Resource Allocation: Marketing Engineering Technical Note 1

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1 Resource Allocaton: Marketng Engneerng Techncal Note 1 Table of contents Introducton Response Functons Specfcaton and Calbraton Optmzng Resource Deployment Call Plannng for a Salesperson Resource Plannng for Sales Force Management Summary Responses Introducton A well-desgned resource allocaton model enables an understandng of the ndvdual and combned effects of marketng resources (or marketng mx elements) such as advertsng, sales effort, or prce, on a response measure of nterest to the company (e.g., sales, proft, customer acquston, ROI), and the capablty to apply ths understandng to dentfy good ways to expend those resources. Resource allocaton across the marketng mx elements ntegrates three modelng concepts: (1) sales response modelng, (2) Estmaton/calbraton of marketng response functons, and (3) optmzng the use of marketng resources to maxmze one or more desrable response measures. For purposes of ths note, we focus on resources that can be contnuously vared (e.g., advertsng expendture, sales effort, web ste nvestment), rather than on resources that can only be vared only n a dscrete manner (e.g., new copy desgn, ntroducton of a new product). Response Functons Specfcaton and Calbraton At the heart of a resource allocaton system are response functons that represent the relatonshps between one or more marketng mx elements and the correspondng outcome measure n each sales entty of nterest. A sales entty s anythng wth whch we can assocate potental sales for the frm customer, 1 Ths techncal note s a supplement to Chapter 7 of Prncples of Marketng Engneerng, by Gary L. Llen, Arvnd Rangaswamy, and Arnaud De Bruyn (2007). (All rghts reserved) Gary L. Llen, Arvnd Rangaswamy, and Arnaud De Bruyn. Not to be re-produced wthout permsson. Vst for addtonal nformaton. 1

2 prospect, market segment, geographc area, product sold by the frm, and so forth. If the frm estmates response functons for each such sales entty, t can use these functons to calculate the levels of effort to allocate to each entty to maxmze profts or to acheve other objectves. The sum of the effort across a set of non-overlappng enttes s then the level of marketng effort or sales resources the frm needs. The frm can dvde ths total by the average effort (e.g., 750 sales calls per year) to estmate the amount of resources (e.g., salespeople) t needs. Specfcaton and calbraton of response models: There are many types of sales response functons used n marketng (see Response Modelng Marketng Engneerng Techncal Note) to model sales response n each sales entty. Typcally a non-lnear S-shaped response functon, such as the ADBUDG response model, s a good choce for representng marketng response to advertsng and sales effort. Before response models can be used for resource allocaton, they must be calbrated or estmated keepng n mnd the context n whch they are to be used. If, for example, the objectve s to determne the marketng budget for the sales force and the allocaton of the total sales force effort across products, then we need to estmate sales response functons that ndcate the future sales for each product under dfferent levels of effort the frm mght deploy on that product. There are broadly three approaches for estmatng response models: (1) statstcal estmaton usng hstorcal data of response behavor, (2) manageral judgment, and (3) expermentaton (more common among onlne frms). Often, a combnaton of methods (e.g., statstcal estmaton combned wth judgment) works best to account for both the endurng constrants of the marketplace, as well as the opportuntes afforded by the future. EXAMPLE: A common functonal form used n resource allocaton s the ADBUDG response model, whch has the followng functonal form: where c X r ( X ) = b + ( a b ), (1) c d + X =a sales entty, =1, 2, 3,..., I (# of sales enttes); 2

3 X =total effort devoted to sales entty durng a plannng perod measured n number of calls, ndexed so that current effort=1 (for smplcty we treat ths as a contnuously varyng quantty rather than as an nteger); r (X ) =ndexed level of sales at entty f the salesforce devotes X amount of effort to that entty; b a c d =mnmum sales that can be expected wth no sales effort allocated to sales entty ; =maxmum sales that can be expected wth an unlmted amount of sales effort allocated to sales entty ; =parameter that determnes the shape of r (X ) whether t s concave or S-shaped; and =an ndex of compettve effort levels drected toward sales entty (the larger ths value, the smaller the mpact of the frm s own sales effort on sales). On way to calbrate ths model s va nonlnear least squares regresson usng hstorcal data of both X and r(x) n each sales entty. Another approach s to use judgmental methods, whch nvolves askng experenced managers (e.g., from sales, marketng, or marketng research functons) what the response r(x) wll be for varous specfc levels of X. Often such calbraton s done wth reference to a base level of X=1, for whch response r(x) s 1, e.g., at current levels of effort, we expect to observe the current level of sales. Typcally, n judgmental calbraton, t s useful to obtan group consensus estmates for the response functons usng the Delph method (Armstrong 2001). Wth the Delph method, before askng for the judgmental estmates, t s useful to provde all the partcpants wth a summary of the hstorcal data pertanng to the entty for whch the sales response s to be obtaned. //end Example Optmzng Resource Deployment A response functon merely ndcates the response on an outcome measure that the frm s lkely to acheve at varous potental levels of effort deployment. By tself, t provdes no gudance on how much effort should be deployed to a 3

4 partcular entty. Typcally, a frm has many enttes competng for the same resource, and t has to evaluate alternatve ways of deployng the same resource across dfferent enttes. To do ths systematcally, we specfy an optmzaton model, whch allocates a resource across enttes to optmze a specfc objectve (e.g., short-term proft, customer retenton). There are many dfferent types of optmzaton models used n marketng (e.g., lnear programs, nonlnear optmzaton, nteger programs, stochastc optmzaton, mult- objectve optmzaton), each approprate n dfferent contexts. We llustrate resource optmzaton n the context of sales force effort allocaton n two dfferent contexts: (1) A sngle salesperson makng decsons about how much effort s/he should devote to each account (customer). (2) Company management decdng how bg a sales force t should have, and how t should deploy that total effort across products and markets. Call Plannng for a Salesperson CALLPLAN (Lodsh 1971, 1974) s an nteractve call-plannng system that helps salespeople to determne how many calls to make to each clent and prospect (equvalently, to each category of clents and prospects) n a gven tme perod to maxmze the returns from ther calls. The system determnes call frequences wth respect to an effort perod, whch s the plannng perod used by the salesperson (e.g., one quarter). The model s based on the assumpton that the expected sales to each clent and prospect over a response perod, whch s the plannng perod of the frm (e.g., a year), s a functon of the average number of calls per effort perod durng that response perod. The response perod selected should be long enough to accommodate potental carryover effects from each effort perod. Specfyng the response functons: We wll use a smple verson of CALLPLAN based on the ADBUDG response functon to llustrate the central ssues. CALLPLAN tres to develop an effectve way for the salesperson to allocate effort across the dfferent accounts. The model assumes that the salespeople seek to maxmze contrbuton (profts) from ther sellng efforts; however, they have lmted tme and therefore they wsh to use ths resource as effectvely as possble. A sales terrtory s assumed to be dvded nto mutually exclusve geographc areas (e.g., zp codes). The salesperson makes trps to some or all areas n the terrtory n each effort perod. In each trp to an area the salesperson ncurs varable costs for expense tems such as travel and lodgng. 4

5 In a trp to an area, the salesperson calls on any gven account at most once. Before we descrbe the formal model, we defne ts parameters: n j = number of trps per effort perod to area j, where j=1, 2, 3,..., J. Because the salesperson calls on an account at most once durng a trp, n j s also equal to the maxmum number of calls made to any account n terrtory j; c j = varable costs ncurred when makng a trp to area j; t = tme that the salesperson spends wth the customer when makng a call to account (t may be set to be the same for all customers); U j = tme t takes to get to area j; e = number of effort perods n a response perod (f the effort perod s a month and the response perod s a year, then e=12); T = total work tme avalable to a salesperson n an effort perod, whch ncludes both sellng and nonsellng tmes; a = a customer-specfc proft-adjustment factor that reflects the proft contrbuton of sales to that customer. r (X )= ADBUDG response model for each account (other concave or S- shaped functons can also be used). The optmzaton model maxmzes profts (Z) for a sngle sales terrtory takng nto account both the costs of vstng the accounts and the expected contrbuton from all the accounts and prospects: Fnd the set of X to maxmze total proft contrbuton margn Z = a r ( X ) e n jc j, (2) subject to t + n ju j X T, (3) j n j = max( X n geographc area j), (4) LB X UB (5) j Constrant (3) ensures that the total tme (call tme plus travel tme) used n 5

6 an effort perod does not exceed the tme avalable to the salesperson; constrant (4) equates the number of trps to terrtory j to the maxmum number of calls made to any specfc account n that terrtory, thus ensurng that n any trp to terrtory j the salesperson does not call on any account more than once; constrant (5) allows the salesperson to ncorporate judgment-based lower and upper bounds on the number of calls made to any account n an effort perod. Model usage: It s useful to frst run the model wth no upper bounds n constrant (5) and wth a lower bound of 0 for all. Then the model s lkely to suggest that the salesperson never call on some accounts and call on some accounts too often. The salesperson may feel that such an allocaton s not reasonable and can then specfy mnmum and maxmum constrants for each account to modfy these results. These judgments account for the effects of factors not explctly ncluded n the model. (For example, some accounts may be beta-test stes that help wth testng a new product before release. However, sales effort on those accounts may not necessarly lead to ncreased sales.) A salesperson should nclude both accounts and prospects n a callng portfolo. However, prospects typcally respond weakly to sales efforts as compared wth exstng accounts; therefore the model wll tend to exclude them from the callng plans t develops. One way to gve adequate treatment to both s to run the model separately for accounts and for prospects: Run the analyss for prospects by settng asde tme equal to T P <T n constrant (3) to be allocated to prospects. Do the same for accounts by settng asde tme equal to T A for exstng accounts such that T A +T P =T, the total tme avalable to the salesperson. A comparson of the results wth and wthout tme set asde for prospects shows how much of the current proft the salesperson s wllng to forgo to cultvate long-term prospects. EXAMPLE To understand the ncremental analyss the CALLPLAN model uses to determne the optmal allocaton of effort, consder a smple example wth four accounts, summarzed n Exhbt 1. Suppose that the salesperson s currently devotng 15 calls to these accounts as shown, brngng n total sales of $11,985. If the cost of a sngle sales call s $200, the net contrbuton s then $8,985. 6

7 EXHIBIT 1 Example of optmzaton procedure n CALLPLAN. The table at the top s a numercal representaton of sales-response functons n four accounts. The bar charts at the bottom show the current and model-recommended allocaton of effort to the four accounts when the salesperson makes a total of 15 calls. An optmzaton procedure would allocate the frst call to account 3, whch has the hghest margnal contrbuton ($3,600). It wll also allocate the second call to ths account, whch has the next hghest margnal contrbuton ($1,800). The thrd to the ffth calls wll be allocated to account 2 wth a total contrbuton of $3,350, the sxth call to account 3, the seventh and eghth calls to account 2 wth a total contrbuton of $1,140, the nnth to twelfth calls to account 1 wth a total contrbuton of $1,400, the thrteenth to account 2, the fourteenth to account 1, and the ffteenth call to account 2. Ths allocaton procedure 7

8 results n total contrbutons of $13,000 wth a net contrbuton (after payng for the sales calls) of $10,000, whch represents a 11.3 percent mprovement over the current net contrbuton of these 15 calls. Note that the model recommends makng no calls on account 4. The frm could use less costly methods such as telemarketng to contact such accounts. Note also that t would not pay to make any call whose margnal contrbuton would be less than $200, the cost of a call. Let us explore what would happen f the salesperson were able to make more than 15 calls. Then the eghteenth call wll be to account 4, wth a margnal contrbuton of $180. Thus the maxmum number of calls the salesperson makes to ths set of accounts should be 17. (If the salesperson makes only 15 calls to these accounts, the opportunty loss of not makng the sxteenth and seventeenth calls s equal to $25, the net contrbuton of makng the two addtonal calls. The sxteenth call would be to account 1, and the seventeenth to account 3.) Resource Plannng for Sales Force Management The salesforce management problem allocates the effort of the entre salesforce to sales enttes to maxmze frm profts over a plannng horzon, subject to several constrants. We call to the model below ReAllocator to focus attenton on the combnaton and szng and allocaton of effort. Each run of the model requres a constrant specfyng a proposed salesforce sze. Ths constrant ensures that the model allocates effort n the best way possble for a gven salesforce sze. The base model follows: Fnd the set of X s to I maxmze Z = r ( X ) S a CF(profts), (6) subject to = 1 I = 1 X e = F( salesforce sze constrant), (7) where S = forecasted sales for entty accordng to the strategc plan; 8

9 a = contrbuton margn per ncremental dollar of sales for sales entty ; C = full costs (salary, benefts, etc.) of a sngle salesperson; F = planned salesforce sze (number of salespeople); and e = planned deployment of sales effort to entty accordng to the strategc plan. r (X )= ADBUDG response model for each account (other concave or S- shaped functons can also be used). The base model gves the optmal allocaton of effort for any gven salesforce sze F. Ths model s then solved repeatedly for varous levels of F, and the frm should keep addng salespersons as long as the ncremental proft assocated wth each person s postve. At the optmal level of salesforce sze, the margnal proft of an addtonal salesperson s 0 (Exhbt 2). EXHIBIT 2 Ths graph shows how the results from ReAllocator can be organzed to ndcate (1) the opportunty cost (the shaded area) of mantanng the salesforce at the current level and (2) the requred change to the current salesforce sze to maxmze profts. 9

10 Constrant (7) can nclude more entty-level constrants. For example, the constrants mght nclude mnmum and maxmum levels of effort allocated to any partcular entty. The modfed constrant set can be specfed as follows: I = 1 X e F, (8) LB X e UB. (9) LB and UB are the lower and upper bounds on effort devoted to any partcular sales entty. For example, the frm mght specfy that total effort devoted to product A should not exceed the equvalent of 100 salespersons (UB) and be at least 50 (LB). Model usage: ReAllocator can be used both for determnng the sze of the sales force (F) as well as the allocaton of that total effort across products, markets, or other sales enttes. Indeed, the strength of the model s ts ablty to help management to determne both the total effort, as well as, the approprate ways to allocate that effort. The model can also be used to assess the overall value of the salesforce. It doesn t make sense to ncrease the sales force sze, f those salespeople are not utlzed for the maxmum beneft for the frm. In today s compettve envronment, frms must justfy ther nvestments n terms of ther opportunty costs. One way to meanngfully estmate opportunty cost n the context of salesforce nvestment s by computng the dfference between profts calculated for effort levels correspondng to the selected salesforce sze and the profts the frm would earn by expendng zero sales effort on all sales enttes (all upper bounds set to 0). In some stuatons, there wll be nteractons between the enttes of nterest, whch broadly fall n two categores: complementary effects (postve synerges) or substtuton effects (negatve synerges). For example, sales force effort on two complementary products wll lkely beneft both, whereas sales force effort on two substtutable products sold by the frm s lkely to cannbalze sales of both products. As another example, n the pharmaceutcal ndustry, the postve or negatve experence that specalsts have wth new drugs affects the prescrbng behavor of the much-larger populaton of general practtoners. Recognzng that phenomenon, many pharmaceutcal companes target key 10

11 specalsts wth promotons, hopng for postve spllover effects to the more general physcan populaton. One way to extend the Syntex resource allocaton model to account for nteractons s by ntroducng co-effcents, {b k }, nto the response model, where b k = effect that an ncremental dollar of spendng on sales entty k has on sales entty relatve to the drect effect of spendng n entty (1 > b k > 1). The restrcton on b k ensures that the absolute magntude of the complementarty or substtutablty effect s less than the drect effect. Then, ReAllocator s modfed as follows (parallelng equatons (6 9): Let X be the (ndexed) level of marketng resource (number of salespeople, $000 of ad spendng, etc.). The problem s then: Fnd the set of X s to MaxmzeZ = I r X + bk X k Sa d X e (10) = 1 k where b k s defned as above d s the cost per unt of X and the other terms are as defned earler. Agan, constrants of the form: I = 1 X e F (total resource constrant), and (11) LB X e UB (sales entty constrant) (12) can be mposed. Even wth these enhancements, ReAllocator has several lmtatons. It s best suted for repettve buyng stuatons where the number of calls made to accounts s an mportant determnant of sales. In repettve buyng stuatons 11

12 the purchase cycle s short, customers buy from an assortment of products, and the salesperson provdes a much more sophstcated verson of remnder advertsng than one gets from other meda such as TV. Here the regular contacts wth customers help cement relatonshps and allow the salesperson to recognze potental problems n advance and deal wth them. Some common examples of sales calls n repettve buyng stuatons are pharmaceutcal reps callng on physcans, packaged goods salespeople callng on grocery stores, agrcultural product reps callng on stores and farmers, and ndustral parts reps callng on dstrbutors. Summary In ths techncal note we descrbed the use of response models n resource allocaton, and llustrated ther applcaton n the context of sales effort allocaton. The approach descrbed here can be used for allocatng the overall marketng budget, or for allocatng a marketng mx element (e.g., meda spend) to dfferent products, markets, or other sales enttes. The basc concepts of market response modelng, calbraton/estmaton, and optmzaton of one or more objectves, can be used n addressng more complex problems n resource allocaton. There are many areas of marketng where resource allocaton models are becomng crtcal, ncludng shelf-space management, campagn plannng and management, meda plannng, and lead management, to name a few. References Armstrong, J. Scott, ed., 2001a, Prncples of Forecastng, Kluwer, Boston, Massachusetts. Lodsh, Leonard M., 1971, CALLPLAN: An nteractve salesman s call plannng system, Management Scence, Vol. 18, No. 4, Part 2 (December), pp Lodsh, Leonard M., 1974, `Vaguely rght approach to sales force allocatons, Harvard Busness Revew, Vol. 52, No. 1 (January February), pp

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