A User-Oriented Model for Sales Force Size, Product, And Market Allocation Decisions

7/27/2019 A User-Oriented Model for Sales Force Size, Product, And Market Allocation Decisions

1/10

A User-Oriented Model for Sales Force Size, Product, and Market Allocation DecisionsAuthor(s): Leonard M. LodishSource: Journal of Marketing, Vol. 44, No. 3 (Summer, 1980), pp. 70-78Published by: American Marketing AssociationStable URL: http://www.jstor.org/stable/1251113.

Accessed: 27/11/2013 08:30

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at.http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

.

American Marketing Associationis collaborating with JSTOR to digitize, preserve and extend access to

Journal of Marketing.

http://www.jstor.org
http://www.jstor.org/action/showPublisher?publisherCode=amahttp://www.jstor.org/stable/1251113?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/1251113?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=ama


2/10

LEONARD.LODISHA simple-to-understand and easy-to-implement model isdeveloped to handle decisions on sales force size, product,and market allocations. One firm's experience in using themodel for tactical allocation decisions and strategic salesforce restructuring is described.

USERORENTEDODEL O RS LES F OR C E S I Z E PRODUCT

A N D M RKET LLOC TIDECISIONS

M OST sales managers are concerned with jus-tifying their firm's investment in the salesforce. Do their salespeople "pay" for themselves?Do they need more people? Or less? A relateddecision is how best to allocate this total sales effortto products and various market segments servedby the firm. The sales effort allocation to productsis typically a negotiated compromise among productmanagers who compete for sales force attentionto their products. This article describes a relativelysimple-to-understand macro model which has beenused to help management with these decisions. Themodel builds up to the sales force size decision

by considering the sales response, by product, oftypical market segment members.

LeonardM. Lodishis Professor of Marketing,The Whar-ton School, Universityof Pennsylvania,Philadelphia.Theauthor acknowledges the help in model formulation andimplementation of Terry Overton, Jim Largent, RuthSmith, and Jan W. Bol. This research was supportedby Management Decision Systems, Inc.

PreviousResearch n SalesForce SizeModelsBecause this model was designed with easy, profit-able implementation as its goal, it occupies a middleground in relation to existing sales force size andproduct allocation models.Beswick and Cravens (1977) developed a salesforce size model based on sales response functionsfor geographic subareas (typically parts of existingterritories). Generally such subareas would not besplit between two salespeople. Their model wouldtypically involve much data collection and analysisbefore running, if the response functions weredetermined empirically.Attempting to develop subjective response func-tions for geographic subareas also would be aformidable undertaking. For example, if a firm has500 salespeople with an average of 10 subareas perterritory, subjective estimates of 5,000 differentsales response functions would be required.On the other hand, some sales forces are alreadyusing subjective sales response estimates of each

Journal of MarketingVol. 44 (Summer 1980), 70-78.0 / Journal of Marketing, Summer 1980

This content downloaded from 86.55.176.81 on Wed, 27 Nov 2013 08:30:02 AMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp


3/10

individualaccount to call effort in order to developimproved call frequency policies. For these firms,a by-product of developing these subjectively esti-mated account response functions is that they canbe used to build up the geographical subarea re-sponse functions needed for territoryalignmentandsales force size decisions (see Lodish 1971, 1974borGlazeandWeinberg1978 or examples). To utilizethese models to evaluate sales force size, withoututilizing their primary call frequency or territoryalignmentbenefits, is probably not cost effective.Previous Research n SalesForceProduct AllocationTwo management science models have been builtfor sales force allocation to products. In the contextof developing a generalmodel for sales force alloca-tion, Zoltners and Sinha (1979)have recently devel-oped a model conceptually very similar to thisauthor's. However, their solution procedures de-scribed in Sinha and Zoltners (1979) are quitedifferent.

Montgomery, Silk, and Zaragoza (1971) havedeveloped "Detailer," a model for allocatingsellingeffort, which was applied in the pharmaceuticalindustry. The models' decision variable is theproportion of physicians contacted who would bedetailed for a particularproduct, once per detailingperiod (typically a quarter). A detail is part of asales call discussinga particularproduct.The choiceof which particular physicians to call on was leftto the salesperson (subject to management guide-lines set outside the model). This choice capitalizeson the salesperson's knowledge of his/her terri-tories and allows freedom to manage personal time.The model, as presented, only considers policiesof complete coverage (detailing every consumer),half coverage, quarter coverage, and no detailing.The affect of detailing on the consumer is modeledutilizing a nonobservable construct called relativeexposure value which is a nonlinear function ofthe detailingpolicy. Accumulatedrelativeexposuresare modeled as an exponentially smoothed averageof relative exposures over time. Sales response isthen anonlinearfunctionof the accumulatedrelativeexposures. This model enables managementto eval-uate alternative dynamic policies such as pulsingversus continued detailing. See Hobday and Reah(1977)and Hamelsmith(1973)for uses of "Detailer"with different response functions.Our model takes a different view of manage-ment's fundamentalproblemsin sales force productallocation. We feel that the primaryissue is whichproducts are more (or less) responsive to detailing

effort to which marketsegments, e.g., "If we detailthis product to this segment twice as much asformerly, what will be the change in sales, oncethe new policy has had a chance to take effect?"The dynamics of such changes are a secondaryeffect and not modeled explicitly.Our model can thus be viewed as an evolutionof the Montgomery, Silk, and Zaragoza model toconsider market segmentation and sales force size,and to simplify its dynamic treatment.The resultingmodel is quite general and could be utilized by mostsales forces selling more than one product.The DecisionModelThe decision model has two components. The first,a predictive model, predicts the sales and profiteffects of a product allocation-sales force sizepolicy. The second is a search procedure to isolatemore profitable policies within constraints imposedby the firm.The PredictiveModelThismodel operatesat the level of marketsegments.These aredefined as mutuallyexclusive, collectivelyexhaustive subgroups of the total possible set ofpeople or firms on which the sales force can call.The model assumes that all members of a segmentwill respond similarlyon the average. The firm hasatrade-offin definingsegments for use in the model.The more ways management divides its market,the more precise will be the response estimates,but more work will be involved to make the esti-mates. One of the pharmaceutical firms used asalesperson's priority ranking as one of the seg-mentation criteria. The salespeople had prioritizedphysicians in their territoryinto quartiles based onprescribing behavior toward the firm's productclasses. Each quartile was treated as a separatesegment. This method of segmentation enables thismodel to utilize each salesperson's best knowledgeof his/her territory,similar o the "Detailer" model.The primary decision variable of the model,denoted MENp is the rate or number of mentions(details) per time period made for product p ona typical member of segment s by an averagesalesperson (See Montgomery, Silk and Zaragoza1971) for a discussion of the organizational andmanagement ssues of centralizationassumed in thistype of model). A mention is defined very generallyas the discussion of a product during a sales call.There is also a trade-off in determiningthe levelof detail to use in defining different products foruse by the model. In general, we have found thatfirmsfeel most comfortable with different products,

A User-Oriented Model / 71



4/10

if they have a different sales message. Thus, dif-ferent sizes or models of a generically similarproduct or product class would typically be consid-ered as one product by the model.Sales of the product to a segment are assumedto be responsive to the average levels of mentionsmade to a typical segment member over the timeframe considered. All sales response estimates forthe model are made as indices with respect to anormal level of yearly sales and a normal productmention policy. These are usually given as thecurrent levels or the current plans for next year.Specifically, denote RI,p (MENpS) as the responsechange (index) in sales of product p to segments over a time frame, if average mentions to a typicalmember of the segment for product p are MENp,s.The time frame used can be varied depending onthe planninghorizon utilized by the firm. Five pointson the response function are estimated by the firm'smanagementand smooth curves are fit to interpolatebetween the points. See Lodish (1971) for detailson this fitting procedure. Some of the details ofthe assumptionsnecessary for makingthe estimatesand how they were described to management inone application are shown in Appendix A.The applicationutilized a four-year time horizonbecause management did not change sales forcesize and product allocations very often. They feltthat the time for changes to take effect might beas long as two or threeyears for some large changes.Most other applications have had only a one-yeartime horizon and thus only one set of sales responseestimates instead of four. Like Montgomery, Silk,and Zaragoza (1971), we also assume there are nocross product sales effects. We differ in that weassume that the same product mention policy willbe followed over the total planning horizon. Asnoted, we do not have the flexibility to modeldynamic policies such as pulsing.In order to translatethe response indices to salesand profits, they must be multiplied by a "normal"sales level and a gross margin fraction. LetNSALESp, denote normal sales of product p tosegment s and let GMpdenote the gross marginof product p. For a given size sales force, theobjective of the firmis to maximize thegross margincontributed by the sales force over the planninghorizon.Maximize:

P sE E GMp NSA LESP *RIps (MENP) (1)

p=l s=lwhere P denotes the number of products and Sthe number of segments.

Constraints on the DecisionThe sales force is constrained in the above maxi-mization because they have a limited number oftotal calls available and because they can only makea small number of mentions per average call. LetMENPC, denote the average number of mentionsper average call on segment s and CALLSS denotethe average number of calls to be made on a typicalmember of segment s. For some segmentationschemes, the time that a typical member wouldhave to listen to a salesperson may vary, thus thenumber of productmentions per call may also vary.The number of average mentions for all productson a segment must be limited by the calls madeto that segment.

MEN,s < CALLSs? MENPCs (2)POn an individual call, it is assumed that a productcan only be mentioned once, thus:MENp,5 CALLS, (3)

The last constraintreflects the total call capacityof the sales force. Let NAs denote the number ofaccounts in segment s and let NP denote the numberof salespeople to be evaluated by the model. Al-ternative sales force sizes can be considered byjust changing the value of NP. Each average sales-person is assumed to be able to make MAXC callsin a period (typically one year). This maximumdepends on the typical travel time.CALLS NA s< MAXC NP

s(4)

The average incremental costs (both compensationand expenses) per person added to the force canbe subtracted from (1) to obtain a net incrementalprofit due to the sales force of size NP. This canvary as a function of the sales force size beingevaluated.The SolutionProcedureThe solution procedure has three parts. The firstinvolves obtaining a profit response function fordifferent level of calls on different segments. Thesefunctions are obtained by solving subproblems foroptimal numbers of mentions for a given numberof calls for all call levels possible in each segment.This method of solution is identical to the first partof CALLPLAN (see Lodish 1971).This incrementalanalysis routine is described in Appendix B.Once the response functions for calls on eachsegment have been determined, the same incremen-tal analysis routine can be used to solve for the

72 / Journal of Marketing, Summer 1980



5/10

TABLE 1Interactive Computer Session for a Sample Problem-- AllocateForWhich Year(s): > 4ForWhich Segment(s): > AllMaximumNo. of Salespeople to Allocate > 135Allocation of Calls to Specialities, Y1982

Marginal No. of TotalProfit People IncrementalStep No. Per Call Added Profit (000) Total People1 196 6.3 1,959 6.32 155 8.0 3,940 14.33 77 6.3 4,708 20.54 75 4.1 5,203 24.65 58 4.1 5,588 28.86 45.8 22.5 7,228 51.47 31.3 44.0 9,474 95.18 25.3 6.3 9,728 101.39 19.0 8.0 10,746 109.310 14.1 4.1 10,839 113.411 9.1 6.2 10,929 119.612 4.6 4.1 10,960 123.813 1.3 6.2 10,972 129.914 -1.4 6.2 10,959 136.1For Which Step Do You Wish to ReportDetailed Allocation? > 7Detailed Report of Allocation, Y1982People Allocated 95

Segment AProduct No. of Details Incremental ProfitA 2 768,090B 0 0C 4 595,195D 3 396,537E 5 940,584F 0 0G 0 0H 1 1,195,300I 1 763,790J 0 0Total 16 4,659,495Segment BNo. of Details67114

Incremental Profit597,2681,772,253102,7232,472,243

optimal number of calls to make on each segmentwithin constraint (4) on the total number of possiblecalls for the whole sales force. The third part ofthe solution procedure, solving for differentnumbers of salespeople, just implies that the incre-mental analysis for this second stage will stop atdifferent numbers of maximum calls which are tobe evaluated. Thus, once the first part of the solutionprocedure is completed and the sales responsefunctions for each segment to number of calls have

been determined, the computer time needed to findthe number of necessary calls for each segmentfor various sales force size levels is extremely small.Also, the profit associated with different numbersof people in the sales force is available quickly.Table 1 shows parts of the trace of an interactivecomputer session in which the solution procedurefor a real problem was run. This problem with foursegments and 23 product/segment combinations,took approximately five to 10 seconds of IBMA User-Oriented Model / 73

ProductKLMTotal



6/10

370/158 CPU time for stage one of the procedure.Stages two and three together took less than twoseconds. The products and segments have beencoded to protect confidentialities. Notice that theinteractivecomputerprogramallows the analyst thefreedom to look at theprofit and sales consequencesof many different sales force size levels and theninvestigate, in detail, the product segment alloca-tion policy that is assumed as part of each levelof sales force size.ImplementationDiscussionThis model has been implemented by three firms,includingone that had been using "Detailer." Mostof the model's usage has been in sales effortallocationto different products. Because of the verypolitically sensitive nature of sales force sizechanges, they areimplementedmuch less frequentlythan product/ segment allocation.

Input for the model is generally decided in thefollowing manner: Sheets like those in AppendixA (with typically only one or two different timehorizons) are filled out by all of the decision makersknowledgeable enough about the products and seg-ments in questionto makeintelligentdecisions. Eachperson first estimates all of the numbers separatelyfor each productand segment. Then all of the peoplewho have made estimates together view summarystatistics, such as the mean and 25% and 75%quartilesof theircolleagues answers. The managersthen discuss outliers and reasons for making theirresponse estimates. This "modified Delphi" tech-nique (Dalkey 1969)thenprescribesthat each personreestimate considering colleagues' comments.Sometimes the process will converge to responseestimates that all of the decision makers feel areappropriate. In other cases, two or three typicalresponse estimates for different groups of decisionmakers will be used in the model to test for sensitiv-ity of alternative assumptions on the model's rec-ommendations.When the model results are determined, thedecision makers know what caused the model'srecommendations.Because of its relativesimplicity,the decision makers consider the model to be nomore than a giant calculator evaluating alternativepolicies much more efficiently than they could. Useof the model does not stop the bargaining andnegotiatingthat typically goes on between differentmanagement groups who have different prioritiesin terms of products and market segments.However, the bargaining s done at a different level.Instead of negotiating over the outputs, the man-agers negotiate over the inputs, i.e., assumptions

about how the marketplace reacts to sales effort.In many cases, the managers realize that in orderto get as many mentions as they want for petproducts or segments, they have to make unreason-able assumptions about how responsive those areasare to sales effort. This is a very useful type of"learning."One Firm's ImplementationExperienceSome details and experiences of one firm's useof the model for decision support should help thereaderinterested in model implementation.In orderto disguise the firm and not change any substantivedetails, let us assume incorrectly that the firm sellsa wide line of package goods through food anddrug stores. Implementation of the model wascoordinatedby amanagementscientist who reportedto the corporatedirectorof marketingservices. Themodel was utilized differently for two differentcorporate sales force decisions: (1) yearly tacticalallocations of the sales force to products and storetypes (marketsegments) and (2) strategic decisionsinvolved in changing sales force size and composi-tion.TacticalAllocations to Products and MarketSegmentsYearly sales response estimates for the tacticalallocations were made by the following:

* Productmanagers estimatingfor allproductsexcept their own);* Group product managers;* Seniormarketingmanagers ncludingthe vicepresident, marketing;* Market researchers;* Senior sales management, including the vicepresident, sales;* Seven regional sales managers;and* Two district sales managers.

Each person's estimates were first reviewed bythe coordinator for internal consistency to makesurethatthe estimatorcorrectly understoodhis task.Any problems were discussed with the estimatorand estimates were redone.Next, estimates of all the regional and districtsalespeople were averaged, as were those of themarketresearchers, the product managers, and thegroupproductmanagers.Seniormarketingand salesmanagement's estimates were not averagedor com-bined. Allocations were then performed for eightdifferent response assumptions; those of middlesales management,productmanagementandmarket




7/10

research, group product management, and five in-dividual senior marketingor sales managers.There was much commonality in the estimatesof all people in the relative responsiveness, butnot necessarily in the absolute responsiveness, i.e.,most groups agreed that product A was more re-sponsive than product B to an increased level ofproduct mentions, but sometimes disagreed on themagnitude of the sales response difference.However, when allocating a fixed size salespersonresource, only the relative differences will affectthe allocation.Thus, rather handoingDelphiroundsto achieve commonality on the response estimates,the coordinator looked directly for commonality inproduct/segment allocations based upon those re-sponse estimates. For some product segments therewas a general agreement that more or less saleseffort was needed. The coordinator used theseallocations to develop a recommendation for a"consensus" acceptable to the estimators.That recommendation, as well as the individualallocations for each of the eight groups, was thenpresented to the group product managers responsi-ble for an allocation recommendation to seniormanagement. For the past two years, actual salesforce allocations have been in the "consensus"direction, but not as pronounced in their changes,i.e., if the consensus increase was 30% in oneproduct's effort, the actual implemented increasemighthave been 15%.This is typical of a conserva-tive, risk averse approach to management. Thereis no explicit treatment of risk or uncertainty inthese models. The conservative management re-sponse was therefore appropriate.StrategicSales Force RestructuringWhen the model was used for strategic purposes,the decision makersneeded to agreeon both relativeand absolute sales response estimates because mar-ginal revenue minus marginal costs were beingcalculated for different sales force sizes and config-urations. The problem that prompted the strategicuse of the model was an inability of the sales forceto call as often on high volume stores as the tacticalallocation model (and management) would haveliked. Some of the store managersjust would notlet salespeople in as often as the salespeople wouldhave liked. The strategic question, then, was whatwould be the sales and profit implications and thesales force size implications if the maximum callconstraint on some segments could be alleviated?This could be done by two different salespeoplerepresentingdifferent products calling on the samestore.Because the separation and enlargement of the

sales force was a highly volatile political issue, onlysales management (district, regional, and senior)was involved in parameterizingthe model. In thisuse, two Delphi rounds were required to achievearesponse consensus of management.The responseestimates were made with both three- and five-yeartime horizons. The five-year horizon was utilizedfor most runs,because preliminaryrunsof the modelshowed that effort for new products would almostexhaust the present sales force after three years.The model runs showed that only if the calls peraccount constraint could be eliminated, would allthe products achieve the effort needed to maximizetheir profits.The average cost per call was increased slightlyand the average calls per salesperson decreasedslightly to reflect the increase in travel costs andtime required if a second sales force were inau-gurated.Because manyof the assumptionsabouta secondsales force (costs, ability to see retailers, relativeeffectiveness percall, and administrative easibility)were not very certain, the sales managers recom-mended experimenting with a second force in tworegions (out of eight) for two years with the restof the companyas acontrol. One of thejustificationsfor this experiment (actually more of a nationalroll out) given to senior managementwas the modelruns with input describing the two sales forces.Senior management (having used the model fortactical decisions) viewed the model as addingcredibility to the requests of sales management.After one year of the experiment, the model wouldbe updated to reflect experience with the separatesales forces. The model runs would then be usedtactically to help adjust the roll out of the secondsales force.Model DiscussionLimitationsAs described earlier, some trade-offs were madein orderto develop a model that could be profitablyimplemented. The macro model does not take intoaccount detailedphenomenasuch as pulsingof calls,or combining accounts into geographicalareas thatare visited on the same trip. Because it takesadvantage of economies of scale, the solutionprocedure employed will not generate optimalsolu-tions for every possible level of sales force size.However, because of the simplifications, manage-ment is able to relatively easily generate inputs forthe model and consider importantphenomena. Theturnaround ime to investigate alternative assump-tions using the model is minimal.

A User-Oriented Model / 75



8/10

The neglect of detailed treatmentof travel timeandcosts, andcombiningaccounts intogeographicalareas is not very serious at the macro planninglevel. Along with compensation, the sales costs persalesperson which is subtracted from (1) includesaveragetravelandentertainmentcosts. The changesin these average costs over the total force as aresult of changes in the product/ segment allocationfor the same size of sales force will usually bequite minor. If some salesperson's expenses go up,others will go down. Similarly, the maximumaverage calls per salesperson per period includesan implicit consideration of the average amount oftraveltimeavailablepersalesperson. This maximumcalls per salesperson is typically obtained by ana-lyzing past data from salesperson's call reports andaveraging the calls actually reported for a timeperiod. For a similar-sized sales force, changes inthe product/segment allocation will cause somesalespeople's travel time to go up and others togo down. The average number of calls availabledoes not change very much.However, as in the case of the "package goods"markets, if the sales force size is changed signifi-cantly, then changes in the travel time and costsmay become more pronounced. If the sales forcesize is decreased significantly, travel time as afraction of total time and costs per salesperson willtypically increase because a smaller number ofpeople are covering the same area. Conversely, alarge increase in force size will be associated withsmaller travel time and costs per salesperson. Themodel can be changed to handle this phenomenonby changing MAXC and the costs per salespersonto be functions of the sales force size evaluated.In the majority of applications, this has not beennecessary because feasible size changes consideredby management have been in ranges where thedifferences in travel time and costs were not be-lieved to be very different from current averages.The ResponseEstimatesA natural question about this procedure is "howgood are the response estimates?" Ourbest answeris "better than nothing " This procedure forcesmanagement to explicitly consider the sales andprofit effects of alternativeproduct/segment effortallocations. The final choice of allocation is madeconsistently with these assumptions. When avail-able, empirical evidence on response functions canbe very useful in aiding management in their esti-mates. This procedure is preferable to a situationwhere managementmakes decisions which may beinconsistent with its assumptions, by using pastdecisions or rules of thumb as a guide. Because

manyother elements, both externallyandinternally,can affect sales by segment from year to year itis very difficult to validate statistically these as-sumptions. However, as discussed below, trackingcan possibly help managersto update their intuitionabout sales response.In contrast to the test versus control situationwhere Fudge and Lodish (1977)estimatedthe incre-mental effect on profitability of salespeople usinga planning model similar to this one to help inindividual call frequency planning, it is impossiblehere, except in a controlled experiment, to directlyestimate what would have happened had manage-ment not used the model. Managementof the threefirms where the model has been applied have feltthe investment in time and money necessary toutilize the model was sufficiently valuable that theyhave decided to use the model each time newplanning and budgeting decisions must be made.Two of the firms have used the model at least twoyears in a row. During the second year, the firsttopic of conversation among the managers doingthe input is how good were estimates last year ofwhat would happenduringthis year for the detailingpolicies that were adopted.AppendixA: AbridgedDescriptionofthe Input Requiredfor the ModelinOne Application n the PharmaceuticalIndustryGuidelinesfor QuestionnaireCompletionWhat You Are Asked To DoFor each pertinentproduct in our marketsegments,you will be asked to forecast what would happento our sales over a four-year period if one of fivecall policies is followed.How Should You Go About Making Up ForecastsThe questionnaire is designed for you to do allforecasts in terms of an index. The starting pointfor the index is always 100. I have filled the indexin for 1979next to the call policy which most closelymatches our 1978 policy. For your assistance, Ihave indicated below each year what the indexwould be if we kept pace with marketgrowth (i.e.,there is no share increase or decrease). I suggestthe following system which will facilitateforecastingin a logical fashion with a minimumof effort.

1. Start with the current level, then the zerolevel, saturation evel andthe other two policylevels.2. For each level ask yourself two questions:76 / Journal of Marketing, Summer 1980



9/10

TABLE A-1ProductA, Market1Estimated MarketShare:Our CurrentShare: 63%OurPrincipalCompetitors X, Y, Z

'79$5,050,000Zero Level SLevel 1 (2 Details) SLevel 2 (4 Details) SLevel 3 (6 Details) SSaturation Level S

'76$3,500,000

'80$5,707,000

Year1ales =ales =ales = 100ales -ales =

'77$3,955,000

'81$6,449,000

Year 2

Growth Rate = 13%/yr.'78

$4,469,150

Year 3'82

$7,287,000Year4

a. If we follow this policy for four years,what will our market share be in the fourthyear?b. Starting with 1978's market share, howquickly will it increase or decrease to theending level?

The market shares' increases can then be translatedto the indexes. Example: Product A (see TableA-I). Starting with the present call level, one mayforecast in view of our present share, followingthe present call policy of four details would maintainour share at current levels. Therefore, the forecastfor level two would be:

The same procedure could be followed for otherlevels and other products.What Assumptions Should You Make As You DoYour Questionnaire

1. Assume that competitive activity remains atpresent levels.2. Assume that the relationship between personaland nonpersonal promotion expenditure levelsremains the same.3. Remember that for many of the markets, onlya portion of the business is up for grabs eachyear.

100 113 128 144Going next to the zero level, one may concludethat if we eliminated all personal promotion of theproduct, our share would drop from 63% to 50%at the end of four years. Translated into the index,we would expect the share to drop about 13% sothe index for year four would be 115 (i.e., 0.87x 144). Now that we've forecasted how much theshare would decline, the next question is how fast?Will it drop off faster at the beginning, at the end,or will the decline be steady? In this case, onemight guess that since most of each year's businessis new scripts, each year we would gradually loseabout two share points. This would lead to a forecastfor level zero of:

Year I Year2 Year3 Year4161 /59 /57 155Level0 97 - x 100 106 x 113) 116-x 128 125(-x 14463 \3 63 \63

AppendixB: The IncrementalAnalysisRoutineAppliedto ThisModelPart 1 of the solution procedure solves the followingproblem many times for each possible level of callsc for each segment s. Find MENps to maximize:p

GM,*NSA LES, RI (MEN,,)p=l = VAL,(c) (B1)subject to:

pMEN,, c MENPC,p=l

MENps< c(B2)(B3)

VAL (c) is thus the maximum value of profit ofhaving c calls made on segment s.Part 1 is "loosely" solved by incremental analy-A User-Oriented Model / 77

Year 2 (4 Details)VYear 1 YV-ar 3 VYSar YeVar AI



10/10

sis. Each RIp , function is approximated by a piece-wise linear, concave function RIps which is alwaysabove or touching the original function at integervalues. See Lodish (1971, p. 30-31) for an illustrationand details of the approximation.The incremental analysis routine allocates men-tions to each product incrementally using the stepsof the RI',s function as its guide. Mentions arefirst allocated to the product with the highest slopeof RIp,, (multiplied by NSALES,p GMp) until theslope changes or until c mentions are allocated forthe product p.The incremental slope for this product is thenchanged to the next slope on the RI' curve. Mentionsare again allocated to the product (either the sameone or a different one) with highest slope until eitherthe slope changes or a total of c mentions havebeen allocated for the product. The routine stopswhen c times the number of mentions meets orexceeds C MENPC,. Note that for large valuesof c, the incremental analysis also obtains valuesfor part 1 for smaller values of c, thus limitingthe computer time for the solution.Part 2 solves the following problem: Find

CALLS, for each segment s to maximize:sE VALs (CALLSs)

s=1Subject to:

ss CALLS -NAs-MAXC NPs=l

(B4)

(B5)The solution procedure to part 2 is identical topart 1, except that calls rather than mentions areincrementally added. A cost per call can be sub-tracted from (B4) if that is needed with no changein methodology.As shown in Lodish (1971), for the levels ofcalls allocated by the incremental analysis, thesolution is optimal. However, because the routinealways takes advantage of economies of scale andallocates calls rather than people, the number ofpeople allocated may be slightly over or under theoriginal constraints. If the routine allocates a verydifferent number of people, it is because the econo-mies of scale make it worthwhile, i.e., a segmenthas increasing returns to manpower additions.

REFERENCESBeswick, C. A. and D. Cravens (1977), "A Multi-Stage

Decision Model for Sales Force Management," Journalof Marketing Research, 14 (May), 135-144.Dalkey, N. C. (1969), The Delphi Method: An ExperimentalStudy of Group Opinion, Santa Monica, CA: Rand,RM-5888 PR (June).Fudge, W. and L. Lodish (1977), "Evaluation of the Effec-tiveness of a Model Based Salesman's Planning Systemby Field Experimentation," Interfaces, 8 (November),97-106.Glaze, T. and C. B. Weinberg (1978), "A Sales TerritoryAlignment Program and Account Planning System,"working paper, Stanford, CA: Stanford University.Hamelsmith, N. (1973), "Diagnostic Models in ManagementLearning," in Proceedings XX, International Meeting ofthe Institute of Management Science, E. Shlifer, ed.,Tel Aviv, Israel.Hobday, C. F. and G. R. Reah (1977), "Experience in theDevelopment and Application of the Multi-Product SalesForce Allocation Model," in Entscherdungshilfen imMarketing, R. Kohler and H. Zimmerman, eds., Stuttgart:C. E. Poeschel Verlag, 211-232.

Lodish, L. M. (1971), "CALLPLAN: An Interactive Sales-man's Call Planning System," Management Science, 18(December), 25-40.(1974), "A Vaguely Right Approach to Sales ForceAllocation Decisions," Harvard Business Review, 52(January-February), 119-124.(1974b), "Sales Territory Alignment to MaximizeProfit," Journal of Marketing Research, 12 (February),30-36.

Montgomery, D., A. Silk, and C. Zaragoza (1971), "AMultiple Product Sales Force Allocation Model," Man-agement Science, 18 (December), 3-24.Sinha, P. and A. A. Zoltners (1979), "Integer ProgrammingModel and Algorithmic Evolution: A Case from SalesResource Allocation," working paper, Evanston, IL:Graduate School of Management, Northwestern Univer-sity.Zoltners, A. A. and P. Sinha (1979), "Integer ProgrammingModels for Sales Resource Allocation," working paper78-49, Evanston, IL: Graduate School of Management,Northwestern University.


This content downloaded from 86 55 176 81 on Wed 27 Nov 2013 08:30:02 AM
http://www.jstor.org/page/info/about/policies/terms.jsp

A User-Oriented Model for Sales Force Size, Product, And Market Allocation Decisions

Documents

Transcript of A User-Oriented Model for Sales Force Size, Product, And Market Allocation Decisions