vidale_wolfe

8/2/2019 vidale_wolfe

1/12

AN OPERATIONS-RESEARCH STUDY OF SALESRESPONSE TO ADVERTISINGM. L. VIDALE and H. B. WOLFE

Arthur D. Little, Inc. , Cambridge, Massachusetts(Received January 29, 1957)

This paper presents the results of studies for major industrial concernson the sales response to advertising. A simple model of the interactionof advertising and sales is described that is consistent with the results ofcontrolled experiments performed on a large number of products andseveral media. The model is based on three parameters: Sales DecayConstant, Saturation Level, and Response Constant. Ithas proved usefulfor analyses of advertising campaigns and for allocations of advertisingappropriations.

OPERATIONS RESEARCH has not as yet found many applicationsin the field of advertising. Only a few papers[1-6)on the subjecthave appeared in the literature. Itis difficult to obtain reliable experi-mental data. It is probably true that designing original advertisingcopy and making a priori estimates of the behavior of the buying publicare not promising material for operations research; there do exist, how-ever, problems that are of great interest to the advertising man andthat can be studied quantitatively. For example:

1. How does one evaluate the effectiveness of an advertising campaign?2. How should the advertising budget be allocated among different productsand media?3.. What criteria determine the size of the advertising budget?

The last two questions cannot be answered without a knowledge of ad-vertising effectiveness;this is where most of the difficultieslie and whereresearch is most needed. Once the relation between sales response andadvertising has been established, the optimum budget size and allocationcan be determined.

During the past few years, the Operations Research Group at ArthurD. Little, Inc., has studied these problems and examinedsales promotionsfor several large industrial concerns. In this paper we wish to presentsome generalizations that have been suggested by the results of our ex-periments.

We shall first describe the type of experimental results we have ob-tained, and then discuss a simplemathematical model consistent with ourobservations.

370


2/12

Sales Response to Advertising 371EXPEIUMENTAL RESULTS: ADVERTISING PARAMETERS

IN ORDER to measure the sales response of individual products to advertis-ing and to compare the effectivenessofvarious media, wehaveperformedalarge number of controlled experiments in which the intensity and type ofpromotion were varied. With the cooperation of sales and advertisingdepartments and their advertising agencies,wehave beenable to run large-scale tests over considerableportions of the U. S. market. The results ofthe tests have in most cases been significant and reproducible. In theanalysis ofadvertising campaigns, we have found it helpful to describetheinteraction of sales and advertising in terms of three parameters:

1. The Sales Decay Constant2. The Saturation Level3. The Response Constant

Weshall introduce these parameters by means ofa few sales histories thatexemplify them. The relations and the data in the examples are real.However, for reasons ofindustrial security, it has beennecessary to concealthe types of products tested and, in a few cases, to paraphrase the ad-vertising media.Sales Decay Constant

In the absence of promotion, sales tend to decreasebecause of productobsolescence, competing advertising, etc. Under relatively constantmarket conditions, the rate of decrease is, in general, constant: that is, aconstant per cent of sales is lost each year. Figure 1 presents the eight-year sales history ofproduct A, plotted on a semi-logarithmicscale. Thisproduct exhibits a small seasonality in sales; however, over the years thesales have been decreasing exponentially. Figure 2 presents the saleshistory of a very seasonal product, B. Here again, the monthly sales,averaged over a full year, 'decay' at a constant rate.

This behavior,whichwehaveobservedin a great number ofunpromotedproducts, leads us to introduce as a parameter the exponential SalesDecayConstant X;that is, the sales rate at time t of an unpromoted product isgiven by S(t) =S(O) exp(-Xt). In the examples above, the Sales DecayConstants are 0.24 per year and 0.06 per year for products A and B re-spectively. As might be expected, the sales decay rate ranges from largevalues for products that become quickly obsolescent or products in ahighly competitive market to almost zero for noncompetitive, well-estab-lished products.

Product C (Fig. 3) exhibits some interesting features when analyzedwith this parameter inmind. The salesof this product were 'decaying' at a


3/12

372 Vidale and Wolfe

constant rate (A=0.9 per year) up to the beginning of 1953, when anarticle favorable to the product appeared in a popular magazine of widecirculation. Sales increased by a factor of five within a month. Thislevel of sales, however, was not maintained, but began to decrease muchmore quickly ( A = 4.7 per year) than the original rate until it reached anew level, double that before the promotion. At this point, the Sales

1110090 ,

{XJO000 !/ \,000

I V \ .000

~ I\ ~,000 V t,000 ~

,000r~ ~\ I J I'

~ ~\

000 -,~I'\

ANNUAL AVEitA6,~~

OF"'aNT" L...... SALE6

, O C X l

60

10 ,

60

50

20 ,

101'150 1':l51 1':l51 1953 1':l54

Fig. 1. Unpromoted product A-sales history,Decay Constant returned to the original value of 0.9. Eight months later,the product was mentioned favorably in another popular magazine, and thesame phenomenon occurred, Clearly, we are dealing here with two classesof customers: those who were induced to purchase after reading the mag-azine articles, but who soon lost interest in the product; and the 'normal'customers, who behaved much like the original customer population, Botharticles succeeded in raising the number of 'normal' customers.


4/12

Sales Response to Advertising 373Saturation Level

The concept of Saturation Level is illustrated by the sales history ofproduct D, Fig. 4. This product was promoted continuously for one yearby weekly newspaper advertisements beginning in July 1954. In the firstsix months, sales rose 30 per cent and then leveled off, although the ad-vertising campaignwascontinued for another sixmonths. This additionaladvertising may have helped to maintain sales at the new level, but thiseffectcannot have been large, because the decay rate both beforeand after

.500.000

100.000

) A AV I/~ I/ ~ 1 /( h. . I . . . . A I !1(I \ r r-~ V \ ' v V

+ ~=~~ :~H~~E5 ' :~ :1

:300.000

: z 100,000. . . .~).~"~ 50,000~

30,000

20,000

1,)53 1,)54 1')55951 1,)52Fig. 2. Unpromoted product B-sales history.

the advertising campaign was small. We conclude that this campaigncould have been considerably shorter and equally effective, and that be-yond a certain point, it lost its value.

Figure 5 presents the sales history of product E. Because of thecomplexity of the sales responses, sales are here plotted on a cumulativescale.

Area 1 received a spot radio commercial campaign for six months . Beginning at the same time, Area 2 received the campaign for twelvemonths.


5/12

374 Vida le and Wolfe1 /> 5,000 c------c------~------_----~

3,000 I--- ~1 \2,000 I I ~' : \ _ -: \,000 ." . . . .00 ."..1 Z 800 ~ . " : . ., 700 0 600 ~

> - 50 0 t : . _-J ~. :: 400-. .~ -300 ~loa

100

~60.000

~'"~ 30.000> ..~" 20.000~

4fJoO I------------f--------------- ~-------- ----------i

1952 1955954Fig. 3. Product C-sales history.

50.000

1 / \ - - v- ~ r -7- '\1/\ I - - - - . . . A /I~ 1\/ \ jA~"ERtSI~6 CtMP~\6N

40.000

10.000

oA50NOJFIV\AMJJA50NOJfMAMJJA~ONll1~53 1954 1955

Fig. 4. Product D-sales history.


6/12

Sales Response to Advertising 375 At the end of the campaign in Area 1, Area 3 received the campaign forsix months. Area 4 was kept as control and received no promotion.

In Areas 1 and 2, sales increased approximately 150per cent over those inArea 4; the additional six months' promotion received by Area 2 did notincrease sales further. Area 3 experienceda similar sales increaseafter the

~-..a 15,000~>-~I-:~~ 10,000~- . . .. . . . . .~-..J: : : : ; ,~ 5,000

o

1 I . I- t- T Ar~a 1,--r--r-- LV-- o Are.a 2A Area '3 Vk~I- t- X Area 4 - VV/'V/ VV/ VV/ V

~V 1/II _ j _/; V// /V IIV V /V / V __ , __ ....-V V / , . . . . . . ~__..:~VV / -:, . . . . . .V/V / -VA : / ' " -~VJ:1V k - " LPVrJJASONOJFMAMJJASONO

1~54 1955TEST PERIOD 1 TEST PERIOD 2

Fig. 5. Product E-sales history.promotion started. Therefore, even though the advertising campaign waspostponed for sixmonths, it lost none of its effectiveness.

From the results exemplifiedin Figs. 4 and 5, we are led to describe theinteraction of advertising and sales in terms of a second parameter-theSaturation Level, M, or practical limit of sales that can be generated.This Saturation Level depends not onlyon the product beingpromoted, butalso on the advertising medium used; it represents the fraction of the


7/12

376 Vida te and Wolfe

market that the particular campaign can capture. This Saturation Levelcan often be raisedfurther by other advertising media.Response Constant

In addition to the Decay Constant and the Saturation Level, weneedathird parameter to describe the salesbehavior ofa product. WedefinetheResponse Constant, r, as the sales generated per advertising dollar when8=0. We note that the number of new customers who are potentialbuyers decreases as sales approach saturation. When advertising isdirected indiscriminately to both customers and noncustomers, the ef-fectiveness of each advertising dollar in obtaining new customers alsodecreasesas sales increase. In general, the salesgenerated per advertisingdollar, when sales are at a level 8, is given by reM-8)/M, where M isthe Saturation Level.

As an example, for product D the Saturation Level was $42,000permonth (see Fig. 4). The advertising expenditure was $5,000per month.In 1954,before the start of the advertising campaign, monthly sales aver-aged $29,000 or 70 per cent of the Saturation Level. The unsaturatedportion, or the percentage of the potential represented by noncustomers,was 30per cent. The new customers converted to the product as a resultof the July promotion increased sales by approximately $3000per month.The Response Constant was therefore r=($3000/mo)/(0.30X$5000)=2/mo.

MEASUREMENT OF PARAMETERSIN THE NEXT SECTION, we will present a model of the interaction of ad-vertising and sales, based on the three parameters: SalesDecay Constant,Saturation Level, and Response Constant. These parameters differ fromproduct to product and must therefore be determined separately for in-dividual products. The Sales Decay Constant can be measured from thesales data either before or after a promotion. The Saturation Level andResponse Constant can be determined froma detailed analysis of the saleshistory, or when necessary, experimentally. We have found that testpromotions, when carefully designedwith experimental controls and on asufficiently large scale, give results that are both significant and repro-ducible, though the degreeofaccuracy attainable is smaller than ordinarilyconsidered acceptable in many other fields of research. Product adver-tising, when effective,shows results within days or at most weeks, so pro-posedadvertising programs can be thoroughly pretested. When as large amarket share as possiblemust be captured before competing products aredeveloped and marketed, it may be necessary to foregopretests. In suchcases, rough estimates of the three parameters can be made from a knowl-edgeofpast performances ofsimilarproducts. Asthe campaign progresses


8/12

Sales Response to Advertising 377and the estimates of the parameters are improved, the campaign can bemodifiedaccordingly.

MATHEMATICAL MODELWEHAVESEENhat the response ofsales to a promotional campaign can bedescribed by three parameters: A , the exponential Sales Decay Constant,M, the Saturation Level, and r, the Response Constant.

A mathematical model of sales response to advertising, based on theseparameters, is represented by:

dS/dt= rA(t) (M -S)/M -AS, (1)where S is the rate of sales at time t, and A(t) is the rate of advertising ex-penditure. This equation has the following interpretation: the increasein the rate of sales,dS/dt, is proportional to the intensity ofthe advertisingeffort, A, reaching the fraction of potential customers, ( M - S)/M ,less the number of customers that are being lost, AS.

This modelhas been chosenbecause it describesin simplemathematicalterms our experimental observations. Undoubtedly the probability oflosing customers is decreased by advertising. Further experiments mayprove that rand M are altered by changes in market conditions, by com-peting advertising, and by the introduction of new products. However,every increase in complexity requires the introduction of one or more ad-ditional parameters into equation (1). Since this modelhas beensufficientto describe the observed phenomena to the degree of accuracy allowed bythe quality of our experimental data, there seems to be no reason at thistime to complicate the picture unnecessarily. As our knowledge of ad-vertising increases, it should be possible to improve this model and todevelop more sophisticated theories.

From equation (1)we can derive several results that haveprovedusefulin the design and evaluation ofadvertising campaigns:

Steadu-etaie 80lution.W e can determine the advertising effort requiredto maintain sales at a steady predetermined level by setting dS/dt=O.From equation (1), we then have A = (A ir) SM /(M -S). We see thatthe closer sales are to the saturation level M , and the larger the ratio Air,the more expensive it is to maintain the required sales rate.Solution of equation (1). For a constant rate, A, of advertising ex-penditure, maintained for time 1', the rate of sales is obtained by integra-tion of equation (1):

Set) = [M /(l+AM /rA)]{ 1_e-


9/12

378 Vida Ie and WolfeThe sales response to an advertising campaign ofconstant intensity and ofduration T is shown in Fig. 6.

The rate of sales increase is most rapid at t=O; as saturation, M, isapproached, this rate is reduced. This means that the first advertisingdollar expended is most effective,the seconddollar is next most effective,and so on. A second implication of this advertising model is that forequal expenditures, a protracted advertising campaign is more profitablethan a short, intense campaign. We have not yet tested this conclusionexperimentally.

Sales RateS (t)M ---------------------------------------

oT

TIME (t)Fig. 6. Sales response to an advertising campaign of duration T.

Advertising PulseMany advertising campaigns are short and very intense. To get an

expression for a single-pulse campaign of negligible duration we can in-tegrate equation (1) to obtain

(4)where 80 is the rate of sales immediately preceding the promotion and ais the total advertising expenditure. The immediate sales increase result-ing from the promotion is

8(0)-80= (M- 80)(1_e-ra/M).The total additional sales generated by this campaign aref' [8(0)-801 e-At dt=M ~80 (l_e-ra/M),which reduces to (ra/X)(M -80)/M for sales well below saturation. Thetotal extra sales generated by the advertising campaign are therefore the

(5)


10/12

Sales Response toAdvertising 379immediate sales increase, multiplied by the mean life of the product, X-1.Also, given a choice of several products, the advertising campaign willgenerate the most sales for the product with the largest value of(r/X )(M - So)/M.

ALLOCATION OF ADVERTISING BUDGETWEHAVEDISCUSSEDxperimental results of sales response to advertisingand have described a simplemathematical model that adequately fits ourobservations. Once the parameters are measured for individual products,the problems of advertising budget sizeand of the allocation of the budgetamong different products can be considered.

Advertising is a form of investment. Those products should be ad-vertised that will result in a return on capital invested equal to or greaterthan the returns from other possible investments, such as new equipmentand research.

As an example, let us consider the simple case of a family of productsthat might be advertised by short, intense campaigns. We define thefollowingquantities:

ak = total cost of the proposed advertising campaign for product k.Rk(i) =additional sales resulting from the advertising campaign.Ck(i) =rate of additional expenditures resulting from the advertising campaign.These include (a) the cost of the advertising campaign itself, (b) the cost ofmanufacturing and distributing the additional items sold.hreturn on capital invested in advertising product k. For example, $100 attime i1 is equivalent to $100 exp[Ik(i2-i1)] at time t2 .The sum total of expenditures incurred by the promotion of product kdiscounted at the rate Ik from the start of the advertising campaign

(t=O) is1 ' " Ck(t) e-Ikt dt.

The additional sales resulting from the advertising campaign, also dis-counted at the rate Ii, are

1 ' " Rk(t) e-Ikt dt.In order to determine the rate of return on capital invested in the promo-tion ofproduct k, weequate expenditures and salesincreases:

1 ' " Ck(t) e-Ikt dt= 1 ' " Rk(t) e-Ikt dt.Under the assumption that production and distribution costs are pro-portional to sales,we have

(6)


11/12

380 Vida Ie and Wolfe(7)

where !k is the ratio of production and distribution costs to selling price.Assuming that the rate of sales of the unpromoted product decays ex-ponentially at the rate ")..k, we have(8)

where RO k is the instantaneous sales increase resulting from the campaign.Substituting (7) and (8) into equation (6), we obtain+1 " " .f R -Akt -Ikt dt - 1 " " R -Xkt -Ikt dtak Jk O k e e - O k e e .o 0

Integrating and solving for h:h= (ROk /ak ) ( l- ! k) - ") .. k. (9 )

Itshould be noted that the relation between RO k and ak is not linear, so therate of return I is a function of the intensity of the advertising campaign.Once the values of Ik are known, one can in principle select the productsthat may be advertised profitably. The rate of return considered ac-ceptable by management varies considerably from company to company,but remains relatively constant in time.We see that the amount of advertising appropriate to each product,and consequently the total advertising appropriation, can be determinedonce the I are known.SUMMARY

IN SUMMARY, we wish to stress the following points:1. When carefully designed and executed, advertising experiments give resultsthat are both reliable and reproducible. The degree of accuracy attainable is,

however, considerably smaller than would be considered acceptable in many otherfields of research. Product advertising gives quick results; the pretesting ofproposed product advertising campaigns, therefore, is especially attractive.2. The response of sales to advertising varies widely from product to product,but some generalizations are possible. The response of individual products to anadvertising promotion may be characterized by two parameters: ResponseConstant and Saturation Level. A third parameter, the Sales Decay Constant,gives the rate at which customers are lost.3. A mathematical model of sales response, based on these three parameters,has proved useful in the analysis of advertising campaigns. By means ofthis modelone can compute the quantities needed to evaluate and compare alternate pro-motional campaigns.4. A knowledge of sales response to advertising for each product permits one to

evaluate the return that can be expected from capital invested in advertising foreach product. With this information it is then possible to select profitable ad-


12/12

Sales Response to Advertising 381vertising programs and to estimate the optimum total size of the advertisingbudget.

We do not know whether the model of sales response discussed in thispaper will prove applicable to all situations; our experience is limited to afew industries, and we have not tested all advertising media. It is our hopethat as these studies progress and as the volume of experimental datagrows, it will be possible to refine the model and thus increase its useful-ness.

We wish to express our appreciation to SHERMANKINGSBURY,GEORGEE. KIMBALL, and FRANK T. HULSWIT, who, in their studies of advertisingeffectiveness, first developed many of the ideas expressed in this paper andhelped to demonstrate the value of the operations-research approach tosales problems.

REFERENCES1. HORACEC. LEVINSON,"Experiences in Commercial Operations Research,"Opns. Res. 1,220 (1953).2. BERNARDO. KOOPMAN,"The Optimum Distribution of Effort," Opns. Res.

1, 52 (1953).3. JOHNF. MAGEE, "The Effect of Promotional Effort on Sales," Opns. Res. 1,64 (1953).4. ROBERTDORFMANANDPETERO. STEINER,"Optimal Advertising and OptimalQuality," Amer. Econ. Rev. 44, 5 (1954).5. R. S. WEINBERG,"Multiple Factor Break-Even Analysis," Opns. Res. 4, 152(1956).6. A. A. BROWN,F. T. HULSWIT,ANDJ. D. KETTELLE,"A Study of Sales Oper-ations,"Opns. Res. 4, 296 (1956).

vidale_wolfe

Documents

Transcript of vidale_wolfe