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Modelling the Effectiveness and Profitability of Trade Promotions

Author(s): Robert C. Blattberg and Alan EvinSource: Marketing Science, Vol. 6, No. 2 (Spring, 1987), pp. 124-146Published by: INFORMSStable URL: http://www.jstor.org/stable/183683 .

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MARKETING SCIENCEVol. 6, No. 2, Spring 1987Printed in U.S.A.

MODELLING THE EFFECTIVENESS ANDPROFITABILITY OF TRADE PROMOTIONSROBERT C. BLATTBERG AND ALAN LEVIN

University f ChicagoInteractiveData CorporationTrade promotions have become an increasingly important element of the marketing mix.Yet, there is very little researchdescribing how to measure the profitabilityand effectiveness oftradepromotions. This paperdescribes how retailers behave when tradepromotions are offered.

Then, a model is developed to capture the two key components of the process: the consumerand the retailer. An example is given showing how to apply the model to actual manufacturerand retail sales data. Then estimates of the profitabilityfor different items in a product categoryare calculated.Many research questions are raised in this paper which can serve as future directions forresearch.Why are trade promotions generally unprofitable?How can scanner data improve theestimates given? How do different types of trade promotions affect the retailer and ultimatelythe consumer? Which brands and items should be trade promoted?

(Modelling; Trade Promotion;Scanner Data)

1. IntroductionBrand managers devote substantial dollar resources to trade promotions and, inmany companies, trade promotion budgets are much greaterthan advertising budgets.Yet, there have been very few models developed to measure the profitability and saleseffects of trade promotions.The purpose of this article is to present a model which assists management in under-standing and measuring the effects of trade promotions. The specific uses of the modelpresented are: (1) to evaluate individual promotions, (2) to identify the best tradepromotions for each size and in each geographical area, (3) to evaluate future promo-tional plans, and (4) to develop trade promotion tactics.The model developed is applied to a data set using Nielsen consumer sales data(bi-monthly) and company shipment data. The consumer sales data used have manyimitations which are discussed later. However, the general modelling approach can beapplied to scan data such as Nielsen's Scan Track. The model can actually be applied

more easily to these data than the data described in the paper since more accurateconsumer promotions and weekly sales data are available from Scan Track.Before continuing, it is useful to define a trade promotion. Trade promotions arespecial incentive programs offered by the manufacturer to their distribution channelmembers. They take many forms, including direct price discounts and free case offers.124

0732-2399/87/0602/0124$01.25Copyright ? 1987, The Institute of Management Sciences/Operations Research Society of America


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EFFECTIVENESS AND PROFITABILITY OF TRADE PROMOTIONSChannel members are then expected to "push" the product through the pipeline byoffering financial and merchandising incentives. Ultimately, the goal is to get theretailer to offer the consumer a price discount and, in many situations, merchandise theproduct through displays and newspaper advertising. In certain situations the manufac-turer will require the retailer to sign a compliance agreement which will make theretailer guarantee some form of price reduction to the consumer or merchandisingactivity on the proposed item.Most of the studies of promotional activity have concentrated on consumer responseto deals. Kuehn and Rohloff(1967) and Frank and Massy (1965) have attempted tomeasure the sales effect of price-off and other types of promotions. Webster (1965),Montgomery (1971) and Blattberget al. (1981) have attempted to measure the charac-teristics of the deal buyer. None of these studies considers how channel membersrespond to trade deals.

Goodman and Moody (1970) developed a system to measure the effect of tradepromotions on sales of the manufacturer. Their system incorporated the buying behav-ior of other members of the channel. They postulated that the main factors affectingsales were trend and seasonality. When trade promotions occurred, the other channelmembers varied the quantity purchased, either to build inventories at lower costs orreduce inventories in anticipation of trade promotions. Their model was theoreticalwith no empirical validation.Brown (1973), using a similar concept, offered a methodology to attempt to estimatethe dealer's inventory during a deal and the trough after a deal caused by the tradeselling inventories bought during the dealing period. The problem with the methodol-ogy developed by Goodman and Moody and by Brown is that it attempts to measureconsumer purchasing indirectly. They do not attempt to estimate the size of tradeinventories, a crucial factor in determining the effect of the promotion.Abrahim and Lodish (1987) use a similar approach to Brown in estimating the effectsof alternative promotions. They use a time series model in which managers and con-sultants analyze the manufacturer's shipments in order to measure the effect of apromotion. Through different statistical procedures they create a baseline forecast ofwhat sales would be without promotions and then the difference in the baseline andactual shipments is a measure of the effect of an individual promotion. They thus alloweach promotion, even of the same type, to vary in its effect on shipments and profits.

The major problem with Brown's and Ibrahim and Lodish's models is the possiblelack of robustness in predicting future promotional effects. By relying heavily on mod-eling residuals and allowing differing effects of identical types of promotions, it be-comes very difficult to generalize the results to future time periods. However, accordingto their published articles, they have excellent success in analyzing promotional effec-tiveness.Chevalier and Curhan (1976), using a survey, describe how trade promotions affectretailer promotion activity. While not formally modelling the relationship betweenretailer promotions and trade promotions, they show that retailers promote only alimited number of items for which they accept trade promotion allowances. Further,slow moving items are unlikely to be displayed and substantial financial inducementsare required to obtain retail price cuts. Most importantly, they question whether tradepromotions are profitable to the manufacturer.The study conducted by Chevalier and Curhan is an excellent starting point for thisarticle. Many of the issues they discuss such as "forwardbuying" (retailersloading theirinventories) and the effectiveness of differenttypes of trade promotions will be the basisof the model developed in this paper. The primary conclusions they draw will beconsistent with the findings in this paper.The model outlined in this article will combine consumer sales, factory shipments

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and estimated pipeline inventories to evaluate the sales effect and profitability of tradepromotion activity. In addition to developing a theoretical model, actual consumersales and shipment data are used to estimate the model's parameters and test itsaccuracy.The model described in this paper is general in form. It has been applied to differentdata sets such as SAMI as well as Nielsen bi-monthly store audit data which are used toestimate the consumer sales equation in this paper.The model can be used with scannerdata which are currently becoming available from sources such as Nielsen. As betterconsumer sales and promotional data become available, the model described in thepaper can be applied with some minor modifications to these new data sources.The remainder of the article is divided into seven sections. ?2 describes the modeltheory and structure;?3 describes the data utilized and the estimation procedures;and?4 the results. ?5 explains how the model is used to evaluate promotions. ?6 demon-strates the model's forecasting capabilities. ?7 discusses the uses of the model; and ?8offers some concluding comments.

2. The Model2A. Introduction

Most consumer packaged goods are distributed through a two- or three-step channel.The two-step channel results from the manufacturer shipping to a retailer(Step 1) whosells to the consumer (Step 2). More complex systems exist in which manufacturersshipto wholesalers (or distributors) who sell to retailers who then sell to consumers. Themodel was developed to represent a two- or three-step distribution system mathemati-cally. Below, the theory of the model will be described, specific hypotheses generatedand equations derived.2B. Model Theory

Figure 1 shows the relationship between the model's components. It begins withpromotions influencing shipments. When a trade promotion is offered (such as anoff-invoice discount) the wholesaler or retailer increases his orders from the manufac-turer.' This increase in orders occurs for two reasons. First, the retailer will "forwardbuy" and hold inventory in order to take advantage of the special incentives beingoffered. Second, since the goal of the trade promotion is to increase retail promotionsand merchandising activities, it is expected that retailerswill increase their inventoriesin anticipation of increased consumer sales from their retail promotions.2If trade promotions can generate consumer sales they will ultimately increase long-run manufacturer shipments. In general, if consumer sales do not increase, trade pro-motions merely increase short-run pipeline inventories which are run down after thedeal, resulting in a post promotion sales trough. The result is that the retailerbuys at areduced price from the manufacturer without sales increasing to compensate for thereduced price. In this case trade promotions become unprofitable.3I rade promotions are defined as inducements offered to the intermediaries in the channel of distribution

resulting in special activities supplied by these intermediaries. The most common types of trade promotionsare bill-backs, allowances, off-invoice allowances and free goods.2 Retailer promotions and merchandising activities take the form of short-term price reductions (deals).3In some circumstances, inventory savings to the manufacturer may mean a trade promotion is profitableeven though it did not increase consumer pass through. If the retailer or other channel members have lowercarryingcosts than the manufacturer, it may be profitableto trade promote even without increasedconsumersales.Another way to think of trade promotions is that the manufacturer is giving a quantity discount to certainmembers of the "trade". The advantage of these discounts has been documented by Lal and Staelin (1984)and Dolan (1986).

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EFFECTIVENESS AND PROFITABILITY OF TRADE PROMOTIONS

FIGURE1.

Factors in addition to trade promotions are often included in the models, such asadvertising, price changes, trend, category seasonality and any other variables consid-ered important in the product category.Competition is an important factor in modeling sales and shipments but it is verydifficult to include for several reasons. First, there are rarely data collected aboutcompetitor's trade promotion activity. Second, even if data were collected historically,one would need to forecast competitors' behavior in order to use it normatively. Third,it is necessary to design competitive game models, including competitors' activities, tounderstand how their actions might affect the firm's activities. Primarily because of thelack of available data, but also for the other reasons mentioned, competitive activitywill not be included in the model.The effect of eliminating competition in the model primarily influences the effect oftrade deals on retailers' promotions. Retailers will buy less from a specific trade dealoffered by the manufacturer because a competitive trade deal was offered. The effectwill be greatervariation in shipments when a given trade deal type is offered. This willincrease the standard errorof the residual. However, if this residual is uncorrelated withthe independent variable, the estimates will be unbiased but have a wider standarderror. It is impossible to know whether the residual is correlated and hence will beassumed, as in most marketing models, to be independent of competitive activity.2C. Forward Buying

Because "forward buying" by the retailer is a crucial factor in determining theprofitability of a trade promotion, it is useful to show why it exists.Figure 2 gives a plot of the shipment history of a firm for a specific product in amarket (the solid line). One sees the peaks and valleys and the rather erratic nature ofthe shipment plot. The circles indicate trade promotions which occurred during the

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ROBERT C. BLATTBERG AND ALAN LEVIN100.000

80.000

60.000

..- UNIT SHIPMENTS---- ADJ UNIT SALES0---0 PROMOTION PERIOD

FIGURE . Nielsen Adjusted Sales vs. Factory Shipments Product X-Market 1.

period.4 The plot demonstrates that there are usually troughs after a trade promotionends, because channel members forwardbuy during the promotion and then run downtheir inventories after the promotion ends.Figure 2 also shows consumer sales (Nielsen)-the dotted line-for the same productin the same market. One sees that consumer sales have much less variability thanshipments because the retaileris buying for inventory with much less being passed on tothe consumer. The result is large swings in shipments resulting in retailer's stockpiling.Because Nielsen estimates of consumer sales are smoothed, they result in less fluctua-tions than may be occurring in a given retailerwhen a promotion occurs. However, inany market retailerpromotions are not simultaneous. Thus, some of this "smoothing"over a two-month period is due to different retailers' running one week promotions.Many products also do not have sizeable consumer sales increases when a retail pro-motion is run. To see this, suppose 50%of the stores promote the trade dealt brand forone week in the bi-month (8 week) period. Sales in these stores increase 100%for theweek. Over 8 weeks, this is a 12.5% ncrease in sales multiplied by 50% or a 6.25%salesincrease. A sales increase of 200% would cause sales to increase only 12.5% over thebi-month period if 50% of retailers promote. If 4-week sales data were used (SAMI) alargerspike would occur but the general conclusions that retailersare heavily stockpil-ing would not change.

4 This product is heavily trade promoted as are most grocery, drug, and health and beauty products. Tradedeals occur in over 70% of the periods. Yet, the regularprice is not the tradedeal price and retaileractions arebased on the difference between regularprice and the trade dealt price. The reason is that the trade deal lastsfor a fixed period of time and therefore the retailer must forwardbuy (inventory) in order to receive the lowerprice. A long-term price reduction would result in different retailerbuying behavior.

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EFFECTIVENESS AND PROFITABILITY OF TRADE PROMOTIONSThe reason the retailerstockpiles can be explained by an EOQ inventory model. Theretailerevaluates three main costs: (1) product cost, (2) inventory carryingcosts, and (3)set up costs. For most retailers (1) and (2) dominate. If there is a temporary price

reductioh, the retailer purchases up to the point where the savings from the promotionare less than the additional holding costs associated with keeping the product ininventory.Because the retailer is buying more than the quantity sold when a promotion occurs,after the promotion ends the retailer will order much less than the quantity being sold.The result is a trough after a deal which is evident in Figure 2.From this explanation one also sees the conditions for a profitable promotion: Mostof the incremental units sold by the manufacturer during the promotion period mustalso be incremental units sold by the retailer. If the retailer does not pass the promotionthrough to the consumer, then the channel members are only buying at reduced costswhich results in a lower implicit selling revenue to the manufacturer without long-runincreased units sold to compensate for the reduced price.2D. Model Hypotheses

Based on the above conclusion, it can be said that retailers use some form of inven-tory model to determine how much to purchase on a given deal.5 This helps to explainseveral of the empirical findings just described and results in the following hypotheses.First, retailerswill "forwardbuy" when trade promotions are offeredif the savings fromthe promotion exceed the holding costs. The "forwardbuying" will cause a trough afterthe deal. Second, the response to a promotion will be lower at the beginning of thepromotion than at the end of the promotion assuming that the retailer can reorder.Thelower sales results from the retaileronly buying enough to get through the deal and thenforwardbuying at the end of the deal. Thus, retailerinventory behavior can explain thehigher sales at the end of a promotion and the trough in the sales following a deal. Inany model of shipments, it is important to capture this inventory effect.For the consumer sales equation, the retailers anticipate their promotions and buyinventories to cover both forward buying and expected sales during the promotion.Thus, inventories can serve as a surrogate for retailer promotions.Based on the conclusions drawn above, the following hypotheses were generated.Shipment Hypotheses.1. Inventories inversely affect shipments.2. Trade promotions increase shipments.Consumer Promotion Hypotheses.1. Retailers build inventories in anticipation of offering consumer promotions.These hypotheses will be used to develop a model structure.2E. Model Structure

In developing the model there were four equations initially postulated: (1) manufac-turer's shipments, (2) retailerpromotions, (3) consumer sales, and (4) inventories. Thefollowing general model is postulated.Shipmentst = fi(inventoryt_l, trade promotionst, other factorst), (2.2a)Retailer Promotionst = f2(trade promotionst, inventories-t_), (2.2b)

Consumer Salest = f3(trade promotionst, retailerpromotionst_l,other factorst, other factorst_l), (2.2c)

5 Some retailers(e.g. warehouse stores) may buy from deal to deal. This would not cause a trough after thedeal but cause higher peaks. However, many retailers do forwardbuy and thus there is generally a trough aftera deal.

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Inventoriest = f4(inventoriest_1,shipmentst, consumer salest), (2.2d)where t = the time period andfi( ) is a function.For each of these equations, trade promotions refer to the various types of tradepromotions used such as off invoice and bill backs. Each differenttype will be includedin the empirically estimated model.

3. The Estimated Model and the Data3A. The Data

To perform the analysis, data were gathered from a variety of sources. The data werefor a three-year period for each major product, and its associated sizes (10 products)and markets (6 markets). Each product size and market combination were analyzedseparately. The following data were used to estimate the model:-Factory shipments-Nielsen sales-Manufacturer's price-Trade promotions-Advertising expendituresBecause Nielsen data are bimonthly and factory shipments are monthly, it is neces-sary to decide on the appropriate time period to use. If the time period of a month ischosen, then Nielsen data must be adjusted. Using a month as the time period maxi-mizes the use of data on manufacturer shipments and promotions. Thus, the analysiswas performed using one month time periods.A variety of methodologies were discussed to develop monthly Nielsen numbers. Itwas decided to adjust Nielsen bimonthly sales using linear extrapolation. However, thestandard errors and t-statistics may be biased, because the monthly observations areweighted bimonthly data.6As mentioned earlier,inventory data are considered to be extremely important in thedevelopment of the models and for the analysis. The inventory data supplied by Nielsenwas insufficient for the analysis because Nielsen inventories representstock inventoriesin the store and do not account for other inventories in the system, especially at thewarehouse level. Thus, an estimate of pipeline inventories was made.To estimate the pipeline inventories Nielsen monthly consumer sales and manufac-turer shipments were used. Since the relationship for inventories in a given period issimply: INVt = INVt_ + Shipmentst - Consumer salest, (3.1)one can estimate inventories if initial inventories Io were available. Because initialinventories were not, a procedure was established to estimate it. Io was chosen so thateach period's initial inventory was greater than or equal to zero. Thus, the inventorydata used are relative inventory. If Io were available, then actual inventory could beestimated.Because the firm did not collect information about retailer promotional activity, itwas necessary to eliminate equation (2.2b) from the set of equations. This requiredrevising equation (2.2c). As a surrogatefor retailerpromotions, last period's inventorieswere used. When the retailer promotes, he builds inventories in anticipation. Tradedeals were not included because the retailer'spromotional periods do not correspondtothe manufacturer's promotional periods. The manufacturer may run a promotion forthree months and the retailerwill promote only one week in the period. Therefore, one

6 The econometric implications of this procedure were not derived. Future researchwill attempt to evaluatethis issue in more detail.

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EFFECTIVENESS AND PROFITABILITY OF TRADE PROMOTIONSwould not be able to use the timing of trade deals to predict retail promotions. Thisleads to a revised equation:

consumer salest = f5(inventories_-1,other factorst). (3.2)The remainder of this section describes the equations used in the final model.3B. Shipments Equation

The primary variables used to explain shipments were pipeline inventories and dif-ferent types of trade promotions. Inventories were lagged because ending inventoriesfrom the previous period influenced shipments in the present period.Incorporating trade promotions into the model raises several issues. First, the firmoffered numerous types of promotions. The major types were off-invoice discounts,sales drive discounts and a special fall premium promotion.7 These promotions wereincluded in the model as separatevariables. In addition, the issue arises how to incorpo-rate the value of the trade promotion into the model. To make alternative trade pro-motions comparable across types and over time, a percentage dollar discount to thechannel member was used. This percentage discount was used to represent the magni-tude of a promotion.8Second, the shipments occurring during the trade promotions were not constant.Because the firm allowed a channel member to purchase only once during the promo-tion, a specific pattern for shipments was observed. A variable was created whichindicates the percentage of a trade deal shipped each month. This percentage varieddepending on the length of the deal (2 months, 3 months, etc.). For example, suppose atrade deal lasts three months. Then, the percentage of the total shipped on deal inmonth 1 represented 30%, in month 2-20%, month 3-50%. The percentages werecalculated using actual data based only on the shipments during the dealing period. Thepercentages used for each deal of varying lengths are given below:

Percentage Shipped by MonthLength of Trade Deal 1 2 3 4

2 40% 60% -3 30 20 504 30 20 10 40To measure the effect of a deal, a new variablewas created which is the product of thetrade promotion percentage discount times the percentage shipped each month duringthe trade deal. This approach is used in the model for off-invoice percentage.The reason an adjustment was made for percentage shipped per month is that re-tailers do not buy evenly throughout a trade promotion. At the beginning of thepromotion they buy to cover their retail promotion and at the end they buy for inven-tory. Thus, the shape of the response function is not uniform over the period of thetrade promotion.Second, a separate end-of-deal variable was developed to capture the carryovereffect

being caused by orders taken during the promotional period at the discount price butshipped the month after the promotion ended. Daily invoice data were used to deter-mine the length of the carryover effect. Generally, it was found that over 98% of theorders placed during the deal period had been shipped within one month following the7 Bill backs, free goods, or other commonly used promotions would be entered as separate variables in themodel. They would be converted to dollar values and then entered.8 Because percentages are independent of the absolute magnitude of prices, using a percentage discountadjusts for inflationary change.

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ROBERT C. BLATTBERG AND ALAN LEVINend of the deal. Therefore, a one-period carryover effect should capture this phe-nomenon.The variable used to define end-of-deal was the percentage trade promotion discounttimes a dummy variable which is 1 if a promotion just ended and zero otherwise.Third, when manufacturer's case price increases, the retailer is likely to forwardbuy.Therefore, a price increase is often preceded by an increase in sales. In general, this canbe modeled by having a dummy variable for the period prior to the deal times thepercentage price increases. Thus, the effect of a price increase leads shipments becausethe retailer or wholesaler forwardbuys.Fourth, sales drives were used to push the product from the wholesaler to a retailer.For all units sold by a wholesaler to a retailer, the wholesaler would receive a paymentof X%of the wholesale price as a financial incentive from the manufacturer. This typeof trade promotion was used to push the wholesalers to load retailers.

Fifth, a fall premium was offered to the manufacturer's sales force every September.The purpose of this premium was to have the sales force increase effort on specificproducts. Because it was difficult to translate the fall premium into a percentage, adummy variable was used which was 1 when a fall premium was present and zerootherwise.Sixth, trend was modelled using time which was 1 in the firstmonth, 2 in the secondmonth and up to 35 in the last month. It was found that a linear trend adequately fit theshipment data.As was stated earlier, competitive factors were not included in the model becausedata were not available. Also, seasonality was not included in the shipments equation

because an independent sales measure indicating shipment seasonality was not avail-able. Using dummy variables to measure seasonality would have added too manyvariables to the equation.The final list of variables used for estimation in the model along with expected signsis shown in Table 1. This leads to the shipment equation:shipment, = f(inventory,t_ , off invoice,, end of dealt, sales drive,,

pricet_,, fall premium, trendt). (3.3)3C. Consumer Sales Equation

The consumer sales equation had to be reformulated because certain data were notavailable. While sources exist for retailer promotions (Majers),9the firm did not sub-scribe to this service. Since retailerpromotions could have a major effect on consumerpurchases, alternative variables were needed. Because pipeline inventories depend onretailer promotions one can substitute this variable into the model as a measure ofretailer activity. The reason for using pipeline inventories is that high inventory levelswould cause the retailer to respond with special promotional activities to reduce theinventory buildup.?0 Thus, whereas high pipeline inventories are expected to reducemanufacturer shipments, they will also cause increased consumer sales due to retailerpromotions. The consumer sales equation therefore contained an inventory variableassurrogatefor retailer promotions.Determining which consumer marketing activities to include in the consumer salesequation raised similar issues to those outlined in developing the shipments equation.Because it was measured with substantial error, retail price was omitted even though it

9Majers provides data to measure retailer's promotional activity.10In the near future Nielsen Scan Track data will make it be possible to measure retail sales and promotionsmuch more accurately. One can then analyze the effect of different manufacturer promotions on retailerpromotional activities rather than using inventory as a surrogate.

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EFFECTIVENESS AND PROFITABILITY OF TRADE PROMOTIONSTABLE 1

ExpectedSignsof Variables n FactoryShipmentModelVariable Used Expected Sign

1. Lagged pipeline inventories2. %Deal completed X off-invoice % +3. End of deal % +4. Sales drive % +5. Price change %(in t + 1) X dummy variable6. Fall premium +7. Trend +

was known to be important. The price measure available was Nielsen's price estimate.A regressionwas run between manufacturer price and retail price and very low correla-tions were found. The reason for these low correlations appears to be how Nielsenweights store prices. As additional outlets stock the product or the outlet's market shareincreases, the Nielsen estimated prices fluctuate. These fluctuations do not represent"true price" changes in the market, merely shifting outlet shares or brand marketshares. Thus, using Nielsen prices was extremely difficult. If price is uncorrelated withother factors in the model, then no bias in the coefficient estimates exists. Therefore,omission of price may not cause serious problems in the use of the model.Consumer advertising was incorporated into the model using total advertisingdollarsand then deflating by an inflation factor forindustry advertising costs. Both currentandlagged deflated advertising were used, though only lagged advertising was incorporatedin the final model. Current advertising entered with the wrong sign. The cause of thewrong sign could not be determined.The other factors included in the equation were seasonality and trend. Seasonalitywas estimated using Nielsen category sales data not brand or item data. By usingcategory sales data, any item marketing effects would not contaminate the seasonaladjustment. X- 11 was used to estimate the seasonal patterns. Trend was simply a timeindicator beginning at 1 and going to 35. A dummy variable was also utilized to removelarge residual effects which could not be reasonably accounted for by the other vari-ables. This was only used in a small number of models.The final list of variables used for estimation in the consumer sales model along withexpected sign is shown in Table 2. This leads to:Consumer sales =f(inventory,t_, advertising-t_, seasonalityt, trendt). (3.4)

3D. Inventory ModelThe inventory model is a straightforwardaccounting relationship:

INVt = INVt_1+ Shipmentst - Consumer Salest. (3.5)The procedure for estimating inventory was given in ?2.

3E. Functional FormThe functional form used for the model given in equations (3.3) and (3.4) was to logthe dependent variable. The specific choice of this functional form is partly arbitrarybecause it is difficult to state which functional form is most likely to represent actualbehavior. A log model made it easy to combine the two equations into a forecastingsystem and also to make sure negative sales are not predicted by the model.The next section presents the model estimation procedures and the results of theestimation. Comparisons of actual vs. fitted and forecast accuracy are presented toevaluate the quality of the models.

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ROBERT C. BLATTBERG AND ALAN LEVINTABLE 2

Expected Signs of Variables in Consumer Sales EquationVariables Assessed Expected Sign

1. Lagged pipeline inventoriesa +2. Lagged deflated advertising $ +3. Category seasonality +4. Linear trend +a Lagged pipeline inventories are used as a proxy variablefor consumer promotions.

4. Model EvaluationThis section is divided into two parts. The first gives the estimation results and thesecond describes the results of the simulation test used to evaluate the model.

4A. Estimation ResultsFor the product line studied, there were 10 items in each of 6 markets. The 10 itemsrepresented line extensions and sizes. Thus, 60 different sets of coefficients were esti-mated for both the shipments and sales equations. Because there were so many differentsets of coefficients estimated, the results are presented in three separatetables. Table 3gives the actual estimates for the shipments and sales equations for the same item in twoseparate markets. The overall results are summarized in Tables 4 and 5.The coefficients in the shipment equations in Table 3 show that the lagged inventoryvariable, indicative of the pipeline inventory in the distribution system, has the correct

TABLE 3Coefficient Estimates for Two Markets and Sizes

SHIPMENTS EQUATIONMarket I/Size 2 Market 2/Size 2

Variable Coefficient T-Ratio Coefficient T-RatioLagged inventory -3.29 X 10-5 -2.94 -4.26 x 10-5 -3.15Trend -5.964 X 10-3 -0.72 7.24 X 10-3 0.88Off-invoice 36.9071 6.51 25.6119 4.93End of deal 3.4142 0.75 4.2845 0.99Sales drive 21.4402 3.27 3.4890 0.55Price change 13.5317 2.31 4.6786 0.89Fall premium 0.2029 1.34 0.2290 1.61Constant 8.8366 45.32 8.7882 45.54

R2 = 0.845 K2 = 0.611# of obs. - 35 # of obs. = 35CONSUMER SALES EQUATION

Lagged inventory 3.295 X 10-6 2.10 4.880 x 10-7 0.17Seasonality 0.0127 2.69 0.0270 4.60Trend -0.0005 -2.01 1.737 x 10-3 0.92Lagged advertising 0.0005 0.33 1.990 x 10-3 1.08Constant 7.89 16.45 6.2365 10.65

2 = 0.446 = 0.511# ofobs. = 35 # ofobs. = 35

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EFFECTIVENESS AND PROFITABILITY OF TRADE PROMOTIONSTABLE 4

Shipments SalesEquation EquationNumber of signs 360 180Number correct 345 155

sign and is statistically significant. The promotional variables-off invoice, sales driveand fall premium-also have the correct signs although their effects vary across mar-kets. The off-invoice promotion variable, adjusted for the length of time of the deal,usually had the largest t-ratio in the shipments equation.In the consumer sales equations, lagged inventory, acting as a surrogate for retaileractivities, again has the correct sign. However, its significance is typically not as greatasin the shipments equation. The lagged advertising variable also had the correct sign,although its significance for this product category was not very high.Tables 4 and 5 give a summary of the coefficient signs and adjusted R-squares. This isa test of the model. One sees that in general the signs are correct, with 345 out of 360signs correct in the shipments equation, and 155 out of 180 signs correct in the con-sumer sales equation." Given that the model was not initially designed using thesedata, this is a strong validation of the model.The adjusted R-squares ranged from 0.23 to 0.95 for the shipments equation andfrom 0.15 to 0.94 for the consumer sales equation. The average adjusted R-square is0.66 for the shipments equation and 0.57 for the consumer sales equation. The widervariation in adjusted R-square for the consumer sales equation is due to the use ofNielsen bimonthly data and the omission of some explanatory variables discussedearlier.4B. Evaluation of the Model: Fitted versusActual

The previous section partially evaluated the model using the number of correct signsfor the coefficients and adjusted R-squares. However, these measures do not necessarilyindicate how the model will do in predicting future shipments and consumer salesbased on future inventory levels. Therefore, a "simulation test" was used.The "simulation" test discussed in this section is a more stringent test of the modelthan evaluating the residuals because the inventory values arecomputed from predictedconsumer sales and predicted shipments rather than actual consumer sales and ship-ments. The simulation begins with an initial estimate of inventory in period 1 and thenpredicts shipments and consumer sales for the next period. Next, the predicted values of

TABLE 5Frequenciesfor Adjusted R2 in Models

Shipment EquationR2 0-0.20 0.20-0.40 0.40-0.60 0.60-0.80 0.80-1.00

Number 1 6 13 27 13Sales Equation

A2 0-0.20 0.20-0.40 0.40-0.60 0.60-0.80 0.80-1.00Number 7 12 14 17 10

" There are 60 equation estimates (6 markets, 10 sizes) for consumer sales and shipments. One coefficienthad an ambiguous sign, trend and was not included in the calculation of number of correct signs.

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ROBERT C. BLATTBERG AND ALAN LEVIN100.00

zNa

1978 1979 1980 1981 1982FIGURE 3. Factory Shipments Model.

consumer sales and shipments are then used to calculate inventory for the next period.The process continues for all the remaining periods.For the simulation to fit the sales and shipment data accurately requires that eachperiod's consumer sales and shipment estimates be reasonably accurate in order tocompute the inventory values. If this is not the case, the simulated versus actual datawill begin to depart. However, the simulation test is less stringentthan a holdout samplebecause the parametershave been estimated on the data used in the simulations. Later,in ?6, these models will be evaluated by making forecasts and then comparing theseforecasts to the actual results.Figure 3 shows actual versus simulated shipments for a specific size in a given

market. Figure 4 shows actual versus simulated consumer sales. For the shipmentsequation certain peaks and valleys are missed, but, in general, the model closely fitsactual shipments. For the consumer sales equation, the model does not track as well,but, again, it follows actual consumer sales. The reason the consumer sales equationdoes not do as well is that Nielsen data are not very accurate measures of true consumersales. This was emphasized earlierin discussing estimation issues, and it is important torealize that Nielsen data are also estimates smoothed over a two-month period and notsums of actual monthly consumer sales.Based on the simulation test, the model appears to be able to forecast future ship-ments and consumer sales given initial inventory values.12 This will be important in thenext section which describes how the model will be used to evaluate promotions.

60.000

50.01 0ACTUAL.440.000 ..., [ ''' [ I ' I' I '' ] I ' ' ' ' I I1978 1979 1980 1981 1982~. - ACTUALqL - FITTED

FIGURE 4. Nielsen Sales Model.12 Every model built for a market/size was simulated. The data given in Figures 3 and 4 are just oneexample. They are representative of the fits across most market/size combinations.

?II ,~~~~~~~~~~~~~~'

0 1 I It ? a? ? I... ,?I ? I.I I

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EFFECTIVENESS AND PROFITABILITY OF TRADE PROMOTIONS5. Evaluation of Trade Promotions

As stated in the introduction, the primary objective of this model is to evaluate salesresponse and profitability of a trade promotion. The purpose of this section is todescribe the methods used for evaluating the effect of a specific promotion on ship-ments, consumer sales and profits.5A. Sales and Shipment Response

The first issue will be a promotion's effect on sales and shipments. The method usedis to simulate the simultaneous equation system with and without the trade promotion.This approach gives the "average"effect of the trade promotion. Actual shipments andconsumer sales for the period will not be used because factors other than trade promo-tions affect them.Figure 5 shows the monthly effect of the promotion. During the first month of thepromotion, shipments increase dramatically over what they normally would have beenhad there not been a promotion. The next few periods of the promotion also showincremental shipments, although less dramatic, due to the nature of the trade dealpromotion and the firm's contractual buying limitations. The final peak occurs afterthe promotion period and shows the carryover effects, i.e., those orders placed at thedeal price which were not shipped until the following period. This discrepancy betweenorders and actual shipments is an important phenomenon which must always be ac-counted for in the development of the models. The major peak at the end of thepromotion period also indicates that distributors are loading their inventories as thedeal period is about to expire. The result of this loading is shown by the troughfollowing the deal period. Finally, as time goes on shipments graduallyreturnto normallevels.The dotted line in Figure 5 indicates sales response as a result of the promotion. Twophenomena should be noted. First, consumer sales effects lag shipment effects by atleast a few time periods. This should be expected since it takes time for the product tomove through the distribution pipeline into the consumer's hands. Second, consumersales activity is much smoother than shipments. This is due to the lagged effect'of thepromotion and retailer stockpiling of the product.Figure 6 demonstrates the incremental effect of a promotion on both shipments andconsumer sales over time. As Figure 6 indicates, although shipments may increasesignificantly during a promotion period, this increase must ultimately be passedthrough the system, as shown by the dotted sales lines. The entire process generallytakes several months before the incremental inventories are passed through the whole-saler and retailer.

2.0l1.8 Promotion ends1.6 / \ caov.

o 14 / \ i< 1.2 Trade deal Consumer salesc 1.0 begins /0.8 nvent \y0.6-0.4 - I t I _. ; r

FIGURE 5. Ratio of Shipments With to Without Trade Deal.

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t 40.000 \20.000- /-Trade deal /begins _-o.-C-umulative incremental consumer saleso -5. Iv-- from the trade dealII ' III IV * I II III IV ' I1979 1980 198i- FACTORY SHIPMENTS- - NIELSEN ALES

FIGURE . Cumulative Incremental Effect of Trade Deal.

Figure 6 also shows that in the long run, the incremental increase in consumer salesequals the incremental increase in shipments. This occurs because over the long run it isnecessary for shipments to equal consumer sales. If the trade promotion does notincrease consumer sales, then it merely shifts the timing of the retailer'spurchases. Thisis the key to analyzing the profitability of a trade promotion. In general, the more theretailer passes through to the consumer relative to the quantity shipped on deal, themore profitable the promotion will be.In conjunction with the determination of sales response due to a trade promotion, itis also important to understand the financial implications of running a trade promo-tion. This issue is discussed below.

5B. Profit Analysis of the Trade PromotionEvaluating the profitability of individual promotions allows the marketing managerto understand the financial effect of a trade promotion. Although one might argue thatpromotional expenditures may be utilized to gain or retain market share over competi-tors, an understanding of profitability should make a marketing manager more effec-tive in deciding the types of trade promotions campaigns to use.Analyzing the profitability of a trade promotion requires cost accounting informa-tion and the number of units sold at the reduced price. The accounting information isused to determine the cost of goods sold so that the marginal cost of each unit of theproduct can be measured. The quantity sold at a reduced price during the promotion isrequired because not all units sold during the promotion period are purchased usingpromotional allowances.The following procedure was used to assess the profitability of individual promo-tions:1. The difference in shipments between running a promotion during a particularperiod of time and not running that promotion was computed each month, using the

models estimated from the historical data (see ?5A).2. Incremental unit shipments due to a promotion were computed by summing theunit differences created in Step 1 over an extended period of time until the cumulativeeffect did not change from month to month.3. Incremental dollar shipments due to a promotion were computed by multiplyingthe unit differences in Step 1 by that month's price. Next, the dollar differences weresummed, giving total incremental promotional dollar shipments.1313It should be noted that since prices change over time, the incremental dollar shipments would usually notmatch incremental unit shipments multiplied by the current period's price.

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250.000200.000150.000100.000

o) 50.0000

-50.000-100.000-150.000-200.000-250.000

-1

in n i

SIZE Xl I RSIZF X? I SIZE X3 I S7F X4

/~~~~~~~~R7~~z

0 INCREMENTAL SHIPMENTS ($)El INCREMENTAL GROSS PROFIT ($)Q COST OF DEAL ($)O INCREMENTAL NET PROFIT ($)

FIGURE . Comparison of Promotion Across Product Sizes Sep 79-Dec 79 8.3%Off-Invoice Deal.

4. Incremental Gross Profit was computed by multiplying the incremental dollarshipments by each period's product gross margin.5. Deal Cost was computed by multiplying the total promoted shipments sold duringthe period by the effective discounted dollar price. The total percentage of a month'sshipments sold on the trade deal were 80%for months during the promotion and 50%for the month immediately after the deal ended. Thus, the amount sold on trade deal iscomputed by multiplying total unit shipments sold during the promotion period by80%plus 50% of the total unit shipments delivered during the month after the promo-tion to allow for carryovereffects. The 80%and 50%factorswere utilized as estimates ofshipments sold at the promoted price, based upon an analysis of total, regular andspecial price shipments across products.14Using the data displayed in Figures 5 and 6 one can compute the profitability ofrunning the trade promotion. Figure 6 shows that incremental sales during the promo-tion period were 55,000 units and 15,000 for the month following the promotion. Theregularsales, not given in the graphs,were approximately 20,000 units per month. Thusduring the four months of the promotion (September through December), 80,000+ 55,000 = 135,000 units were sold. In the period after the promotion, 35,000 unitswere sold.The promotion being analyzed was an 8 %off-invoice promotion. Regular price was$12.00 and so the discount was $1.00. Utilizing the algorithm outlined above, total14 These percentages are usually obtained from historical promotional information available in most com-panies. The 80% and 50%were averages across trade deals. Due to random fluctuations a given trade dealmight deviate slightly from trade deal to trade deal.

139

J. ,4 -.-- .- 11 41 L. Z% I


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shipments sold on promotion were equal to 80% of product shipments during thepromotion period puls 50% of the product shipments for the period immediatelyfollowing the end of the promotion period. If the off-invoice allowance is $1.00 percase, then the total cost of the promotion is $1.00 X [(0.8 X 135,000) + (0.5 X 35,000)]= $125,500.The gross margin percentage for this product was 50% or $6.00 per case. From Figure6 one sees that long-run incremental increase in shipments was 15,000 units. Then, theincremental profit for the additional unit was $90,000.Combining the two calculations of deal costs and incremental profits shows that thedeal lost $35,500 in total. Thus, while shipments actually increased approximately15,000 units, the cost of discounting shipments normally sold was greater than theprofit gained from the promotion.For this particularfirm, an evaluation of the profitability of their promotional activi-ties across products, markets, promotion types and time was performed and displayedgraphically. Examples of these results are shown in Figures 7-10. Each graph showsfour bars for each of the product-area-time-promotion types being assessed. The firstbar indicates incremental dollar shipments. The second bar shows incremental grossdollar profit. The third bar displays the dollar cost of the promotion and the fourth barindicates the incremental net dollar profit of the promotion. It should be noted thatincremental net dollar profit really represents an opportunity cost, and not a directprofit or loss to the individual product-market being assessed; that is, a loss due to apromotion indicates expenditures which could have been utilized for other activitiesbut instead were spent on a promotion. A profit indicates that the promotion generatedenough incremental business to cover the cost of running that promotion.

250.000 ___200.000 '150.000-100.00050.000--50.000-100.000-150.000o

etc Ico+ , , / 0fi

,N l- I


19/24

EFFECTIVENESS AND PROFITABILITY OF TRADE PROMOTIONS250.000200.00(

? \150.000f

^ 5C50.000-0-

0*1C INCREMENTAL S IPMENTS (

-so5.o -

8.3%OFF INVOICE I 3% SALES DRIVEO INCREMENTAL SHIPMENTS ($)a INCREMENTAL GROSS PROFIT ($)? COST OF DEAL ($)0 INCRFMFNTAI NFT PROFIT (l

FIGURE . Comparison of Invoice vs Sales Drive Sep 79-Dec 1979 Product X-Market 1.

Figure 7 shows an evaluation of a promotion for 4 sizes, aggregatedacross all mar-kets. It shows that certain sizes "lost" money and others were profitable as a result ofthis particular promotion. It is comforting to know that not all product promotionsresult in lost profits. In this case it meant a change in strategy for the firm since thelargest selling size was also the greatest "loser" in profits when this promotion was run.Figure 8 shows a comparison of a particulartype of promotion for one product-areaacross time. As Figure 8 indicates, different off-invoice percentages cause differenteffects depending upon when the promotion is run, how long it is in effect, and howsoon after another promotion is run.Figure 9 compares two promotional types for a particular product. As one can see,the off-invoice promotion generates much higher incremental dollar shipments thanthe sales drive promotion, but at a greater cost. The off-invoice promotion might bemore effective in gaining market share, whereas the sales drive might be better inmaintaining share while minimizing losses.The analysis of the trade promotions given in Figures 7-10 gives mostly negative

results. They show that most trade promotions do not pay out. This result is commonlyfound by most researchersstudying trade promotions.15There are several reasons:1. Trade deals probably do not directly pay out, and are used defensively ratherthanto increase profits.2. The models do not directly adjust for maintaining distribution through tradedealing.'1 See, for example, Chevalier and Curhan (1976).

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120.000

(,)


21/24

EFFECTIVENESS AND PROFITABILITY OF TRADE PROMOTIONSTABLE 6a

Actual vs. ForecastProduct I-Market XActual Forecast Difference % Difference

81 4 33135.2 35900.0 2764.8 8.381 5 22328.3 26400.0 4071.7 18.281 6 74791.9 79100.0 4308.1 5.881 7 57437.6 53600.0 -3837.6 -6.7818 8 1320.2 72800.0 -8520.2 -10.581 9 55376.1 52700.0 -2676.1 -4.881 10 27397.7 33500.0 6102.3 22.381 11 47948.5 42100.0 -5848.5 -12.281 12 72004.6 80600.0 8595.4 11.982 1 49131.3 53400.0 4268.7 8.782 3 92490.8 82500.0 -9990.8 -10.8824 31801.8 35300.0 3498.2 11.0Total 695224.0 690300.0 -4924.5 -0.7

absolute error was 11.8% for product 1 and 11.3% for product 2. By grouping timeperiods together, the forecasting accuracy of the model improves. Utilizing the modelson a total product line basis across a twelve month forecasting period, the percentagedifference between the actual shipments and the forecast shipments was less than 4percent. Naturally, from month to month there were variations, but on the average itwas found that the models performed well as a forecasting tool.The overall accuracy of various product-areamodels varied. Generally, the higher thevolume sales of the product, the more accurate the model. Smaller products, in terms ofunit sales, did not perform as well as the largerproducts. Since product management isusually much more interested in their high volume sizes than in their flanker sizes, itwas felt that the models worked well.A number of other forecasting tests were performed by the organization using differ-ent scenarios and different product-area models. The results led to the utilization of

TABLE 6bProduct 2-Market X

Actual Forecast Difference %Difference814 11453.9 10300.0 -1153.9 -10.181 5 9497.2 11800.0 2302.8 24.281 6 24882.6 29400.0 4517.4 18.281 7 21236.1 20500.0 -736.1 -3.581 8 22881.5 25300.0 2418.5 10.681 9 19271.8 15800.0 -3471.8 -18.081 10 8029.2 9000.0 970.9 12.1811 1 15442.5 12400.0 -2042.5 -13.281 12 21672.9 20700.0 -972.9 -4.582 1 16556.6 15400.0 -1156.6 -7.082 2 16055.1 18600.0 2544.8 15.982 3 26184.0 29100.0 2916.0 11.182 4 12720.2 13000.0 279.8 2.2Total 225883.0 232300.0 6416.5 2.8

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ROBERT C. BLATTBERG AND ALAN LEVINthese models in the development of future marketing plans, coupled with managementinput and experience.

7. Uses of the ModelThe specific uses of the model presented are: (1) to evaluate individual promotions,(2) to identify the best trade promotions for each size and in each geographical area, (3)to evaluate future promotional plans and (4) to develop trade promotion tactics.16The model cannot be used to evaluate the effect of eliminating all past promotions orto evaluate new types of promotions. The reason is that the statistical methods utilizedcannot go beyond the scope of the data used to fit the model. Therefore, a strategy ofeliminating promotions which will affect other variables, such as distribution andcompetitive reaction, is so extreme that it is not possible for the model to evaluate thisstrategy.Another use of the model is to design test promotions for selected sizes and areas. Onthe basis of the results of the model, the firm realized that it is possible to eliminatepromotions and to increase profitability. However, to follow that strategy across 10sizes and 6 areas may reduce the overall profitability of the product. Even though themodel indicates certain strategiesor tactics that can be followed by the firm, it is muchmore sensible to design controlled experiments in which promotions are eliminated in1 or 2 areas with control areas following the "normal" promotional strategy. Thenbased on the experimental results, the strategy can be implemented gradually in othermarkets. Therefore, a recommended use of the model is to identify trade dealing tactics

and then design experiments to test their effects. The model can be used to track andevaluate the test strategies. This is similar to the adaptive control approach recom-mended by Little (1966).Using the model developed, the firm found out that most of their promotions werenot profitable. This had been suspected by the firm but not documented. The modelallowed the firm to analyze correctly the profitability of their trade promotions. As aresult of the analysis of the firm's past promotions, the following recommendationswere made.1. More stringent contractual requirements. These might include such areas as re-quirements for consumer pass through of discounted items, use of count/recount sys-tems so that the promotional allowances were paid only on the units sold to theconsumer during the promotional period, and incentives which allow distributors tobuy on deal only if they increase their purchases relative to prior periods.2. Increase consumer promotional spending. These included increased advertising,couponing, and special packaging where increased demand by the consumer would"pull" the product through the system.173. Fine tune promotion strategy. Given the current trade promotion program, it wasdetermined that reducing the discounts being offered, shortening the promotion dura-tions and lengthening the time between promotions might be more effective than thecurrent promotional program.

Overall, this model allows the firm to evaluate its promotional history. The results ofthis process can then be used to develop future promotional strategies.In addition, the16 The model simulates sales and shipments under different alternative trade deals. It then calculates

expected profits. This thus allows the model to be used to evaluate alternative trade deal tactics such asshortening the length of the trade deal.17 Couponing and special packs were not incorporated in the model but were examples of pull-orientedpromotions the firm could use.

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model-generated forecasts can be used in product scheduling or development of realis-tic sales quotas. Regional and national promotional evaluations can also be developedthrough aggregations of individual product-market simulations.8. The Model Applied to Scanner Data

The model developed in this paper was applied to manufacturer shipment data andNielsen bi-monthly consumer sales data. In the last year several firms have begun tooffer scanner data by retailer in selected U.S. markets. An example is Nielsen's ScanTrack data.The availability of scanner sales data will enhance the model currently developed. Itwill eliminate many of the data problems described in ?3. More importantly it willprovide more accurate estimates of the retail promotions that result from trade promo-tions. It will provide more accurate sales estimates of the effect of these retailerpromo-tions for a brand and the effect on competition.The model as described in this paper can easily be applied to scanner data. Theconceptual structure still applies. The major difference will be more accurate estimatesof the model's parameters.9. Summary

The purpose of this paper has been to develop a model in which the sales effects andprofitability of trade promotions have been evaluated. The model has provided firmswith a number of analyses and results that have highlighted many of the problems firmscurrently have with trade dealing. These include:1. Lack of consumer pass through of trade deals.2. Heavy forward buying by retailers, making many trade deals unprofitable.3. Variability in effectiveness of trade deals across sizes and markets (sales districts).There are, however, many questions not currently answered or understood. Furtherresearch is required in a number of important areas of trade dealing.1. Competitive environment of trade dealing-Can a firm reduce trade deals toincrease long-run profitability when competitors do not reduce trade deals?2. Trade deal effectiveness-When are trade deals effective? In which product cate-gories? Which sizes? Which types of retailers?

3. Data availability-In the next several years scanner data will be available for mostlarge SMSA's. How will the availability of these data change the models currentlybeing used?4. Nonpackaged goods categories-How can models and analysis of trade promo-tions be conducted for durable goods and non-packaged goods products such as cloth-ing, electronics, etc.?It is hoped that the model presented in this paperwill serve as the beginning of futureresearch in this area. 818This paper was received November 1984 and has been with the authors for 3 revisions.

ReferencesAbrahim, Magid, and Leonard Lodish (1987), "PROMOTER: An Automated Promotion Evaluation Sys-tem," Marketing Science, 6 (Spring), 101-123.Blattberg,Robert C., Gary Eppen and Joshua Lieberman (1981), "A Theoretical and Empirical Evaluation ofPrice Deals for Consumer Non-durables," Journal of Marketing, 45 (August), 116-129.Brown, Robert G. (1977), "A Model for Measuring the Influence of Promotion on Industry and ConsumerDemand," Journal of Marketing Research, 10 (November), 38-0387.

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146 ROBERT C. BLATTBERG AND ALAN LEVINChevalier, Michel and Ronald Curhan (1976), "Retailer Promotions as a Function of Trade Promotions: ADescriptive Analysis," Sloan Management Review, 18 (Fall), 19-32.Dolan, Robert J. (1987), "Quantity Discounts: Managerial Issues and Research Opportunities," MarketingScience, 6 (forthcoming).Frank, Ronald E. and William F. Massy (1965), "Market Segmentation and the Effectiveness of a BrandsPrice and Dealing Policies," Journal of Business, 38 (April), 186-200.Goodman, David A. and Kevin W. Moody (1970), "Determining Optimum Price Promotion Quantities,"Journal of Marketing, 34 (October), 31-39.Kuehn, A. A. and A. C. Rohloff (1967), "Consumer Response to Promotions," Promotional Decisions UsingMathematical Models, P. J. Robinson (Ed.), Boston: Allyn and Bacon.Lal, Rajiv and Richard Staelin (1984), "An Approach for Developing an Optimal Quantity Discount PricingPolicy," Management Science, 30 (December), 1524-1539.Little, John D. C. (1966), "A Model of Adaptive Control of Promotional Spending," OperationsResearch, 14(November-December), 1075-1097.Montgomery, David B. (1971), "Consumer CharacteristicsAssociated with Dealing: An EmpiricalExample,"Journal of Marketing Research, 8 (February), 118-120.Webster, Frederick E., Jr. (1965), "The Deal Prone Consumer," Journal of Marketing Research, 2 (May),186-189.