C. MERLE CRAWFORD

A Shotgun Marriage 37 of and Marketing?

III the management of many firms, especially in production, inventory control, and ware- oP corporate management is dedicated to housing. Mathematical models are set up to the continuing search for better ways of T describe common business situations, the doing business. Over the years this search intent being to provide a framework for has uncovered many new and valuable tools analysis and prediction in areas where the -scientific factory management, budgeting, complexity of many variables defies com- marketing research, data processing, and prehension by the mind alone. many others. To date, the marketing department seems Today, much attention is being given to to have found mathematics of little assis- mathematical tools, variously called opera- tance, and top management may well be tions research, management science, or bus- wondering whether the reluctance to use it iness mathematics. All indications are that comes as a result of ( 1 ) basic inconsistencies this approach is rapidly finding a p/ace in between the new tools and marketing prob- lems or (2) a built-in reluctance on the part Mr. Crawford is Associate Professor of Marketing, of marketing executives. Stated more co- University of Michigan. gent/y, is there any justification for the

SUMMER, 1966 C. MERLE CRAWFORD

skepticism with which marketing executives marketing organization can spawn is often seem to be greeting the use of mathematical a measure of its success."1 models? Such striving for change is motivated My contention is that there is indeed justi- partly to put the company a step ahead of fication, which stems primarily from the lack , partly to match change intro- of realism among model builders (mathema- duced by competition, and partly to call the ticians) and from a lack of understanding significant turns in an industry before they and involvement by marketing executives happen. Yet the driving persistence of with this new science. Whether mathematics the need for change and innovation seems to will ever play a significant role in marketing have avoided the onslaught of mathematics, is yet to be determined. for the time being anyhow. As might be ex- Does this view make marketing executives pected, the executive will perceive little as- laggards? Should top management push sistance from mathematics on this important more to stimulate a speedup of the learning marketing function. He may find models to and involvement process? In some firms the assist in allocating the media budget, but he answer is yes, but generally it must be no, for probably will not find models to develop the simple reason that mathematics is not ideas for new products or over-all promo- yet ready for such a shotgun marriage. There tional platforms. are powerful and devastating roadblocks to Even the general area of decision making 38 communication between mathematicians must be greatly stretched to permit the and marketers, and, until they are dimin- premise that "Marketing management can ished, any forced application to marketing be viewed simply as the continuing attempt operations will reduce eflqciency, not in- to recognize and solve specific marketing crease it. These roadblocks to communica- problems. ''2 If decision-making techniques tion arise from the very nature of marketing are necessary, for example, to determine the and the top marketer's task, from the ma- next innovation in a particular industry, then thematical techniques and processes them- the executive would most assuredly be in- selves, from oral and written mistakes made terested in mathematical models. At present, by mathematical researchers, and from the however, they seem to offer little promise in sometimes rather unscientific posture of the this critical aspect of marketing. mathematical scientists. In sum, change, creativity, and innovation are the essence of marketing, and the execu- tive might be pardoned his belief that mod- BLOCKS ARISING FROM els are fine in selected mechanical areas of NATURE OF MARKETING marketing, but not in these most critical ones. MODEL INABILITY TO HANDLE CBEATIVITY

Mathematical models work best when ap- MODEL INABILITY TO HANDLE GOALS plied to mechanical functions, where all significant variables are tangible and quan- A basic premise in the development of most mathematical models is that they relate the tifiable. But the top marketing executive would probably say that his major function is creativity. As the editors of Sales Manage- 1 "Significant Trends," Sales Management (Aug. ment recently said: "Marketing's greatest 21, 1964), p. 81. strength is also one of its greatest weak- 2 H. V. Roberts in R. E. Frank, A. A. Kuehn, and W. F. Massy, eds., Quantitative Techniques in Mar- nesses. Its greatest strength is change; in keting Analysis (Homewood, II1.: Richard D. Irwin, fact, the amount of successful innovation a Inc., 1962), p. 3.

BUSINESS HORIZONS I'elAtLRIAGE OF MATHEIVfATICS AND ~¢IARKETING.p

goal of the enterprise to the topic under reports concerning the widespread adoption study. Such goals (for example, maximiza- of model building among business firms in- tion of long-term or short-term profits, or dicate no awareness of the many human rea- sales) must be few in number since they sons for such programs; rather, they infer serve as constraints in the system of equa- that the socially acceptable motivation of tions. increased business efficiency is responsible. The executive's problem is to understand But other motivations are possible, too. how one or a few such tangible goals can be Has the pride of the president ever been the selected from a complex system of goals to basis for a new system? Was there a desire control the calculation. The goals sometimes to impress the board of directors? During become quite personal, and are usually lush times, is there motivation from the "We geared to blend the desires of several indi- can afford it" school? Does it ever happen viduals, including the executive and others that a finn installs a computer system for the in the firm whose feelings must be consid- routine handling of accounting data, and ered. They also change frequently, as organ- then, finding huge unused capacity, decides izations themselves change. to use this idle time? Finally, has any de- Faced with this dynamic complexity of partment or division head ever used a new goal structure, model builders remain un- tool like mathematics in an effort to polish daunted, insisting that goals be spelled out his image among his peers or impress higher and quantified. The attitude seems to be, management? To the extent that the latter 39 "The equations must go on"-but the mar- reasons prevail, business use of models is keting executive may have left at intermis- not a testimonial to their helpfulness. sion. Second, every operating marketing unit consists of people, with the usual collection DIFFICULTY WITH THE HUMAN FACTOR of strengths, weaknesses, doubts, insecur- ities, drives, and ambitions. Even the best In two respects, current attempts at selling scientific solutions to problems must still go mathematical models for use in marketing throngh the human wringer before they can seem to ignore the human problem. First, be used; in fact, the problem statement it-

!t

SUMMER, 1966 C. MERLE CRAWFORD

self, and much of the data and assumptions ing executives are easily repelled by "assis- used in the calculations, must pass through tance," which, as they see it, simply is not human minds and hands before the calcula- practical. For instance, a lengthy article on tions can even start. If problem solutions, model building, published a few years ago, like organizations, can be made to work ff listed the various mathematical approaches people want them to work, what, on balance, available, and began an explanation of the is the contribution of the new science to the first one (matrix algebra) as follows: "Past enterprise? Might the executive be pardoned records show that on the average it takes a concern over the aseptic, research labora- hour of sales effort and $1 of ex- tory solutions to his problems? penditure to produce a sale in the first mar- ket; ,~ hour.., in the second market .... -3 This type of statement, perhaps necessary INAPPROPRIATENESS OF CASE HISTORIES for construction of a matrix algebra model, Mathematical enthusiasts are rapidly over- would appear strange to most marketing coming the problem of a lack of case his- executives since, though they might dearly tories drawn from the marketing field. All want such information, they simply do not too often in the past, illustrations have been have it. drawn from nonprofit areas such as the gov- C. West Churchman, a staunch proponent ernment, the military, and so forth. To the of mathematical models in marketing, re- 40 marketing executive, there is little connec- cently put the danger this way: "Hence, tion between managing a nonprofit opera- there must be a real concern about the relia- tion and staying alive in his business; the bility of mathematical models.., one great sooner he hears of relevant marketing case risk of being able to think rigorously is that histories, the sooner will his interest we may continue to go down the wrong path- heighten. way, forgetting the assumptions that started the thinking process in the first place."4 Although further development of mathe- MATHEMATICAL TECHNIQUES matical techniques may eliminate most of these troublesome assumptions, a peculiar It is, of course, impossible to differentiate tendency still remains in the thinking of unequivocally between problems in apply- model builders that assumptions are neces- ing a particular technique and the problems sary to achieve understanding by executives, of understanding those who attempt to ex- that a complete model is too complex for plain the technique. In the case of mathema- comprehension. If so, models may fail to gain executive acceptance for some time. tical models, a few matters at the core of the new approach cause difficulty, and would not change appreciably whoever was doing EXCESSIVE DETAIL the explaining. Whereas it is frequently necessary to assume away a particular aspect of a marketing TIIE PROBLEM OF ASSUMPTIONS problem, it also appears necessary to simply Mathematical techniques of problem solv- ing face the age-old problem of assumptions, 3 Philip Kotler, "The Use of Mathematical Mod- no less than other scientific techniques de- els in Marketing," Journal of Marketing (October, veloped over th~ past twenty-five years or 1963), p. 32. 4 In Peter Langhoff, ed., Models, Measurements so. The matter is widely discussed, even in and Marketing (Englewood Cliffs, N.J.: Prentice- the mathematical literature itself. Market- Hall, Inc., 1965), p. 35.

BUSINESS HORIZONS ~AlqRIAGE OF MATHEMATICS AND MARKETING~

ignore many of these matters. In one case, a handling the equations, the matter of data researcher was trying to analyze the effects inevitably remains. Since the executive of advertising; after posting the variables he knows he rarely has the data he wants, when had selected for study, he mentioned several he wants it, and in the form he wants it, how" peripheral effects such as the effect on the can he visualize complex equations using attitude of salesmen, on retail data he cannot find, or cannot afford him- for the product under study, and on the de- self? With research reports giving the clear sired company image. impression that data currently constitute the Regarding these latter effects, he said, principal roadblock, the executive may un- "These details constitute a major nuisance derstandably wonder where the needed mil- from the point of view of the analyst .... lions of statistics are going to come from. They clutter up the pro.blem. "5 An executive, grounded in the concept that good INABILITY TO HANDLE ALTERNATIVES managers and good sales managers stay on top of every situation at all times, might not Mathematical researchers take a stand on feel comfortable in a problem analysis that the claim that various systems of equations, ignores significant details in such a manner combined with probability , can han- as this. dle a limitless range of alternatives in any given marketing problem. Although this DANGER OF GENERALIZATIONS view is perhaps true, the marketing execu- 41 tive may be a student of the "diminishing Less tangible, but more prevalent and po- returns" school, which wonders where, along tentially more dangerous, is the strong ten- the road of complexity, mathematics passes dency for models to imply broad generaliza- this critical point? tions regarding cause and effect. This Moreover, these executives know that tendency might seem alarming to the mar- quality counts more than quantity; one good keting executive who is very much aware he idea, thought of at the last moment, will lives in a world where cause and effect, like cause the collapse of weeks and months of parallel lines, never seem to meet. Though careful calculations on previously available he puts forth the causes (with help from alternatives. If model systems can be built competition and the economic system gen- to offer practical flexibility, an important erally) and must live with the effects, clear need will be satisfied. lines rarely seem to connect one with the others. Models should not oversimplify these relationships. THE DANCER OF ONE WEAK laNK

Even though a particular system of mathe- CONTINUING LACK OF NECESSARY DATA matical analysis may have been worked out in great detail, an executive might not feel Regardless of the skill in. developing appro- certain that there wasn't one weak link in the priate marketing theory, regardless of the dexterity used in developing mathematical chain of reasoning or processing, one statis- equations that represent this theory, and tic assumed because it was not available, regardless of the speed of computers in one spurious cause-and-effect relationship, or one bad guess regarding the probable reaction of competition. Where is the con- 5 William J. Baumol in Wroe Alderson and Stan- trol over the system? What outside party ley Shapiro, eds., Marketing and the Computer (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1963), understands it well enough to offer inde- p. 204. pendent appraisal?

SUMMER, 1966 C. MERLE CRAWFORD

PROBLEM OF PBEDETER1VLINEDANSWERS remaining communication barrier of all is, perhaps, the barrier traceable to mistakes One recent report on mathematics in mar- made by overenthusiastic proponents of keting described the results of research de- mathematics as they attempt to explain signed to detect the presence of any carry- their new technology. These mistakes take over effect in advertising. But in the process many forms. of developing the equations, relationships had been so established that a carry-over ACCUSATIONS OF GROSS INEFFICIENCY effect had to exist. The assumptions pre- determined the conclusion, a fault not un- Presentations supporting the use of mathe- known to the executive who has spent years matical models in marketing offer over- going over marketing research survey re- whelming and irresponsible condemnation ports. In other instances, we see models of of current marketing practices-overwhelm- media scheduling, which require such a ing because it seems to be the premise at the complete mass of data on costs, impacts, start of every such presentation, and irre- competitive schedules, and so forth that the sponsible because almost never are the task is one of computing, not modeling. The standards presented by which the researcher problem seems to be inherent in the ap- reached his conclusions regarding market- proach. ing's efficiency. Virtually every such presen- tation begins with the explicit or implicit 42 TIME REQULRED TO SOLVE PBOBLEI~fS reference to the inadequate tools and proc- esses by which problems are currently being A good mathematical model, once on the solved, and the millennium that mathema- computer, can apparently spew out a hun- tics will soon bring about. dred solutions to a problem while a non- Experienced marketing executives have mathematical analyst is looking for a pencil lived through too many eras of problem- and paper. This is the frame of reference in solving innovation to fall victim to this type which speed is discussed. of overenthusiasm. (Remember the first However, descriptions of model building year of motivation research?) But, be it un- are quite vague when it comes to the total derstood, this is not to defend inefficiency! time that went into structuring the necessary Rather, the executive would be right simply theory, fitting the model, gathering the to ask critics of current marketing decision needed data, and smoothing out the wrinkles making to document their denunciations to a point where the computer can take over. with more than sweeping generalizations One gets the impression that this time can regarding intuition, seat-of-the-pants rea- be quite lengthy indeed, as much as a year soning, and so on. Where is the evidence in some instances. During this period when that a sales manager paying his men a mathematical models are going through straight commission is inefficient? Where is their technological shakedown, executives the evidence that soap companies are in- may be getting badly mistaken impressions efficient in the selection,of Tv shows? Where of their time efficiency. is the evidence that prices are wrongly set? The marketing executive might ask, MISTAKES IN PRESENTATIONS "Where lies the burden of proof?"

Problems arise even ff we assume an execu- THREAT TO JOB SECURITY tive mental modus operandi attuned to mod- els, and ff we assume no problems inherent Given the fact that marketing executives do in the techniques themselves. The greatest not really understand the newer techniques

BUSINESS HOBIZONS MARRIAGE OF MATHE~'VLATICS AND kX$ARKETING.~

of data manipulation and model building, "It would be tragic if instinctive, ego-protec- what might be their reaction to a statement tive phobias were to obstruct and delay the natural line of development in this field. ''7 such as the following: A marketing executive has more than his "The disruptive force of computers is ac- centuated because it is focused largely on white share of critics and feels a daily stream collar and managerial segments of organiza- of economic, political, and social criticism. tions. Managers may have been casual during He certainly will not welcome yet another the first Industrial Revolution about the effects adversary, especially ff it comes bearing ac- of new technology on hourly workers, but it is cusations of phobias and inefficiency, to say not likely that they will be as casual about a new technology that may eliminate or drasti- nothing of incompetence and stupidity. The cally modify some of their own jobs. ''~ idea of his being a marketing sinner is re- pugnant, and he can be expected to fight How can executives possibly want to such attacks actively. Nor will he submit to learn management techniques from those the belief that unless he heeds the call to who say or imply that their machines and science (and immediately) he will be pas- equations will sometime replace the execu- tured to the tape-splicing room. tives themselves? Whatever the ultimate effect, the immediate emotional reaction is Finally, we might anticipate the execu- hardly a healthy one for mathematics. tive's reaction to an implication in one of the In the same vein, rather like a prelude to quotes above (heard frequently) that he is ultimate demise, are found the widespread falling behind his counterparts in other di- implications and accusations of incompe- visions of the firm, such as production and 43 tence. Incapable executives must surely face finance. For a man who earnestly believes difficulty holding on to their jobs during the his sales force and his advertising keep those next revolution; to see what executives are other divisions operating, this might indeed currently having to face, consider the fol- be anathema. lowing quotations:

"Now there is one thing that may block ac- DISAGREEMENT ON DEFINITIONS ceptance of a model that deserves special at- tention; this is stupidity or ignorance• The man- Although not unique to mathematical model ager may be incompetent to understand the implications of the model, or he may be igno- building, it is a fact that the new field seems rant of some things the scientist has discovered." to be confused regarding terminology. In "Broad social experiments are associated with time, as the dust settles, this problem will great social upheaval, unrest and revolution. subside to minor squabbles among active Experiments in the activities of the finn are like- wise attainable only at considerable risk and participants, but in the meantime conflicting managerial resistance." definitions abound. Weinberg said recently:

•.. intuitive decisions are made today when adequate data is available. These decisions are "From this it becomes apparent that we may dramatic, but only as they highlight incompe- have as many definitions of management sci- tence." ence as there are practitioners. Although I do "This delay [in using computers in market- not want to add to this confusion, for the pur- ing] may be due to the marketing executive's poses of discussion, I would like to define man- fear of a strange and unfamiliar tool, a wide- agement science as follows.... "8 spread belief that marketing problems do not lend themselves to computer-oriented manage- ment science techniques or the monopolization 7 The preceding quotations, in order of appear- of existing computer facilities by executives ance, are from C. West Churchman, Peter Langhoff, from the other functional areas of the business." and Guy-Robert Detlefsen, in Models, Measurement and Marketing, pp. 35, 18, and 210; and Wroe Alderson and Stanley Shapiro, and Martin K. Start, in Marketing and the Computer, pp. v and 64. 6 William R. Dill in Marketing and the Computer, 8 Robert Weinberg, Marketing and the Computer, p. 224. p. 101•

SUMMER, 1966 C. MERLE CRAWFORD

Add to management science the various related techniques to marketing decision- definitions for models, operations research, making is now swiftly being overcome." quantitative techniques, and so on, and "[Critical Path Analysis is] a powerful tool to ensure the successful launching of a new chaos can prevail. An executive needs a product.... It is a giant stride taken by man- modern marketing dictionary at his side agement science." when reading the newer techniques, as will "What our befuddled marketing executive be demonstrated later, but his struggles doesn't have, and isn't even aware he needs, is would be aided by some standardized over- a way of handling the facts at hand in a logical sequential way. Nor does he understand the all headings. process by which he arrives at a decision. Some- day-probably much sooner than most realize- he will have both, and more. "9 PUBLICITY AND PROGRESS These statements, and many more like Researchers in the mathematical field are them, run as a thread through most writing tempted to oversell their progress, as will be on this subject. Even though a given piece discussed; granting for the moment that of research may be concerned only with an contributions have been genuine, the execu- early trial of a technique, there is a tendency tive might well be confused concerning the to generalize both in terms of applicability specific functional areas in which these con- and regarding the extent of success. Excep- tributions have come about. On the one tions can be made, of course, and most re- 44 hand, he hears of advertising evaluation, searchers in the field make a perfunctory over-all marketing program systems, and so bow to scientific posture somewhere during on. On the other, he reads that most of the their discussions. A completely candid de- actual successful applications have come scription of progress, however, is difficalt to forth in the logistical area-inventory, ware- find. housing, and the like. Media scheduling will The most perplexing part of it all is not surely be in this camp soon, but, even with the occasional unrestrained comment in the some current work completed, it seems a press or at a meeting; these are momentary fact that mathematics has a great distance enthusiasms. Rather, the concern for mar- to travel before it moves in on the truly keting executives comes in reference to as- executive-level marketing problems. sessments of current actual practice in use of the techniques• Are they in widespread application or not? If so, let bona fide sur- IRRESPONSIBLE OVERSELL veys of management practice establish this Emerging schools of thought, in perhaps all fact. of man's endeavors, have overzealous ad- Equally deceptive is the occasional habit herents who frequently lose perspective in of including the newer mathematical tech- citing the advantages of their new approach. niques in with a group of long-standing mar- Therefore, it should not be surprising to note keting research techniques (calling them their presence in the field of mathematical tools of quantitative analysis) and then proclaiming the widespread use of the bun- model building:

"Without the systems approach to marketing • . . companies will go on being production- 9 The preceding quotations, in order of appear- oriented or finance-oriented, lacking an ade- ance, are from Wroe Alderson and Stanley Shapiro, quate intelligence mechanism to orient them- and R. J. Aboucher, in Marketing and the Com- puter, pp. 7 and 31; Printers" Ink (July 13, 1962), selves to the market." p. 21; Yung Wong, "Critical Path Analysis for New "In less than one minute the computer will Product Planning," Journal of Marketing (October, produce the sales forecast for 1960." 1964), p. 59; and Printers" Ink (March 12, 1965), "[The] lag in application of computers and p. 15.

BUSINESS HORIZONS MARRIAGE OF ~IATHE~IATICS AND !3/IARKGTING?

dle. This is an actual disservice to marketing limitations surrounding any particular piece executives, who-right or wrong-look to use of research. Examples abound, but for mar- of a new technique by other firms as a clue keting executives one recent case would be to whether they should give the item a closer of interest, ll This study used a model to look themselves. They want information, but show the superior economics of having they would like it to be accurate, unbiased, salesmen paid a commission based on prod- and reliable. ucts' gross margins rather than total sales. This alternative has been argued for years, FAILURE TO TELL FULL STORY and executives would logically be interested in the outcome of the research. But nowhere For some reason, reports on mathematical in the report was there recognition of such models suffer from exclusion of information factors as complexity of routine commission that would greatly help a marketing execu- calculation, the desire to keep margins con- tive accurately assess the usefulness of mod- fidential, conflict with the salesman's general els in his operation. Such omissions are of drive toward "getting the order," and others. five types. Research reports should address all appli- cable and important limitations. False Starts and Failures Granting that researchers would rather report successes Costs of This Research Though stressing than failures, perhaps it should not be sur- the cosmic speed of calculations on today's 45 prising that virtually no reports are made computers, research reports in this field of the latter. Mathematical research must rarely mention costs. That they should is have yielded negative answers more often suggested by the following: "'We go than is reported, and, ff marketing is to be- through an industry like a swarm of locusts come more of a science, the negatives must through a wheat field,' says (John) Handy, share billing with the successes. This, most who admits he would never have installed would agree, is a hallmark of science. a computer system had he known that it One outstanding example of forthright- was going to cost $300,000. "12 For a com- ness in the reporting of research on mathe- pany executive who wants to take his firm matical techniques in marketing was a recent into a reasonably broad program of mathe- article that should be required reading for matical model building, what should he plan anyone interested in the field. Alfred Oxen- on as a probable expenditure for the first feldt, almost in diary form, relates his ex- two or three years? What will the continuing periences in trying to develop a demand costs be ff the research produces usable pro- function for analyzing the sales of TV sets. grams? Such estimates should include some Although he was able to retain his convic- figures for the indirect costs of lost executive tion that mathematics has a fine place in time during the period of learning and ex- marketing, he nevertheless was willing to perimentation. Short of having this type of report an amazing story of false starts and information, an executive who has read of ultimate failure. 1° the huge investments made by DuPont, Ford, and others might well wonder about Applicable Limitations Just as it is com- his position vis-~t-vis mathematics, with a mon to rarely report total failures, so is it total budget of, say, $10-15 million. common to be selective in describing the

li John V. Farley, "An Optimal Plan for Sales- lo Alfred Oxenfeldt, "Scientific Marketing: Ideal men's Compensation," Journal of Marketing Re- or Ordeal?" Harvard Business Review (March, search (May, 1964), pp. 39-43. 1961), p. 51. 12 Business Week ( March 6, 1965), p. 98.

SUMMER, 1966 C. MERLE CRAWFORD

Evaluations of Solutions Several years within the firm and in its market place? ago the author was involved in research to Whether yes or no, the marketing executive determine the applicability of a new mathe- could make a better appraisal ff he had this matical technique for use in sales forecast- information. ing. After several false starts, the method reached "operational" status only because EXCESSIVELY TECHNICAL LANGUAGE so much time and effort were put into it that monthly calculations seemed warranted. Top marketing executives occupy powerful Since the previous system of calculations positions in their respective companies, and was continued, it was rather surprising some thus are besieged regularly by people sell- time later to hear this case cited as an ex- ing something-an idea, a new technique, a ample of the successful application of this person. Not only have they learned to look new technique. beyond the window dressing invariably put Virtually no reports of mathematics in around these presentations, but, to put it marketing cite the opinion of line marketing bluntly, they have learned not to be fooled executives whose judgments the models by trappings. were set up to help, although opportunities Since they know there is apt to be an in- for it abound. For instance, a recent report verse relationship between the amount of showed how operations research introduced window dressing and worth of the proposal, 46 "the concept of measurement and logical what is their reaction on this score when analysis in sales problems which had been they meet up with mathematical models? previously considered amenable only to in- Reading and listening to researchers in this tuitive treatment."a3 field can be likened to a trip through the These problems were of sales force super- Land of Lavish Labels. Every idea, no mat- vision and control, subject to more than in- ter how important, seems to require a new tuitive treatment since the turn of the cen- label. tury, and the firm's sales managers were cer- To cite just one example of the many tainly well aware of this fact. But nowhere available, a recent paper on models con- were their opinions of the new methods tained the following words: stated, an omission that might be of concern to marketing executives. Group 1 Those that are probably mean- ingless to the nonmathematical executive The .Staying Power of Solutions Also normative associated payoff admissible states posterior analysis missing in the reports from researchers in outcome matrix preposterior analysis this area is any information regarding the sequential set sensitivity analysis staying power of these new applications. nonzero probability states of nature utility theory choice of criterion Even when a new computational process ap- tree diagram computer simulation pears to pass muster in a firm and becomes Bayesian minimal regret cognitive supersedure operational, what is its status a year or two Laplace criterion antecedent stages later? Five years later? Can the techniques stand the test of time in a marketing organi- Group 2 Those that the executive might zation faced with explosive change, both think he understands but will not, at least in the context of mathematical models decision theory stage of complete optimization ignorance 12 A. A. Brown, F. T. Hulswit, and J. D. Kettelle, components dynamic programming "A Study of Sales Operations," in Frank Bass and optimal conditional payoff others, eds., Mathematical Models and Methods in rational decision joint occurrence Marketing (Homewood, II1.: Richard D. Irwin, Inc., continuous variable original payoff entry 1961), p. 397. random sequence prior judgments

BUSINESS HORIZONS MARRIAGE OF ~IATHEI~IATIGS ANqD k%IARKETING.9

multistage decisions recursive If the field of mathematical models is to delay problem eontext progress according to the plans of its advo- maximize his mini- unique events mum payoff prescriptive cates, marketing executives must somehow prior analysis systematic find the time, interest, and inspiration for future states suboptimization digging into this highly technical material. personalistic view expected value criterion incremental eollectively exhaustive Although the task must somehow be made prior probabilities power principle as simple as possible, one wonders whether marginal probabilities decision matrix it is the nature of mathematical science to hypothesis testing observed evidence offer a comprehensible simplicity in concept substantive knowledge degree of uncertainty discrimination or communication, and, if not, what are the flexibility criteria of choice equiprobable implications relative to its ultimate place in conjunction disoriminatory power business management? maximum criterion objective probabilities betting odds time dimension discounting development planning feedback horizon POSTURE OF MATHEMATICAL SCIENTISTS This is, of course, a problem in communi- cation, since a company interpreter will be As a capstone perhaps to much of the fore- necessary to help implement any system us- going, and building specifically upon several ing such a vocabulary. Can a marketing ex- ideas covered in the third section (mistakes ecutive ever hope to feel comfortable in this 47 made in oral and written communications), environment? Unfortunately, words are not the only we come to the matter of appraising a sci- ence by the yardsticks of science. The brief problem along this line; formulas or equa- nature of this article precludes an exhaus- tions also rank high as communication blocks. Not that this is insurmountable, since tive investigation on this score, but an ex- the interpreter can again handle the details ecutive's attitude toward mathematical mod- of a project within a company, sparing the els might be easier to anticipate if thought executive the task of understanding the of in the context of the question: Is he really mathematics. But, beyond the fact that ex- being offered a science? ecutives have a knack for failing to properly Certainly an early step in any application utilize research which they do not under- of scientific method is appraisal of existing stand, the mathematical researchers them- apparatus or methodology. How well is a selves may be so absorbed in their work that function currently being performed? To they fail to appreciate the speed with which date, marketing mathematicians seem to the chasm between themselves and execu- show more interest in testing a new applica- tives is widening. tion than in appraising current performance. For instance, a recent technical article in Second, blunt accusations concerning a the ]ournal of Marketing Research offered current state of inefficiency in marketing do no less than forty-four complicated mathe- not become those who would be called sci- matical formulas. As a journal for specialists, entists. Nor do the incautious predictions this may be expected, but the author said: concerning the near-future widespread "... the equations developed are sufficiently adoption of these methodologies. tractable to enable their day-to-day use by Finally, the field of science seems to offer busy managers, m~ two posture types regarding the merits of research findings themselves: (1) the "scientist-scientist" who simply reports his 14 R. L. Mela, "Sales Budgeting for Controlled findings, with minimal editorial comment, Growth Objectives," Journal oJ Marketing Research (May, 1965), p. 138. and lets them tell their own story; and (2)

SUMMER, 1966 C. MERLE CRAWFORD

the "promotion-scientist" who can hardly their problem as one of "what next," rather find the breath to report his findings, so in- than "whether next"? terested is he in making their import clear. Assuming that more of a truly scientific The scientist-scientist is sometimes accused posture will eventually prevail in this dy- of being so skeptical of his own work that he namic new field, one should be in a position is its severest critic. to predict a gradual broadening of under- Which does the executive see in the fore- standing concerning models, their demise as front of the work on mathematical models in a "hot" press item, and more frequent re- marketing? How many research presenta- ports of concrete payout. Only then will tions can he approach with assurance that marketing executives undertake a wide- he is the object of information, not influence? spread test of their operational character; Is it possible that researchers in this field and only after this assessment will we know are so convinced of the ultimate dominance their ultimate place in this art-science com- of mathematics in marketing that they see plex called marketing.

48

THE SEEMING stability of the modern marketing structure is an illusion. For instance, the number of retail firms appears to remain substantially unchanged from year to year or to increase modestly with the expansion of the economy. On January 1, 1960, there were approximately 1,998,000 firms engaged in retail trade. Exactly one year earlier there had been about 1,977,000 such businesses. This apparently modest increase of 21,000 retail firms was actually the result of 162,000 new establishments entering the retail field and 141,000 such firms closing for various reasons. On the basis of this fairly representative turnover, the life expectancy of a retail store is just short of fifteen years. In depression circumstances, it would be much less. Somewhat more stability is observed in the wholesale field, but the mortality rate of all marketing institutions is phenomenally high. -Martin L. Bell ~V£AIRKETING: CONCEPTS AND STRATEGY

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