30

Reprinted from JOURNAL of MARKETINGVolume 28, No. 1, January, 1964

Logical Flow Models forMarketing AnalysisWILLIAM F. MASSYandJIM D. SAVVAS

Can analytical models ofmarketing phenomena beconstructed, tested, and un-derstood by persons whoare not sophisticated inmathematics?

"Yes," say the authors—LOGICAL FLOW MODELSmeet the specifications.

They are appropriate forthe analysis of large classesof marketing behavior. Theycan yield specific predic-tions, or be made the basisfor computer simulation andsensitivity analysis in muchthe same manner as theirmathematical counterparts.They can be important aidsto decision making.

Journal of Marketing, Vol. 28 (January,1964), pp. 30-37.

I HE USE of analytical models in marketing has become widelyaccepted. As direct aids to decision-makers, their use provides

an increased understanding of the forces underlying marketingphenomena, and in some cases leads to improved forecasts ofspecific conditions like the level of sales or competitive prices.

Similarly, effective marketing research requires a systematicstatement of hypotheses, logic, and conclusions. Such statementsare the sum and substance of the analytical model.

What may not be widely enough recognized is that a high degreeof mathematical knowledge is not necessary for the constructionand analysis of many useful marketing models. The purpose ofthis article is to describe the logical flow model, to show where itfits into the spectrum of modeling activity, and to indicate howthis kind of analysis can be conducted by even the mathematicallyunsophisticated.

Types of ModelsModels can be classified in a number of different ways :

" Deterministic or probabilistic

" Descriptive or normative" Empirical or theoretical

" According to the language used in their construction. 1

The models tobe discussed in this article are: (1) deterministic—they do not explicitly consider uncertainty as to outcome;2(2) descriptive—they represent attempts to describe what israther than what should be;3 and (3) empirical—they are basedon direct observation and testing rather than on abstractprinciples.4

The major question to be discussed is that of the language usedin the construction of models. Models useful for marketinganalysisare usually made up of English statements,mathematical equations,

1 For a generalized treatment of model building and simulation, seeRonald E. Frank, Alfred A. Kuehn, and William F. Massy, Quanti-tative Techniques in Marketing Analysis (Homewood, Illinois:Richard D. Irwin

Co.,

Inc., 1962), especially pp. 106-124 and pp.461-548.

2 A treatment of uncertainty can be found in Robert D. Buzzell andCharles C.

Slater,

"Decision Theory and Marketing Management,"JOURNAL OF

MARKETING,

Vol. 26 (July, 1962), pp. 7-16.3 See Herbert A.

Simon,

"Theories of Decision-Making in Economics,"American Economic Review, Vol. 49 (June, 1959) , pp. 253-283.

* See William Lazer, "The Role of Models in Marketing," JOURNALOF

MARKETING,

Vol. 26 (April, 1962), pp. 9-14.

Logical Flow Models for Marketing Analysis 31 32 Journal of Marketing, January, 1964

or logical flow sequences. Each of these languageswill be considered in order to show the strong andweak points and the range of usefulness of each ofthem for marketing.

Prose ModelsEveryonehas constructed simplemodels of human

or marketing behavior, using only "everyday Eng-lish" as the language of representation. For exam-ple, a sales manager for a firm manufacturing con-sumer products might describe a competitor's re-action to his price cut by saying: "If I cut myprice, my competitor will cut his an equal amount."

When the sales manager is pressed, he may givea more detailed description of his competitor's re-action: for example, the prose model in Part A ofFigure 1.

While a one-sentence model is easy to grasp,more complicated formulations like the many-sentence model in the figure may be unduly cum-bersome. It may be difficult to keep all of theirimportant characteristics in mind when attemptingto draw conclusions or make predictions about thebehavior under study. Yet the many-sentence modelmeets the basic requirements for a model of be-havior: It sets up initial conditions and inputs("If I cut my price," "providing the price cut islikelyto be permanent," etc.) and predicts responses("my competitor will cut his [price] to meet mine,"etc.).

Mathematical ModelsBased on the sales manager's verbal statements,

the mathematically inclined marketing analystmight build a model as described in the middleportion of Figure 1. Notice how the "everydayEnglish" of the verbal model is still used in thedefinitions of the variables, but how relationshipsamong them are described with equality signs, sub-scripts, and other mathematical relationships, inaddition to English.

While the mathematical model in Figure 1 isquite

brief,

it can in principle be subjected to thegamut of mathematical techniques, ranging fromoptimization to sensitivity to comparative staticsanalysis.B It can easily be passed on to a technicianor a computer for mathematical computations. How-ever, it is backed up by a long string of definitionsand restrictions which were used in its constructionand which must be used again to translate the con-clusions of the mathematical analysis back into"everyday English." In fact, these definitions must

5 See Jay W. Forrester, Industrial Dynamics (Cam-bridge, M.I.T. Press, and John Wiley & Sons

Co.,

Inc., 1961), as well as the comparative statics anal-ysis of classical economic models as discussed in H.A.

Simon,

Models of Man, Social and Rational (JohnWiley & Sons

Co.,

Inc., 1957), p. 103.

be kept constantly in mind during the mathematicalanalysis if absurd manipulations and conclusions areto be avoided.

Logical Flow ModelsThe third model of Figure 1 is also based on the

sales manager's English statements. This model usesthree types of language:

1. Everyday English—to describe questionsasked and actions taken by the subject ofthe model.

2. Circles, diamonds, and squares—to enclosephysically the sets of questions and actionsdescribed by the model.

3. Arrows—to indicate the flow of questions andactions: the sequence in which questions areasked and actions are taken.

The logical flow model of C in Figure 1 is easilyconstructed from the prose model by simply de-scribing the questions posed and actions taken.The statements of the latter are set down in thelogical sequence in which they appear in the be-havioral process. The simple devices of geometricalshapes and arrows help put together a picture onecan "see." This picture is easily grasped or evenmemorized, and can be referenced readily. Conclu-sions obtained from the prose model can be recon-structed by following each possible path leadingfrom "start" to "end."

" ABOUT THE AUTHORS. William F.Massy is Assistant Professor ol Marketingat the Graduate School of

Business,

Stan-ford University. A Yale graduate, heholds an S.M. degree in Industrial Management and a Ph.D. degree in Eco-nomics from the Massachusetts Instituteof Technology.

Dr. Massy has been a member of the W/w _____faculty of the School of Industrial Man- —agement, M.1.T., and has served as con-sultant to a number of firms, including Arthur D. Little, Inc.and Dynatech Corporation of Cambridge, Massachusetts. Hehas published articles in professional journals, is author ofPLANNING IN MARKETING—A SELECTED BIBLIOGRAPHY,and is coauthor (with Ronald E. Frank and Alfred A. Kuehn) ofQUANTITATIVE TECHNIQUES IN MARKETING ANALYSIS.

Jim D. Savvas is the principal of themanagement consulting firm of Jim D.Savvas and

Associates,

Bay City, Michi-

gan.

His experience is as a marketingand management consultant to businessand industry, and he has been with West-inghouse, General Motors, and Bachrach,Sanderbeck and Company.

A graduate of Middlebury College,Mr. Savvas has an M.S. in IndustrialAdministration from the Carnegie In-stitute of Technology. He has done additional graduate workat the University of Pittsburgh, and has coauthored papers dis-tributed by the Ford Foundation and the Office of NavalResearch.

Figure 1. Three models of a competitor's reaction to a price cut.

Comparison of Models the well-known lines of literature research, theThe important features of prose, mathematical, collection and analysis of field and/or secondary

and logical flow models have been summarized in source data, and the important cycle of modelingFigure 2 as an aid to comparing the three types of — testing — remodeling— retesting — and so on.languages which are available to the marketing ___._.." «"_"_ *,_..." ./ ■ o l "

i

_.

m. __ ii " j- " "____._,_. Applicability to Modeling Various Behaviorsanalyst. The following discussion is limited to the: T . ,_. , , ,_ ...____ . Logical flow models do not represent an answer. Expertise required of the researcher to M kinds of model.building problemB. Each of" Applicability to modeling various behaviors the three basic models under discussion is more

Applicability of conducting various types of applicable to some types of model-building situa-analyses tions than to others.Understandability by businessmen Prose models are best suited to the description

of relatively simple aspects of the behavior ofExpertise Required of the Researcher individuals and homogeneous groups. For example :

The ability to reason logically in terms of every- "I will sell you a dozen apples in return for forty-day English (or whatever the national language) nine cents," and "All scheduled airlines in theis a prerequisite for every model building endeavor. United States will begin collecting 5% federal ex-One advantage of prose and logical flow models is cisc tax, instead of 10%, on all taxable passengerthat this basic ability is sufficient to handle the tickets beginning in 1964."technical aspects of their construction and manipu- Mathematical models are most applicable wherelation, whereas mathematical sophistication is a the results of many independent decisions aremust for the mathematical-model builder. "averaged out" to produce aggregate behavior pat-

It is taken for granted that no matter what type terms which are of interest. Continuous quantita-of model the researcher is attempting to construct, tive variables are usually handled best by mathe-he is able (and willing) to do intensive work along matical means.

34 Journal of Marketing, January, 1964Logical Flow Models for Marketing Analysis 33

Figure 2. Comparison of features of verbal, mathematical, and logical flow models.Applicability to Feature to:*

(i) (2) ts) wCombinationmathematical

andProse Mathematical Logical flow logical flow

models models models modelsFeature of modelExpertise required of researcher

LogicMathematics

Applicability to modelingSimple behavior of:

individualshomogeneous groupsheterogeneous groups

Complicated behaviorof :individualshomogeneous groupsheterogeneous groups

Applicability of conductingComputer simulation

Understandability byBusinessman of:

ModelsAnalysis of modelsRecommendations based on

models

Some examples of applicabilityTo various subjects:

A competitor's behaviorMarket demandBreak-even points

* (+ ) is "yes" or "good," (— ) is "no" or "poor."

Also the behavior of heterogeneous groups of in- for example, the model builder must incorporate thedividuals, or behavior with respect to a broad class same calculations, even though he is constructingof decisions, is best modeled mathematically. Ex- a logical flow rather than a mathematical model,amples are the cost-volume-profit (break-evenpoint) There is an important difference between includingconsiderations of the examples in Figure 1, which such calculations in a logical flow model and build-represent in a continuous fashion the effect of many ing a mathematical model of the cost-volume-profitdecisions; and the price-sales volume relationship structure for a firm. The former was concernedwhich was deliberately left out of the models of only with the way the competitor conducts hisFigure 1 but which would be essential in complet- business—as good or bad as that may be. Theing this model of competitive behavior. latter would abstract the essence of the true cost-

By themselves, logical flow models are applicable volume-profit relations for the competitor,for the description of both simple and fairly com- Logical flow models can be used jointly withplicated aspects of the behavior of an individual, mathematical models in a more meaningful senseor a homogeneous group of individuals, with re- than just considered (Figure 2, column 4). Con-spect to particular decisions. An example will be sider the case where a series of logical flow modelsgiven later. Simple mathematics may be combined has been built to describe how buyers for depart-with logical flow statements if the individual whose ment stores, discount houses, and chain stores setbehavior is being modeled makes use of mathemati- prices on, say, electric refrigerators. Assume acal calculations in reaching a decision. These same metropolitan area in which 90% of all electriccalculations must then be incorporated, but the refrigerators are sold by the stores alreadymodeled,general nature of the logical flow model (Figure 2, and the other 10% of sales can safely be ignored.column 3) is not altered. In such a situation, it might well be desirable to

If the competitor calculates average costs per have a model of how consumers react to the pricesunit from his accounting data in order to deter- set by the various stores. Instead of studying themine whether he can break even at a given price, millions of heterogeneous consumers in the metro-

politan area and building a great many logical flowmodels to describe their reactions separately, itwould be better to build and statistically test asummary mathematical model which first predictedthe total yearly sales of electric refrigerators andthen allocated the total sales to the various storesaccording to their prices. The two types of modelscould then be connected together to produce areplica of the overall retail market structure forrefrigerators in the metropolitan area.

Applicability of Various Types of AnalysesSimulation has been defined as "the process of

conducting experiments on a model instead of at-tempting the experiments on the real system."6 Inmost business simulations, the model is translatedfrom the language in which it was originallycon-structed into a languagethat can be interpreted bya digital computer (balgol, Fortran, mad, ipl,

LISP, or

SIMSCRIPT,

to mention but a few). A set ofexperimental conditions may then be fed into themachine, which after performing the operationsindicated by the model produces the desired set ofoutcomes.

It is easy to see how mathematical equationmodels can be translated to a computer inputlanguage. After all, the computer was designed toperform arithmetic calculations—it can add, sub-tract, multiply, and divide, and with appropriateprograming can take logarithms, perform exponen-tiation, and find determinants. The so-called "alge-braic" programing languages like IBM's FORTRAN(FORmula TRANslation) are designed to speed thewriting of mathematical programs.

What perhaps is not so well known is that com-puters enjoy an equal facility for non-arithmeticcomputation.7 Computers can read, write, process,and compare a variety of kinds of symbols or pat-

terns. These can be interpreted not only as num-bers, but also as words, as sentences, or even asgeometric diagrams.

Since computers can be programed to follow dif-ferent courses of action (that is, branches), de-pending upon the relationships between patterns,it is possible to translate logical flow models likethe one given in Part C of Figure 1 directly intoa computer input language. Any of the "algebraic"languages can be used as nonnumerical symbolmanipulators by concentrating upon their set ofconditional branching instructions. In addition, cer-tain languages (for example, ipl and lisp) havebeen constructed expressly for the purpose of trans-

8 Same reference as footnote 5, at p. 18.

Geoffrey P. E. Clarkson and Herbert A. Simon,"Simulation of Individual and Group Behavior,"American Economic Review, Vol. 50 (December,1960), pp. 920-932.

lating logical flow models into terms that computersunderstand.8

Understandability by BusinessmenMarketing practitioners grasp even complicated-

looking flow charts much more easily than mathe-matical or even prose models. This contrasts par-ticularly with the kinds of initial barriers that areoften "thrown up" against the use of mathematics.

A Model of Buyer BehaviorSavvas has conducted research into the behavior

of a departmentstore organization, under the spon-sorship of an important manufacturer of electricalappliances. Suggested by the pioneering efforts ofCyert, March, and Moore,9 it has led to work on alogical flow model of the store's procedures fordeciding what manufacturers' lines to carry in itsmajor appliance department.

A portion of the model is presented in Figure 3.In addition to certain sectors that are not re-ported, some of the questions posed in the figure(such as, "Is it bad on service?") are determinedthrough lower level flow sequences (how "bad" isdetermined) .

The model includes two basic types of ele-ments : lists, and questions or conditional branches.The product lines which the buyer carries, andothers which he knows are potentially available,are arranged into lists—there are five lists repre-sented in Figure 3. Particular lines are moved fromone list to another according to the outcomes ofthe conditional branching operations. Sometimesthe order of occurrence of lines in a list is impor-tant, as when the lines are rank-ordered by grossmargin or some other attribute. The idea of proc-essing lists is ofkey importancefor the constructionof computer programs from logical flow models. Forexample, the LISP programing language mentionedabove stands for List processing.

While the general nature of this part of thebuyer's decision process is made apparent by in-spection of Figure 3, a number of points are worthconsidering in detail.

1. Gross margin (last year's sales multiplied bymarkup) is used as the buyer's primary cri-terion for ranking lines. For lines not carriednow, he looks at his weakest major competi-tor's sales. Thus, his method for forecastinggross margin is biased in favor of productshe now carries.

2. Lines now carried enjoy a second advantage.

8 See Allen Newell, editor, Information ProcessingLanguage: V. Manual (Englewood

Cliffs,

N. J.:Prentice-Hall, Inc., 1961).

9 R. M. Cyert, J. G. March, and C. G. Moore, "AModel of Retail Ordering and Pricing by a Depart-ment

Store,"

in Frank, Kuehn, and Massy, samereference as footnote 1, pp. 502-522.

1

Journal of Marketing, January, 1964Logical Flow Models for Marketing Analysis 35 36

Figure 3. How a major appliance department decides WHICH SUPPLIER'S LINES TO CARRY.

Provided that (a) they are among the top 10or 15 lines on the working list (this cutoff israrely effective for currently carried items),(b) their sales have not declined during thelast year, and (c) service has been satisfac-tory, these products are automaticallyplaced

tives that might be available.in the "carry" list regardless of other alterna-

3. Satisfactory lines that are not currently ear-ried are placed in the "consider-buying" list.They are considered further only if the buyerhas not been ableto meet his sales and markup

goals exclusively from the "carry list." Ifadditional lines are needed, the best potentialnew line is compared with the best of the oldlines on the "consider-to-drop" list; and theone with the highest gross margin is chosen.

4. Potential new lines must have satisfactoryservice and must not be strong in discounthouses. The discount house question does notcome up in evaluating currently carried prod-ucts, although service considerations remainimportant. Exceptions are made when thelines are needed for comparison purposes(trading the customer up or down).

Figure 3 places significant limits on the decisionprocesses which the buyer is expected to use. Whileno one would pretend that he always acts in theindicated way, the model will be useful if it repli-cates his behavior in a substantial number of cases.Unusual behavior can be discovered and analyzedagainst the backdrop of the average decision pat-terns as summed up by the model.

Finally, since this model was developed fromobservations upon the behavior of only two people—the buyer and his assistant—generalizationof thepresent model without further research would bea serious mistake.

Development of a Logical Flow ModelThe model from which Figure 3 was excerpted

was constructed with the aid of three kinds ofdata: (1) interviews with the buyer, wherein heattempted to explain how he performed his job;(2) observations of current decisions as they wereactually made; and (3) a careful analysis of thedepartment's written records, which summarizedthe results of many past decisions.

Individuals can rarely describe all the details oftheir jobs with great accuracy—some things areeasily forgotten and others are difficult to makeprecise or put into words at all. On the other hand,written records may be interpreted in many differ-ent ways, and the researcher cannot choose betweenthem without help from the decision-maker himself.

Observation of current decisions is the most diffi-cult kind of data to acquire—the researcher mustobtain access to the decision-maker, and then be atthe right place at the right time. Moreover, manydecisions are made largely without benefit of oralor any other overt activity which can be noted bythe observer. In such cases, it is sometimes possibleto ask the respondent to "think aloud," although thebiases possibly introduced by such a procedure arenot well understood. Where such "live" observationscan be obtained, however, they are well worth theeffort since they can provide a basic understandingupon which other avenues of exploration can bebased.

Testing the ModelOnce a model has been developed, it should be

tested against new data about the phenomena understudy. The untested model represents a set ofhypotheses, from which predictions about the realworld may be obtained. Obviously the empiricalverification of hypotheses is a crucial element inthe development of a scientific discipline. It is noless important in the application of scientific meth-ods to practical problems.

The formulation of research results in terms ofa logical flow (or mathematical equation) model andthe translationof the model into the input language

of a digital computer provide an opportunity fortesting. Once this has been done, the researcher cango back "into the field" and collect fresh data abouta new set of decisions which have been made bythe individual or group studied originally.

When the new data are fed into the computerand the program is allowed to run its course, thecomputer's decision can be compared with the oneactually made by the subject of the simulation. Ifdiscrepancies between the two results are noted,the model can be improved and tested again withnew data. If the test is successful, the success servesas evidence for the validity of the model. Thus, thelogical flow model can be tested against actual be-havior in the same way that theories in the physi-cal sciences are tested against the results of newexperiments.

The computer model of behavior allowsmore strin-gent tests than simple comparisons of predicted andactual decisions. Since the model is "couched" interms of the decision process actually utilized by

the individual in question, it is possible to comparethe results of each of the intermediate tests thatare performed on the way to determining the finalsolution (that is, the "questions" of Figure 3) withtheir real-world counterparts.

In theory, it is possible to compare the computer'sdetermination of what is to be done; when, how,and where; and in what form the results are madeavailable, with equivalent data derived from freshobservation and analysis of the real organization.

If the model doeswell on these microscopic compari-sons, the degree of confidence in its validity is in-creased immeasurably.

Strictly speaking, the computer is not necessary

for any of these results. A man with a pencil andpaper, and perhaps a slide rule or desk calculator,could follow the steps of the flow chart if the prob-lem is not of too great magnitude. Since this methodis often time-consuming and subject to clerical er-rors, however, the intermediate step of computerprograming is usually desirable. Once a programis written and "debugged," the rules given in theflow chart can be applied to a variety of situations

Logical Flow Models for Marketing Analysis 37

in a short time, without danger of mistakes or mis-interpretations.

Use of the computer has another "payoff" as well.The computer is unable to fill in or gloss over situa-tions where the researcher has failed to specify pro-cedures clearly. Since the computer is essentially ablank slate to be filled in by the programer, it isabsolutely necessary that the flow chart be madecomplete, consistent, and unambiguous. The ma-chine cannot determine whether the model is cor-rect, in the sense of bei _g a true replication of thereal decision process; but it can and most certainlywill find any gaps or inconsistencies in the model.

Since completeness and logical consistency areprerequisites for a valid model, the stringent re-quirements imposed by machine programing—andindeed by the modeling process itself—are entirely

consistent with those for the advancementof knowl-edge of decision-making in marketing.

Importance For Management

The logical flow model will take its place in thebattery of techniques that promise to put marketingdecision-makingon a more scientific plane than hasheretofore been possible.

Its use can lead to an increased understanding ofthe behavior of consumers, membersof the channelsof distribution, and even parts of firms' own mar-keting organizations. This kind of knowledge willallow better forecasts of marketing phenomena andhence improved management decisions. It is easierto make a good choice between alternatives if theirrespective outcomes are known or can be closelyapproximated.