CAPPLAN: a decision-support system for planning the pricing and sales effort policy of a salesforce

Transcription

1 of Marketng 68 CAPPLAN a decson-support system for plannng the prcng and sales effort polcy of a salesforce Sönke Albers Unversty of Kel, Kel, Germany European of Marketng, Vol. 30 No. 7, 1996, pp MCB Unversty Press, The problem If a frm sells a certan product mx through a salesforce to heterogeneous accounts, t s faced wth the problem of optmal allocaton of sellng effort across accounts. Zoltners and Snha (1980) have surveyed models for adng ths decson, ncludng the popular CALLPLAN model by Lodsh (1971). Furthermore, t s a common marketng practce n a varety of ndustral and nsttutonal marketng stuatons as well as n sales of consumer goods wthn channels of dstrbuton to delegate some prce-settng authorty to the salesforce (Stephenson et al., 1979). Ths mples that the salespeople can make use of ther specfc knowledge regardng the prce responsveness of each customer n order to negotate customer-specfc prces optmally. Lal (1986) presents some detaled examples n whch such a dfferentaton of prces s usual. Now, f sales management has as much nformaton about the sellng envronment as ts salespeople, t has no reason to delegate the prcng responsblty. In ths stuaton, frms need an optmzaton model for jontly determnng prce levels as well as sellng effort levels. So far, no such model has been proposed n the lterature exstng on ths subject. One reason mght be that, under specfc condtons, both nstruments can be optmzed ndependently (Srnvasran, 1981). If, however, producton costs per unt ncrease wth ncreasng levels of requred producton capacty, then both marketng nstruments become nterrelated. To address ths problem, the development of the decson-support system CAPPLAN (Call and Prce Plannng) was undertaken. The second and thrd sectons of ths paper are devoted to a dscusson of the proposed response functon and the method of estmatng ts parameters. A formal descrpton of the decson model s then gven, and a smple heurstc based on ncremental analyss s provded for the resultng optmzaton task. The paper concludes wth experences from actual applcaton of the system at an ndustral photo laboratory offerng the development of flm and the producton of prnts through a varety of retalers.

2 Sales response functon The core element of CAPPLAN s the sales response functon dependent on prce and the number of calls as operatonalzaton of sellng effort. As both nstruments should be dfferentated across accounts or account groups, CAPPLAN operates wth ndvdual response functons. We have chosen a multplcatve, exponentally weghted response functon wth zero-call sales and asymmetrc response to ncreases and decreases n both prce and the number of calls CAPPLAN a decson-support system 69 h p x( h, p) = z S + ( z) S β η 1 B Q ( I), ( 1) quantty current quantty nfluence nfluence of sales of sales of calls of prce β = η = β β η η f h f h B > B D I f p f p Q > Q D I ( I), ( 2) ( I). ( 3) I Index set of account groups ( ndex). h Actual mean number of calls for one account of the th group. p Actual mean reference prce for the th account group. x (h, p ) Quantty of sales wth an account of the th group dependng on number of calls h and prce p. S Reference (current) quantty of sales wth the th account group as a result of h = B and p = Q. B Reference (current) number of calls for one account of the th group. Q Reference (current) reference prce for the th account group. z, β D, β I, η D, η I r Parameters to be estmated that may be nterpreted as follows z Fracton of S that can be sold wthout calls (h = 0) at the current prce of p = Q (zero-call sales). β D, β I Elastcty of effort dependng on sales wth the th account group, wth respect to a decrease (D) or an ncrease (I) n the current number of calls. η D, η I Elastcty of sales wth the th account group, wth respect to a decrease (D) or an ncrease (I) n the current prce.

3 of Marketng 70 In order to avod complex mult-perod, stochastc models, t s assumed that the response s the long-run response and determnstc. Due to the mpossblty of observng the sellng effort and negotated prces of compettors, no compettve effect s consdered n the response functon. All these assumptons are normal wthn the salesforce lterature (Lodsh, 1971; Mantrala et al., 1994). Furthermore, the response may have zero-call sales (z. S ) as suggested by Lodsh (1971), thereby encompassng the nfluence of other marketng nstruments. Functon (1) dffers from the one n CALLPLAN (Lodsh, 1971) by workng wth a concave rather than an S-shaped form because t represents the aggregate of ndvdual accounts sales response functons. Even when the latter are S-shaped, the aggregate response functon s approxmately concave when effort s always optmally allocated across accounts (Mantrala et al., 1992). The multplcatve form of (1) allows for mplct and symmetrc response nteracton effects between prce and callng effort. A property such as ths s necessary because sales losses owng to very hgh prces cannot be compensated for fully by gans n sales from very ntensve callng effort. Response functon (1) offers another attractve property, namely, t always passes through the pont currently realzed. If h = B and p = Q, then x (h, p ) = S by constructon. Ths enables management to compare the current and recommended polces easly, thereby ncreasng ts acceptablty. Workng wth such a functonal form also allows for the specfcaton of dfferent elastctes of sales wth respect to ether a decrease or an ncrease n the level of the marketng nstruments. Such an asymmetrc response s descrbed n Smon (1989) regardng the prce. Smlarly, I have very often found n practcal applcatons that sales management beleved that decreasng callng effort would cause more sales varaton than ncreasng callng effort. To summarze, CAPPLAN s based on a multplcatve, exponentally weghted response functon that s very popular n marketng because t s parsmonous, exhbts decreasng margnal returns and allows for a response nteracton between marketng nstruments (Hanssens et al., 1990). However, t dffers from the smple multplcatve functonal form by consderng a constant sales response to zero-calls, asymmetrc elastctes for decreases and ncreases n marketng nstruments and an mplct scalng parameter α = B β.q η ( I). Estmaton of the parameter values When applyng response functon (1), the values of ts parameters z, β D, β I, η D, η I ( I) must be estmated. In general, the most desrable dervaton thereof from observed tme seres or cross-sectonal data (Naert and Weverbergh, 1981) s not possble because the correspondng data are usually not avalable. Ths s even more true for expermental data. It s assumed that management has enough experence and ntmate knowledge of the market to be capable of estmatng the ncrease or decrease n sales as a consequence of a varaton of prces and callng effort (Lodsh et al., 1988). Prevous studes (Fudge and Lodsh, 1977; McIntyre, 1982) have shown that decsons can ndeed be

4 mproved by systems that rely on subjectve estmates, especally f they are used for allocaton decsons, whch s the case here. The dervaton of the parameter values can be smplfed by decomposng the response functon nto separate functons wth respect to prce and callng effort. Ths s possble f one of the nstruments s set at ts current level, such that the correspondng elastcty expresson s equal to one and cancels out. In the case of h = B we obtan CAPPLAN a decson-support system 71 x( P) p = S Q Here, a response functon expressed n relatve terms s arrved at, wth sales (x ) relatve to current sales (S ) dependng on prce (p ) relatve to current prce (Q ). For applcaton purposes, t s proposed to ask the management to gve estmates on x (p )/S for at least sx prce levels (.e. p /Q = 80 per cent, 90 per cent, 95 per cent, 105 per cent, 110 per cent, and 120 per cent) whle calculatng S from the frm s nternal fles. The frst three and last three estmates serve as data ponts for a non-lnear regresson, to obtan η D and η I, respectvely. Ths consttutes an mprovement over more common approaches where the number of pont estmates equals the number of parameter values, whch always results n a pseudo-perfect ft. Here, the estmaton procedure provdes 3 (ponts) 1 (parameter) = 2 degrees of freedom, so that the error varance and thereby the approprateness of the functon s shape can be assessed (Naert and Weverbergh, 1981). The solated response functon wth respect to callng effort can be obtaned by settng p = Q, such that formula (1) smplfes to x ( h )/ S z 1 z η h = B β ( I). ( 4) ( I). ( 5) Analogous to the estmaton of the parameter values of (4), t s proposed agan to ask for subjectve estmates on x (h )/S for at least sx callng effort levels, and to estmate the values of β D and β I from separate non-lnear regressons regardng the respectve three ponts of decrease and ncrease n callng effort. In addton, management must provde nput on the relatve number of unts that can be sold even where the frm reduces ts callng effort to zero. Formal descrpton of the decson model On the bass of response functon (1) wth (2) and (3), a decson model s formulated whch allows for a dfferentaton of prces and an allocaton of callng effort across groups of accounts. A stuaton s examned n whch there s an already exstng salesforce wth a gven workng-tme capacty. As decsons on the prce levels may have consderable nfluence on the requred producton capacty, a correspondng constrant s employed. However, whle

5 of Marketng 72 ths capacty can be vared, t causes ncreasng unt cost c(cap) over ncreased producton capacty. More formally, we encounter the followng proft maxmzaton problem G( CAP, WT) = ( p c( CAP)) x ( p, h ) max! ( 6) I I I proft parametrc contrbuton quantty of n CAP and WT per unt sales subject to scarce resources x ( p, h ) CAP (producton capacty), (7) a t h WT (workng-tme capacty). (8) In order to obtan meanngful solutons that wll be trusted by management, the levels of prce and number of calls are constraned between a lower and an upper bound whch are not formalzed here. c(cap) Unt cost functon ncreasng n producton capacty CAP. a Number of accounts composng the th account group. t WT Length of one call to an account of the th group. Maxmum total workng tme that can be devoted to callng by all salespeople. The decson model s formulated for the general case of dfferentatng prces and callng effort across groups of accounts. In many cases, the number of accounts s too large to allow for the estmaton of ndvdual sales response functons per each account. Therefore, the clusterng of accounts wth smlar response functons and the applcaton of the same polcy to all accounts wth such clusters (groups) s unavodable. However, the case of ndvdual accounts can be handled by settng a = 1 ( I). The formulaton of (6)-(8) shows that the decson maker really faces two dfferent types of problem. For fxed capacty levels CAP and WT, there s an allocaton/dfferentaton problem. Here, only the relatve values of the decson varables (prce and number of calls) across the dfferent account groups are of nterest, gven the utlzaton of a certan capacty level. Ths s rather an operatve plannng problem. However, f one ntends to vary the levels of CAP and WT, one encounters dfferent absolute values for prce and the number of calls for each account group, respectvely. Ths problem has a more strategc character, because t requres the evaluaton of nvestments wth long-term effects and sde-effects not modelled n (6)-(8). Moreover, the assessment here must be based on less relable nformaton. Therefore, CAPPLAN offers the opton of a parametrc optmzaton, allowng for evaluaton of how the dfferentaton of prces and the allocaton of calls change over dfferent capacty levels. Ths nformaton, then, provdes management wth the nput necessary

6 for decdng on possble nvestments n the enlargement of the producton capacty level. In the development of CAPPLAN, some trade-offs were made n order to arrve at a decson-support system that can be mplemented proftably. Frst, the response functon has a smple functonal form and does not allow the exploraton of dynamc and compettve polces. Second, the model s formulated at the market segment level, such that t s not possble to consder the combnaton of accounts nto geographcal areas that are vsted on the same trp. As a consequence thereof, a detaled treatment of travel tme and costs s neglected. As long as management does not want to change salesforce sze, such a smplfcaton s not crucal, as Lodsh (1980) has already ponted out for a smlar model for callng-effort allocaton. Fnally, t must be stressed that c(cap) may have any shape and s assumed to be a non-convex and noncontnuous arbtrary functon. CAPPLAN a decson-support system 73 A heurstc procedure for searchng for mproved solutons The applcaton of a standard non-lnear programmng algorthm to our decson problem (6)-(8) appears mpossble because the objectve functon mght not be concave, s not dfferentable owng to the asymmetrc elastctes, and s composed of both contnuous varable (prces) and nteger varables (number of calls). Although a specal, exact optmzaton algorthm mght eventually be constructed, t was decded that a specal purpose heurstc whch systematcally searches for mproved solutons should be developed. Because of the requrement for a parametrc optmzaton and the non-convexty of c(cap), any exact optmzaton algorthm would have to solve the problem for a large number of dscrete levels of CAP, whch would consume an unreasonably hgh amount of CPU-tme. Furthermore, management does not ntend automatcally to apply the soluton n practce. Rather, t wants to gan some nsght whch would be merged wth conclusons from other aspects that are beyond the scope of ths model. The addtonal work and cost of exact optmzaton are therefore dffcult to justfy, whereas a heurstc provdes a better beneft-cost rato. Parametrcally optmal solutons for a whole set of levels of CAP and WT can be provded n an effcent way only by procedures bult on the prncples of ncremental analyss. The basc dea of the heurstc s a decomposton of the decson model nto the followng two sub-problems (1) PRICE Heurstcally dfferentates prce wth number of calls pre-specfed by the user; (2) NCALL Optmzes the allocaton of calls wth prces pre-specfed by the user. The ncremental analyss n PRICE starts wth the hghest acceptable prce levels per account group, leadng to the lowest producton capacty requrement. In every teraton, the algorthm searches for the partcular prce reducton over account groups that offers the hghest ncrease n proft contrbuton per addtonal unt of producton capacty requred. Ths s

7 of Marketng 74 executed enumeratvely owng to the non-concave and non-dfferentable response functons. The procedure contnues untl all prces have reached ther lower bounds. The ncremental analyss n NCALL s smlar to PRICE. It starts wth the lowest acceptable number of calls per account group, leadng to the lowest workng-tme capacty requrement. In every teraton the algorthm searches for the partcular ncrease n calls over accounts that offers the hghest ncrease n sales volume per addtonal unt of workng-tme capacty requred. Ths agan s executed enumeratvely untl the number of calls have reached ther upper bounds for all account groups. A detaled descrpton of PRICE and NCALL s provded n an appendx avalable from the author on request. A good jont soluton can be obtaned by alternatvely applyng PRICE and NCALL wth the best found soluton of the other procedure, respectvely, as prespecfed values. If the current polcy as a startng-pont s far from optmalty, ths alternatng optmzaton leads to substantal mprovements over the startng-pont. However, no clam s made about the convergence to the true global optmal soluton. In practce, the decomposton nto PRICE and NCALL offers management the opton to nvestgate as many combnatons of prcng and callng-effort polces as are necessary to gan suffcent nsght nto the problem and to fnd a satsfactory smultaneous soluton. Such a feature generally facltates mplementaton of a decson-support system. Experence derved from an applcaton The plannng stuaton CAPPLAN was developed for a medum-szed ndustral photo laboratory n Germany, whch offers the development of flm and the producton of prnts through approxmately 500 heterogeneous retalers (.e. specalzed photo shops, chemsts, department stores, supermarkets) to the consumer. Over the years, the qualty offered by laboratores has become more and more unform. Furthermore, a rather standardzed product of 9 13 cm colour prnts has evolved. Because of ts commodty character, the laboratores felt that pull marketng wth the help of advertsng was mpossble. All attempts at ntroducng new products n order to avod strong competton have faled so far. In ths stuaton, management felt that t could compete only on prce and servce such as quck delvery of processed orders, effcent and generous handlng of consumer complants, and effectve consultng of retalers. A neat functonng of the servce depends heavly on the frequency of vsts (calls) by salespeople. However, the frm under our consderaton judged ts retalers to be heterogeneous wth respect to ther response to the number of vsts. Some retalers do not pay much attenton to the number of calls. Others, workng wth more than one laboratory at the same tme, tend to send most of ther orders to the laboratory that s servng them best. Therefore, servng heterogeneous retalers means that the tme capacty of the salesforce has to be allocated dfferently across retalers.

8 Despte competton and a prce decay n the last perods, our frm realzed that there were some opportuntes for actve prcng decsons. It came to ths concluson after determnng that companes stll charge dfferent prces. Although the delvery prce cannot be observed drectly, a substantal varaton theren across retalers was consdered to be lkely. Ths was nferred from the fact that retalers generally fx ther sellng prces accordng to the delvery prce plus relatve extra charge (contrbuton), and these sellng prces vared more than 50 per cent. Such dfferences n prce dd not seem to be justfed by cost dfferences, but were the result of some knd of non-transparency n the market. Actual prce offers could only be acqured va negotatons for whch a retaler does not have enough tme there may be thousands of offered tems and perhaps more than ten supplers per tem. Agan, our frm was convnced that ts retalers were heterogeneous wth respect to ther response to prce varatons. Frst, varatons of the delvery prce are, n general, followed by a correspondng varaton of the retalers prce for whch, n turn, the response of the consumers dffers accordng to the retalers characterstcs. Second, retalers who work wth multple laboratores and cannot adjust ther sellng prce wll face a decrease n ther margn f one of the laboratores ncreases ts delvery prce. As a consequence, these retalers wll reduce the number of orders to be sent to ths laboratory. Thrd, the lkelhood of retalers entrely swtchng to other laboratores depends on the retaler s sze and ts compettve stuaton wthn ts local market. If prces must be negotated, t s common practce to delegate prce-settng authorty to the salespeople because they are n the better poston to adjust ther offers to the respectve forecasted responses. However, as already observed by Stephenson et al. (1979), salespeople tend to offer prces that are too low. Therefore, management wanted to specfy dfferentated prce levels centrally for smlarly respondng account groups, so that the actually negotated prces may not fall short of these specfed levels. Such prce dscrmnaton s proftable because t extracts all of the retalers surplus. Ths s legal n Germany as long as the company does not domnate the market. In ths case, the management of our frm thought t unlkely that small changes n prce and sellng effort would be observed by competng laboratores, because most retalers would ntate negotatons wth competng laboratores only f they faced substantal changes n the prevous polces. Furthermore, management assumed that ts retalers rarely exchange nformaton concernng prces and the number of vsts. Our frm therefore expected that a dfferentaton of prces and sellng effort wthn lower and upper lmts farly close to the prevous polcy would not provoke compettve reactons. CAPPLAN a decson-support system 75 Need for decson support The development of CAPPLAN was ntated by the management of our frm because t judged ts current polcy to be far from optmum

9 of Marketng 76 The frm dd not follow an actve and systematc prcng polcy. In the past, the company had lowered prces for the customers ndvdually from tme to tme when competng offers jeopardzed the relatonshp to a certan customer. As a result, prces dd not reflect the supposed response functons. Despte a prce decay, management assumed that t was feasble to proactvely rase prces once a year and justfy such actons by ncreases n costs. When t came to convertng prospects nto new accounts, the frm was already operatng proactvely by establshng prce ranges that had to be fulflled by all offers of the salespeople. In order to mprove current practce, t s necessary to base dfferentated prcng decsons on the respectve sales response functons. Any such attempt wll be facltated by the fact that the frm negotates only a sngle prce, although t offers a complete product lne. Ths reference prce holds for the basc product (9 13 cm colour prnts), whch alone accounts for more than 60 per cent of total sales volume. All other prces are, then, determned accordng to a fxed relatonshp to the reference prce. Wth respect to sellng effort, the frm had been followng a very smple polcy. All accounts receved an equal number of calls wth the excepton of a dfferentaton between old and new accounts. The number of calls for new accounts was double that for old accounts because the frm had experenced that new accounts termnated ther contracts more often than old accounts. The reason was that n the startng perod problems wth servce arose more frequently, whch n turn resulted n the termnaton of a contract unless a salesperson took care of the problems. But now, management had become convnced that sales response functons were sgnfcantly dfferent not only between old and new accounts but also across other account segments, such that t would ndeed be proftable to explore the advantages of dfferentated callng polces. In addton to these requrements, the frm had to take nto account a gven producton capacty that could only be enlarged f accompaned by ncreasng unt costs. More precsely, c(cap) ncreases to a hgher level when exceedng 105 per cent of the current quantty of sales (S ) because the personnel must then be pad an overtme surplus. After exceedng 110 per cent, 120 per cent and 150 per cent of S, respectvely, fxed nvestment costs for enlargng the producton capacty must be ncorporated nto c(cap). Ths has been realzed by calculatng average unt costs for a set of dfferent capacty levels. Wth ths non-contnuous unt cost functon c(cap), prce and callng-effort decsons become nterrelated, resultng n a complex decson-makng problem whch can be supported proftably by CAPPLAN, especally through ts parametrc optmzaton opton.

10 Implementaton CAPPLAN, as descrbed so far, has ndeed been mplemented n the frm under our consderaton. Ths was possble manly because the decson model (6)-(8) completely reflected the management s understandng of the actual plannng stuaton, the management tself beng postvely predsposed to more nnovatve plannng tools. Implementaton was also advanced by alterng the response functon s specfcaton untl management fnally agreed on t, whereby the ncorporaton of asymmetrc elastctes was crucal. Furthermore, t was a clear advantage that, owng to the system s constructon, one works wth response functons passng through the currently realzed pont. Thus management could compare easly the proftablty of any recommended polcy wth the current one. As has already been ponted out by several researchers (Keen, 1975; Lttle, 1979; Lttle and Lodsh, 1981; Lodsh, 1981), the benefts of a decson-support system do not come only from the applcaton of the optmal soluton but also from varous learnng processes throughout all phases from development up to the applcaton of the system. Consequently, the usefulness of a system cannot be evaluated solely n terms of hard proft ncreases. Rather, one needs to take nto account soft benefts, such as a better understandng of responses after explcaton of ntutve knowledge, or a new structurng of the perceved decson model after beng forced to formalze t. In ths partcular case, the followng soft benefts were acheved The requrement of subjectvely estmatng the response functons ntated a long dscusson about the heterogenety of the varous responses. Owng to ts heavy workload, management rejected provdng ndvdual estmates for about 500 retalers. It agreed nstead to search for groups wth smlar responses. Prevously, salespeople only treated old and new accounts dfferently. Now, dscussons between salespeople, the respectve sales manager and the charman of the frm revealed that the retalers responses dffered not only between old vs. new accounts, but also across type of retaler (specalzed stores, department stores, chemsts, supermarkets), sze of accounts (A, B, C), and exclusveness of customer relatonshp (exclusve orders, splt orders). Sales management learned from ths exercse that ts prcng and callng-effort polcy could be dfferentated across not just two but 39 dfferent account groups, consstng of three to 40 retalers each. Later, the management expressed that ths nsght alone would have justfed the development cost of CAPPLAN. In many cases, estmaton of the response functons revealed flat decreases n sales as a result of prce ncreases, suggestng to the management that, after the perod of permanent prce decay, the market now would be stable enough to accept prce ncreases. However, examnng all groups together, the responses ndcated too much heterogenety, so that no such smple polcy could be derved. The fnal CAPPLAN a decson-support system 77

11 of Marketng 78 estmates for the ndvdual response functons have been provded by the responsble salesperson and the sales manager. The estmates have been revsed untl agreement has been reached. As a result, the R 2 of the calbrated response functons was n almost all cases hgher than 0.9. Results Management ntated the use of CAPPLAN by subsequently applyng the subroutnes PRICE and NCALL. PRICE was run wth the current number of calls, and provded parametrcally the best dfferentaton of prce levels for producton capacty levels wthn the nterval of 80 per cent to 130 per cent. On the bass of the most proftable prce schedule, whch requred a producton capacty of 108 per cent, NCALL was mplemented n a second step. It provded the parametrcally optmal number of calls per account group for workng-tme capacty levels wthn the nterval of 50 per cent to 130 per cent (relatve to current). The result of ths sequental optmzaton process n terms of recommended polcy changes s found n Table I. Table I. Number of account groups wth specfc recommendatons for the prcng and callngeffort polces Recommendaton regardng callng effort Prcng Decreased number Same number Increased number recommendaton of calls of calls as before of calls Total Prce decrease Same prce as before Prce ncrease Total However, management felt uncomfortable wth ths soluton fearng that the recommended prce decreases, although wthn tght lower bounds, mght stmulate the general tendency of a prce decay. Therefore, management wshed to nvestgate the possble mplcatons of the best soluton found so far yet wthout allowng prce decreases. In addton, sales management wanted to evaluate a unform prcng polcy that would consst of ncreases across all account groups. The dea was to operate wth a more proftable prcng polcy whereby the quantty losses could be compensated by ncreased effort on the part of the salesforce. As an alternatve, management was also nterested n revewng the consequences of doublng ts acquston effort (number of prospects regularly called on). For the resultng sx strateges (three prcng strateges two acquston strateges) optmal callng-effort levels have been determned. Note that ths was only possble as a result of the decomposton of the optmzaton process nto the subroutnes PRICE and NCALL. The correspondng proft results of these solutons, referrng to four dfferent levels of workng-tme capacty (80 per cent, 100 per cent, 110 per cent and 120 per cent), are found n Table II.

12 Workng-tme Producton capacty Sales Proft requrements requrements volume contrbuton Prcng Acquston (n % to current (n % to (n % to (n % to strategy strategy workload) current) current) current) Optmal Current prces acquston effort Optmal Doubled prces acquston effort Optmal Current prces acquston wthout effort decreases Optmal Doubled prces acquston wthout effort decreases Prce Current ncreases acquston across the effort board Prce Doubled ncreases acquston across the effort board CAPPLAN a decson-support system 79 Table II. Results of dfferent prcng and acquston effort strateges From the results of these what-f -runs of CAPPLAN, the frm learned the followng more strategc lessons A comparson of the mpact of the varous polces ndcates that proft vares substantally only across prcng polces, but not wth respect to an ncrease n total sellng-effort levels. As a result, the frm wll be payng attenton prmarly to a good prcng polcy. All strateges that lead to substantal ncreases n the requred producton capacty turn out to be less proftable. Ths mples that aggressve growth strateges, lke prce decreases and ncreases of acquston effort, are not preferable. On the other hand, t dd not prove to be advantageous to ncrease prces for all accounts. The resultng loss of quantty of sales cannot then be compensated by correspondng sales ncreases through more callng effort. The most advantageous strategy n Table II entals a constraned dfferentaton of both prces and callng-effort levels. The restrctons of non-decreases n prces and of remanng at the current acquston effort

13 of Marketng 80 level help to avod costly producton capacty extensons. It should be noted that CAPPLAN predcts an ncrease n proft of more than 12 per cent for ths best strategy. Ths demonstrates that, wth the same level of sellng effort as before, substantal proft mprovements can be acheved by smply dfferentatng the marketng nstruments optmally across account groups. Increases n workload (total sellng-effort level) from 90 per cent to 110 per cent (as compared to current effort) only lead to small ncreases n quantty of sales and of total contrbuton. Obvously, the salespeople are operatng n the range of flat slopes of ther sales response functons. Because a reducton of the number of salespeople was consdered mpossble, sales management concluded not to change ts salesforce sze. Instead of applyng the best soluton drectly, the frm mplemented a modfed polcy based on the precedng conclusons. At the begnnng of the followng year the frm announced prce ncreases justfed by cost ncreases to nearly all accounts for whch the recommendaton was not to decrease prces. Ths was accompaned by a careful montorng of the reactons of customers. When there appeared to be a real danger of losng such customers, the frm offered to contnue agan wth the old contract. Instead of reallocatng callng tme, the frm began to tran ts salespeople so that they would become able to consult ther customers really and properly (retalers). Management thus hoped to ncrease the prevously flat slope of the response functon, thereby changng the current callng polcy nto a more proftable one. In order to be able to evaluate the usefulness of CAPPLAN better, t would have been preferable to calculate the hard benefts n terms of proft mprovement nduced by the mplemented polcy. Unfortunately, ths would requre comparson wth a non-mplemented polcy, whch s not possble. From ts vewpont, the frm s management was satsfed wth the strategc nsghts ganed from the varous runs of CAPPLAN, enablng them to mplement an mproved polcy. The only fgure avalable for judgng the usefulness of CAPPLAN was an actual ncrease n contrbuton of about 20 per cent whch, of course, mght have been caused by a varety of other sources frst, prce ncreases were accepted more readly than had been antcpated; second, the frm was not n a dangerous poston because most of the compettors also ncreased ther prces; and, thrd, most retalers experenced gans from a small overall ncrease n sales volume. Consequently, there was no way to determne the unconfounded effect of CAPPLAN. However, management subjectvely estmated that about half of the contrbuton mprovement, namely 10 per cent, may be attrbuted to the nsghts ganed from usng CAPPLAN. Conclusons We have descrbed the development and applcaton of the decson-support system CAPPLAN, whch provdes optmally dfferentated delvery prces and

14 callng-effort levels across heterogeneous customers. A jont optmzaton of these two marketng nstruments s necessary f they are coupled va a jont producton capacty constrant whch can be expanded only at non-lnearly ncreasng unt costs. It has proved to be crucal to the mplementaton to have spent most of the development effort on the constructon of an approprate sales response functon. As a result, management felt confdent n subjectvely estmatng the response parameters and n relyng thereon. The management later expressed that, alone, the nsghts ganed from calbratng the response functons would have justfed the effort and costs of development. On the other hand, t turned out to be worthwhle not to have nvested too much tme n the constructon of a specal-purpose optmzaton algorthm. The use of a smple heurstc based on ncremental optmzaton prncples was judged to be suffcent, snce the best soluton found predcted a total ncrease of 12 per cent over current proft contrbuton. Furthermore, ths heurstc allowed for a parametrc optmzaton wth respect to dfferent levels of producton capacty, such that the mpact of extenson decsons could be evaluated more accurately. In addton, the heurstc enabled the frm to perform what f -runs of CAPPLAN for dfferent prcng and acquston strateges. The fnal outcome of the applcaton of CAPPLAN was the mplementaton of a polcy based on strategc nsghts ganed throughout the applcaton process. An evaluaton of the proft mprovement brought about by ths polcy was dffcult because other factors mght have confounded the actual ncrease of contrbuton acheved, whch as at 20 per cent. It s encouragng that management, based on ts own subjectve judgement, attrbuted half of the ncrease, namely 10 per cent, to the use of CAPPLAN. CAPPLAN a decson-support system 81 References Fudge, W.K. and Lodsh, L.M. (1977), Evaluaton of the effectveness of a model based salesman s plannng system by feld expermentaton, Interfaces, Vol. 8 No. 1, Part 2, pp Hanssens, D.M., Parsons, L.J. and Schultz, R.L. (1990), Market Response Models Econometrc and Tme Seres Analyss, Kluwer Academc Press, Boston, MA, Dordrecht, London, p. 39. Keen, P.G.W. (1975), Computer-based decson ads the evaluaton problem, Sloan Management Revew, Vol. 16 No. 3, Sprng, pp Lal, R. (1986), Delegatng prcng responsblty to the salesforce, Marketng Scence, Vol. 5, pp Lttle, J.D.C. (1979), Decson support systems for marketng managers, of Marketng, Vol. 43, Summer, pp Lttle, J.D.C. and Lodsh, L.M. (1981), Commentary on judgment based marketng decson models, of Marketng, Vol. 45, Fall, pp Lodsh, L.M. (1971), CALLPLAN an nteractve salesman s call plannng system, Management Scence, Vol. 18 No. 4, Part II, pp Lodsh, L.M. (1980), A user-orented model for sales force sze, product, and market allocaton decsons, of Marketng, Vol. 44, Summer, pp Lodsh, L.M. (1981), Experence wth decson-calculus models and decson support systems, n Schultz, R.L. and Zoltners, A.A. (Eds), Marketng Decson Models, North-Holland, New York, NY, Oxford, pp

15 of Marketng 82 Lodsh, L.M., Curts, E., Ness, M. and Smpson, M.K. (1988), Sales force szng and deployment usng a decson calculus model at Syntex Laboratores, Interfaces, Vol. 18, January-February, pp Mantrala, M.K., Snha, P. and Zoltners, A.A. (1992), Impact of resource allocaton rules on marketng nvestment-level decsons and proftablty, of Marketng Research, Vol. 29, pp Mantrala, M.K., Snha, P. and Zoltners, A.A. (1994), Structurng a multproduct sales quotabonus plan for a heterogeneous sales force a practcal model-based approach, Marketng Scence, Vol. 13, pp McIntyre, S.H. (1982), An expermental study of the mpact of judgment-based marketng models, Management Scence, Vol. 28, pp Naert, P. and Weverbergh, M. (1981), Subjectve versus emprcal decson models, n Schultz, R.L. and Zoltners, A.A. (Eds) (1981), Marketng Decson Models, North-Holland, New York, NY, Oxford, pp Smon, H. (1989), Prce Management, North-Holland, Amsterdam, p. 106ff. Srnvasan, V. (1981), An nvestgaton of the equal commsson rate polcy for a mult-product salesforce, Management Scence, Vol. 27, pp Stephenson, P.R., Cron, W.L. and Frazer, G.L. (1979), Delegatng prcng authorty to the sales force the effects on sales and proft performance, of Marketng, Vol. 43, Sprng, pp Zoltners, A.A. and Snha, P. (1980), Integer programmng models for sales resource allocaton, Management Scence, Vol. 26, pp