure prOper

interpretation of the regression parameters.35

Perhaps suc-
cessive rectilinear equations over restricted ranges of X
could be used to approximate the curved relationship.

The existence of multicollinearity implies depend-
ence among or between the independent variables. Multi-
collinearity reduces the efficiency of the estimates for
the regression parameters: however, for efficiency in
forecasting sales (Y) the interrelationships among dependent
variables pose no real problems. Of importance is the
amount of information about Y available through the use
of the independent variables taken in concert, not sepa-
rately. If two independent variables correlate perfectly.
one can be drOpped because it doesn't add any insight not
already present by including the other one.

A number of measures have been pOpularized for
examining the strength of the relationship between the

dependent and independent variables. These are the coeffi—

cients of correlation (r), determination (r2),

81
nondetermination (k2), alienation (k), and association (A).
These variables can be represented symbolically. For any
X value, three Y values are of interest. These are Y, the

actual or observed Y value: Y the value computed by using

cl

the regression line; and E. the mean of the historic Y

values. The total variance, Oyz, or the variance of Y

values about their mean, Y, is 6(Y¥§)z/n. The unexplained

o 2

YC , or the variance of Y values about the re-

variance,

gression line, is e(Y—Y¢)2/n. The explained variance,

oyxz, or the variance of Yb values around the mean, §, is
e(YcJY)2/n. It can be shown that

.(y-i'r') 2 = E(Y-Yc) 2 + ewe-FF
n n n

 

 

or

thus

yc y “yx y

coefficient of determination
a the relative reduction in squared
error (variance) due to estimating
values of Y from values of X.

o
"<
X
a)
\
Q
"<
N
H
M
II

coefficient of nondetermination

= the relative amount of squared error
(variance) remaining due to esti—
mating values of Y from values of X.

o
\
q
N
I
“I
ll

r = /45 = coefficient of correlation.

82

k = /k2 = coefficient of alienation = the remaining
relative amount of absolute error due to

estimating values of Y from values of X.
A = l-k = coefficient of association = the relative
amount of reduction in absolute error due

to estimating values of Y from values of

X.

It is difficult to say which of these measures pro-
vides the greatest insight into the strength of_the associ-

ation between X and Y. The interpretation of r2

as a rela-
tive type of measure is, perhaps, more logical than that of
r, which is dimensionally meaningless. However, r is eaSily
analyzed by using statistical testing. Because of their
interrelated nature, all coefficients can and should be

2 or k2 is known.

calculated once r

A primary reason for utilizing correlation and re-
gression analysis is Objectivity. The technique practically
guarantees a cold, hard look at a situation without the
danger of human bias. Of course, a forecaster could elimin-
ate some possible independent variables from the study by
allowing his intuition to guide him. Generally, regression
and correlation analysis leads to an objective and measur-
able result.

The preliminary investigation required to develOp

a set of potential independent variables leads to a more

thorough understanding of the factors influencing sales.

83
The subtleties of the relationship between sales and other
factors become clearer. There may be a temptation to
interpret a strong association as causality, but this may
not be true. It is possible, however, to discover a
causal relationship. Such a finding would obviously be
invaluable to all those who rely on the forecast for
information.

Because the effects of different independent vari-
ables on sales may vary throughout the country or by
product, many variables may have to be selected; neverthe-
less, regression and correlation analysis is still very
useful. Different sets of equations on a regional basis
may enhance forecasting accuracy. Certainly in the limit
every product in every location could be studied individu-
ally to determine the most suitable variables and equations.

A final reason for the possible adOption of this
technique is the availability of a measure of the strength
of the predictive equation. By looking at the five coef-
ficients derivable from the historic data, management can
evaluate the reliability of the projections. A critical
assumption here is that past relationships will continue
to hold, at least on a relative basis.

This previous point introduces a negative considera-

tion: the impact of residual or excluded independent

84
variables. Surely no analyst is capable of achieving a
perfect relationship (r2 = 1.0) among sales and all needed
independent variables on every attempt. Even the slightest
imperfection sets the stage for later forecasting error.
For example, within the current range of values an excluded
independent variable may have a negligible impact on sales.
Suppose the strength of the association increases consid-
erably beyond the current range. Unless someone notices
this, the forecast goes awry without a reasonable explan-
ation.

The availability of data related to the independent
variables could be regarded as another limiting feature of
this technique. If indexes are used as predictors, espe-
cially aggregates of economic activity, oftentimes only
annual data are available. unless the independent variables
are leading series, they may have to be predicted in order
to be used as input to the regression equations.

A considerable volume of data is required to Oper-
ationalize this type of model. Detailed historical analysis
is necessary to derive the regression equations. Continuous
updating is advisable so that the parameters will reflect
the most recent tendencies. Lack of data timeliness,
availability, or accuracy could each have a detrimental

effect on forecasted output.

85

Last, it is apparent that considerable technical
expertise is a must in order to understand and to develOp
the relationships. This point can be re—emphasized merely
by studying any intermediate or advanced text dealing with
regression and correlation analysis. Likewise, those using
the forecast may be mystified by the inner workings of the
model.

Comparison of Sales
Forecastinngechniques

To attempt to generalize about the relative merits
of the aforementioned forecasting techniques is to be some-
what arbitrary at best. Surely, the rankings depend upon
the experiences of the user, as well as his reading know—
ledge of the alternatives. Regardless, a relative ranking
is presented in Table 3.1. Cross-rankings between quantita-
tive and nonquantitative classes are not attempted because
of noncomparability. For instance, it is not patently
obvious, except for a specific case, whether or not polling
a sales force costs more than running a computerized regres—
sion model.

The ranking scheme is from one to four. A "l" is
the best in the sense of least-cost, most detailed,
fastest, etc. Equal rankings are indicated by an average

of the specific rankings involved.. For example, two 2.5's

86

 

 

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87
indicate a tie between the second and third methods. Also,
no rankings were develOped for the selection criteria of
accuracy, turning points, and clarity. These are best mea-
sured, as noted before, in terms of absolute standards
germane to a specific company and situation.

The rankings deserve some comment to clarify or, as
the case may be, to justify the tabled results. Cost would
seem to increase going from Factor Listing (FL), to Jury of
Executive Opinion (JE), to Sales Force Composite (SF), and
finally to Users' Expectations (UE). Increased manpower
requirements characterize this sequence. In addition, UE
entails devising a sampling instrument and the attendant
costs of testing and tabulating.

SF yields a more detailed forecast because it is
a buildup approach. UE may come close to this level of
detail, but at the cost of an extremely thorough sampling.
FL and JE, because of their general nature, practically
preclude any detail.

UE can reveal the important market factors if the
test instrument is well-rounded and prOperly constructed.
The FL approach suggests management's list of possible
factors, but JE and SF only indirectly incorporate these
market factors.

It is logical that required inputs would parallel

88
cost movements. FL requires only a set of factors with
intuitive weightings. JE calls for tOp executives to pool
their knowledge and to expend a certain amount of effort
and time. To implement an SF approach, considerable man-
power must be used, including both field sales personnel
and sales managers. An adequate UE forecast calls for
marketing research peOple, a test instrument, research
validation, tabulation, and interviewer or postal service
costs.

Analyzing relative strength in terms of the plan-
ning horizon is a difficult task. It seems that the FL
and JE methods might be more useful for long-term fore—
casting, while SF and UE lend themselves to a shorter time
period. The first two approaches tend to be more general
and planning oriented. On the other hand, salesmen and
customers may have more precise estimates for the near
future. Overall, none seems to be good for both long- and
short-term forecasting.

The timing criterion has been applied assuming that
the forecast being sought is not a first-time one. In
other words, the projection mechanism is already is exist-
ence. An FL approach should be the fastest to Operate be-
cause of its basic simplicity. An SF or JE estimate should

be next fastest if the process has already been formalized.

89
The prOper signals need only to be sent to those involved
to trigger the return of the individual forecasts. Last,
UE requires prodding many customers to respond, not always
an easy task, even if good customer-firm relations exist.

The degree of rigor is inversely related to cost.

A valid customer survey would be most appealing to the
theoretician because of its representativeness. A detailed
sales staff survey might approach a customer survey in
rigor, but the information gathered would still be second-
hand. Even more removed from the market place are the
results obtained from the FL and JE approaches. They are
the least exacting.

The quantitative techniques are also listed in
order of increasing cost--Moving Average (MA), Exponential
Smoothing (ES), Time Series Analysis (TS), and Regression
and Correlation Analysis (RC). Again, this sequence corre-
sponds to increasing input requirements. MA requires only
the most recent n values for sales and a calculator (or a
computer for many computations). ES may be even simpler in
terms of raw data requirements, but greater technical know-
how is needed. TS calls for much data, technical capability,
and computing equipment. Finally, RC is even more demand-
ing than TS with respect to data and technical ability

because of possible multivariate, nonlinear applications.

90

Perhaps BS is the most flexible in level of detail.
It can be implemented at nearly any level, and it is espe-
cially useful for generating product-by-product projections.
TS and RC are just as effective theoretically as ES, but
there are certain practical limitations. Sales of low
volume items can't be estimated with confidence, and rela-
tionships between independent variables and a specific
product may be weaker than for product classes or areas of
the country. MA is practically limited because it is an
averaging method. Low volume or high volume, volatile
products make averaging historic data a useless exercise.

Only RC actually considers market factors in the
form of the independent variables incorporated into the
model. The other three quantitative approaches emphasize
data patterns, not relationships or causalities.

The four techniques appear, at first glance, to be
about equally apprOpriate for different length planning
horizons. Actually only ES offers true flexibility, but
it generally is used at the shorter end of the time scale.
TS, by virtue of its component structure, can be utilized
only over a longer-range interval. Projections should not
be computed for periods shorter than those of the historic
data used to derive the equations. The same warning is

relevant for MA. Last, RC's usefulness is largely a

91
function of the periodic availability of values for the
independent variables. Often such data are obtainable only
on a yearly basis.

TS and RC can both generate forecasts throughout
their relevant ranges. As long as the assumed relation-
ships hold, the equations can be used. MA and ES are data-
bound in that they both require the latest value for actual
sales before a new forecast can be produced. TS and RC
are capable of forecasting at a more advanced date than
either MA or ES.

The most rigorous of the quantitative techniques is
RC. Nonlinear and multivariate alternatives are possible,
as well as simple linear models. Several restrictions on
data and model structure must be met. Finally, five coef-
ficients for evaluating the strength of the relationship
can be derived. TS is based on a best-fit criterion, and
it decomposes historic data into four component flows. ES
can be weighted to be very responsive to current input, or
just the Opposite. The MA approach is obviously the least

sophisticated; it is a simple average over several periods.

Selection of ForecastinggTechnique

 

The remaining task at the present time is to choose

the sales forecasting technique to be used in conjunction

 

 

 

 

92
with the LREPS model. The foregoing presentation, analysis,
and comparison of techniques provide the framework for this
selection. The discussion which follows is organized on a
priority basis.

First, since the LREPS model is a quantitative,
computerized simulation, the forecasting mechanism must lend
itself to either logical or symbolic expression. All eight
techniques satisfy this test, although the quantitative
methods are somewhat easier to program.

Next, all data input must be available at the start
of a simulation and be capable of being updated through
feedback linkages in the model. The nonquantitative tech-
niques start to fall short at this point. For example, to
anticipate and to program all the thought processes in
which an executive or a salesman might engage while up-
dating his initial forecast is an impossible task. Like-
wise, to conduct an Opinion poll of simulated product users
is to know in advance the way in which they think, making
the poll results trivial. The nonquantitative approaches
to sales forecasting can be eliminated from consideration.

Third, the need is for a short-term mechanism cap-
able of forecasting in detail by product and by geographic
region. Fourth, the Operating cost is inconsequential

because any technique will not contribute substantial

93
additional cost when compared with existing model Operating
costs. Based on level of detail required and the desired
planning horizon, exponential smoothing is the most appro-
priate choice. In addition, this approach is less demand-
ing in terms of inputs than the more rigorous techniques.

Timing becomes less important because of the rela-
tively short time interval being studied. Also because of
the one year time span, the importance of market factors
is diminished. This forecasting mechanism is for control
purposes, not for long-range planning.

As a result, the importance of detail, inputs, and
the planning horizon seem to indicate an exponential
smoothing model. This, then, is the adOpted forecasting
technique. The format of the model is

New Forecast = a(New Demand) + (l-a)(Old Forecast).

Summary

The objective of this chapter was to describe the
alternative forecasting techniques so that a wise selection
of the technique to be used in conjunction with the LREPS
model could be made. As was shown, there are two main cate-
gories of techniques, nonmathematical and mathematical.
Included in the nonmathematical group are factor listing,

jury of executive Opinion, sales force composite, and users'

94

expectations. The mathematical approaches are moving
average, eXponential smoothing, time series analysis, and
regression and correlation analysis.

Each technique has its strengths and weaknesses.
To choose correctly the most apprOpriate technique, manage-
ment needs to compare a set of selection criteria with the
relative rankings of these techniques. The situation
facing the firm dictates which technique is suitable.

For purposes of short-term computer experimentation,
exponential smoothing appears to be the most useful of the
various techniques. Forecasts for short time periods are

possible, as are regional and product forecasts.

95

CHAPTER III--FOOTNOTES

1M. H. Spencer, C. G. Clark, and P. W. Hoguet,
Business and Economic Forecasting (Homewood, Illinois:
Richard D. Irwin, Inc., 1961), p. 4.

2Stanton and Buskirk, p. 555.

3C0pe1and, p. 76.

4COpeland, pp. 78-83.

5Spencer, Clark, and Hoquet, p. 17.

6Stanton and Buskirk, p. 555.

7R. R. Still and E. W. Cundiff, Sales Management:

Decisions, Policies, and Cases (Englewood Cliffs, N.J.:
Prentice-Hall, Inc., 1958), pp. 555-556.

 

8Forecastipgpsales. pp. 12-14.

9E. C. Bratt, Business Cycles and Forecasting
(Homewood, Illinois: Richard D. Irwin, Inc., 1953), p. 239.

loForecasting Sales, p. 20.

 

llIbid., p. 21.

lzrbid.

13Cope1and, p. 98.

14C. M. Crawford, Sales Forecasting: Methods of
Selected Firms (urbana, Illinois: The university of
Illinois, 1955), pp. 28-30.

15Forecasting Sales, p. 31.

16R. G. Brown, Statistical Forecasting for Inventory
Control (New YOrk: McGraw-Hill, Inc., 1959), p. 13.

17Ibid., p. 45.

18Ibid., pp. 46-51.

96
19R. G. Brown, Exponential Smoothing for Predicting
Demand," Tenth National Meeting of ORSA (San Francisco,
Nov. 16, 1956).

20Management Operating System: Forecastinge-
Exponential Smoothing--De§ail (White Plains, N.Y.: Inter-
national Business Machines Corporation), p. 17.

21Brown, Statistical Forecasting . . ., p. 66.

22A. A. Hirsch and M. C. Lovell, Sales Anticipations
and Inventory Behavior (New York: John Wiley & Sons, Inc.,

23J.‘W. Forrester, Industrial Dynamics (Cambridge,
Mass.: The M.I.T. Press, Massachusetts Institute of Tech-
nology: 1961), p. 411.

24R. W. Llewellyn, Fordyn:l An Industrial Dynamics
Simulator (Raleigh, N.C.: North Carolina State University,
1965), pp. 6.40-6.44.

25M. Hamburg, Statistical Analysis for Decision
Making (New York: Harcourt, Brace & World, Inc., 1970),
p. 540.

26Ibid., p. 543.

27G. R. cooper and C. D. McGillem, Methods of Signal
and System Analysis (New York: Holt, Rinehart and Winston,
InC. ' 1967) ' pp. 90-93.

28T. Thornton, unpublished lecture notes (East
Lansing, Michigan: Michigan State University, 1971).

29ForecastingSales, p. 34.

30Hamburg, p. 460.

31R. E. Frank, A. A. Kuehn, and w. F. Massy,
Quantitative Techniques in Marketing Analysis (Homewood,
Illinois: Richard D. Irwin, Inc., 1962), p. 85-93.

32J. Johnston, Econometric Methods (New Ycrk:
MCGraw-Hin. Inc., 1963), pp. 179-199.

33Frank, Kuehn, and Massy, p. 87.

34Ibid.

351bid.. p. 89.

97

CHAPTER IV

FORECASTING ACCURACY

Introduction

 

The critical nature of sales forecasting as the core
of the planning process has been mentioned, as have been
approaches for estimating future sales volumes.. In order
to ensure sound forecasts, however, the firm needs bases
for evaluating the reliability or accuracy of these projec-
tions. Further, the assessment of the forecasting mechanism
should be a continuous process: a model which is apprOpriate
now may not be valid in future time periods. To validate a
model with the historic data used to develOp it is surely
an incestuous approach.

The question of how to measure forecasting accuracy
is not a simple one. Certain mathematical forecasting
techniques have built-in measures to guide the user in
their application. These specific measures are not univer-
sally applicable. In this study only general techniques
for determining the accuracy of any approach to forecasting
are presented.

98

99
Hirsch and Lovell suggest several criteria Which
can be used to appraise alternative measures of forecasting
1
accuracy:

1. It is obviously advantageous to work with a
measure that may be regarded as an index of
the cost to the firm of erroneous forecasts.

2. It is useful to have a measure of forecast
accuracy that is independent of units of
measurement so that the relative accuracy
of forecasts by large and small firms will
be comparable.

3. It is helpful, at least for certain purposes,
if the yardstick of precision rates the fore-
caster relative to the difficulty inherent in

the type of series he is trying to forecast.

4. It is useful to judge the forecasts both with
and without systemstic bias.

The first rule implies that the magnitudes of the
error levels are important if the impact of a given error
is to be determined. The second guideline suggests the
need for a dimensionless, relative measure of error.
Third, the sales pattern of the firm must be analyzed.
Finally, bias should be removable. The overall need is,
then, for an absolute, relative, difficulty-weighted, and
unbiased error measure. Apparently no one gauge will be
able to satisfy these all-inclusive, even contradictory,
criteria.

The remainder of this chapter looks at accuracy

measurement in terms of several perspectives. First,

100

common statistical techniques are presented. Next, a
generalized turning-point approach is covered. Last, evalu-
ation based on firm objectives is suggested in addition to

the previous approaches.

Statistical Accuracy Evaluation

 

As might be suspected, there are several ways to
measure forecasting accuracy with mathematical derivations.
A listing of such methods would include the following:2'3

1. Standard deviation

2. Mean-square error

3. Mean absolute deviation

4. Correlation coefficient

5. Theil's inequality coefficient

6. Adaptations of previous measures.

Each measure is now discussed in detail, highlighting the

reasons for the possible use of each.

Standard Deviation
The standard deviation is an obvious choice as a
yardstick for appraising forecasting accuracy. The general

formula for computing the standard deviation of a sample is

s = ZQY?§)2
n

where s is the sample standard deviation, Y is an individual

101
observation, Tris the average of all such sample observa-
tions, and n is the number of observations. For use in the
context of a forecasting evaluant, each Y can be inter-
preted as the difference between a forecasted and an actual
sales value, Yf - Ya' 80'? is the mean of all such values
in the sample and is equal to §;_:—§;.

As is the case with other measures which follow,
the standard deviation does not satisfy all of the criteria
noted at the outset of this chapter. It is an absolute
measure, so interfirm comparisons are not possible. The
first point, suggesting an error index related to cost, is
tested in Chapter VI for a combination of error measurement
methods. No reading on the inherent complexity of the
forecasted time series is supplied by the standard devia-
tion. In general, this criterion is beyond the sCOpe of
this research and is left to econometricians. Unfortun-
ately, the standard deviation can hide consistent over- or
underestimation, so it does not remove systematic bias.

Statistical testing is possible by utilizing the
variance, the square of the standard deviation. The F test
permits comparison between forecasting approaches by com-

paring the resulting variances in ratio form.

102
Mean-Square Error
An alternative to the standard deviation is the
mean-square error (MSE), which can be shown to be related
to the standard deviation. An expansion and rearrangement

of terms yields

The first term on the right of the equality is the mean-
square error. Since it is a component of the standard
deviation, it is simpler to compute. The size of the nume
bers involved when using the mean-square error is one draw—
back of the technique: hence, comparisons between firms is
not meaningful.5
Work has been done which indicates that the mean-
square error may be prOportional to certain production and
inventory costs.6 A more comprehensive model, such as
LREPS. could be used to verify these claims. Because it

squares an absolute difference, the mean-square error would

flag any steady positive or negative forecasting mistakes.

Mean Absolute Deviation

The general form for the mean absolute difference is

eLXl

n

where, according to convention, Y is the difference between

103
actual and forecasted sales. This approach ignores the
sign of the difference and gives the average value of the
unsigned forecasting error. This technique is the simplest
so far, and it is the easiest and fastest one to calculate.
However, comparisons between large and small firms are im-
possible because the measure is absolute, not relative.
Consistently bad estimates are pinpointed because of the

absolute value.

Correlation Coefficient
There may be an association between predicted and
actual changes in sales volumes. A correlation coefficient
which measures the strength of this association can be com-
puted. The formula
r2 = 1 - sez/sa2

2
e

2

where r is the coefficient of determination, s is the

is the variance of

2

variance of the forecast error, and sa2

7 is the same as

the sales data. The interpretation of r
for the coefficient of determination discussed in the
previous chapter in the section dealing with regression
and correlation analysis. The range of values possible for
r2 is from zero to one.

This gauge is a relative one, so it encourages

matching among companies. If a firm consistently under-

104
estimates sales, it could receive a perfect score of unity.

Thus, the correlation coefficient does not eliminate bias.

Theil's Inequality Coefficient
Theil develOped a test statistic which is bounded

at the lower extreme by zero.8 The measure is

 

U = fuss
(Ya)2/n

A perfect forecast yields a U of zero, while fore-
casting error results in U values greater than zero. If
0:1, the same result could have been achieved by forecast-
ing a value of no change from the previous actual value. If
U is greater than one, the forecast of no change was better
than the forecast used.

The relative value is desirable for making compari-
sons. It imposes a penalty for systematic linear bias be—
cause of the incorporation of the mean-square in the rela-

tionship.9

Adaptations of Previous Measures

Hirsch and Lovell have suggested several transforma-

tions and combinations of the aforementioned measures.10

The first such coefficient is

E(Yé)

 

105

The value of this adaptation is in the very meaning-
ful interpretation which can be given to values of r12. An
r12 of one indicates perfect forecasting. A value of zero
suggests the same results could have been realized by making
the naive forecast of no change. Finally, negative values
imply the forecaster is doing worse than could have been
done with the naive estimate.

Another possibility is
r22 = 1 - MSE/saz.

This coefficient compares the accomplishments of
the forecaster with the root-mean-square-error obtained by
a naive forecaster who consistently predicts the most
recent average sales value as the estimate. Unless the
actual data exhibit a trend, this coefficient is useless.
It does show that the forecaster working with a series dis-
playing a consistent trend is working with a simpler problem.

Additional manipulations can be performed which
reflect seasonal or cyclic fluctuations. If certain charac-
teristics of the actual sales pattern are known or suspected,
error measurement can be refined considerably.

A general improvement can be made to correct all of
these measures to relative form. This is to define the

actual and forecasted values in relative terms. That is,

let at be the actual relative change in sales and ft be the

106

forecasted relative change, both for period t. Then,

 

 

at """ Ya,t ' Ya,t-l ft = Yf,t ' Ya,t-1
Ya,t-l Ya,t-1
where Y is actual sales in period t and Y is fore-
a,t f,t

casted sales for period t.

This conversion is especially important for using
the F test to compare variances for different forecasting
periods. For example, comparing variances for the differ-
ence between actual and forecasted sales in absolute terms
for two different intervals, one being one day and another
being three months, would probably be a waste of time. If
average daily sales is 100 units and the range is :10%,
then to forecast the average would be to err by no more than
10 units. With quarterly sales equal to 6,300 units (be-
cause one quarter equals 63 days within the LREPS model)
and the range being :10%, forecasting the average could
result in an error of 630 units. The standard deviation
of the forecast for the larger prediction interval would
be much larger than for the one day interval. However,
using the relative definition of the standard deviation
would eliminate this noncomparability.

If a and f are substituted for Ya and Yf, respec-
tively, in the foregoing presentation, the adjustment for

relativity is included. Thus, in the previous formulae Y

107

now becomes a - f instead of Ya - Yf.

Nonmathematical Accuracy Evaluation

The ways just presented to determine forecasting
accuracy are ones which all firms and managers may not
understand. They probably would feel comfortable in terms
of peer group evaluation if they used such methods. In
other words, if the benefits of using such evaluatory tech-
niques are ignored, there may be pressure to use these
methods "just because we should."

This hypothetical situation, if it exists, is a sad
one indeed. For persons who may be trapped by such circum-
stances, a possible solution can be cited. A less sophisti-
cated technique, at least in terms of the mathematics, is
the analysis of turning points. One can argue that the
critical element of sales forecasting is to determine the
direction of change of sales volume.11 Given the direction,
either a continuation Of the present or a change in trend
(a turning point), any of the previous forecasting tech-
niques could be used with an acceptable degree of precision.
Accordingly, the "hit" prOportion on predicting turning
points is a simple measure of forecasting prowess. An
arbitrary "batting average" can be set as a minimum accept-

able prOportion of correct directional estimates. If a

108
company is not anticipating turning points a high enough
prOportion of the time, then the application and choice of
technique should be re-evaluated.

The value of correctly foreseeing turning points
often is not appreciated by forecasters. A simple example
dramatizes the crucial nature of such anticipations. Sup-
pose a firm's sales volume is increasing by about 10% per
time period with the range of the increase being between 8%
and 12%” The length of the time period, the number of
products involved, and the geographic region in question
are not important for purposes of this illustration. Now
suppose for next period the firm projects another 10% incre—
mental increase in sales when, in fact, a 10%.decrease is
realized. The net effect is an overestimate of 20%. This
error is considerably larger than the historical i2% per
period. If the firm had based its Operating plans on the
tolerance level of 2%, then the 20% could prove to be
disastrous.

Another illustration highlights individual product
studies. A firm might be able to forecast within an accept-
able range for a product group. For simplicity imagine a
grouping of 10 products. Suppose five products have been
increasing in volume over time, and five others have been

declining in sales. If the sales of each set of five were

109
comparable, a reversal by each would leave total sales
generally unchanged. The internal changes would make a
shambles of physical distribution performance. There
would be stockouts, excess inventories, poor service,
premium replenishment costs, and backorders.

Thus far, only the prOportion of turning points
correctly prognosticated has been mentioned. At least two
statistical tests can be used to evaluate the firm's record
of anticipating these directional switches. A logical
first choice would be an application of the binomial test.
A brief example shows the usefulness of this test. If the
process by which a turning point is forecast involves some-
one merely flipping a coin, then the probability of cor-
rectly forecasting a turn when it occurs is 0.5. A compari-
son of an actual z (or t) value with a critical 2 (or t)
value based on the desired confidence level could be made.

The actual value is computed from

 

z (or t) = (p - 0.5)/f(.5)(.5)/n
where p is the prOportion of turning points correctly esti-
mated and n is the number of turning points or sample size.
If n is sufficiently large, say, greater than 30, then the
z statistic is appropriate: otherwise, t is used. The
hypotheses and the corresponding acceptance and rejection

regions depend upon the objectives of the researcher.

110
The runs test, used in conjunction with the binomial
test, may be more enlightening. It is possible that the
firm is forecasting only one-half of the turning points.
Thus, the results of the binomial test would not be signifi-
cant. If the prOportion of mistakes (or correct estimates)
follows a nonrandom pattern, then the runs test would re—

veal this. The runs test identifies the extreme cases of

Jr- ‘5 “-273“!

many or few runs (sequences of like events) in a sample.
As an extreme case, with C indicating a correct turning
point forecast and I denoting an incorrect one, imagine the
following sample of 20 forecasts:

CCCCCIIIIICCCCCIIIII

The prOportion of correct projections is exactly
0.5, and the number of runs is four. The probability of
observing four or fewer runs with two subsamples of 10 ele-
ments each is 0.001. Thus, it is very unlikely that the
above pattern is a chance occurrence.

It should be pointed out that analysis of turning
points is more apprOpriately applied to planning or long-
term forecasting. When the forecasting interval is large,
a directional error has a greater impact. Operating fore-
casts made weekly can be updated to compensate for direc-
tional errors. Annual forecasts for a planning horizon of

several years had better be directionally correct:

lll

otherwise, they are worthless.

Accuracy Evaluation by Objectives

During the course of selecting and evaluating a
forecasting model, a company can easily become involved
with the details of the process and lose sight of broader
objectives. Certainly the assumptions underlying the vari-
ous techniques must be considered, and the planning horizon
should be studied carefully. The forecast is not, however,
an end in itself. The value of the forecast is measured by
how much it contributes to the planning process. Should
not forecasting accuracy be measured in a like manner? How
is effective planning manifested? One gauge is the con—
strained level of cost or profit. The constraints may com-
plicate the problem considerably, but cost and profit are
measureable accounting concepts.

The LREPS model presents an Opportunity to examine
the relationship between forecasting accuracy and physical
distribution system costs. For each forecasting model used
measures of forecasting error are collected. At the same
time, physical distribution costs are monitored. Thus,
cost and error are tracked simultaneously. If accuracy is
truly reflected in the system objective, minimized con-

strained physical distribution cost, then error and cost

112
profiles should be quite similar. The ideal forecasting
mechanism is the one which yields minimum total costs.

This concept can be generalized to any system
utilizing a forecast as an input. To be safe, patterns Of
cost and error should be reviewed for similarities.
Possibly one system component of relatively larger size
might not rely on the accuracy of the forecast: hence,
little benefit would accrue to the firm which emphasizes
increased precision in its estimates. Usually an insightful
way to compare forecasting alternatives would be to compare

respective system costs.

Summary

A forecasting model cannot be ignored once it is in
Operation. It should be monitored regularly to assess its
performance. Several approaches for carrying out this
evaluation have been presented. Statistical analysis is
quite pOpular, and many variations of standardized statis-
tics have been developed. As an alternative, turning point
analysis offers the less quantitative forecaster a means of
evaluating performance.

Regardless of the forecasting technique and error
analysis employed, the objective of the forecast should not

be overloOked. Forecasts provide, in the limit, valuable

113
input to the planning process. To a lesser extent, differ-
ent segments of the firm need projections. A sOphisticated
planning model, such as LREPS, can utilize a complex and
accurate forecasting mechanism. On the other hand, for
other uses a less complex forecasting model could probably

sacrifice some accuracy, yet still be a valuable tool.

114

CHAPTER IV--FOOTNOTES

1Hirsch and Lovell, p. 36.

2;p;g., pp. 37-42.

3Brown, Statistical Forecasting . . ., pp. 89-94.
4M. Mendenhall, Introduction to Probabiliry and

Statistics (Belmont, California: Wadsworth Publishing
Company, Inc., 1968), pp. 39-40.

5

 

Brown, p. 90.

6c. c. Holt, F. Modigliani, J. F. muth, and H. A.
Simon, Planning Production, Inventories, and Work Force
(Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1960).

7Hirsch and Lovell, p. 38.

8H. Theil, Applied Economic Forecasting (Amsterdam:
The North-Holland Publishing Co., 1966), pp. 26-32.

9Hirsch and Lovell, p. 38.
loIbid., pp. 39-42.

11Erickson and Lewis, ch. 7.

CHAPTER V

RESEARCH METHODOLOGY

Introduction

The general form of the short-term build-up fore-
casting model has been conceptualized and programmed. The
research to this point has been aimed at fulfilling the
first part of the overall research Objective, that of
develOping a forecasting archetype. This chapter begins
the presentation of a continuing illustration of how the
general model can be applied in a particular situation, the
remaining part of the overall objective. It should be
noted that the data used in this example are disguised
because of the competitive nature of the industry in which
the sample firm Operates.

First, the forecasting model is described in its
entirety. Next, the researchable hypotheses which guided
the experimentation are outlined. Finally, the research
sequence used in carrying out the computer experimentation

is presented.

115

 

 

116
The General Model

The forecasting mechanism discussed is flexible in
terms of three dimensions. In Chapter I it was suggested
that the forecasting technique, the level of detail, and
the prediction interval should be variables which can be
assigned different values. The model was designed with
this in mind. Each of these three dimensions can be varied
as the situation dictates.

In Chapter III exponential smoothing was chosen as
the apprOpriate technique for short-term forecasting. The
ZIP regional system and the broad range of possible tracked
products found in LREPS allow the use of many techniques at
the same time. However, only exponential smoothing was
deemed suitable for this search. To maintain maximum flexi-
bility, the smoothing constant was allowed to vary by
product and by region. At one extreme, the same smoothing
constant can be used for all products and regions. At the
other extreme, each product area can be assigned a different
smoothing constant.

The second dimension, level of forecasting detail,
is Operable at four levels. These are the firm, the
product, the DU (ZIP Sectional Center), and the product-DU.
More levels are theoretically possible, but were not modeled.

One of the unique features of this model is that it

 

 

117

facilitates the develOpment of aggregate forecasts by accu-
mulating lower-level estimates. For example, product fore-
casts can be generated by summing all product-DU forecasts
for that product. Alternatively, the forecast can be made
at the product level, but product-DU projections would then
be only arbitrary fractions of this product total. Even
though the aggregate forecasts might be equal under the two
approaches, the detailed forecasts under the build-up method
should prove to be more accurate and, thus, more useful.

Variations in the prediction interval are quite
easy to achieve. The forecasting module within the LREPS
model is simply called at different times during the simu-
lation run. Frequent callings generate frequent forecasts,
but for shorter periods, and vice versa. Again, different
product-DU's can be assigned unequal forecasting intervals.

The computer experimentation described in Chapter
'VI deals with these three dimensions as they relate to a
specific company. The dimensions are interrelated to

formulate a specific forecasting model.

Researchableguestions and Hypotheses
Several questions were devised which served to
focus the research on specific tOpics. These questions are:

l.' What are the "best" values for the smoothing

118
constants of the predictive equations for the
sample data? These values can be determined
through experimentation--evaluated on the
basis of forecasting accuracy and physical
distribution costs--or by examining previous
research aimed at this problem.

2. What prediction interval (day, week, month,
etc.) is most appropriate? What is the
functional relationship between physical
distribution costs and the size of the pre-
diction interval?

3. What is the nature of the build-up function
which provides the national forecast from the
local forecasts? In other words, how much
detail is required for a satisfactory forecast?

4. What is the relationship between physical dis-
tribution costs and system service levels?
Cost has been traditionally considered to be
an increasing function (at an increasing rate)
of service level.

A set of testable research hypotheses can be de-

rived from each question. From Question 1 a relationship
ibetween.equation parameters (smoothing constant values)

and cost can be hypothesized:

119
H : There is no association between smoothing
constant values and physical distribution
costs.

H1: There is an association.

Since both data sets are at least interval in
nature, regression and correlation analysis is applicable.
The smoothing constant can be treated as the independent
variable and cost as the dependent variable. The signifi-

cance of the sample correlation coefficient (r) can be

learned by using the t statistic

 

t = r/711-r2)/(n-2).
A two-tailed test is in order with HD being rejected if the
absolute value of the computed t is greater than the criti-
cal t value.

The following relationship between physical distri-
bution costs and the size of the prediction interval is
based on Question 2:

H0: There is no association between the size

of the prediction interval and physical
distribution costs.

H1: There is an association.

.As for the previous question, the sample correlation coeffi-
¢:ient can be examined by the use of the t statistic.

The emphasis of Question 3 is on the derivation and

«comparison of alternative build-up functions. This can be

done by comparing sample variances for the same forecasting

120
level for any two alternatives. The variances are in rela-
tive terms. The hypotheses are:

H : The variances for any ZIP area (DU) and

product are equal for the two build-up
functions.

0

H1: The variances are unequal.
Additional hypotheses about other equivalent forecasting
levels are formatted similarly.

The ratio of the two variances being compared ex-
hibits an F distribution. The test statistic is

F = 812/822

where the 32's are the sample variances with 312 arbitrarily
chosen as the larger value for convenience in comparing
actual F values with tabled critical F values. H0 is
rejected if the actual F value exceeds the critical value.

Another set of comparisons relating to the selec-
tion of an adequate level of detail is based on Ques-
tion 3. Given the accuracy and associated physical dis-
tribution cost at one level, does the next level of fore-
casting detail offer a significant improvement? The sup-
;xosed relationships of the sample variances are:

H0: The variances are equal for the two levels
of forecasting detail.

H1: The variances are unequal.

Once more, the F test can be used as described for

121
the previous hypotheses.
The relationship between physical distribution
costs and forecasting accuracy can be hypothesized as a
result of the preceding analyses:

H - There is no association between forecasting
error and physical distribution costs.

H1: Higher levels of forecasting error are
associated with higher levels of physical
distribution costs.

This set of hypotheses can be tested by computing
the value of Spearman's rank correlation coefficient (r8).
The nonparametric test is in order because several measures
of error are reasonable, as can be seen from the discussion
in Chapter IV. Thus, a weighted composite index of error

measures can be displayed only in rank order. The computed

r is based on

 

 

8
n n n
E . - Z - Z .
r = nifllxiyl (i=lx1)(i=lyl)
S

n n n n
2 2 2 2
n E x. - (2'. X-) n.£ Y -' (z Y.)
[i=1 1 i-l 1 ][ i=1 1 i-l 1 ]

In this instance x- refers to forecast error and Yi

3.

:refers to physical distribution costs--both ranked ordi-

2na11y. The computed r is compared with the critical value

(of re, based on sample size and significance level. Since

‘the hypothesized relationship is a direct one, the critical

122
r8 has a positive sign. If the computed r8 is greater than

the critical r H0 is rejected.

8'
The subject of Question 4 is the relationship be-
tween physical distribution costs and service. The specific

hypotheses are:

H0: There is no association between physical
distribution cost and service.

H1: Higher physical distribution costs are
associated with higher service levels.

With service as the independent variable and cost as the
dependent variable, regression and correlation analysis is
applicable. Again, the t statistic in one-tailed form is

suitable for the testing of these hypotheses.

Research Sequence
The questions are ordered to provide a sequence for
the experimentation. The analyses of Questions 1, 2, and 3
were carried out concurrently. That is, smoothing constant
values, prediction intervals, and build-up functions were
derived simultaneously. Initial values were selected on

1 and others. Changes were

the basis of research by Packer
Inade to yield different combinations of these three factors.
'The result was a convergence on an Optimum combination for

the selected alternatives. This phase of the research is

3presented in Chapter VI.

123
The second set of experiments was designed to iso-
late the effect of physical distribution service on costs.
Since the structure of the components of total cost could
also have changed, these costs components were traced too.
The results of these experiments are covered in Chapter

VII.

124

CHAPTER V--FOOTNOTES

1A. H. Packer, "Simulation and Adaptive Forecasting

as Applied to Inventory Control," Operations Research
(July, 1967).

CHAPTER VI

DEVELOPMENT OF THE
DETAILED FORECASTING MODEL
Introduction
The general short-run forecasting mechanism with
exponential smoothing as the selected technique serves as
the framework for the detailed sales forecasting model.
Specific levels for the three dimensions of prediction
interval, level of detail, and smoothing constant are chosen
for consideration. Various combinations are tested to
(determine a heuristically Optimum set. Since an infinite
number of combinations are possible, only a limited number
are examined.
The following relationships are studied in this
chapter:
1. The relationship between the exPonential
smoothing constant and physical distribu-
tion costs.

2. The relationship between the prediction
interval and physical distribution costs.

3. The relationship between levels of fore-
casting detail.

125

126

4. The relationship between forecasting accu-
racy and physical distribution costs.

For all experimentation the same pattern of actual
simulated sales is used. The daily sales total is con-
sidered to be increasing by a constant amount (rectilinear
trend). Variation in sales is achieved by assuming sales
values to be normally distributed about this trend line.
These random fluctuations represent chance variations in
daily sales. Even if a firm experiences rigidly increasing
sales (a strict linear trend), day-to-day variations are
likely to occur. Each day the trend value for sales is
adjusted by the product of a normal random deviate times
the standard deviation of daily sales.

To simplify experimentation the LREPS structure has
been condensed. Instead of examining many products and 390
Demand Units (DU's), 10 sample products and 31 DU's are
utilized. This represents a partial product line and a
.region of the country. This greatly reduces computational
(:ost and time, while still facilitating the testing of the
build-up concept .

Smoothing Constant and
Prediction Interval Experimentation
Smoothing constant and prediction interval values

are handled concurrently because, as stated in Chapter II,

127

they interrelate as variables in the planning process. The
choice of values for one of these variables affects the
range of choices for the remaining one.

Several writers have researched the range of appro-
priate smoothing constant values.l'2 Brown notes that a
value of 0.01 results in a sluggish and nonresponsive model,
while 0.5 is a volatile and overly sensitive choice. He
suggests further that 0.10 is a satisfactory alternative to
these extremes.3 For this research the following five
values were selected:

0.01 0.05 0.10 0.30 0.50

The choice of a prediction interval is more diffi-
cult. Since the overall period of analysis is one year,
this is the maximum value. Such a choice would not facili-
tate the initialization needed to allow the exponential
smoothing model to function prOperly. For this reason the
lengthiest interval examined is three months. Even this
selection results in only four forecasted periods, a rela-
tively small number of observations.

The LREPS model has been designed to process no
events shorter than one day, so this is the lower bound on
the prediction interval. Because of this design constraint,

one week is the shortest selected interval. The prediction

intervals used are as follows:

 

128

1 wk. 2 wks. 1 mo. 2 mos. 3 mos.

There are 25 combinations of smoothing constant and
prediction interval values, as shown in Table 6.1. For
each combination variable physical distribution cost was
collected. These data are presented in Tables 6.2 and 6.3
with fixed prediction interval and smoothing constant
values, reSpectively.

Variable physical distribution cost was selected
for analysis because of the short-term nature of these
experiments. Of the cost components within LREPS, including
inbound transportation (Manufacturing Control Center to
Demand Unit), outbound transportation (Distribution Center
to Demand unit), throughput, ordering, facility, and
inventory, only inbound transportation and inventory costs
vary with service requirements in the short run. Higher
service levels (delivery to more customers with less vari-
ation) are achieved with the larger inventories and frequent
replenishments (inbound shipments); therefore, cost is in-
creased. The other components remain fixed for periods of

one year or less.

SmoothingyConstant Analysis
The first set of research hypotheses tested related

the smoothing constant to physical distribution costs:

129

TABLE 6.1.-~Combinations of Smoothing Constant
and Prediction Interval Values

 

 

 

Smoothing Prediction
Experiment Constant Interval
11 0.01 1 wk.
12 0.01 2 wks.
13 0.01 1 mo.
14 0.01 2 mos.
15 0.01 3 mos.
21 0.05 1 wk.
22 0.05 2 wks.
23 0.05 1 mo.
24 0.05 2 mos.
25 0.05 3 mos.
31 0.10 1 wk.
32 0.10 2 wks.
33 0.10 1 mo.
34 0.10 2 mos.
35 0.10 3 mos.
41 0.30 1 wk.
42 0.30 2 wks.
43 0.30 1 mo.
44 0.30 2 mos.
45 0.30 3 mos.
51 0.50 1 wk.
52 0.50 2 wks.
53 0.50 1 mo.
54 0.50 2 mos.
55 0.50 3 mos.

 

130

TABLE 6.2-—Physica1 Distribution Cost as a
Function of Smoothing Constant

 

 

 

Prediction Smoothing Variable Physical
Interval Constant Distribution Cost/1b.
1 wk. 0.01 $0.010553
0.05 0.011552
0.10 0.012318
0.30 0.011991
0.50 0.012170
2 wks. 0.01 0.010363
0.05 0.010854
0.10 0.010833
0.30 0.011105
0.50 0.011418
1 mo 0.01 0.010187
0.05 0.010320
0.10 0.010333
0.30 0.010466
0.50 0.010743
2 mos. 0.01 0.010197
0.05 0.010178
0.10 0.010359
0.30 0.010345
0.50 0.010430
3 mos. 0.01 0.009877
0.05 0.009962
0.10 0.009860
0.30 0.010088

0.50 0.010165

 

 

131

TABLE 6.3.-—Physical Distribution Cost as a
Function of Prediction Interval

 

 

 

Smoothing Prediction Variable Physical
Constant Interval Distribution Cost/lb.
0.01 1 wk. $0.010553
2 wks. 0.010363
1 mo. 0.010187
2 mos. 0.010197
3 mos. 0.009877
0.05 1 wk. 0.011552
2 wks. 0.010854
1 mo. 0.010320
2 mos. 0.010178
3 mos. 0.009962
0.10 1 wk. 0.012318
2 wks. 0.010833
1 mo. 0.010333
2 mos. 0.010359
3 mos. 0.009860
0.30 1 wk. 0.011991
2 wks. 0.011105
1 mo. 0.010466
2 mos. 0.010345
3 mos. 0.010088
0.50 1 wk. 0.012170
2 wks. 0.011418
1 mo. 0.010743
2 mos. 0.010430
3 mos. 0.010165

 

‘AI

,9 . A“. wavy-4n...
; ‘ .

132

H : There is no association between smoothing
constant values and physical distribution
costs.

H1: There is an association.

For each set of research hypotheses there are cor-
responding statistical hypotheses, based on the population
parameters in question. For the above hypotheses, the
sample correlation coefficient, r, expresses the strength
of the relationship between the two variables. The smooth-
ing constant is treated as the independent variable in the
analysis. The statistical hypotheses about the pOpulation
correlation coefficient, 0, are these:

HO: 0 = 0.

H1: p # O.

This test was conducted at a .10 level of signifi-

cance. The t statistic is apprOpriate with the actual t

value computed from

 

t

r//(1-r2)/(n-2)

where n is the sample size. In this analysis physical
distribution costs were regressed on smoothing constant
values with the prediction interval held constant. Five
samples, each containing five data pairs, result from such
an approach.

The structure of the hypotheses implies a two-tailed

test. The critical t value for three (n—2) degrees of

133

freedom at the .10 level is 2.353. The resulting decision
rule is:

If |t|> 2.353, reject HO and accept H
otherwise, accept H0.

17

The results of this group of tests appear in Table
6.4. The data were fit to the following four general line

forms using the least-squares criterion:

1. Y = a + bX
2. Y = a + b(log X)
3. Y = a(b)X
4. Y= a(X)b.

There is substantial evidence to suggest a direct
relationship between smoothing constant values and variable
physical distribution costs. With sales following an in-
creasing trend pattern, variations are due mainly to chance
fluctuations. Larger smoothing constant values tend to
exaggerate the effect of a random fluctuation and would
trigger a system over-reaction, such as a large replenish—
ment order to cover a sudden increase in sales. Smaller
smoothing constant values overlook this "noise" and smoothly
increase the forecast to match the sales growth.

Other than it is a direct one, the exact relation-
ship is difficult to describe. Equation four seems to be
the best overall choice for all five data groupings; how—

ever, the simple linear trend line, equation one, reflects

Hm>ma no. on» pcommp ucMUHMNcme

 

 

134

 

 

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we gamma“ mmm.N osq.N «NsmHm. s
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on soohmu mmN.N mN¢.N amNmHm. N
m uumnmu mmm.N nNQN.s NommNa. H msuaoa m
mm “8?: SUN momN $33. s
on sumhmu mmm.N mmo.N «NoHsm. m
on uummmp mmm.N mom.N ooqmmm. N
m uumnmu mmm.N mao.N mmmHsm. H msucoa N
mm “8?: EN pass 208.... .V
on somnmu mmN.N ammo.w mmwNna. m
on gamma“ mmm.N nNNm.m cmemw. N
m uuonmp mmm.N mMHo.m quNNm. H asses H
mm “gummy mmm.N mea.o aNmon. s
on somhmu mmm.N anm.m quQHa. m
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m nommmu mmm.N ncmm.m mooon. H ax: N
mm somnmu mmN.N HNm.N HwHoom. s
on uawoom mmm.N NNN.H NNONam. m
on “comm“ mmN.N mso.m «Hess». N
m uawuum mmm.N mmN.H NmNmmn. H Haws H
cowmfioma u HmoHuHuo u pmusaaoo uamwoawmmoo show Hm>umuaH
coaumHmuuoo coaumavm coauuwnmum
maaamm Hmumamo pmxfim

 

 

pmme Hm>umuaH sowuuwpmum nu“: Axv mmaHm> usmumaoo
wsflnuooEm co va wumoo cowusnfiuumfln Hmowmmsm mo aoummmuwmmll.¢.o Manda

135
a strong association for four of the five samples.

It should be emphasized that this is an aggregate
relationship because the same smoothing constant was applied
to all products in a given experiment. Since all products
were assigned a similar sales pattern, the overall pattern
proved to be an accurate reflection of the individual
product patterns. Relative sales amounts did, however,
vary considerably among products. This did not pose a
problem because there was no apparent relationship between
volume and smoothing constant. The only problem was an
artificial one, created by the use of the simulation pro-
cess. Only a fraction of any product's sales can be simu-
lated during an experiment. Extrapolation is used to attain
total sales. A product with a relatively small sales volume
is difficult to simulate accurately. The simulated volume
for slow-moving items could possibly be too light to fore-
cast within this model. This parallels the real-world
lyroblem of inactive products; therefore, these products
‘were maintained within LREPS in spite of this forecasting-

‘volume problem.

Based on this analysis the firm with this product
cmonfiguration and sales pattern should choose smoothing
«constant values in the 0.01 to 0.10 range. Higher values

cyverexcite the physical distribution system, and these

136

extreme reactions can only lead to higher cost.

Prediction Interval Analysis

The next set of hypotheses refer to the possible
relationship between the prediction interval and physical
distribution costs:

H - There is no association between the size

of the prediction interval and physical
distribution costs.

I? -_

P. _--_~.~:--. -

H : There is an association.

Again the sample correlation coefficient, r, can be
tested to determine the strength of the relationship. The
statistical hypotheses are as follows:

H ° p = 0.

H1: p # 0.

As in the earlier experiments the t test is employed
at the .10 level of significance. Five samples of five
pairs of values for the prediction interval and variable
physical distribution costs were analyzed for fixed values
of the smoothing constant. The decision rule is identical
to that presented in the previous section.

The experimental findings are shown in Table 6.5.
The same four general equations were fit to the data.
'These results show an even stronger relationship than the

lorevious ones. Several t values are significant beyond

137

”I .2.C'wl.l.lh

‘
«v
N

 

 

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138

the .01 level. There is almost conclusive evidence indi-
cating an indirect relationship between the prediction
interval size and physical distribution costs. The explan-
ation is a straight forward one. For any prediction inter-
val, each forecasted value for a given product is the Same
for each day of that interval. Since there is an increas—
ing trend in the data, a longer prediction interval causes
the average forecasted value to be used to estimate sales
for more days. If the average value reflects a random
fluctuation, it is too high or too low. An overestimate
results in soaring inventory costs. An underestimate leads
to increased inbound transportation cost to handle back-
orders. The longer prediction interval means that a bad
forecast can't be corrected as fast as is possible with a
very short interval.

This company should utilize short forecasting
intervals for its products. The smooth sales pattern is
traced best with a small prediction interval (5 to 10 days)
which allows random movements to be eliminated quickly.

Once again, this is an aggregate relationship,
examined only for the case where all products use the same
interval. It is possible that different products could use
different intervals to reduce further the overall system

cost. This possibility is covered later in this chapter.

139

Multivariate Analysis

With statistically significant relationships exist-
ing between variable physical distribution costs and the
smoothing constant and between variable physical distribu-
tion costs and the prediction interval, a natural extension
is a multiple regression with two independent variables. A
multiple linear regression line was derived as follows:

Y = 0.011165 + 0.00117281X + 0.0000239346X2

l
where Y is variable physical distribution cost, X1 is the
smoothing constant, and X2 is the prediction interval. The
prOportion of the total variance in Y associated with this
line is .61751, yielding a coefficient of multiple correla-
tion of .785818. The standard error of the coefficient of
multiple correlation is given by
3,1,2'3 = (1-r2)/¢QE:§T.

The value for the standard error from this data is
.0816. The ratio of r to 31.1.2,3 is 9.63, meaning that r
differs from zero by 9.63 standard deviations. This value
is significant well beyond the .01 level.

A comparison of this coefficient of multiple corre—
lation with the simple correlation coefficients observed
for the simple linear regressions performed earlier reveals

that the multiple coefficient is smaller than all but two

of the ten simple coefficients. This seems, at first, to

140
be inconsistent; however, an explanation can be given.
First, the simple regressions were based on samples of only
five observations each, while the multiple regression was
performed on 25 sets of data. It is easier to fit a line
to a smaller number of observations. As the sample size
increases, the likelihood of observing extreme values in-
creases.

Second, the highly correlated linear relationships
varied from sample to sample. For example, the linear
relationships between variable physical distribution cost
and the smoothing constant for fixed prediction intervals
of two weeks and three months, respectively, are

Y = 0.0105813 + 0.00173588X and

Y 0.00987518 + 0.000600107X.
Both correlation coefficients are about .92. The "a"
values in the two equations are comparable, but the "b"
values differ by a factor larger than three. Trying to fit
one line to this data to approximate ten unrelated lines
weakens the overall relationship. The multiple relation-
ship still permits fairly good estimates of cost, based on
a standard error of the estimate of 0.00043782. Using the

mmltiple regression line, a forecaster can estimate costs

to within $.001/lb. about 98% of the time.

141

Level of Detail Experimentation

 

Two of the three dimensions of the forecasting model
have been analyzed. The apprOpriate level of forecasting
detail must now be determined. This analysis is viewed
from two perspectives. First, the same level of detail is
compared for alternative build-up functions. Second, for
the same level of detail a build—up model is compared with
a breakdown application.

The initial experiments included 25 sets of values
for the smoothing constant and the prediction interval. It
seems reasonable, however, that different products might
be traced more accurately with different smoothing constants
or prediction intervals. An additional simulation run was
devised to allow for this possibility. Each of the ten
tracked products was assigned the smoothing constant and
prediction interval values which minimized the product's
relative variance between forecasted and actual sales.

This is the so-called "best" build—up function, shown in
Table 6.6. Comparisons of relative variances can then be
made for the same level of forecasting detail to see if
the added flexibility is statistically significant.

Further, different approaches in using the "best"
model can be studied. One approach is to forecast at the

product-DU level. A second method is to forecast at the

142

TABLE 6.6.—-The "Best" Build-Up Function

 

 

 

Product Smoothing Prediction
Number Constant Interval
l 0.30 3 mos.
2 0.10 3 mos.
3 0.05 3 mos.
4 0.01 2 mos.
5 0.10 2 mos.
6 0.10 1 wk.
7 0.10 1 wk.
8 0.05 1 wk.
9 0.05 1 wk.
10 0.50 1 wk.

 

product level and allocate product sales to the DU's on
some arbitrary basis.

The measure of variance used is a relative one.
The general formula for the sample variance is

s2 = E(YJY)2/n

where Y is an observation, Yris the mean of all observa-
tions, and n is the number of observations. To use 32 as
a relative measure, the Y values must be redefined. Y is

now defined as the difference between relative actual

sales, a, and relative forecasted sales, f. The formulae

 

143

for a and f are

at = Ya.t ‘ Ya,t-1 ft = Yf,t " Ya,t-1
Ya,t-1 Yalt-l

 

 

where Ya,t is actual sales for period t and Yf,t is fore—
casted sales in period t. This conversion facilitates
comparisons between products with different volumes or
prediction intervals. These relative values have no mean-
ing whenever Ya,t-l is zero because division by zero yields
unpredictable results. When Ya,t-1 was observed to be
zero, the relative values were not included in the calcu-

lation of the relative variance.

Intralevel Detail Analysis

The following research hypotheses guide the com-
parison of identical levels of detail between the "best"
function and any other function:

H : The variances for any ZIP area (DU) and

product are equal for the two build-up
functions.

0

H1: The variances are unequal.

If Sijlz represents the relative forecast variance
2 is the

of product i in DU j for alternative one and sij2

variance for alternative two, then the F test statistic is
either

- 2 .2 - 2
F - sijl /si]2 or F - Sijz /Sij1

144
depending upon which variance is larger. The larger value
is arbitrarily assigned to be the numerator for comparison
with tabled critical F values.

The statistical hypotheses, with 0'3 representing
the population relative variances, are these:

Ho‘ Oijlz ' Oij22'

H1= °ij12 f Uij22-

Since critical F values depend on the degrees of
freedom (sample size) for both variances, no one critical
value can be stated. The general form of the decision

rule is

If computed F > critical F, reject H07
otherwise, accept HO.

.A .10 level of significance was used for all comparisons.

The "best" function (experiment 26) was compared
'with the simulation run utilizing a smoothing constant of 0.10
and a prediction interval of three months (experiment 35).
This run is one of the lowest in terms of variable cost per
unit, and its backorder percentage is comparable to that of
the "best" function. In terms of service for a given unit
cost, however, the "best" function offers the more desir-
able result.

The relative variances of the forecast error were

compared for each product—DU in the two simulations. The

 

.fl
-- -']

 

1’.
Jr

 

145

TABLE 6.7-—Summary of Product-DU F Tests

 

 

Larger Variance Significant

 

 

Yes No Total
Experiment with 26 51 113 164
Larger Variance
35 53 93 146
Total 104 206 310

 

4'71

P‘s.”

results are shown in Table 6.7.

With 10 products and 31 DU's a total of 310 F
ratios were computed. For 104 product-DU's the difference
in relative variances is significant at the .10 level; how-
ever, each run has almost the same number of significant
ratios. In addition, twice as many of the F values are
not significant at the tested level. The conclusion based
on the product-DU evidence is that the two simulations
seem to be equally effective in forecasting capability.

A test for the significance of the prOportion of F
tests favoring one or the other of the experiments offers
corroborative evidence in favor of the above conclusion.
If p is the prOportion of larger F ratios for experiment
26, then the probability of observing 164 or more F ratios

is the probability that z (a standard normal deviate) is

 

greater than (l64-150)//510(.25). This is equivalent to

146

P(z > .902) = .1788, a value much larger than conventional

significance levels of .05 or .10.
This data can be examined at the DU level of the
product level, but the same conclusion is reached. For the

DU level the results are summarized in Table 6.8.

TABLE 6.8.-~Summary of DU F Tests

Larger Variance Significant

 

 

Yes No Total
Experiment with 26 10 3 13
Larger Variance
35 13_ _fi_ 18
Total 24 7 31

 

The prOportion of significant F ratios is consider-
ably higher for the DU level as compared to the product-DU
leve, but the total is fairly equally divided between the
two experiments. The prdbability of Observing 18 in one of
two classes in a sample of 31 is considerably greater than
.10 (about .18).

At the product level the data tend to favor experi-
ment 26 as the better choice, but the results are not sta-
tistically significant. Experiment 35 has the larger
‘variance for seven of the 10 products: however, the prob-

ability of this happening is .17, above the .10 level.

_ -13.:sz

147
The only conclusive evidence is the difference in
overall variance for the two experiments. The F value is
1.853 with the variance for experiment 35 being the larger
of the two. This F value is significant well beyond the
.02 level. This may appear to be in conflict with earlier

findings, but there is a very good reason for such a re-

1:53

sult. A re-examination of the product-DU variances reveals

11:516.:
. ..
,. .

that, while the two experiments have approximately the same

.ra

prOportion of large variances, experiment 35 generated many
extremely large variances. For the 51 product—DU's that
exhibited significantly larger variances from experiment
26, most were significant at the .10 level only. On the
other hand, the 53 significant variances from experiment
35 were often significant well beyond .02 or even .01 levels.
The variances must be compared at all four levels,
the distribution center, the DU, the product, and the
product-DU, to establish which experimental results are
superior. Even this guarantees only an indication of sta-
tistical significance. Managerial significance must also
be considered.
Although experiment 35 is less effective than 26
in forecasting seven of the 10 tracked products and has a
larger overall variance, these seven are ranked fourth to

tenth in sales volume. Experiment 35 does predict the tOp

148
three products in sales volume more accurately. The net
effect is that each approach forecasts about one half of
the total sales volume more effectively than the alterna—
tive. Again neither experiment can be picked as the better

one .

Interlevel Detail Analysis
The research hypotheses for this stage of the
study are:

H0: The variances are equal for the two
levels of forecasting detail.

H1: The variances are unequal.

The variances are computed for the same level of
detail, the product level; however, forecasts are generated
at the product level for one alternative and at the product-
DU level for the other. The F test can be used to compare

the relative variances. The test statistic is

2

_ 2 _ 2 2
F ' 511 /312 °r F ‘ 512 /Sil

depending upon which yields the larger F value. Here silz

is the variance for product i accumulated from all product-

2

DU forecasts, and s12 is the variance based on product

level forecasts.

The statistical hypotheses are these:

2 2
Ho: “11 = “12 '

r.-

149
If the computed F value exceeds the critical F
value (based on sample sizes and .10 significance level),
then H0 is rejected: otherwise, it is accepted.
Experiment 26 is based on the smoothing constant

and prediction interval values shown in Table 6.6. The

forecasts are develOped at the product—DU level. Experi—

m
ment 27 is the same as 26 with one important exception: E
The forecasts are computed at the product level and allo- é

cated to the DU's on the basis of the weighted index for
each DU. Experiment 26 is a build-up approach. The re—

sults are presented in Table 6.9.

TABLE 6.9.-~Summary of Build-Up Breakdown Comparison

 

 

 

Experiment with Significant

Product Larger Variance Difference
1 27 no
2 26 no
3 26 no
4 27 no
5 26 no
6 27 no
7 26 no
8 27 no
9 26 no
10 27 no

 

150

Since the products are ranked high to low by sales
volume, clearly neither 26 nor 27 has an advantage. This
position is further enhanced by the F value of 1.049 for
the ratio of the two overall variances, easily an F value
due to chance alone. It appears that for this data the
product forecasts could be allocated to the DU's with
little to no loss in forecasting accuracy as compared with
a more detailed forecasting approach.

This conclusion is due primarily to the allocation
of simulated actual sales to DU's on the same basis as
forecasted sales, the DU weighted indexes. With different
allocative bases experiment 26 would most likely be a con-

siderably more accurate approach.

Cost-Accuracy Considerations
Determination of the specifications of the build—
up function facilitates the analysis of the effect on
physical distribution costs of forecasting accuracy. The
related research hypotheses are:

H0: There is no association between forecasting
error and physical distribution costs.

Higher levels of forecasting error are
associated with higher levels of physical
distribution costs.

Spearman's rank correlation coefficient is used

to test these hypotheses because the measure of error

 

151

develOped is an index or composite value. A gauge such as
the variance is a useful estimate of error, but it over-
looks systematic bias. A consistent 10% overestimate, for
example, is not identified by the relative variance of the
forecasting error. To overcome this deficiency, the vari-
ance can be used in conjunction with a measure sensitive to
systematic bias, such as Theil's inequality coefficient.

Values for the relative variance and for Theil's
coefficient were collected for each of the first 25 experi-
ments detailed in Table 6.1. The 25 variances were ranked
in order, from low to high, from one to 25. The same rank-
ing was applied to values for Theil's coefficient. An in—
dex for each experiment was obtained by multiplying the
ranking of each of the two measures by 0.5 and summing the
two products. The equal weights were arbitrary, based on
the assumption that the two error measures are equally
important. The values for the two error measures, their
respective rankings, and the weighted indexes appear in
Table 6.10. Variable physical distribution costs and
rankings are also included in this table.

Spearman's rank correlation coefficient is computed

from ° n

 

 

 

152

 

O OOHOHO. 0.0H NH NH OOHO. N OOOO. ON
OH OOOOHO. O N OH OONO. O NOOO. ON
NH OONOHO. O.NH O.NH N OOHO. OH OONO.H ON
HN OHOHHO. 0.0H NH NH OOOO. NH OONO.H NN
ON ONHNHO. OH 0.0H OH OOOO. OH OOOO.H HN
O OOOOHO. O.NH O.NH OH OHOO. O OOOO. ON
HH OOOOHO. O 0.0 N OOOO. O HOOO. OH
NH OOOOHO. H N O OOOO. H OOON. OH
ON OOHHHO. OH 0.0H O OONO. OH OONO.H NH
ON HOOHHO. O.N 0.0H HH NNOO. OH HOOO. OH
H OOOOOO. OH OH OH OOOO. HN ONHN.H OH
NH OOOOHO. OH OH OH ONHO. O OONO. OH
OH OOOOHO. O.N 0.0H O HOHO. OH OOOO.H OH
OH OOOOHO. O O H HOOO. HH OOOO. NH
ON OHONHO. O 0.0 O ONHO. N OONO. HH
O NOOOOO. 0.0N 0.0H ON ONOO. NH OOOO.H OH
O ONHOHO. OH O.NH HN OHOO. OH OONO.H O
O ONOOHO. 0.0N 0.0H OH ONOO. ON HOON.H O
OH OOOOHO. O HH O OONO. OH ONNO.H N
NN NOOHHO. O 0.0 O OOOO. O OOOO. O
N NNOOOO. NH OH ON NHOO. O OOOO. O
O NOHOHO. ON O.NN ON NOOO. ON NONH.H O
N NOHOHO. NN ON, OH NNOO. ON HOOO.H O
OH OOOOHO. ON 0.0N ON OOOO. ON NONO.H N
OH OOOOHO. ON NN NN OOOO. NN OOON.H H
xcmm umoo am xsmm xmocH xomm .wmooo xcmm woamwum> unmawumoxm
OHOmHum> Omuanmz O.HHOOO O>HOOHOO
ouHmoaaou Hmuoa

 

momuooo< wawuwmomuom mo mmxmosHll.0H.o mHm<H

153

where the xi's are weighted index rankings and the yi's
are physical distribution cost rankings.

The statistical hypotheses are as follows:

The critical rS for a one-tailed test at a .05 sig—
nificance level for a sample of 25 is 0.400. The related
decision rule is

If computed rs > 0.400, reject H

. 0’
otherwise, accept HO.

The computed value of rS based on this data is
0.470, which is significant at the .05 level. H0 is re—
jected, and it is concluded that there is a direct relation-
ship between variable physical distribution cost and fore-
casting error. While the relationship isn't strong, it is
statistically significant, implying that the hypothesized
relationship (H1) does exist. Inaccurate forecasts over-
state inventory and result in higher inbound transportation
costs to deliver the needed backorders.

This is further proof of the importance of accurate
forecasts. There are no automatic physical distribution

system responses to compensate for the consequences of

erroneous forecasts.

 

154
m
This chapter presented the application of the
general forecasting model to a Specific situation. Differ-
ent smoothing constant values, prediction intervals, and
levels of detail were examined for usefulness. The firm
selling the 10 sample products in the specified area of
the country should heed the following recommendations: h

1. Select smoothing constant values from the I
0.01 to 0.10 range. 5“

2. Select prediction intervals from the one
to two week range.

3. Forecast at the product level rather than
the product-area level.

Finally, physical distribution costs were found to
be increasing with forecasting error increases. This

emphasizes the importance of forecasting precision.

155

CHAPTER VI - - FOOTNOTE S

1Brown, pp. 53-54.
2Hirsch and Lovell, pp. 141-169.

3Brown, p. 54.

“Ofrwrmgfl!

CHAPTER VII

PHYSICAL DISTRIBUTION
COST-SERVICE TRADEOFF

“It.

If.

M..—

Introduction

 

I. (2.
4
.4

The detailed forecasting model can be used in con—
junction with other models or by itself to verify or to
disprove theories in business. As noted earlier, however,
the forecast serves as a vital input to many processes
of the firm. Further experimentation with the model alone
beyond validation would seem to be pointless. The other
possibility, the merger of the forecasting model with a
model of firm activity, is much more promising.

The LREPS model, as a representation of the distri—
bution system, provides the backdrOp for studying proposi—
tions heretofore tested with simple, incomplete models.
Since the application of the systems concept to physical
distribution, the relationship between system cost and the
attendant customer service level has been under close
scrutiny},2 This relationship is a natural one to be

studied with such a comprehensive model as LREPS and is

156

157

considered in detail in this chapter.

Traditional PrOpositions

 

Before presenting the current thinking on the rela-
tionship between cost and service, these two terms should
be defined. Cost refers to total physical distribution

cost, the sum of the component costs for facilities, inven-

ink;

o o a u o o a 3
tories, transportation, communication, and unitization.

fix:-
1 ‘ ‘

Tradeoffs are allowed between and among these five com-
ponents to achieve service levels at minimum cost. Since
this is a short—term analysis, only those costs which vary
during this time span are examined. This includes inven-
tory and inbound transportation costs.

In this analysis service refers to transport capa—
bilities, rather than the broader marketing definition.
Such aspects as condition of goods are assumed to be un-
changed as service level is altered.

Service is a two-fold concept, covering both speed
and consistency of service. Speed and consistency are
analogous to the mean and standard deviation of a prob—
ability distribution, respectively. Speed refers to the
average time needed to move an item between two points,
normally a warehouse and a buyer. Consistency describes

the variation in speed over a number of observed transfers.

158
To specify fully a service level, both speed and consistency
must be defined. For example, a service objective may be to
provide five-day delivery to at least 80% of the customers
and seven-day delivery to all others. Taken alone, the

five-day average time doesn't explain service.

 

The last definitional problem is the functional
relationship between cost and service. A given service {i
level can be attained through many system configurations at 4
differing costs. The reference here is to the least—cost
system for each level of service. The cost-service line,
if plotted graphically, is the lower bound of the cost-
service space, which represents all combinations of cost
and service.
Cost has been considered an increasing function of
the service level at an increasing rate. Costs spiral up—
ward as perfect service, delivery to 100% of the customers
in the minimum possible time using the swiftest mode of
transportation available from every inventory location, is
neared. Magee has suggested that the effect of distribu-
tion on sales is a function of location, inventories, and
system responsiveness. He contends that to fill 95%.rather
than 80% of orders from stock, a 15% change, is to increase
inventory costs by about 80%.;4 An interesting hypothetical

example was formulated by Hill showing that something less

159
than perfect service should be the goal. The inordinately
high cost of increased service levels would not be offset
by the added product demand.5

Heskett, Ivie, and Glaskowsky relate alternative
system configurations to after-logistics-costs profit to
show that the best system in terms of service isn't neces-
sarily the most profitable.6 This example is especially
expressive of the viewpoint hOpefully adOpted by marketers:
Service provided should also be a function of service ex-
pected by the customer, not only be a function of attain—
able service.

Bowersox, Smykay, and LaLonde noted that the
typical firm usually balances "reasonable" performance
levels against "realistic" costs.7 The prohibitive nature
of extremely high service forces the firm to back away

from it.

Eerrimental Results

 

Service can be analyzed from another perspective,
that of the customer order cycle. The buyer views the
order cycle as consisting of five elements:8

1. Order initiation and dispatch time

2. Order transmission time

3. Order processing time

. f “g“?

n
I

160

4. Order shipment time

5. Order receipt time.

The supplier controls the order processing stage
and exerts influence on the alternatives used in the order
transmission and order shipment stages. These three stages
are elements of the normal customer order cycle of LREPS.

A fourth element, the stockout delay, is an additional

LREPS feature which can be added to the normal cycle to

r -2;
.
I

find the total order cycle of the supplier. For the LREPS
model variations in each of these four components determine
what prOportion of customers are served within a specified
time, as well as the statistical variance of the total
order cycle.

Order processing is based on Monte Carlo random
variate functions. The following discrete probability

distribution is used:

 

 

Probability Order Processing Time
10% 0 days
60% 1 day
30% 2 days

Any function describing reality can be used. If a distri-
bution center is Operating above a specified volume, an
additional one-day order processing delay is added to a
percentage of the orders equal to the percentage of Opera-

tions above the defined level.9

161
Order transmittal and outbound (from Distribution
Center) transportation times were develOped in a similar
fashion. Sets of three concentric circles were placed
around each Distribution Center to indicate one, two, and
three day service. If a Demand Unit fell within the inner-
most circle, it would receive one-day service on average.

If it was within circle two and outside circle one, it fl

.r ;- 4.".-1: .
:1. _

could expect two-day service. Communications rings can be
interpreted identically. With many ring sets available
each Distribution Center can be assigned different communi-
cations and delivery rings. Variances about these average
order transmittal and delivery times are formulated on the
basis of several Monte Carlo functions, like the order pro-
cessing functions. Each Distribution Center can achieve
different consistency of service.

Finally, the stockout delay is computed during the
simulation cycle, not prior to execution, as are the
previous elements of the order cycle. The stockout delay
is the sum of out-of-stock days divided by the sum of out—
Of-stock units.

LREPS provides summaries of Distribution Center
Performances after each experiment. More specifically,
the following service measures are computed:10

1. Customer service penalty time (stockouts)

162 F

2. Mean and standard deviation of normal
customer order cycle time

3. Mean and standard deviation of
customer delivery time

 

4. Total customer order cycle time
5. Percent of case units backordered

6.‘ Mean and standard deviation of product

stockout days ,n

7. Normal order cycle time prOportions t
8. Domestic average service time Rh
9. Average lead time for each DC—MCC link.
An accurate measure of system service performance

can be obtained by allowing inventories to be negative, if

needed (in other words, no stockouts). Every time a poten-

tial stockout occurs, the order is filled and backordered.

The measure of performance is the percent of case units

backordered. A high backorder percentage implies poor

service. Improved service is realized at an increased

cost: therefore, percent case units backordered should be

an inverse measure of service achievement.

For the cost-service experiments the normal order

cycle time distribution was specified as follows:

 

 

PrOportion Normal Order
of Orders Cycle Time
.13 4 days
.70 5 days

.17 6 days

163

The standard deviation of the normal order cycle was set
at 0.8 days.

The research hypotheses describing the cost—service
interaction are as follows:

HO: There is no association between physical
distribution cost and service.

H1: Higher physical distribution costs are
associated with higher service levels.

:1

Regression and correlation analysis is apprOpriate

r.— “L”...
I;

because both sets of data are ratio in nature. Percent
case units backordered is the independent variable, and
cost is the dependent variable. Since high service levels
imply low percentages of backorders, the statistical hypoth-
eses about p, the population correlation coefficient de-
scribing the relationship between cost and badkorders, are
formulated as follows:

HO: 0 = 0.

H1: 0 < 0.

The structure of the hypotheses implies a one-

tailed t test with

 

t = r//Q1-r2)/(n-2)
where r is the sample correlation coefficient and n is the
sample size. The sample data are 25 pairs of variable
physical distribution cost-percent case units backordered

values (Table 7.1). The critical t value for a one-tailed

164

TABLE 7.1.--Physical Distribution
Cost-Service Values

 

 

 

2 Cases Variable Physical
Experiment Backordered Distribution Cost/lb.
41 0.325 $0.01199l
51 0.350 0.012170
31 0.425 0.012318
21 0.500 0.011552
42 0.525 0.011105
52 0.600 0.011418
32 1.100 0.010833
22 1.275 0.010854
43 1.275 0.010466
53 1.500 0.010743
11 1.525 0.010533
12 2.000 0.010333
44 2.050 0.010345
54 2.150 0.010430
12 2.175 0.010363
13 2.350 0.010187
23 '2.375 0.010320
45 2.800 0.010088
55 2.825 0.010165
35 2.850 0.009860
34 3.125 0.010359
25 3.125 0.009962
15 3.575 0.009877
14 3.975 0.010197
24 4.200 0.010178

 

test at the .05 level of significance for 23 degrees of
freedom is 1.714. The decision rule is

If t < -l.7l4, reject HO;
otherwise, accept Ho.

The four general equation forms described in
Chapter VI were fit to this data. The results of this

analysis are shown in Table 7.2. All four t values are

165

TABLE 7.2.—-Cost-Service Regression

 

 

 

 

Sample
Correlation
Equation Coefficient Computed t Critical t Decision
1 -.845808 -7.603 -1.714 reject H0
2 —.947242 -l4.l73 -l.7l4 reject H0
3 —.856195 -7.948 -1.714 reject H0
4 -.950914 ~14.737 -1.7l4 reject H0 t
i

 

_‘ .-

significant well beyond the .05 level, suggesting a very
strong inverse relationship between percent backorders and
variable physical distribution costs. In addition, since
the fourth equation provides the best fit (least unexplained
variance), the relationship of cost to service is likely

one which increases at an increasing rate.

These 25 cost values can be considered short-run
minima for given service levels. Facilities are fixed
during this time span, and transportation and communications
networks are the most economical of the available alterna-
tives.

This cost-service relationship must be used in
conjunction with the firm's overall profit function. The
cost of transport service is only one of several components

of the total profit picture. A systems perspective is

 

 

166
required to reach the Optimum profit position. For example,
transport service has an impact on sales revenue. To pro-
vide high service to the extent that the marginal cost of
service exceeds the marginal revenue generated is not an

economically sound policy.

Summary

A specific application of the forecasting-LREPS
model has been presented in this chapter. The direct rela-
tionship between physical distribution cost and service has
been substantiated statistically using the sample data.
Based on the different functional forms fit to the data,
the cost—service relationship appears to be increasing at

an increasing rate.

if" - “ft“;I-Zc—il

167
CHAPTER VII--FOOTNOTES
l . . . .
D. J. Bowersox, "PhySical Distribution DevelOp-

ment, Current Status and Potential," JOurnal of Marketing
(January, 1969), pp. 63-70.

 

2Bowersox, Smykay, and LaLonde, ch. 1.

3. Ibid., ch. 5.

 

4J. F. Magee, "The Logistics of Distribution [W
Systems," Harvard Business Review (July-August, 1960), p
pp. 89-101. F

k.

5"The Case for 90% Satisfaction," Business Week
(January 14, 1961), pp. 82-85.

6J. L. Heskett, R. M. Ivie, and N. A. Glaskowsky,
Business Logistics (New York: The Ronald Press Co., 1964)
pp. 173-174.

7Bowersox, Smykay, and LaLonde, p. 116.
8D. McConaughy and C. J. Clawson (eds.), Business
_ngistics--Policies and Decisions (Los Angeles: Research

Institute for Business and Economics, University of
Southern California, 1968), pp. 120-125.

9Helferich, pp. 179—180.

1°Ibid.. pp- 268-270.

CHAPTER VIII

SIMULATED SALES FORECASTING:
FINDINGS AND IMPLICATIONS

Introduction

 

truer-:7:

The overall purpose of this research has been to
devise a way to deal with the measurement problem of evalu-
ating a sales forecasting mechanism. Until now management
has been forced to wait until forecasted time periods be-
came history before assessing forecasting capability. The
combination of a forecasting archetype with the LREPS model
provides the firm with an approach for evaluating the fore-
casting model before it is used. Only after-the-fact in-
vestigation yields positive proof regarding forecasting
accuracy, but the approach suggested in this dissertation
reduces substantially the uncertainty involved in develOp-
ing a forecasting system.

This chapter first summarizes the results of apply-
ing this new forecasting approach to sample data. As a
result of this application, a generalized approach to

Short-term sales forecasting can be suggested. Next, the

168

169
extension of the short—term to long-run applications is
develOped. Finally, the research areas worth further in-

vestigation are discussed.

Summary of Experimental Results

The forecasting model was constructed with flexi—
bility along the three dimensions of forecasting technique,
prediction interval, and level of detail. Exponential F
smoothing was chosen as the specific forecasting technique. ha
Experimentation was conducted with the sample data to deter-
mine the apprOpriate levels for these three dimensions.
The basis for evaluation was minimized physical distribu-
tion costs, measured by LREPS. Since the period of interest
was one year, only those costs which varied in the short-
run were isolated. These include inventory and inbound
transportation costs. The assumed sales pattern was that
of an increasing linear trend with random fluctuations
allowed to occur about the trend line.

The linear assumption is actually more rigorous
than a nonlinear assumption. With small sample sizes, as
was the case with the data used in this research, curved
lines often provide a better fit. If a straight line can
be applied, stronger statements can be made regarding the

functional relationship.

 

 

It ‘.b’:
i

 

170

Smoothing Constant Analysis

Smoothing constant values (the parameter of the
simple exponential smoothing formula) were regressed
against variable physical distribution costs. The relation-
ship was found to be a direct one with higher smoothing con—
stant values associated with higher variable cost values.
Sample correlation coefficients were found to be statis—
tically significant, based on the t statistic, at the .10
level. Some coefficients were significant beyond the .01
level. The tested values for the smoothing constant were
0.01, 0.05, 0.10, 0.30, and 0.50. Based on this analysis
the firm supplying the sample data should consider small

smoothing constant values in the 0.01 to 0.10 range.

Prediction Interval Analysis

Similar regressions were performed on pairs of
values for the prediction interval and physical distribu-
tion cost. The values for the prediction interval which
were examined were one week, two weeks, one month, two
months, and three months. Exceptionally strong inverse
relationships were discovered between the two variables.
Most sample correlation coefficients were significant
beyond the .05 level. It was recommended that the firm

in question should utilize a very short prediction interval,

171
one or two weeks.

A multiple correlation was carried out treating
variable physical distribution cost as the dependent vari-
able and the prediction interval and the smoothing constant
as independent variables. A significant (r = .78) relation-
ship was observed, although it was not as strong as those
of the simple regressions. A larger sample encompassing
many strong individual relationships which were not as

strongly interrelated accounts for this.

Level of Detail Analysis

 

The forecasting archetype permits forecasting at
four levels of detail: the Distribution Center, the
product, the Demand Unit (DU), and the product—DU. Two
types of experiments determined the most apprOpriate fore-
casting model for a given level of detail and also the
needed level of detail.

For the first analysis two simulation runs were
compared: (1) a model using the same smoothing constant
and prediction interval for all tracked products and (2) a
model using the smoothing constant and prediction interval
for each product which minimized that product's relative
variance between forecasted and actual sales. Forecasts

were generated at the product-DU level, and comparisons

172
of the relative variances at all four forecasting levels

for the two simulations were made using the F statistic.

 

Only at the Distribution Center level was there a statis—
tically significant difference (.10 level) favoring the
second forecasting model. However, because the second
model was less precise in forecasting the high volume
products, no definite preference could be reached based on
statistical evidence. The decision was left to management h
to determine which products and market segments are vital
to the firm's future. The model which served these fore-
casting cells best is the probable choice.

The second analysis compared two versions of the
model which utilized the best smoothing constant and pre-
diction interval values for each product. The first ver-
sion forecasted at the product-DU level, while the second
version generated product forecasts which were allocated
to the DU's. The F test was used to compare product vari-
ances for the two methods to see if the added detail of
the product-DU approach was needed. No significant dif-
ference was observed; therefore, the simpler model was just

as effective as the more complex one for the sample data.

173
Effect of Forecasting Accuracy
To determine the importance of forecasting accuracy
to the Operation of the physical distribution system, an
index of forecasting error was regressed against variable
physical distribution cost. The index was composed of
equal-weighted rankings of the relative forecasting vari-

ance and Theil's inequality coefficient. The variance

3"“ TELL-m4 ::

measured the consistency of the forecast error and Theil's
coefficient pinpointed any steady over— or underestimated
forecasts. Twenty-five pairs of values for the two vari-
ables were gathered through simulation runs.

Spearman's rank correlation coefficient was com-
puted to be 0.470, significant at the .05 level. This
tends to suggest a direct relationship between forecasting
error and variable physical distribution costs for the
sample data. A further contention is that this is likely

to be a general relationship found within nearly all firms.

Physical Distribution Cost-Service Relationship

Experts have suggested for several years that
physical distribution cost is an increasing function of
service (and probably at an increasing rate). Since the
LREPS model provides several measures of service as well

as cost, this hypothesized relationship could be tested.

174

By allowing all orders to be filled regardless of
the existing inventory levels (possible only in a simulated
environment), an accurate measure of service was obtained.
Each time an order would have caused a stockout, the order
was filled and a backorder was placed. The measure of ser-
vice develOped was percent of case units backordered, an
inverse measure of service achievement.

The regression of percent backorders against vari-
able physical distribution cost yielded a statistically
significant (beyond the .01 level) negative correlation
coefficient. Cost is an inverse function of percent back-
orders, implying a direct relationship between cost and
service. Of the four mathematical relationships derived,
the strongest was an exponential form. This means that the
direct relationship is prObably at an increasing rate.

This analysis lends strong support in favor of the tradi-
tional prOpositions about the cost—service tradeoff.

A General Approach to
Short-Run Forecasting

 

From the experimental results developed for this
particular company, some general guidelines for organizing
and implementing the short-term forecasting process can be
stated. It should be pointed out again that forecasting

is part, a central component, of the more comprehensive

175
management task of planning. Since the type is defined by
the interval over which the plans are developed, short-term
planning is necessarily a subset of long—range planning.
As a result, short-term forecasting must be synchronized
with long-term forecasting. The combination of several

short-term forecasts should coincide with the overall long-

 

term forecast for the total time span.

Because this research is based on the build-up con—

f;

cept, this agreement is critical. Long-range projections
are defined as the summation of shorter—term forecasts. If
management has thoroughly organized the planning process,
long-range objectives should imply short-term goals. This
channel should flow in both directions; hence, short-range
forecasts, as responses to short-term objectives, should
aggregate over time to yield a suitable long-term forecast,
in line with the long-range planning objectives.

To operationalize the short-term forecasting pro-
cess, the following steps should be taken:

1. Determine the precise use of the forecast.

2. Segment the market into homogeneous areas.

3. Develop similar product groups.

4. Collect required data.

5. Specify the three dimensions of the
general short-term forecasting model.

 

176
6. Review model results regularly.
7. Check results with alternative method.
Each step is discussed in terms of its content and its func-

tion in the entire short-term forecasting process.

Forecast Objective

 

The initial step is to define exactly the purpose of

the forecast. The position of the forecast in the overall

 

planning scheme must be specified in order to complete the
remaining steps. Many uses for sales forecasts were listed
in Chapter II. In this research the forecast served to
control inventory levels and replenishment orders. The
marketing department may want to evaluate the impact of
alternative short-term tactics, such as coupon campaigns

or sales. Perhaps personnel is develOping manpower plans
to cover peak-season production activity. Each department
within the company can utilize these short-range estimates
for its own purposes.

Because departmental needs vary, the forecast needs
depend somewhat upon the requesting department. The mar-
keting example cited above suggests detailed product-market
segment projections. The personnel example implies gross
sales data along with standard production per man infor-

mation, although a varied product line might have to be

 

177
forecasted in detail.

A very explicit statement of forecast objectives
often makes the remaining steps in the forecasting process
self-evident. Data needs become obvious, as does the level
of forecast detail. Considerable savings in man hours could

result from extra effort at this initial stage.

Market Segments

The identification of market areas with similar
characteristics helps to simplify the forecasting problem.
The common features should, however, be transformable into
action. This is important primarily to marketers. Charac-
teristics which suggest marketing tactics are much more
valuable than thOse which offer nothing beyond neat cate-
gories. This latter Case is better than no classifying
scheme whatsoever. These control units can be treated in
a similar fashion for forecasting purposes. Perhaps the
same forecasting techniques and equation parameters will
be applicable.

Another reason for segmenting is to isolate areas
that are very difficult to forecast because of low sales
volumes, unpredictable competitive action, or other reasons.
These "bad" segments can be approached more intuitively,

while the other areas can be analyzed with more conventional

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178
techniques.

It is conceivable that different departments might
prefer unique market segments or control units for fore-
casting. A uniform classifying system is desirable, but
not at the cost of generating useless forecasts. This prob-
lem is one which must be solved at the time it appears be—

cause no universal set of categories currently exists.

Product Groups

 

Product groupings accomplish the same goal as market
segments: simplified forecasting because of similar pat-
terns of sales. Groupings should be made with this in mind,
not on the basis of like product characteristics. Extremely
unrelated products may exhibit like sales behavior. Again
departmental differences may dictate several grouping con-
figurations. For example, forecasts for inventory control
purposes may not interest the financial manager who is

evaluating product line performance.

Data Collection

The main emphasis of this step is on the shape of
anticipated sales patterns and the availability of historic
sales and associative data. This step interrelates con-
siderably with the subsequent one, the general forecasting

model dimensions: however, it is important enough to merit

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179
separate attention.

The sales pattern greatly affects the dimensions of
the model. The specific technique utilized will depend up—
on the regularity of fluctuations (perhaps the seasonal and
cyclic components of the time series model). If random
movements are prevalent, then maybe a very short prediction
interval will be needed to enable quick adjustments to be
made in the forecast.

Historic data, as input to a data bank, also deter-
mine which techniques are feasible. For example, time
series analysis and regression and correlation analysis
utilize considerable historic, and for the latter, assoc-
iative, data.

With product and market groupings outlined manage-
ment has a framework for data collection. These classifi-
cations can serve as common denominators or control units
for the formatting and storing of data. The importance of
a central data bank should be noted. Even though different
departmental objectives probably cause separate short-run
forecasts to be generated, these projections should ideally
be drawn from a common source of information. By designing
flexibility along the three dimensions discussed in the
next section, management can derive different forecasts

from the same data bank by specifying the control unit set

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180
and the levels of these three dimensions. The only remain-
ing problem is that of suitable report formatting, a rela-
tively simple problem in comparison with those just men-

tioned.

General Forecasting Model Dimensions

This is the stage in the forecasting process upon
which this research is primarily focused. Three specific
dimensions have been delineated: the forecasting technique,
the prediction interval, and the level of detail. These
dimensions are Operable within an overall framework of
product-market area grids (forecasting cells). Management
can prescribe the right dimensions levels by defining an
objective function to be Optimized with these three dimen—
sions as the independent variables.

Simple regression analysis can be used to determine
the nature of the relationship between the forecasting
technique parameters and the dependent variable of the ob-
jective function. A similar approach can be applied to the
prediction interval. If possible, a multivariate relation-
ship should be derived. If significant relationships are
found, then the apprOpriate ranges for the technique para-
meters and prediction interval can be specified.

Level of detail analysis encompasses a re-examination

 

181
of the first two dimensions, as well as a third area for
making model specifications. The former refers to the
assignment of prediction interval values to the forecasting
cells. The preceding discussion implies an aggregate level
(same interval for all cells) study. Possibly more reliable

forecasts would result from using several prediction inter-

3

vals for different products. This can be determined by

I d

comparing forecasting error (e.g., variance between fore-
casted and actual sales, Theil's inequality coefficient,
other statistics, or composite indexes of several measures)
for different levels of the first two dimensions. The com-
parisons are made at the same level of forecasting detail.

Once the prediction interval and forecasting tech-
nique parameters have been finalized, the overall level of
detail can be determined (product-market segment, product,
product group, market segment, etc.). The purpose of such
comparisons is to eliminate spurious detail. If forecasts
for individual products yield satisfactory results when
compared with forecasts derived at the product-market seg-
ment level, the additional forecasting level is of little
to no marginal value.

This dissertation has emphasized statistical
analyses as the bases for choosing values for these three

dimensions. While this is the recommended approach, less

 

182
sophisticated methods may be just as valid. Managerial
judgment is vital to forecasting and should be given con—
sideration. The prOper balance between judgmental and
experimental findings is hard to attain, yet each of the

two is necessary.

Forecast Review

 

Because the business environment is so dynamic,

conditions can suddenly change, making the forecasting
model obsolete. This is a rather extreme and unlikely
possibility. More probably, competitive action will cause

a forecast to be incorrect. Periodic reviews enable manage-
ment to "retrac " the forecasting mechanism so that fore-
casts are again within the tolerance limits.

As the forecast is revised, perhaps different
marketing plans should be constructed to anticipate the
change. The purpose of the forecast is to provide useful
input to the total planning process. To be useful, fore-

casts must be timely and must reflect current conditions.

Result Verification

This step does not imply the develOpment of an
alternative forecasting mechanism as elaborate as the
first. Instead, this may be the time to apply managerial

judgment and intuition. The forecast review helps to

183

realign the existing forecasting model, based on experience

 

with that particular system. Verification offers a fresh

viewpoint.

Extensions to LongrRange Forecasting
The transition from short- to long-range forecasting
can be most easily described after contrasting short-

(tactical) and long-range (strategic) planning. Steiner

lists 15 points as bases for distinction.1 A comparison of
strategic and tactical planning appears in Table 8.1.

This comparison has a direct impact on the conver-
sion of the short-term forecasting process, described in
the preceding section, to cover long-range estimating.
First, the specific use of the forecast is more difficult
to state: nevertheless, this is still a crucial first step.
Long-range goals, Objectives, policies, and strategies form
the foundation for the forecast. The very nature of the
planning process entails the formation of objectives and
purposes; hence, this first step is less likely to be over-
loOked for long-range forecasting than for short—temm
forecasting.

The market-product classification is likely to be
less difficult for long-range forecasting. The corporate

and broad nature of strategic planning will usually be

TABLE

184

8.1.-—Comparison of Strategic
and Tactical Planning

 

 

Comparative Basis

10.

11.

12.

l3.

14.

15.

Level of conduct

Regularity

Subjective values

Range of
alternatives

Uncertainty

Nature of
problems

Information needs
Time horizons
Completeness

Reference

Detail

Type of personnel
involved

Ease of evaluation

DevelOpment of

objectives, policies,

and strategies

Point of view

Tactical Planning

lower management

fixed schedule

lower weighted

smaller

less

structured,
repetitive

narrower, internal
shorter

narrower focus

based on strategic
plan

more

lower management

easier (short time)

historically based

functional view

Strategic Planning

upper management

continuous, but
irregular

higher weighted

greater, by :

definition 3
L

more

unstructured,

unique

broader, external
longer
broader focus

original

less

upper management

harder (several years)

new, flexible

corporate view

 

 

 

 

185
concerned with large geographic regions and product groups
or the entire line.

Because of the general emphasis of long-range fore-
casting, the data required are to generate aggregate esti-
mates. Perhaps annual or quarterly data are all that are
needed. The time period for which the data are collected
may be much larger. Long—range forecasting extends far
into the future, making use of a strong historic foundation
for extrapolation purposes. If the future is thought to be
relatively independent of the past, then the extensive
historic base is less important; however, the newer rela-
tionships must be based on valid and current information.

The difference in long- and short-term forecasting
can be handled by the flexible forecasting archetype upon
which this dissertation is based. The model can accommodate
several ranges of alternatives by inputting many simulated
actual sales patterns. Each pattern reflects a different
set of assumptions; therefore, the model can be designed
to anticipate the sales pattern thought to be the most
likely to occur.

The model can be Operated whenever a forecast is
needed. Possible forecasts could be generated on a regular
basis in addition to the "as needed” projections. The fore-

cast interval can be defined for practically any feasible

I1

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A 'J

“a. :‘2 -..-
.9

186

length. For long—range forecasting a one-year interval

 

might be useful. Ten to fifteen, or even more, one-year
periods could be forecasted consecutively to build the
long-run forecast. An alternative approach is to continue
short-term forecasting and accumulate them in the same
fashion. Both approaches could be used to develOp forecasts

for the same long-term period for comparative purposes «-

.3'

(step 7--check results--in the forecasting process).

I t... A‘AF-“ :1. u

Further flexibility is provided by selecting dif-
ferent forecasting techniques. For this research exponen-
tial smoothing was the apprOpriate technique. Methods
more suited for long—range forecasting, such as time series
analysis and regression and correlation analysis, might be
chosen. No matter which technique is selected, it can be
applied at any level desired.

As an example, a complex multiple regression rela-
tionship might be derived utilizing the same equation para-
meters (with adjustments made for relative volume differ-
ences) for all products and market segments. At the other
extreme, different regression equations could be formulated
for each market and product. The aggregate nature of long-
range forecasting lends itself more to the general approach,
but either one is a viable alternative.

The remaining two steps in short-term forecasting

187
are equally valid for long-term forecasting. The model
should be reviewed periodically, and results should be
checked using other methods.

In summary, this build-up forecasting model used
along with LREPS has been designed to traverse the timing—
detail separation between long- and short-term forecasting.
The prediction interval, forecasting technique, and level
of detail can be combined to forecast for tactical or
strategic purposes. Combining these dimensions with
alternative hypothetical sales patterns effects maximum
forecasting flexibility. The other short-run forecasting
steps are relevant for long-run forecasting as well. The
real difference is in the depth and breadth of managerial

perspective and approach.

Implications for Future Research
Expansion of this research into other directions
appears promising. Additional research areas can be classi-
fied according to the following scheme:
1. Extensions of current research problem

2. Tests of additional business-related
hypotheses

3. sOphistications of the general forecasting
mechanism

4. Alternative approaches to forecasting.

 

1.. ”Ll.-.‘ may.
A V: "

188
Examples from each of these three major areas are discussed

below.

Extension of Current Research Problem

Several studies can be conducted with the sample
data used for this dissertation. First, the assumed actual
sales pattern could be altered to reflect changing environ—

mental and marketing conditions. The only pattern tested

! of-é— A...
'd

was an increasing linear trend, subjected to random fluctu-
ations. A seasonal pattern would be an obvious choice be-
cause many firms experience regular variations in sales
throughout the course of a year. Another possibility is a
decaying sales function. All such patterns wouldn't be
relevant at the same time, but such experimentation would
prepare a company for the different stages in the product
life cycle.

A second inventory location would introduce inter-
actions not presently observed with the single warehouse
model. LREPS assigns Demand Units (DU's) to Distribution
Centers on a priority basis. The second placement would
allow orders resulting in stockouts at one location to be
filled from the other site. This complicates the fore-
casting problem; however, it is an added dimension of

reality.

189
More combinations of forecasting levels might also
be attempted. This research presented a comparison of only
two levels and no variation in the level of detail within
a given experiment. The experimental evidence indicated
certain of the products could be forecast in the aggregate,

while others might be handled more accurately with fore-

I

casts at each DU. Experiments using different combinations

of these two levels could be compared, approaching gradu-

IF un- -Am‘ . 1.-
. _ "

ally the precide model which minimizes forecasting error
for this data. Overly zealous pursuit of this so-called
accuracy should be avoided. Since the simulated actual
sales input is hypothetical, pinpoint forecasts would
represent Spurious accuracy.

By increasing the simulated sales volume per unit
of time, certain of the approximations inherent in the
simulation process would be overcome. For example, certain
products with high absolute sales volumes, but low relative
to other tracked products, might not appear to be active
in several DU's. By increasing the volume per time period,
the probability of the product appearing on the generated
simulated invoices increases. It should be emphasized
that this is a valid experimental approach. Increased
simulated sales decreases the prOportion of extrapolated

to simulated sales. This increases the reliability of the

190
experimental results. As long as the total of actual simu-
lated sales and extrapolated sales is realistic, the results
are valid.

As a final improvement in experimental technique,
sample sizes could be increased. Only five pairs of smooth—
ing constant-cost and prediction interval-cost values were
collected for each sample. The very significant relation-
ships discovered tended to minimize the problem of sample
size; nevertheless, larger samples generally are more
reliable.

All of the steps suggested as being desirable were
not taken because of a cost-time constraint. Additional
funding and several more months would have been required

to probe thoroughly into all of these areas.

Tests of Additional Business-Related Hypotheses

 

To enumerate all of the possible areas of business
which could be examined using the LREPS-forecasting mech—
anism as a starting point is an impossible task. The first
step might be to consider additional forecasting-distribu-
tion system interactions. For example, in the short—run
only inbound transportation and inventory costs were found
to vary with the quality of the forecast. Longer term

analysis should result in more component variations within

191

the physical distribution system. LREPS can be directed to
add Distribution Centers to the national network according
to predetermined decision rules. If the forecast is too
high to the extent that an additional Distribution Center is
"built” three to six months too soon, the cost of such an
error could be measured directly. The best forecast in the
long-run might be the one that postpones Distribution Center
additions as long as possible from a cost-service viewpoint.

This example leads to another area of examination:
the interrelationship among forecasting (planning), physi-
cal distribution, and other business areas. A natural
area would be finance, since it monitors all other activi-
ties within the firm.2 Research has been done to establish
relationships between financial variables and changes in
the structure of the distribution system.3 By adding the
forecast as a causal factor in this changing logistics.
structure, forecasting and finance can be related. The
impact of forecasting accuracy on the sources of funds is
an example of a specific research project.

The forecast mechanism could be detached from the
LREPS model and combined with another simulation of firm
activities. A production system model, including the
materials procurement network, would interrelate With the

forecasting model. Eventually, if all such models could

 

 

192
be connected, the firm itself could be analyzed. This last
possibility is still several man-years of work away from

occurring.

sOphistications of the General Forecasting Mechanism

The existing model can be improved in a number of
areas. The first such improvement could be to make the
three dimensions more dynamic. With feedback linkages
built into the model, regular monitoring of results could
be achieved. For example, in this research the exponential
smoothing approach could have been replaced by a form of
dynamic smoothing. That is, the last period's forecast
could be generated using several smoothing constants. The
smoothing constant resulting in the most accurate forecast
would be used to generate the next forecast. Variations
on this basic theme could also be implemented. Some
products could be forecasted using dynamic smoothing and
several smoothing constants, while other products with
stable sales patterns might use the existing approach.

A two-step dynamic smoothing model could also be
used. Four or five initial smoothing constant values could
be used to narrow down the range of possible values. Given
the best initial values, additional values within a smaller

range might be tested. Gradually the most suitable value

 

193

 

would be found.

Another method is to develOp a warning system by
checking forecasting accuracy regularly. When the fore-4
casting error exceeds some predetermined level, the
dynamic smoothing module could be activated. The current
value for the smoothing constant is used until the error
becomes unacceptable. This approach reduces computing time ;
by executing the dynamic smoothing programs only when they r
are needed, not every time a forecast is generated.

The prediction interval can be analyzed dynamically.
The forecasting error can be checked to guard against poor
interval choices. Periodic regressions of the most recent
data (dependent variable) against prediction interval
values could be made to determine the general line form.

If the relationship isn't strong, adaptations in the inter-
val can be initiated.

The apprOpriate level of detail can also be deter—
mined dynamically by checking the forecasting error. If
the forecasts are not satisfactory, the next level of
detail can be the new forecasting base.

A second sOphistication that is warranted is the
elimination of the homogeneity assumption about the DU's.
Simulated actual sales are allocated to the DU's on the

basis of the DU's relative pOpulation. Some variation is

194
achieved by allowing DU pOpulations to grow at different
rates. By adding different allocation bases, a possibility
already provided for within LREPS, DU's with unique fea-
tures could be simulated. For the sample data analyzed in
this research, pOpulation was a satisfactory DU descriptor:
however, for other firms this may not be the case.

Additional flexibility could be attained by in-
putting simulated actual sales in another fashion, actual
sales dollars by product and DU, instead of allocating
sales to these cells. This would eliminate some of the
random simulation approximations referred to in earlier
sections. Actual sales would be recorded precisely. The
Order File Generator within LREPS could still be used to
simulate the invoice detail required to meet sales speci—
fications.

More and varied statistical analyses could be
attempted to aid in the develOpment of the forecasting
model detail. Some of the measures of forecasting error
discussed in Chapter IV, beyond the variance and Theil's
inequality coefficient, could be examined through experi-
mentation. Perhaps certain measures of error are useful
only as a function of the actual sales pattern. Other
variables within the model could be tracked and related

to the prediction interval, equation parameters, and

 

[It

i

i.

 

195
level of detail dimensions. For example, average inventory

levels could be related to these model dimensions.

Alternative Approaches to Forecasting

 

This dissertation has focused on the joint usage of

a forecasting framework and the LREPS model, including the

 

Order File Generator. The forecasts were generated within

Er
fl

the forecasting model, and simulated actual sales were dis- %

seminated throughout the geographic market area by the Order a

File Generator. Serving as the objective function to be
optimized, the LREPS model reflected the reactions of the
physical distribution system to different levels of fore-
casting accuracy. These accuracy levels resulted from dif-
ferent settings for the three dimensions of the forecasting
module.

The LREPS model, taken alone is an equally viable
forecasting tool. Annual sales data can be inputted
exogenously through the Supporting Data Subsystem. The
mechanism which distributes sales dollars across products
and territories can be used to forecast the future. Rela-
tionships between product category sales or product sales
and selected independent variables can be derived for
every Demand Unit (DU) from historic data. Detailed (by

product and by DU) forecasts are easily obtained once the

 

196
historic relationships are determined. The physical dis-
tribution system, as simulated by LREPS, can again be used
as the objective function.

Seasonal and cyclic influences can be incorporated
into this approach. The exogenous sales input can be
adjusted by cyclic indexes to reflect general economic con-
ditions. The seasonal variations can be anticipated by
associating indexes with each day simulated by LREPS.
Quarterly seasonal factors can be included by assigning
the same index to each day in the quarter. More precision
can be obtained by gradually changing the indexes on a day-
to-day basis.

Using LREPS as the forecasting mechanism eliminates
having to design the three dimensions of the forecasting
model develOped in this dissertation. LREPS can be used
directly to generate forecasts. The forecasting module
develOped through this research is easily "uncoupled" from
LREPS to stand alone. The LREPS forecasting mechanism
would be somewhat more difficult to use independently,
although it is possible with some minor modifications of
the model structure.

This alternative forecasting approach involves
using LREPS as the primary forecasting instrument instead

of as a controlled experimental environment. The

197

conclusions reached in this dissertation could be validated
by this other method. If the two approaches to forecasting
resulted in similar forecasted values, more confidence
could be placed in the estimates. Conversely, unlike fore-
casts would cause management to investigate the causes for
divergence. An attractive area for additional study would
be a statistical comparison of the results of these two

forecasting methodologies.

 

 

198

CHAPTER VIII--FOOTNOTES

lSteiner, pp. 37-39.

2 . . . .

The idea for this potential research can be attri-
buted primarily to Dr. Michael L. Lawrence, Assistant
Professor of Finance, University of Missouri, Columbia.

3M. L. Lawrence, Development of a Dynamic Simula—
tion Model for Planning Physical Distribution Systems:
The Financial Implications of Warehousing Decisions (un-
published doctoral dissertation, Michigan State University,

1972).

199

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