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Introduction to management science and marketing online

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David B, Montgomery** and Glen Lo Urban**


Tiinr> 1 Qftl






David Bo Montgomery** and Glen Lo Urban**

( 266—67
June, 1967

* Comments and criticisms are solicited g, but this paper may not be cited
or reporduced without the written permission of the authors o

** The authors are Assistant Professors of Management in the Alfred Po Sloan
School of Management, Massachusetts Institute of Technologyc

JUN 29 1967

M- i. (. LIbKMrtlES



David Bruce Montgomery
Glen Lee Urban


All Rights Reserved


This paper is a working draft of Chapter 1 in

Management Science in Marketing


David Bo Montgomery


Glen Lo Urban

Sloan School of Management
Massachusetts Institute of Technology




Introduction _

A Marketing DialoKue in 1988 1

Mansgement Science Tin Marketing: The Present b

Purpose of This Book 9

The Nature of Management Science

Definition of Management Science 10

Management Science Models 11

Techniques for Analyzing Models 16

Uses of Mano'^ement Science Models 18

Management Science and the Uecision-Information System

Management Science and the Man-Information lnteraction25

The Data Bank 28

The Statistical Bank . 33

The Model Bank 36

The Man 38

Plan of Development of This Book 39


A Marketing Dialogue in 1988

The year is 1988. The place is the office of the marketing
manager of a medium size consumer products manufacturer. , The parti-
cipants in the following discussion are John, the marketing manager;
Bill, the director of marketing science; Rod, Bill's assistant who
specializes in marketing research; and Scott, the sales manager for the
company. The scene opens as Bill, Rod, and Scott enter John's office.
John: Morning Bill. .. Rod. .. Scott . What's on the agenda for this

Bill : We want to take a look at the prospects for our new beef substi-

John : What do we have on that new product?

Rod: We test-marketed it late in 1986 in four cities, so we have that
data from last quarter.
John : Let's see how it did.

(All four gather around the remote cpnsole video display unit,
John activates the console and requests it to display the sales results
from the most recent test market. The system retrieves the data from
random access storage and displays it on the video device.)
John : That looks goodi How does it compare to the first test?

(The console retrieves and displays the data from the first
test on command from John.)


Rod : Let me check the significance of that sales increase of the most
recent test over last year's test.

(Rod requests that the system test and display the likelihood
that the sales increase could be a chance occurrence,)
Rod ; Looks like a solid sales increase.
Bill : Good.' How did the market respond to our change in price?

(Bill commands the system to display the graph of the price-
quantity response based upon the most recent test data.)
John : Is that about what our other meat substitute products show?

(John calls for past price-quantity response graphs for similar
products to be superimposed on the screen.)

John: Just as 1 suspected — this new product is a bit more responsive
to price. What's the profit estimate?

(John calls for a profit estimate from the product planning
model within the system.)

John: Hmm. .. $5,500,000. Looks good. Is that based upon the growth
model I specified to the model bank last week?

Bill : No. This is based upon the penetration progress other food
substitutes have shown in the past as well as the information we have
on the beef substitute from our test markets.
John : Let's see what mine would do.

(He reactivates the product planning model, this time using his
growth model. The profit implications are displayed on the console.)
John: Well, my model predicts $5,000,000. That's close. Looks like
my feelings are close to the statistical results.


5x11 : Let's see if there's a better marketing strategy for this product.
We must remember that these profit estimates are based on the preliminary
plan we developed two weeks ago,

(Bill calls for the marketing mix generator to recommend a mar-
keting program based upon the data and judgmental inputs which are avail-
able in the data bank's file on this product.)

Bill : There, we can increase profit by $700,000 if we allocate another
sales call each week to the new product committees of the chain stores,
Scott : I don't think our salesmen will go along with that- They don't
like to face those committees. The best I could do is convince them to
make one additional call every other week.
John: What would happen in that case?

(The marketing mix generator is called with the new restriction
on the number of calls.)

John : Well, the profit increase is still $500,000, so let's add that
call policy recommendation to our marketing plan. I'm a little worried
about our advertising appeals, though. Can we improve in that area?
Bill : Let's see what the response to advertising is.

(The video unit shows a graph of the predicted sales-advertising
response function.)

Bill : If we changed from a taste appeal to a convenience appeal, what
would the results be, John?
John : I think it would look like this.

(John takes a light pen and describes a new relationship on the
video unit based upon his judgment of the effectiveness of the new appeal.)

i;od : Let me check something.

(Rod calls for a sample of past sales-advertising response curves of
similar products using the convenience appeal.)

Rod : I think you are underestimating the response on the basis of past

John : Well, this product is different. How much would it cost for a
test of this appeal?

(Rod calls a market research evaluation model from the console.)
Rod: It looks like a meaningful test would cost about $5,000.
Bill : Wait I Hadn't we better check to see if the differences between
these two advertising response functions will lead to any differences
in profit?

(The marketing mix model is called for each advertising function.)
Bill : Looks sensitive to the advertising response, all right. There's
a $900,000 difference in profit.

John : 1 wonder what risk we'd run if we made a decison to go national
with the product right now. What are the chances of a failure with this
product as it stands if we include this morning's revisions to the
marketing mix?

(A risk analysis model is called on the system.)
John: Looks like a 35% chance of failure. Maybe we'd best run further
tests in order to reduce the risk of failure. What's next on the agenda
this morning?

The dialogue presented in this section indicates the probable
environment in which future marketing decisions will be made. Market-
ing managers will be able to call upon powerful information systems to
assist them in charting the course and evaluating the results of the
firm's marketing efforts. Such systems will provide the manager with
advanced modeling and statistical techniques to assist him in improving
ii£ decisions. They will also provide him with the capacity to store,
reti^eve, and manipulate data relevant to his decision problems.
Although the dialogue was depicted as occurring in 1988, recent devel-
opments in computer technology and marketing modeling techniques may
make such systems a reality in the much nearer future.
Management Science and Ma rketing : The Present

In the period after World War II, a new methodology for analyz-
ing management problems emerged. The methodology has been commonly
referred to as operations research or management science. This method-
ology has produced models and quantitative techniques such as mathema-
tical programming, PERT, and simulation. These new techniques have
found a number of successful applications in production and finanace.
Marketing, however, has not experienced a parallel development.
Although there is evidence of accelerating interest in the management
science approach to marketing, achievements in this area remain more
modest than in areas such as production and finance.

A number of factors have contributed to this relative lag in
management science progress in marketing. The following six factors

juld seem to be the major factors in this lag:

1. Complexity of Marketing Phenomena . The modeling of market
phenomena often requires greater complexity due to the fact,
that response to market stimuli tend to be highly non —
linear, to exhibit a threshold effect (i.e,, some minimum
level of the stimulus is required for there to be any
response at all), to have carry-over effect (e-g-s response
to this period's promotion will occur in future periods),
and to decay with time in the absence of further stimula-
tion. A further consideration is the fact that market
response tends to be dependent upon many factors. This
multivariate nature of marketing problems injects addition-
al complexity into marketing decisions.

2, Interaction Effects in Marketing Variables . The impact of
any single controllable marketing variable is difficult to
determine due to int'eraction of the variable with the envi-
ronment and with other marketing variables. For example,
the impact of promotional effort may depend upon factors in
the firm's environment such as the level of economic activity,
the availability of credit, and customer expectations. Inter-
action with other marketing variables occurs, for example,
when sales results due to promotion depend upon the level of
price and distribution. These interactions within the
marketing mix make it difficult to uncouple the elements in
the marketing mix so that they may be analyzed independently.
Other management decision areas have had more success in
uncoupling the component subsystems for further analysis,

2. Competition and Marketing Decisions . The final outcomes of
marketing decisions depend upon how competitors react. In
many production and finance problems, competitive effects
are negligible or considered exogeneous,

4. Measurement Problems in Marketing , The consumer oriented

nature of marketing makes response relationships difficult,
if not impossible, to observe. Recourse is often made to
indirect techniques such as recall measures of advertising
exposure. Production and inventory systems, on the other
hand, generally require only data from physical systems
within the firm. Buzzell has noted that, "It is clear,.,
that the .development of inventory models would be far more
difficult if it were necessary to rely on estimates of
stocks on hand as recalled by stock clerks."

Robert D. Buzzell, Mathematical Models and Marketing Management
(Boston: Division of Research, Graduate School of Business Administration,
Harvard University, 1964), p. 74,

5. Instability of Marketing Relationships . The relationships
between market responses and marketing decision variables-
tend to be temporally instable due to changes in tastes ^
attitudes, expectations, etc. This factor makes continuous
market measurements and the revision of decisions crucially
important in marketing.

6. Cultural Incompatibility of Marketing and Operations Research
Personnel Initially, underlying cultural differences -
between marketing and operations research personnel formed

a barrier to innovation. Marketing decision-makers usually
gained their experience in the sales area of the company and
were not able or willing to accept or utilize quantitative
techniques. Operations researchers, on the other hand, did
most of their work in the production area, which is charac-
terized by measurable and quantifiable data. The operations
research people, in general, were not interested in market-
ing problems because of the non-quantifiable nature of
marketing and the cultural incompatability with marketing

The underlying explanation for these factors lies in the fact
that marketing deals with behavioral rather than technological phenom-

The preceding diagnosis of the factors contributing to market-
ing's past lag may encourage the reader to doubt the compatibility of
marketing and management science. Other factors, however, suggest
accelerated progress in the future. In the first place, the profit
squeeze due to spiraling costs and increased competition is forcing
firms to seek better methods for decision making. Since marketing costs
are becoming a major proportion of total costs, firms will tend to focus
more attention on marketing decision problems. Secondly, shortened
product lives have made new products of crucial importance to the firm.

-The staggering failure rate of these new products is leading to the
acceptance of more scientific approaches to product planning. Another
factor which should help management science to advance in marketing


elates to the quantity and quality of marketing data available for
decision purposes. Commercial and governmental data services are
constantly expanding, while advances in psychometric procedures,
especially multidimensional scaling, promise improved quality and
relevance of available market data.

In addition to these factors which indicate greater pressures
coward the acceptance of management science innovations, management
science itself is maturing as a discipline. Advances in mathematical
programming, such as integer programming, branch and bound methods for
combinatorial problems, stochastic programming, and non-linear
programming, enable the management scientist to treat much more com-
plex and interrelated problems than was feasible in the past. As
further evidence of the maturing capability ot management science
to deal with marketing problems, one could cite developments in statis-
tical decision theory, simulation techniques, and heuristic program-
ming. The advent of the third generation computer system^jwith its
greatly enhanced storage capabilities, speed and software, holds great
promise for implementing these new techniques in marketing. Remote
consoles and graphical displays will allow considerable man-machine-
data-model interaction in the future.

It is hoped that this book will contribute to the diffusion of
management science methods in marketing by providing a framework for
the assessment of past and potential contributions of management science
to marketing problems.


^• £po s e.ofThis_Bo^

This book will attempt to present an integrated discussion of
the uses of management science in analyzing and solving marketing
problems. This development will begin by structuring overall market-
, ng problems from the point of view of the marketing manager. This
structure will indicate the overall nature of the problems and will
reflect rhr behavioral, quantitative, and institutional aspects of
m&ikicing Existing management science applications to marketing will
be positioned in this structure. In every problem area, the scope 6^
each work ill be delineated and its relationship to other mathemati-
cal models will be outlined. The methodology of these applications
will be analyzed and advantages and disadvantages of the various
approaches will be discussed.

The outcome of this analysis will be a description of the state
of the art of management science in marketing. In this development of
the state of the art, a number of gaps m the application of modeling
techniques to marketing problems and subproblems will become apparent.
These gaps may reflect an undesirable definition or understanding of
particular marketing problems, an unreasonable set of assumptions, or
an unsatisfactory designation of factors to be considered exogenous in
the analysis. The occurrence of these gaps should not be too surpris-
ing since - the management science approach itself is very young,
most of the literature in management science having been developed
the last fifteen years. The identification of the shortcomings of
previous approaches is intended to define a number of the opportunities


for the future. It is hoped that this book will supply a base for
future analytic work on marketing problems. A number of the most
productive avenues for advancing the management science approach in
marketing will be indicated in each chapter.

It is the purpose of this book to (1) structure overall marketing
problems, (2) position existing management science models in this
structure, (3) indicate existing gaps in the application of management
science in marketing, (4) assist the reader in developing his capacity
to build and implement models for use in analyzing and solving marketing
problems, and (5) indicate productive directions for future management
science efforts in the area of marketing.

Definit ion of Managem ent Science

It is difficult to define and bound an area of study which is
experiencing a constant development of new techniques that extend its
scope and composition. Management science is such an area. Despite this
difficulty, two prominent features are reflected in the name given to
this area of study. "Management," in the context of the methodology,
carries with it a strong implication of problem solving. Thus,
management science is directed at understanding and solving management
problems. The second component of the name is "science." This
carries with it a strong implication of scientific methodology. This
methodology can be described as:

1. Formulation of a problem

2. Development of a hypothesis for understanding or solving
the problem (usually in the form of a model)


3. Measurement of relevant phenomena

4, Derivation of a solution or basis of understanding of the

5- Testing of the results

6. Revisions to reflect the testing of the hypothesis

7. Emergence of valid results

This IS essentially the methodology used in the empirical physical
sciences. These two aspects are central propositions of management
.?cier - and lead to a definition of management science as the understand-
ing and solu;ion of management problems by the application of scientific

It should be noted that this definition does not restrict itself
to a specific enumeration of techniques. Although management science
efforts up to this time have tended to be quantitative, this is not a
necessary condition for work in the area of management science. There
is no natural dichotomy between quantitative and behavioral^ or non —
quantitativa', efforts. The techniques applicable to management problems,
such as operations research, econometrics, mathematics, statistics, and
the behavioral sciences, are all relevant to the area of management science.

The definition of management science proposed here is very broad
and is intended to include all analytical model building efforts directed
at solving and understanding business problems. This will lead to a com-
mon^ compatible field of knowledge that will encourage rigorous, productive
analyses of the problems of management science.
Management Science Models

Before discussing the types of models used in management science,
it would be useful to define what is meant by a model. A model is simply
"a representation of some or all of the properties of a larger system."


^he representation could be physical or abstract. For example, a wooden
model airplane is a physical representation of a larger system — the
actual real world airplane. An alternate model would be a set of blue-
prints which represents the larger system. A third model might be a set
of mathematical equations that represent the larger system.

In management science, four commonly used types of models can
be identified:

1. Implicit models

2. Verbal models

3. Logical flow models

4. Mathematical models

The system may be the phenomena underlying the relevant behavior, or
the system may be the decision procedure itself. In this way a model
can be used as a representation of the environment or the environ-
ment as viewed through a particular decision procedure.

Implicit models are models that are not made explicit by some
communic.abie form of representation. All decisions that are not made
on the basis of an explicit model are made on the basis of an implicit
model. This exhaustive classification is based on the premise
that all decisions are made by the use of a model. This is not an
unacceptable proposition since a "model" was defined in a very general
sense as a representation of a larger system. With this definition it
is clear that all decisions are made on the basis of a model, since some
representation of the problem must be perceived before it can be solved
or a decision reached. If the model is not recorded in communicable
form, it is an implicit model that remains in the decision maker's
cognitive structure until it is communicated and made explicit.


There are several methods of making an implicit model explicit.
The first method is to communicate the model in the form of written or
spoken words. This representation is a verbal model. The communica-
tion of the model is the first step in making it explicit. An
example of a verbal pricing model may be, "follow the price of the
largest firm in the industry unless it would produce losses or the
price change does not appear to be permanent." This verbalization of
an implicit model exposes the behavioral postulates assumed on the

basis of the decision model.


The next type of model is the logical flow model. This

is an extension of the verbal model by the use of a diagram. The
diagram makes explicit the sequence of decisions to be made and the;
way in which they are related. In Figure 1-1, the simple verbal de-
cision model is described by a logical flow diagram. This formulation
of a model is useful since it serves to clarify the relationships
between the model's components.

The next step in model exposition is to quantify the model's
components and the relationships between the components. This leads to
a mathematical model. In the mathematical models, not only the sequence
but also the magnitude of the interrelationships is indicated. In


See W. F. Mass/ and J. Saavas, "Logical Flow Models for

Marketing Analysis ," Journal of Marketing , Vol. XXVIII (January, 1964),
pp. 32-37.


Logical Flow Diagram















• >

f \








. , \




the pricing example, a mathematical model to describe the environment

might be:

PROFIT = U • q


q = if Price > Price of largest firm
= 5000 if Price ^ Price of largest firm

U = Profit
With this model the existing decision structure and new procedures
could be tested. Mathematical models can be described in a number
of ways. Two useful dimensions of classification relate to methods
in which the model treats time and risk. The first classification is
divided into segments: static and dynamic. That is, those models
that do not consider time effects and those that do. The second clas-
sification is divided into stochastic and deterministic models. Sto-
chastic models consider risk or probabilistic phenomena while deter-
ministic models assume certainty of outcomes and events.

The four model types described above may be used compatibly.
For example, a mathematical model may be one part of a logical flow
model which is derived from a verbal description of an implicit model.
The type of model to be used depends on the degree of explicitness
desired in the problem or decision situation. The desired degree of
explicitness depends upon the advantages that accrue to the researcher
or decision maker who approaches his problems using the more formal-
ized mathematical models. First, mathematical specification has the
advantage of making assumptions overt. This renders the assumptions
more open to debate, testing, and revision. Secondly, mathematical

models often provide a useful framework for measuring market phenomena.

Finally, the language of mathematics is the richest frameworJk in which

to manipulate a model. Such manipulation may involve the optimization

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Online LibraryDavid Bruce MontgomeryIntroduction to management science and marketing → online text (page 1 of 3)