Maximizing profit of a food retailing chain by targeting and promoting valuable customers using Loyalty Card and Scanner Data

European Journal of Operational Research 174 (2006) 1260–1280 www.elsevier.com/locate/ejor

O.R. Applications

Maximizing profit of a food retailing chain by targeting and promoting valuable customers using Loyalty Card and Scanner Data Gabor Pauler a

a,b,*

, Alan Dick

c

Department of Computing Science, Faculty of Engineering, University of Pecs, Hungary b Department of Marketing, School of Management, SUNY at Buffalo, USA c School of Management, University at Buffalo, USA Received 26 November 2003; accepted 8 March 2005 Available online 16 June 2005

Abstract In this paper, we set up a House of Profit Model, an approach of maximizing profit of a food retailing chain by targeting and promoting valuable customers. Our model combines

• • • •

segmentation analysis of households using Loyalty Card and Scanner Data, price and promotion elasticity analysis, simulation of effects of pricing and promotion, price and promotion optimization to maximize profit.

These components are well-known in the literature and each of them has received considerable independent study. However, in this study we combine each of these components into one consistent, application-orientated model. We then demonstrate using panel data that the combination has a synergic effect on the efficiency of estimation and the maximization of profit (e.g., price and promotion elasticity estimation is improved by conducting it within market segments rather than across an entire hetereogeneous population). These estimates are further improved by incorporating ‘‘pass through’’—a functional relationship between a retailerÕs unit prices and unit costs.  2005 Elsevier B.V. All rights reserved. Keywords: Marketing; Loyalty Card; Scanner Data; Price elasticity analysis; Price and promotion optimization

*

Corresponding author. Address: Department of Computing Science, Faculty of Engineering, University of Pecs, Hungary. Tel.: +36 309 015 488; fax: +36 72 425 461. E-mail addresses: [email protected], [email protected]ffalo.edu (G. Pauler), mgtdick@buffalo.edu (A. Dick). 0377-2217/$ - see front matter  2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.03.028

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1. Introduction Electronic Loyalty Card systems have been used in retailing for a long time, but only a small portion of their information potential is used in everyday business practice. Supermarkets were the fourth industry after banks, airlines and gas retailing using Loyalty Cards widely. Two major paradigms for managing Loyalty Card systems have emerged in the supermarket industry. In the discount-orientated paradigm, the main objective of the Loyalty Card system is to generate loyalty giving out rewards in mass promotions (Hughes, 1999; Curtis, 1999; Lewis, 1998; Partch, 1999). The database marketing-orientated paradigm states that Loyalty Card cannot generate loyalty with simple mass promotions. Its purpose is collecting widespread transaction- and socio-demographic data from customers and design profitable, customized deals (Beenstock, 1999; Lee, 1996). In this paper, after a brief overview of the relevant literature, we refine the second paradigm by introducing our House of Profit Model. Our combined approach maximizes the profit of a food retailing chain by targeting and promoting valuable customers. The model is based on common components of the marketing literature including: • • • •

segmentation analysis of households using Loyalty Card and Scanner Data, price and promotion elasticity analysis, simulation of effects of pricing and promotion, price and promotion optimization to maximize profit.

However, our approach contains major improvements. We combine these components into a quantitative model with considerable synergic effects. First, Loyalty Card and Scanner Data from a grocery chain is used to identify valuable customers. Three segmentation measures are computed for each customer: Total sales, Total profit and Sales gap coefficient (a measure of consumer spending at stores outside of the grocery chain). Combining these three measures, households are grouped into eight segments. Then, price and promotion elasticity analysis within all segments is performed in parallel. This reveals the competitive/complementary relationship of the different products. The within-segment estimation of the profit functions and price elasticity coefficients provides better model fit than estimation using data pooled across segments. We then employ non-linear gradient optimizations to search within-segments for the optima of pricing and promotions. This provides better overall results than global optimization. In the literature the concept of ‘‘pass-through’’ is well known (see for example, Walters, 1989). It suggests that strong manufacturers force weaker retailers to pass through trade discount to the consumers. We extend this concept based on empirical data by incorporating ‘‘pass-through’’ in price elasticity analysis as the functional relationship between unit price and unit cost of a product to the retailer. This further improves the efficiency of profit estimation and maximization. The result is a Loyalty Card system which enables managers to customize pricing and promotion among targeted households/segments to reach maximal profit or market share. The validity of our model is statistically tested using a data warehouse of a regional food retail chain in the USA. The data consist of more than 150 stores, 3 million households, 200 million transactions and 2 billion purchased items.

2. Overview of literature The literature is overviewed in two main sections corresponding to different components of our model. In the first section we examine the literature related to targeting customers and discuss how our approach

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builds on existing literature. Then we examine literature related to consumer promotions, and discuss how our approach combines the fractionated approach taken in previous research. 2.1. Targeting customers The most common method to target valuable customers is the Recency–Frequency–Monetary Model described by Bellman, 2001; Bult and Wansbeek, 1995; Hughes, 1995; Sachs, 1997; Schoenbachler et al., 1997; Raider, 1999: Recency of the customer (R) is measured as date of last purchase. Frequency (F) refers to the number of transactions falling within a particular time window. Monetary (M) represents the total amount of money spent. Recent, frequent customers who spend the most money are considered the most valuable. Typically, in this paradigm, the R, F, and M variables are cut into (1 . . . 5) quintile intervals. The resulting crosstabulation of the R · F · M quintiles indicates the number of customers falling in each of the 125 cells. The consumers in the most valuable cells (e.g. R5F5M5) are then selected for direct mail promotion. While widely accepted, the RFM Model still faces several criticisms in the literature. RFM deals with separate loyalty cards instead of household-level consumption. This analysis can seriously misrepresent the nature of the household, especially when there is joint consumption and/or decision making. We avoid this error in our approach by combining individual cards within a household to create household-level data. Additionally, RFM does not consider purchases made at competitors, so it provides little insight regarding the full potential spending of customers. In our model, we attempt to rectify this limitation by creating a Sales Gap Coefficient, which represents purchases made at competitors. MacStravic (2000) claimed that RFM cannot be used in industries where the relationship is tenuous with the customer. Since Frequency and Monetary are whole-time aggregates, they do not reflect the value of newly joined customers who have the potential to become big spenders. Consequently, RFM will undervalue these customers. Therefore, in our model we will use time averages instead of simple aggregates. 2.2. Promoting to customers The most effective ways to promote to valuable customers is hotly debated in the price elasticity literature. The efficiency of using price promotion alone is criticized by Ehrenberg et al. (1997) who showed that it is not effective in generating new customers and long term loyalty, and can have a negative effect on profitability. Cheong (1993) showed earlier that the higher the price elasticity of demand, the higher rate of coupon redemption. Store-level determinants of non-price promotions are debated by the following authors: Bolton (1989) examined 12 brands in 12 stores and stated that price elasticity of demand was uncorrelated with promotion, but negatively correlated with displays. Hoch et al. (1995) showed that price elasticity of demand had a negative correlation with household education level and positive correlations with minority membership and family size. Karande and Kumar (1995) examined unit price, sales, coupon redemption, displays and ads of three major brands of three product categories (ketchup, yogurt, soup) in seven stores for 156 weeks. They used loglinear multiplicative models to estimate demand functions, while sales time series were filtered by an AR1 autoregression model. External factors were connected with estimated functions using linear regression. Price elasticities of sales were positively correlated with market share, ad frequency, announcement of promotions, while negatively correlated with price tier, frequency of promotion and display and their coincidence with competing brandsÕ promotion. Shankar and Krishnamurthi (1996) found that price elasticity of demand had a negative correlation with displays, but a positive correlation with Everyday Low Pricing. Francis et al. (1998) used loglinear additive models to estimate demand functions, while sales time series were filtered by an AR1 autoregression model. Seasonal and celebration effects were filtered

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by dummies. External factors were connected with estimated price elasticities of demand using linear regression. Price elasticities of demand were negatively correlated with market share and income of the households, while positively correlated with intensity of promotion and minority membership. The effects of promotions on the in-store competition between private label and national brands are also a very critical issue for a retailing chain. As private labels usually have much higher margins than their national brand counterparts. Mercer (1996) examined the market share of premium priced-, market leader-, and private label brands. He showed that the price promotion of a market leading brand mostly threatened private label brands, not other premium brands. Summarizing this brief literature review, we note that there is sophisticated research in various fields. Some of these studies examine price promotions, others look at private labels, others examine price elasticity, while still others focus on segmentation. However, the literature lacks a combined approach which encompasses data processing, segmentation, price/promotion elasticity, profit maximization into one consistent, application-orientated, quantitative model. We will develop such an approach in the next chapter. 3. House of Profit Model The purpose of the House of Profit Model is to maximize the profit of a retailing chain by targeting and promoting their most valuable customers. In this chapter we first overview the modelÕs basic assumptions, then we describe its segmentation method to target valuable customers, finally its implications for promotion are discussed. 3.1. Assumptions about application environment • The food retailing chain has multiple store locations and a profit maximization objective. • The supply chain is short. The food retailing chain sells directly to end-users, and it buys directly from manufacturers. • There is fierce competition with other retailing chains. • An Electronic Loyalty Card system is installed, and loyalty cards are distributed. • Using Scanner Data from the Loyalty Card system, the chain can track the dates, times of purchase, barcodes of products sold, number of units sold, $ sales, $ profits (including all significant direct and indirect costs), and the redemption of electronic, manufacturer, and store coupons. • Data from the cards can be aggregated into households by matching the addresses given by consumers when they sign up for the cards. • Individual products identified by barcode can be aggregated along a multi-level functional, extendable product hierarchy with super categories at the top.

3.2. Targeting valuable customers with segmentation Step 1. Three segmentation measures are computed for every household: s X Total sales; $=household S h ¼ S ht h ¼ 1 . . . H ;

ð1Þ

t¼1

Total profit; $=household

Ph ¼

s X t¼1

Pht

h ¼ 1 . . . H;

ð2Þ

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Sales gap coefficient; %

Gh ¼

rS ht S ht

h ¼ 1 . . . H;

ð3Þ

where t = 1 . . . s—time periods, weeks. h = 1 . . . H—households. Sht—$ Sales for hth household in week t, based on net unit prices. All electronic coupons and paperbased manufacturer/store coupons valid on the current week and redeemed by the current household are subtracted from the selling price of the chain. Pht—$ Profit for hth household in week t. $ Profit term is based on the difference between net unit prices and direct unit costs. No taxes or indirect cost are considered. Taxing rules vary from state to state and indirect costs are influenced by many non-pricing-related issues. Thus, their inclusion would blur the results. Direct unit costs are calculated as quantity-weighted average unit cost for the orders and stock during the current week. This includes all quantity deals or any kind of allowances received by the retailer from manufacturers. rSht—standard deviation of weekly sales, $/household. S ht —average weekly sales, $/household. Our segmentation scheme is a refined version of the one proposed by Niraj et al. (2001). He segmented customers by profitability and potential size of basket. While it is possible to acquire household level potential spending data across product categories from syndicated data sources, this would cost more than a dollar per household. For three million households this would become cost prohibitive. We overcome this difficulty by noting that in the food retailing industry, household inventory cycles typically do not exceed 4–6 weeks even for non-perishable products. Over a longer time window (e.g. one year), the consumption of loyal customers is cyclic but evenly distributed, except during the peak seasons (Thanksgiving, Christmas, etc.). For less loyal customers, competitorsÕ deals can easily generate short term store shifts, creating wide gaps in by household sales time series data. Thus, disloyalty is manifested in the presence of sales gaps, which we estimate using the well-known concentration measure described in (3). Distortions caused by peak seasons can be prevented by downscaling the sales from those weeks by percentages based on store managersÕ experience. NirajÕs profitability measure is a relative measure and does not indicate the absolute size of profit, which is the overall goal of the chain. Instead of using his profitability measure, we analyze its components separately in (1) and (2). Since signup for cards is a dynamic process, there is a lot of variation in the durations of Loyalty Cards, which is measured by the amount of time passed from date of signup. Since we are aggregating to the household level we also compute Durations of households, which is measured by the duration of the oldest card in the household. Simple aggregation across duration as often done with the RFM model, cannot discriminate truly bad customers from good ones that have recently joined. Therefore, totals of households with duration between 3 months and 1 year are up scaled by dividing them by duration. Households with less than three months duration are discarded from the sample because of insufficient data. Step 2. Households were grouped into eight groups by running k-mean clustering on their three segmentation measures with the following settings. Initial values of the eight cluster centers were set combination of extreme values of the three measures:  H   H   H  H H H MinðS h Þ; MaxðS h Þ  MinðPh Þ; MaxðPh Þ  MinðGh Þ; MaxðGh Þ . ð4Þ h¼1

h¼1

h¼1

h¼1

h¼1

h¼1

Segmentation measures are normalized into [0, 1] intervals using their partial distribution functions.

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Table 1 The largest segments Segment

Total sales 2 [0, 1]

Total profit 2 [0, 1]

Sales gap 2 [0, 1]

1 2 3 4 5

Low = 0.152 Low = 0.132 High = 0.767 High = 0.831 Low = 0.181

Low = 0.131 Low = 0.111 Low = 0.351 High = 0.699 High = 0.634

High = 0.837 Low = 0.116 Low = 0.206 Low = 0.198 High = 0.701

During iteration, Dd/d = 0.005 convergence criterion was used, where d is the Euclidean distance of cluster centers on normalized measures (iteration converged in 385 steps). Households were grouped to the nearest cluster center using Euclidean distance on normalized measures. In Table 1 we show [0, 1] normalized actual values of the biggest five cluster centers. The number of households grouped to cluster centers and denormalized values are omitted to maintain confidentiality. Segments are ordered from largest to smallest. 3.3. Promotion of valuable customers The results of the segmentation analysis suggest the following guidelines for promotion. First, avoid wasting promotion resources. Segment 2 (low sales, low profit, low gap) households should receive little or no promotions. These customers are already spending at their potential which is not very high. Thus promoting to them will not likely create a good return on investment as this segment is unlikely to increase their purchases. Promoting to Segment 1 (low sales, low profit, high gap) households should be also minimized. These customers are likely to be loyal customers of competitors, so promoting to them carries a big risk. The second guideline is sales gap filling. Segment 5 (low sales, high profit, high gap) households are infrequent customers but they buy high margin products. Since they represent a more attractive segment, they should receive promotion attention. Specifically, promotions to these consumers should attempt to switch them over to our chain for a greater percentage of their shopping trips. The third guideline is profit extraction. Segment 3 (high sales, low profit, low gap) customers are loyal to the chain but they consume simple low margin products. Promotion to them should focus on switching them to high margin products. The fourth guideline is to retain and reward the best customers. Segment 4 (high sales, high profit, low gap) consumers deserve special attention to insure that they stay that way. Using our guideline for promotion we develop a three dimensional segmentation scheme. You can think of scheme as a two-story house with four rooms per story (see Fig. 1). With the four promotion guidelines above, we want to move as many people as possible from worst rooms to best rooms of the house. Consequently, we name this House of Profit Model. 3.4. Promotion techniques examined In the analysis, we differentiate three groups of promotion tools. First, there are basic price-related promotion tools which include everyday low price, seasonal price reductions, Loyalty Card electronic coupons, manufacturer coupons, and store coupons. The disadvantage of these tools is that customers form expectations about their occurrence over time and can anticipate the various deals that will be offered. Also, competitors can easily copy these deals which reduce their efficiency. A second category of promotion tools include basic non-price related tools such as ads, displays, gifts, and sweepstakes. These tools are not necessarily product specific.

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Fig. 1. Overall scheme of the House of Profit Model.

Finally, a third category of promotion tools are what we refer to as integrated tools. These include product bundling, conditional rewards, and parallel price promotion of complementary products. Using a Loyalty Card system allows us to differentiate the use of these integrated tools across segments. In this paper, all price-related tools are incorporated in unit prices, non-price related tools form separate group of variables, and their integrated usage is analyzed. Effective usage of the integrated tools requires extensive knowledge about demand levels of different products and their cross-relationships with other products. These are defined with the following terms: Own price elasticity of DemandjSalesjProfit ¼

% Demand DjRevenue DjProfit D of product X ; 1% Unit price D of product Y ð5Þ

where D is change of the current measure. For Demand, most of the time this is negative. For Sales, this should also be negative most of the time but it could approach 0 or even become positive if the price reduction is badly designed. For Profit, this is positive at lower prices and negative at higher prices. Cross price elasticity of DemandjSalesjProfit ¼

% Demand DjRevenue DjProfit D of product Y . 1% Unit price D of product X ð6Þ

Cross price elasticity is negative for complementary products, and positive for competing products. Cross elasticity need not be symmetrical. That is, the cross elasticity of product of product X on product Y can be different from the elasticity of product Y on product X since the different products can have different abilities to draw sales. Price elasticity of total DemandjSalesjProfit ¼

% total Demand Dj total Revenue Dj total Profit D . 1% Unit price D of product X ð7Þ

This is usually negative for successful deals as an individual price reduction positively influences totals. For unsuccessful deals this would be negative as an individual price reduction causes a loss in total sales or profit. Own-, cross and total elasticity of the basic non-price related promotion tools can be defined in a similar way. The only difference is that signs of coefficients will be in the opposite direction of those corresponding to price elasticity.

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3.5. Pricing and promotion model 3.5.1. Basic concept The basics of our approach are consistent with the price elasticity models in the literature described by Bolton (1989), Hoch et al. (1995), Karande and Kumar (1995), Shankar and Krishnamurthi (1996), Francis et al. (1998), Blattberg and Wisiniewsky (1995), Mercer (1996), Cotterill et al. (2000). Demand functions are estimated with Loglinearized OLS models from historic price-, promotion- and demand data. Price elasticity coefficients of Demand/Revenue/Profit are computed from first order partial derivates of the estimated demand functions. We depart from the traditional literature in the following way. Price and promotion elasticity analysis is conducted in parallel within each loyalty/profitability segment rather than computing the coefficients across the entire population. Within-segment estimation of the profit functions and price elasticity coefficients provides better model fit than estimation based on the entire population. In the formulation of the model, indexing elements by segments is omitted for simplicity. We incorporated ‘‘pass-through’’ between manufacturers and retailer (Walters, 1989) in price elasticity analysis as the functional relationship between unit price and unit cost of a product to the retailer. This makes profit estimation and optimization more effective. We use the index of periods as dummy variable in all OLS regressions to eliminate linear trend effects. Also, a seasonal dummy measured on [0, 1] scale is used to eliminate the effects of shopping peaks (Easter, Labor Day, July 4th, Halloween, Thanksgiving, Christmas, New Years Eve, etc.). We omitted dummies from the formulation for simplicity. 3.5.2. Functions of the model Indices t = 1 . . . s—time periods, weeks, i, j = 1 . . . n—products, k = 1 . . . m—simple non-price related promotions. Demand (units sold) function of ith product ! n m X pj X Bi ak Di ¼ exp 1   i ¼ 1 . . . n. uii uij k¼1 vik j¼1

ð8Þ

Independent variables: pj —net unit price of jth product (including all price-related promotions), ak—intensity of kth non-price related promotion (units of non-price promotion). Parameters estimated from historic data: Bi —potential basket size of ith product, $. This is the maximum $ Sales amount that can be extracted from the market (see Fig. 2). uij —relative unit utility of jth product versus the ith product, $. Own utility uii indicates the intrinsic value of the product itself to the customer, so it is usually positive. Cross utilities uij indicate the opportunity cost of shifting from one unit of product i to one unit of the product j. They are negative for

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Measures:

Units sold

Total sales, $

Total profit, $

Bi

10.00 9.00 8.00 7.00

Basket size, $

6.00 5.00 4.00 3.00 2.00

gi

1.00 0.00 -1.000.00

Unit utility, $ 1.00

2.00

3.00

4.00

5.00

6.00

7.00

-2.00

8.00 Unit price, $

-3.00 -4.00 -5.00

Fig. 2. Theoretic example of basic functions at one product.

competing products and positive for complementary products. Without cross-effects, $ Sales of the actual product is maximized if its unit price equals its unit utility (see Fig. 2). vik—1 * unit utility of kth promotion for ith product, $. It is usually negative if the promotion supports the current product, and positive if it supports a competing product. Method of parameter estimation: Demand functions are log-linearized. lnðDi Þ ¼ lnðBi Þ  lnðuii Þ þ 1 þ

n X

pj

j¼1

ai ¼ lnðBi Þ  lnðuii Þ þ 1

m 1 X 1 þ ak uij vik k¼1

i ¼ 1 . . . n;

ð9Þ

i ¼ 1 . . . n;

ð10Þ

bij ¼ 1=uij

i ¼ 1 . . . n; j ¼ 1 . . . n;

ð11Þ

cik ¼ 1=vik

i ¼ 1 . . . n; k ¼ 1 . . . m.

ð12Þ

Parameters are estimated from historic data with OLS regressions: n m X X pjt bij þ akt cik þ eit i ¼ 1 . . . n; t ¼ 1 . . . s; OLS regression: lnðDit Þ ¼ ai þ j¼1

ð13Þ

k¼1

where pjt—net unit price of the jth product in the tth time period, $ (including all price-related promotions), akt—intensity of the kth non-price promotion in the tth time period, $, Dit—quantity sold of the ith product in the tth time period, units, ai —regression constant of demand function for the ith product, bij —regression coefficient of the jth product in demand function of the ith product, cik—regression coefficients of the kth non-price promotion in the demand function for the ith product, eit—error term for the demand function of the ith product in the tth time period, $.

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Bi ¼ expðai þ lnð1=bii Þ  1Þ i ¼ 1 . . . n; uij ¼ 1=bij i ¼ 1 . . . n; j ¼ 1 . . . n;

ð14Þ ð15Þ

vik ¼ 1=cik

ð16Þ

i ¼ 1 . . . n; k ¼ 1 . . . m.

Sales function of ith product S i ¼ pi Di

i ¼ 1 . . . n.

ð17Þ

Direct unit cost function of the ith product and incorporation of the concept of ‘‘pass-through’’. In the traditional Marketing and Economics literature, companies are reported to often use cost plus pricing. In other words, the retailer takes the direct unit cost of a product as given by a manufacturer and marks up the price by a given percentage. Additionally the concept of ‘‘pass-through’’ is widely known (Walters, 1989). Here, a strong manufacturer forces a weaker retailer to pass through trade discounts. This may not be the best strategy for the retailer as it may decrease sales of its higher margin private label products. In both of these examples, selling price is a function of direct unit cost. We extend the term ‘‘passthrough’’ by recognizing that the causality may be reversed if a strong retailer is dealing with a relatively weak manufacturer, or manufacturer of its private label products. In this case the retailer controls his selling price. When the retailer reduces the selling price, or gives out more discounts and coupons to reduce net unit price, sales will likely increase and the retailer will be in a position of ordering larger quantities from the manufacturer. This increases the lot sizes produced by the manufacturer and reduces his average costs. The retailer can force the manufacturers to share the savings through quantity deals, decreasing the unit cost to the retailer. Of course, manufacturers cannot go under their minimal long term Average Cost even for big orders, so the trend we can observe between net unit price and direct unit cost to the retailer in the practice is more parabolic than linear (see Fig. 3). Since the trend between direct unit cost and net unit price is strictly monotonic it could be modeled with a function in either direction to achieve the same results, as we donÕt have to make any assumption about casualty to incorporate pass-through in our model. We use net unit price as the independent variable of a parabolic direct unit cost function (see Formula 18), since it conceptually fits better with price elasticity analysis, where unit prices are typically used as independents. Direct unit cost function of ith product (taxes and indirect costs are not considered): ci ¼ gi þ fi p2i

i ¼ 1 . . . n.

ð18Þ

UnitCost, $

UnitPrice, $

Fig. 3. Observed time series in unit price · unit cost plot of a fruit product. Crosses are observations, the thin line is their sequence in time. The thick line is the parabolic trend line. Exact category and scale values are omitted to maintain confidentiality.

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Independent variable: pi —net unit price of ith product (including all price-related promotions). Parameters estimated from historic data: gi —minimal direct unit cost of ith product, $. This is the manufacturerÕs minimal long term Average Cost (LAC) (see Fig. 2), fi —pricing transmission coefficient of ith product, % (the strength of the relationship between direct unit cost and squared net unit price). Estimation of parameters: Direct unit cost functions are linearized using squares of unit prices qit as independents. Parameters are estimated from historic data with OLS linear regression: OLS regression: cit ¼ gi þ fi qit þ eit

i ¼ 1 . . . n; t ¼ 1 . . . s;

ð19Þ

where qit = pit2, where pit—net unit price of the ith product in the tth time period, $, cit—direct unit cost of ith product in the tth time period, $. It is quantity-weighted average unit cost for the orders and stock on the current week, eit—error term of ith product in the tth time period, $. If the R2 of the OLS linear regression is unacceptably low, we assume that there is no significant connection between unit price and unit cost. In this case, average of observed unit costs cit is used as constant ci. In practice, pass-through effects for major national brands and perishable private label brands in the retail food industry are very strong. Incorporating these effect in the estimation of direct unit costs results in much better fit in the estimated profit functions (see Formula 20), allowing for more efficient optimization. Empirically, this is shown in the tests of our model (see Part 4, Tables 8 and 9). Profit function of ith product Pi ¼ ðpi  ci ÞDi

i ¼ 1 . . . n;

ð20Þ

where pi—net unit price of ith product (including all price-related promotions), ci—direct unit cost of ith product. Total demand function of all of the products analyzed n X Di . D¼

ð21Þ

i¼1

Total sales function of all of the products analyzed n X Si. T ¼ i¼1

ð22Þ

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Total profit function of all of the products analyzed R¼

n X i¼1

Pi 

m X

ðxk þ y k ak Þ;

ð23Þ

k¼1

where R—total profit, xk—fixed cost of kth non-price promotion, $, yk—unit cost of kth non-price promotion, $. To follow the full costing principle of profit computation suggested by Niraj et al. (2001), we incorporated costs of promotions in the total profit function formulated at (23). 3.5.3. First order partial derivates To compute elasticity coefficients we take the partial derivatives of the Demand/Sales/Profit functions of individual products and total basket with respect to price and non-price promotion (see Table 2). 3.5.4. Price and promotion elasticity coefficients Elasticity coefficients (see Table 3) can be computed from first order partial derivates using the general relationship between the elasticity of function A and its partial derivate of function A by variable p:

Table 2 First order partial derivates

Derivate of: By price of: Demand

Own

Cross

Total

ith product ith product

ith product jth product i 5 j

oDi 1 ¼  Di uii opi

oDi Di ¼ opj uij

All products jth product n oD X Di ¼ opj uij i¼1

Sales

oS i ¼ opi

  p 1  i Di uii

oS i Si ¼ opj uij

 n  X oT S i Sj ¼ þ opj uij pj i¼1

Profit

oPi ¼ opi

  pi 1  2f i pi  Di uii

oPi Pi ¼ opj uij

 n  oR X Pi Pi ¼ þ þ gj  fj pj opj i¼1 uij pj

Derivate of: By promotion: Demand

ith product kth promotion

All products kth promotion n oD X Di ¼ oak vik i¼1

None

oDi Di ¼ oak vik

Sales

None

oS i Si ¼ oak vik

n X oT S i ¼ oak vik i¼1

Profit

None

oPi Pi ¼ oak vik

 n  oR X Pi ¼  yk oak vik i¼1

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Table 3 Price/promotion elasticity coefficients

Elasticity of: By price of: Demand

Sales

Own

Cross

Total

ith product ith product

ith product jth product i 5 j pj eDi ðpj Þ ¼  uij

All products jth product Pn

eDi ðpi Þ ¼ 

pi uii

p eS i ðpi Þ ¼ 1  i uii

Profit ePi ðpi Þ ¼ Elasticity of: By promotion: Demand

Sales

ð1  2f i pi Þ p  i ð1  fi pi Þ  gi =pi uii

None

None

Profit

None

eA ðpÞ ¼

oA=A oA p ¼ . op=p op A

eD ðpj Þ ¼

eT ðpj Þ ¼

pj uij

eR ðpj Þ ¼

ith product kth promotion ak eDi ðak Þ ¼  vik eS i ðak Þ ¼ 

D pj i¼1 ð uij

pj i¼1 ð uij

i¼1 vik

ak vik

eR ðak Þ ¼

Di

D Pn

eT ðak Þ ¼

Pi Þ þ Pj þ gj pj  fj p2j R

All products kth promotion Pn ak eD ðak Þ ¼

SiÞ þ Sj

T Pn

ak vik

ePi ðak Þ ¼ 

Di

Pn

pj eS i ðpj Þ ¼  uij ePi ðpj Þ ¼ 

pj i¼1 uij

ak i¼1 vik

Si

T Pn

ak i¼1 ð vik

Pi Þ  y k ak R

ð24Þ

All of this analysis is done separately in each segment. Segment-wise elasticity matrices can be constructed from own-, cross-, or total price elasticities of profit. For example, Table 3 provides these for Segment 3 (high sales, low profit, low sales gap). The profit of selected product categories is indicated in rows, and prices of these products are indicated in columns. The main diagonal contains own-coefficients, nondiagonal elements are cross-coefficients. In the first row, there are private label brand total-coefficients, in the last row all products total-coefficients. In our model, all price elasticities are functions of the unit prices of products, therefore we show their value at the historical average unit prices. Negative coefficients indicate complementary relationships among the selected products while positive coefficients indicate competitive relationships. In Table 4, actual product names are omitted and all coefficients are rescaled by a factor to maintain confidentiality. For example, within this segment (high sales, low profit, low sales gap), a price reduction of product National dessert 1 has a weak competitive effect impact on total profit of all private categories (0.124, see row 0, column 7) and total profit of all categories (0.012, see row 14, column 7). It also has a positive impact on its own profit (1.186, see row 7, column 7). Managerially, use of this elasticity matrix helps design bundled deals by identifying complementary products, are which consumed together. Two products should be selected for a bundled price deal only if they have a strong negative cross-coefficient and a negative total-coefficients. You would not want to promote a particular bundle if it negatively affected total profit within the segment. An analysis like this helps to achieve the promotion goals mentioned in Section 3.3.

1: Price, 2: Price, 3: Price, 4: Price, 5: Price, 6: Price, 7: Price, 8: Price, 9: Price, 10: Price, 11: Price, 12: Price, 13: Price, Private Private National National National National National National Private National National National Private fruit 1 fruit 2 drink 1 drink 2 drink 3 food 1 dessert 1 dessert 2 dessert 3 food 2 food 4 drink 4 drink 4 0: Profit, Private brands 1: Profit, Private fruit 1 2: Profit, Private fruit 2 3: Profit, National drink 1 4: Profit, National drink 2 5: Profit, National drink 3 6: Profit, National food 1 7: Profit, National dessert 1 8: Profit, National dessert 2 9: Profit, Private dessert 3 10: Profit, National food 2 11: Profit, National food 4 12: Profit, National drink 4 13: Profit, Private drink 4 14: Profit, All categories

0.417 1.441 0.064 0.047 0.016 0.173 0.068 0.154 0.088 0.028 0.063 0.297 0.060 0.046 0.164

1.318 0.152 1.719 0.060 0.043 0.380 0.205 0.129 0.231 0.127 0.266 0.521 0.028 0.039 0.419

0.463 0.533 0.386 0.403 0.347 0.388 0.389 0.362 0.084 0.193 0.455 0.299 0.316 0.557 0.368

0.511 0.718 0.423 0.521 3.102 0.335 0.245 0.056 0.578 0.482 0.511 0.293 0.369 0.330 1.151

0.349 0.271 0.747 0.742 0.303 1.201 0.211 0.689 0.355 0.517 0.379 0.344 0.316 0.614 0.449

0.051 0.040 0.136 0.093 0.004 0.029 2.206 0.079 0.035 0.250 0.137 0.063 0.071 0.006 0.048

0.124 0.184 0.107 0.056 0.045 0.116 0.117 1.186 0.085 0.209 0.012 0.071 0.073 0.145 0.012

0.065 0.034 0.090 0.006 0.047 0.045 0.039 0.194 1.241 0.001 0.038 0.031 0.076 0.069 0.046

0.114 0.147 0.049 0.091 0.074 0.044 0.017 0.044 0.085 1.437 0.051 0.012 0.100 0.008 0.021

0.566 0.716 0.745 0.212 0.081 0.373 0.025 0.548 0.050 0.576 2.956 0.400 0.190 0.357 0.116

0.218 0.235 0.242 0.088 0.036 0.079 0.082 0.004 0.009 0.003 0.004 1.338 0.085 0.017 0.036

0.145 0.147 0.235 0.403 0.005 0.210 0.110 0.208 0.053 0.042 0.037 0.192 2.521 0.875 0.167

0.016 0.033 0.150 0.205 0.045 0.001 0.059 0.105 0.019 0.221 0.054 0.060 0.176 2.676 0.038

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Table 4 Elasticity matrix

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For the low sales, high profit, high sales gap segment occasionally purchased prestigious products can be bundled with complementary perishable food products, which have shorter household inventory cycles and generate store traffic. This helps sales gap filling. For high sales, low profit segments, the frequently purchased national brand products can be bundled with high profit private label products to help profit extraction. Also, asymmetry of cross coefficients of private-national product pairs can be examined. For example, for category Drink 4 the national version has a strong competitive impact on private label (0.875, see row 13, column 12), while the reversed impact is not as strong (0.176, see row 12, column 13). In most of the cases, a price reduction of a national brand hits the private label hard, which cannot fight back with price promotion. This supports the earlier results of Mercer (1996) who similarly found such an asymmetry. Observing this asymmetry suggests the following questions to the manager. If the ingredients and packaging of the private and national brand products are comparable, why is the competition so asymmetric: • Is there a problem with the private label brand image in the given category? • Is there a problem with the store image? • Is the problem limited to specific segments? Observing the various asymmetries in these matrices helps to better target expensive customer satisfaction surveys by products, brands and by segments. 3.5.5. Simulation The effects of pricing deals can be simulated computing Di demand, Si sales and Pi profit functions of products and D, T, R totals using the new prices. There are several managerial uses of such a simulation. It helps to avoid profit loosing deals. It is possible that a deals increase demand and sales but decreases profit. In light of a planned price promotion, it helps to forecast demand for inventory and purchasing planning purpose. It provides insight into the full effect of a price promotion. This includes not only the effect on the sales or profits of the promoted brand(s), but also the effects on the other brands as well as total sales and profits. For example, it helps to detect, if accepting a manufacturer deal creates more pain than gain by cannibalizing the retailerÕs higher margin private label brand sales. 3.5.6. Optimization Searching for optimal prices and promotion intensities within a specific segment is a complex problem: maximizing Pi profits of individual products can negatively influence Si individual sales and T total sales due to higher prices, while maximizing sales may decrease profitability. Maximizing R total profit can totally drive out certain products from the market, while maximizing Pi profit of an individual product can negatively influence R total profit through competitive relationships. Therefore, we define the maximization of R total profit as the goal function of our model (see Formula 25 for detailed description). Moreover, category managers at the retail chain will define lower bounds LB as constraints on T total sales (see Formula 26) and on Si individual sales (see Formula 27) based on the profit maximizing or market share expanding category management policies they follow. Since fit of OLS regressions outside the range of available data is not guaranteed, we constrain the optimum search to the historic ranges of price and promotion (see Formulas 28 and 29). Goal function: ! n n m m X X X   Bi pj X ak 2  pi  ðgi þ fi pi Þ exp 1   ðxk þ y k ak Þ ! Max. ð25Þ uii uij k¼1 vik i¼1 j¼1 k¼1

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subject to:

! n m X pj X Bi ak pi exp 1   P LBT ; uii uij k¼1 vik i¼1 j¼1 ! n m X pj X Bi ak  pi exp 1  P LBSi i ¼ 1 . . . n. uii uij k¼1 vik j¼1 n X

ð26Þ ð27Þ

Value ranges of variables of the model: Minðpit Þ 6 pi 6 Maxðpit Þ i ¼ 1 . . . n;

ð28Þ

Minðakt Þ 6 ak 6 Maxðakt Þ

ð29Þ

k ¼ 1 . . . m.

Goal function (25) and sales functions in constraints (26) and (27) are nonlinear, and they have both convex and concave parts. We attempted to solve the model two ways: first, we used the Newton gradient optimization method (Goldberg, 1989) with termination criteria 0.01%, minimal goal function improvement rate between two steps. It terminated after 21 steps. As goal function (25) and constraints (26) and (27) are nonlinear and they have both convex and concave parts, the Newton gradient algorithm may stop at a local optima. Therefore, we tried Simple Genetic Algorithm (SGA) (Goldberg, 1989) also, which does not require any assumption about convexity/concavity of the goal function, but it has higher computational requirements. We set up SGA as follows: • As SGA is an unbounded optimization method by default, we subtract squares of the differences by which lower bounds (26) and (27) are exceeded from the goal function (25). This way we incorporate lower bounds (26) and (27) into the goal function as quadratic punishment terms. • Search population size = 255, initial values are random. • Chromosome encoding: sequential, binary, with 16bit/variable resolution, variable value ranges limited according to (28) and (29). • Chromosome length = 208 bits. • Mutation probability = 0.001. • Crossover probability = 0.5. • Algorithm termination criteria: 0.01% minimal goal function improvement rate between two generations. SGA terminated after 133 generations. In the practice, both Newton gradient method and SGA gave identical solutions of the model.

4. Testing The validity of our model was tested using a data warehouse of a regional food retail chain in the USA. The 85 weeks of data includes more than 150 stores, 3 million households, 200 million transactions and 2 billion purchased items. Testing was done on numerous sets of selected products. Table 5 contains the best R2 and F-tests of the entire models in first two columns. The rest of the matrix contains significance values of the individual t-tests. This table was computed pooled across all eight segments. Actual category names are omitted to keep confidentiality. One may notice that the products ‘‘National drink 1’’ and ‘‘National drink 3’’ have bad model fit. They also destroy ‘‘All categories’’ model fit. When estimations were run at the individual segment level, R2s were improved considerably (see Table 6). This demonstrates the efficiency of our segmentation and within-segment estimations.

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0: Profit, Private brands 1: Profit, Private fruit 1 2: Profit, Private fruit 2 3: Profit, National drink 1 4: Profit, National drink 2 5: Profit, National drink 3 6: Profit, National food 1 7: Profit, National dessert 1 8: Profit, National dessert 2 9: Profit, Private dessert 3 10: Profit, National food 2 11: Profit, National food 4 12: Profit, National drink 4 13: Profit, Private drink 4 14: Profit, All categories

R2

F-values 1: Price, 2: Price, 3: Price, 4: Price, 5: Price, 6: Price, 7: Price, 8: Price, 9: Price, 10: Price, 11: Price, 12: Price, 13: Price, (sig Private Private National National National National National National Private National National National Private levels) fruit 1 fruit 2 drink 1 drink 2 drink 3 food 1 dessert 1 dessert 2 dessert 3 food 2 food 4 drink 4 drink 4

0.827 0.914 0.832 0.500 0.820 0.727 0.838 0.808 0.893 0.872 0.812 0.771 0.843 0.900 0.586

0.045 0.000 0.038 0.964 0.058 0.383 0.030 0.084 0.001 0.005 0.074 0.198 0.024 0.001 0.863

0.182 0.193 0.169 0.275 0.292 0.254 0.192 0.192 0.194 0.222 0.254 0.142 0.221 0.277 0.231

0.132 0.139 0.122 0.200 0.212 0.184 0.138 0.139 0.140 0.160 0.184 0.102 0.160 0.201 0.167

0.075 0.079 0.069 0.114 0.122 0.105 0.079 0.079 0.080 0.091 0.105 0.058 0.091 0.115 0.095

0.037 0.039 0.034 0.057 0.060 0.052 0.039 0.039 0.040 0.045 0.052 0.029 0.045 0.057 0.047

0.054 0.057 0.050 0.083 0.088 0.076 0.057 0.057 0.058 0.066 0.076 0.042 0.066 0.084 0.069

0.094 0.099 0.087 0.143 0.152 0.132 0.099 0.099 0.100 0.115 0.132 0.073 0.114 0.144 0.120

0.154 0.163 0.143 0.234 0.249 0.216 0.162 0.162 0.165 0.188 0.216 0.120 0.187 0.236 0.196

0.211 0.223 0.196 0.317 0.336 0.293 0.222 0.222 0.225 0.256 0.293 0.164 0.255 0.320 0.267

0.131 0.138 0.121 0.199 0.211 0.183 0.138 0.138 0.140 0.160 0.183 0.102 0.159 0.200 0.166

0.041 0.044 0.038 0.063 0.067 0.058 0.043 0.043 0.044 0.050 0.058 0.032 0.050 0.064 0.053

0.142 0.150 0.132 0.215 0.229 0.198 0.149 0.149 0.152 0.173 0.199 0.110 0.172 0.217 0.180

0.065 0.069 0.060 0.099 0.105 0.091 0.068 0.068 0.069 0.079 0.091 0.050 0.079 0.100 0.083

0.057 0.060 0.052 0.086 0.092 0.079 0.060 0.060 0.060 0.069 0.080 0.044 0.069 0.087 0.072

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Table 5 Testing of OLS models (across all eight segments)

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Table 6 Testing of OLS models (within eight segments) R2

Segment 1

Segment 2

Segment 3

Segment 4

Segment 5

Segment 6

Segment 7

Segment 8

0: Profit, Private brands 1: Profit, Private fruit 1 2: Profit, Private fruit 2 3: Profit, National drink 1 4: Profit, National drink 2 5: Profit, National drink 3 6: Profit, National food 1 7: Profit, National dessert 1 8: Profit, National dessert 2 9: Profit, Private dessert 3 10: Profit, National food 2 11: Profit, National food 4 12: Profit, National drink 4 13: Profit, Private drink 4 14: Profit, All categories

0.901 0.951 0.946 0.889 0.930 0.842 0.957 0.912 0.943 0.964 0.898 0.857 0.933 0.945 0.861

0.893 0.976 0.884 0.888 0.915 0.841 0.934 0.924 0.955 0.930 0.896 0.812 0.961 0.975 0.779

0.933 0.969 0.905 0.868 0.942 0.848 0.897 0.914 0.938 0.948 0.905 0.885 0.929 0.948 0.828

0.917 0.931 0.929 0.855 0.874 0.896 0.906 0.924 0.940 0.943 0.916 0.873 0.919 0.957 0.903

0.891 0.932 0.946 0.871 0.882 0.904 0.882 0.879 0.943 0.932 0.857 0.840 0.943 0.948 0.780

0.899 0.960 0.943 0.884 0.892 0.847 0.890 0.896 0.938 0.940 0.874 0.830 0.927 0.960 0.812

0.876 0.933 0.932 0.863 0.900 0.877 0.896 0.880 0.931 0.957 0.929 0.851 0.893 0.940 0.878

0.932 0.962 0.918 0.845 0.930 0.855 0.940 0.850 0.961 0.961 0.882 0.860 0.909 0.953 0.747

Table 7 Optimization results Segment

1

2

3

4

5

6

7

8

Sales Profit Gap R2 Max. profit

Low Low High 0.861 224,352

Low Low Low 0.779 136,768

High Low Low 0.828 268,440

High High Low 0.903 45,401

Low High High 0.780 94,680

High Low High 0.812 36,505

Low High Low 0.878 44,363

High High High 0.747 31,320

Sum of segmentwise maximal profits

Non-segmented model results

811,829

0.586 768,450

The segmentation also had positive effects on profit optimization. Table 7 shows that prices and promotions optimized within segments resulted in bigger profits than optimization based on the non-segmented population. The maximum profit obtained when the optimization was done for each of the segments separately was 811,829 in total. This was gotten by summing the eight individual profits in Table 7 and is larger than the maximum profits obtained when the data were pooled across the 8 segments (768,450). All of the profit figures shown here have been rescaled to protect confidentiality. We also tested how incorporating pass-through in the estimation of direct unit costs improves model fit and optimization. We ran the same by-segment analysis as shown in Table 6 without pass-through, using constant direct unit costs instead of estimates (see Table 8). Comparing Tables 6 and 8 indicates that all model fits decreased when the pass-through effects were not included. Model fits for strong national brands and perishable private label brands were hit especially hard, since pass-through is very strong in these products: A strong national brand manufacturer forces the retailers to pass trade discounts through to consumers. For perishable private label brands, the retailer has the power over the suppliers to force them to provide large quantities of products at reduced unit cost. These decreasing fits for the goal function and constraints led to smaller profit maximums (see Table 9) as the possibility of forcing suppliers by the retailer to share the savings (which is an everyday practice in the industry) was not considered.

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Table 8 Testing of OLS models within 8 segments, without pass-through effect R2

Segment 1

Segment 2

Segment 3

Segment 4

Segment 5

Segment 6

Segment 7

Segment 8

0: Profit, Private brands 1: Profit, Private fruit 1 2: Profit, Private fruit 2 3: Profit, National drink 1 4: Profit, National drink 2 5: Profit, National drink 3 6: Profit, National food 1 7: Profit, National dessert 1 8: Profit, National dessert 2 9: Profit, Private dessert 3 10: Profit, National food 2 11: Profit, National food 4 12: Profit, National drink 4 13: Profit, Private drink 4 14: Profit, All categories

0.772 0.734 0.712 0.847 0.860 0.740 0.856 0.771 0.845 0.950 0.740 0.788 0.906 0.937 0.848

0.839 0.781 0.806 0.793 0.839 0.736 0.755 0.889 0.889 0.916 0.734 0.719 0.955 0.961 0.705

0.799 0.956 0.703 0.832 0.925 0.744 0.761 0.858 0.927 0.943 0.758 0.814 0.866 0.933 0.797

0.861 0.772 0.850 0.807 0.829 0.823 0.853 0.873 0.926 0.938 0.886 0.789 0.900 0.947 0.866

0.754 0.877 0.722 0.840 0.872 0.881 0.755 0.795 0.776 0.920 0.775 0.834 0.924 0.939 0.673

0.894 0.780 0.822 0.852 0.830 0.767 0.717 0.824 0.789 0.935 0.851 0.716 0.892 0.953 0.680

0.686 0.693 0.679 0.854 0.876 0.823 0.846 0.858 0.907 0.936 0.862 0.813 0.822 0.934 0.738

0.775 0.898 0.891 0.838 0.827 0.745 0.877 0.776 0.931 0.940 0.738 0.711 0.842 0.951 0.713

Table 9 Optimization results without pass-through Segment

1

2

3

4

5

6

7

8

R2 Max. profit

0.848 207,418

0.705 118,521

0.797 208,719

0.866 39,941

0.673 87,212

0.680 32,905

0.738 34,943

0.713 28,732

Sum of segmentwise maximal profits

On-segmented results

758,391

0.511 741,160

5. Summary In this paper, we set up House of Profit Model, an approach of maximizing profit of a food retailing chain by targeting and promoting valuable customers. The House of Profit Model provides a framework for a manager to offer differential promotions to consumers, by considering the consumersÕ loyalty and profitability. By using such a segmentation scheme we were able to derive better estimates for price and promotion elasticity. This resulted in higher profit maximization. Additionally, we extended the concept of pass-through and incorporated it into our elasticity estimates. Again, profit maximization was improved. The major limitations of the model and possibilities for extension of the method can be summarized in the following points. The Length of the time series (number of historic data points) limits the maximal number of independent variables (dummies, our prices and promotions, competitorsÕ prices) that can be analyzed together in OLS regressions. One solution might be analyzing aggregated product categories, but in our experience very high aggregation as well as using barcode level data results in poor model fit. Another potential solution, collecting more lengthy time series, also wonÕt solve the problem, because complementary-competitive relationships of products change over time. In our experience using a time window longer than one year significantly decreases model fit. We did not incorporate competitorÕs pricing and promotion data in the model. Even if it is possible to get databases containing weekly unit prices of individual products at competitors, detailed product categorization of different retailers may not be compatible. It is hard to aggregate unit prices of products at competitors into comparable product categories using weighted averages without knowing their sales data.

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A dynamic approach of price elasticity analysis should be used with a rolling time window and ARMA techniques for smoothing time series and controlling autocorrelation. But these methods have higher computational requirements, which is a disadvantage in a large-scale business application even using the latest supercomputing resources. Sometimes data are unsuitable for analysis because prices were not managed, they do not have variation. In this case pricing experiments in selected benchmark stores can help to generate sufficient data.

Acknowledgements This research was completed with the support of the Center for Relationship Marketing, School of Management, SUNY at Buffalo, USA. The authors gratefully acknowledge contributions of members of the research group at the Center: Dr. Arun K. Jain, Director and Samuel P. Capen, Professor of Marketing Research, Dr. Minakshi Trivedi, Associate Professor, Dr. Debrata Talukdar, Assistant Professor. Ganesh Kannan and Samrat Sen assisted as Graduate Assistants to the project. The author is also very grateful for support of the Center for Computational Research at the University at Buffalo for providing access to their supercomputing facilities. Specifically we would like to thank Dr. Russ Miller, Director, Dr. Thomas Furlani, Associate Director, and system administrators Cynthia Cornelius, Tony Kew and Steven Gallo.

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