Assessing category vulnerabilityacross retail product assortments

Mayukh DassRawls College of Business, Texas Tech University, Lubbock, Texas, USA, and

Piyush KumarTerry College of Business, University of Georgia, Athens, Georgia, USA

Abstract

Purpose – A critical issue faced by retailers is determining the composition of the productassortment in every category and setting the price levels for each product without compromisingcategory-level customer demand or operational efficiency. The purpose of this paper is to propose anovel, model-based clustering approach to bring parsimony to retailers’ assortment configuration andpricing process. The objective of the model is to group alternative assortment configurations into setsto which the category exhibits equivalent vulnerability.

Design/methodology/approach – In this method, each possible assortment and pricingconfiguration is first conceptualized as a unified entity and then these entities are clustered basedon the vulnerability of category level sales. The authors illustrate the benefits of this new method forcategory planning using two sets of data for brands of soft drinks and enhanced water, collected froma panel of adult customers.

Findings – The results from both data sets show that several assortment configurations, varyingsignificantly in terms of numbers of products and prices, result in similar levels of categoryvulnerability. In other words, several widely-different product-pricing combinations result in similarlevels of category demand.

Originality/value – The paper’s findings imply that retailers can bring parsimony to their categorymanagement process by shifting their strategic focus from individual brands to assortment clusters.Specifically, they can select the most efficient or the smallest assortment from each cluster withoutsacrificing category demand. Overall, the authors’ approach can help simplify the complexdecision-making process related to product selection and price setting, and help retailers achieve thedual objective of operational efficiency and high category demand.

Keywords Retailing, Pricing policy, Retail assortments, Category management, Category vulnerability

Paper type Research paper

IntroductionA central issue in the management of retail operations is configuring and pricing theproduct assortment offered within each category and across locations (Kahn, 1999).The assortment composition affects a retailer’s positioning, the traffic generated at itsstores (Borges et al., 2005; Briesch et al., 2009), and its overall performance(Broniarczyk and Hoyer, 2005). The traditional approach to address this issue favouredlarger assortments aimed at meeting the preferences of a diverse customer base (Boydand Bahn, 2009). Consequently, the number of products available at a typical retailerincreased significantly over the last two decades (Hoch et al., 1994). However, with thewidespread availability of store-level transactions data, the strategic mindset has

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Both authors have contributed equally to this article.

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Received July 2010Revised February 2011Accepted July 2011

International Journal of Retail& Distribution ManagementVol. 40 No. 1, 2012pp. 64-81q Emerald Group Publishing Limited0959-0552DOI 10.1108/09590551211193603

shifted away from assortment size towards assortment efficiency (Boyd and Bahn,2009). Retailers now optimize their product lines at a disaggregate level, making morefrequent adjustments to the number and prices of brands carried (Amine and Cadenat,2003; Grewal et al., 1999).

A micro-level product line optimization approach increases the variability in the setof brands available across store formats, locations, and the multiple points of salewithin a store. While a high variance in assortment composition may help retailersgain operational efficiencies, it often increases the likelihood of a loss of category salesbecause of an absence of the preferred brands or high prices for some customers.Consequently, retailers have to manage the trade-off between the efficiency gains fromproduct portfolio rationalization and the potential loss of category sales. Recently,Wal-Mart, one of the world’s leading retailers, experimented with a reduced assortmentstructure with only one top national brand and their own private label brand in aspecific category, and faced a backlash from its customers. Their store-level sales in thecategory dropped by 40 per cent (CNN, 2010) and they were forced to revert back totheir original assortment composition policy. This issue also spills intoretailer-marketer conflicts such as those observed in the soft drinks category(MSNBC, 2009).

The management of the assortment composition and the pricing of the brandstherein is a non-trivial problem because of the large number of possible brand-pricecombinations (Mantrala et al., 2009). The problem is further exacerbated because atypical retailer carries multiple product categories in its overall portfolio. Whileprevious research on assortments does provide guidance regarding shelf-spaceallocation (Chong et al., 2001; Gomez Suarez, 2005), market structure (Moore andCarpenter, 2008), product presentation (Huffman and Kahn, 1998), assortmentattraction (Chernev and Hamilton, 2009) and biases in customers’ decision-making(Boyd and Bahn, 2009; Chernev, 2003; Deng and Kahn, 2009; Simonson, 1999), it doesnot fully address issues pertaining to the relationship between alternative assortmentconfigurations and a potential loss of category sales. In other words, it does not directlyexamine how the various possible combinations of available brands and theirrespective price levels influence category sales. As a result, it is possible that retailersinadequately account for the effects of the variance in assortment composition andpricing when making category management decisions.

In this paper, we propose a model-based clustering approach to help alleviate thisproblem and assist retailers in bringing efficiency to their assortment planning andpricing process. As noted, the primary reason why the assortment configuration task isa significant challenge for retailers is because the number of product-pricecombinations in any category is typically very large. However, we believe thatmany of these configurations result in similar levels of category demand. Therefore, wepropose that the retailers’ product configuration task within any category can besimplified by grouping possible assortments on the basis of the equivalence ofcategory demand. In other words, assortments that might otherwise vary in terms oftheir brand composition and pricing, but to which the category exhibits similar levelsof demand, can be grouped together to form assortment clusters. From a demandperspective, retailers can then be indifferent across the alternative assortmentconfigurations within each cluster, and can select the appropriate one on the basis ofother criteria, such as shelf space optimization or the availability of trade promotions.

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Our objective in this paper is to develop such an approach for grouping alternativeproduct-price configurations within a single category on the basis of demandequivalence. The key benefit of this approach is a significant reduction in the numberof decision alternatives and a simplification of the assortment planning process byperhaps several orders of magnitude. A second benefit is the availability of informationon demand equivalence that can help retailers makes decisions regarding itemreduction on shelves. We illustrate the application of our proposed model using datafrom two product categories but it can be easily replicated across multiple categories,with larger number of alternative product-price combinations, or using other metrics,such as category margins or profitability.

In this proposed method, we first conceptualize each alternative assortment, not interms of the individual brands present within it, but as a unified singular entityconsisting of a subset of the available brands at their respective price levels. Then, incontrast to existing theoretical approaches and practice, we articulate the retailer’sassortment planning problem in terms of a choice among these assortment entities ratherthan among individual brands or prices. We then define category vulnerability as thelikelihood that customers will not buy from the category under the available assortmentconfiguration and pricing environment. A category may be more or less vulnerabledepending on which brands are present in the assortment, which among those are onsale, and the depth of discount. We propose that retailers can gain efficiencies in theassortment planning process by grouping alternative assortment entities based on thelevels of category vulnerability which is conceptually the inverse of category demand. Inorder to determine the composition of these clusters, we postulate that each assortmentcan be thought of as belonging to latent assortment space where its location isdetermined by the level of the category’s vulnerability. Assortments to which thecategory is equally vulnerable are located close to each other in this space and those towhich the category exhibits differential vulnerability are located far apart. We then use anew, mixture-type model to discover the underlying assortment vulnerability clustersbased on their effects on category purchase and their unobserved commonalities withone another (Handcock et al., 2007; Krivitsky and Handcock, 2008).

The paper aims to make three contributions to the retailing literature. First, it proposesa new approach to conceptualizing the category management process in terms of choicebetween alternative assortment configurations as unified entities. Second, it develops anovel model to cluster or group these alternative entities on the basis of equivalence indemand or category vulnerability. And third, it illustrates using simple examples, that thecategory structure and the number of assortment clusters could be significantly differentdepending on the depth of discount when products within the assortment go on sale.

The rest of the paper is organized as follows. In the next section, we briefly delineatethe relationship between our work and the literature on assortment management.Thereafter, we introduce the clustering model and its application to the assortmentmanagement problem. We then describe the studies and discuss our results. Weconclude with a discussion of the managerial implications of our findings and providesome directions for future research.

Relationship with the literatureTwo streams of literature relate closely to our research. The first adopts aretailer-centric approach and provides optimization models based on tradeoffs between

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demand and efficiency considerations. These models focus on managing a variety ofmetrics that capture considerations surrounding a retailer’s overall image (Berry,1969), store traffic (Borges et al., 2005), profitability (Mcintyre and Miller, 1999),consumer’s perceptions (Amine and Cadenat, 2003), consumer preference (Miller et al.,2010), and efficiency (Brijs et al., 2004). A key performance measure among these is anefficient utilization of shelf-space, and models have been developed that help retailersoptimize their product portfolios around this metric (Bultez et al., 1989; Gomez Suarez,2005; Urban, 1998). The models account for the tradeoffs among demand, stockoutcosts, and inventory holding costs, and provide guidance for building optimalsingle-category and multi-category assortments (Martınez-Ruiz and Molla-Descals,2008). The recent focus of assortment models has shifted towards financial metrics,such as category revenue (Chong et al., 2001), product variant profitability (Zhaolin,2007), or customer-basket profits (Cachon and Kok, 2007). This shift is consistent withthe belief that many retailers can significantly reduce the number of SKUs they carrywithout suffering in terms of a loss in sales (Hoch et al., 1994) or in customerperceptions of variety (Morales et al., 2005).

The second stream of literature adopts a customer-centric perspective and examineswhether and when large assortments may be preferred over smaller ones and vice-versa.While it is intuitive that smaller assortments increase a retailer’s risk from not being ableto meet the demand across a wide range of customer preferences (Carpenter and Moore,2006; Simonson, 1999), or accommodate a large variance in their decision processes whilethey make a product selection (Kahn and Lehmann, 1991), they might sometimes bepreferred over larger ones. Large assortments tend to increase the cognitive loads oncustomers (Kahn and Lehmann, 1991) and often reduce the likelihood that they will endup making a choice (Iyengar and Lepper, 2000). Customer may therefore sometimesprefer smaller assortments, especially when they do not have well-articulatedpreferences (Chernev, 2003; Simonson, 1999), or when the products in the assortmentdiffer on non-alignable attributes (Gourville and Soman, 2005).

Our research complements previous work on the choice between small and largeassortments (Chernev, 2003; Gourville and Soman, 2005), and brand choice withinassortments (Simonson, 1999). It provides a category-centric view that will helpretailers categorize assortments in terms of the risk to category purchase and also helpbrand marketers develop assortment cluster-specific promotion plans. One advantageof this approach is that it does not need to make specific assumptions about the brandchoice process within assortments. It merely uses information on the share of ano-choice option, howsoever determined, to develop category vulnerability clusters. Asecond advantage is that the model considers an assortment as a unified entity.Therefore, it is flexible and can accommodate a large number of alternative assortmentconfigurations that may be observed in the marketplace. If many potential assortmentsthat are feasible are not actually observed in the marketplace, they can be removedfrom consideration and the model can be estimated using only the remaining ones.And, finally, the approach can be easily implemented using a variety of metricsranging from category volume to overall profits.

Model developmentAs noted, a category is vulnerable when there is a high likelihood that customers willnot purchase from within it given the composition of the assortment in terms of the

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brands that are present and their respective prices. Therefore, we conceptualizecategory vulnerability in terms of the customers’ share of the “no-purchase” optionunder different product and pricing configurations. Our objective is to clusterassortments based on the levels of category vulnerability. In order to extract thesevulnerability clusters, we assume that each assortment occupies a position in latentspace such that its location determines the share of the no-purchase option. We alsoassume that alternative configurations share some observable or unobservablecommonalities among themselves based on their having either common brands orsimilar pricing patterns. Assortments may therefore have some form of implicitrelationships among themselves in latent space that influences the observed effects onthe share of the no-purchase option. Assortments that have a stronger mutualrelationship will be located closer to each other and will form a cluster. Those that arelocated far from each other will likely belong to different clusters.

We use a vertex clustering approach (Monni and Li, 2008) to discover these categoryvulnerability clusters by partitioning the assortment space. This approach isappropriate because it does not impose constraints on the possible number of clusters(Gordon, 1973), and does not require data on the dynamics of the research units, thealternative assortment configurations (Bradlow et al., 2005). Instead, it employs a newlatent, mixture-type clustering model that is capable of discovering the underlyingassortment clusters based on the observed changes in the choice share of the “nopurchase” option and the observed and unobserved commonalities among assortments(Handcock et al., 2007; Krivitsky and Handcock, 2008).

In order to cluster the assortments in latent space, we use the choice share data ync ofthe “no purchase” option, nc, for a set of customers for each of A alternativeassortments. We define an observation as consisting of a relational tie ya1a2

for each pairof assortments a1, a2 ¼ 1. . .A where ya1a2

¼ 1, when assortment a1 results in a greatercategory vulnerability or higher share for the “no purchase” option than assortment a2,and 0 otherwise. We create an A £ A matrix, Y ¼ [ya1a2

], that can be viewed as arandom variable with a sample space ofY # {0; 1}AðA21Þ. We then consider a class ofhierarchical modelsðY ¼ yjxÞ, such that the conditional probability of the relational tiebetween two assortments depends only on the distance between them in theunobserved “assortment space.” We consider assortment positions in latent spaceasZ ¼ {zi} and posit that each assortment has an unobserved position in atwo-dimensional Euclidean latent assortment space, where [ya1a2

] takes the followingform:

ðY ¼ yjb; Z Þ ¼ða1;a2Þ[Y

YPðYa1;a2

¼ ya1;a2jb; Z Þ ð1Þ

The ties between the assortments are independent, given Z ¼ {Za1}Aa1¼1, the locations

of the two assortments in latent space. Considering Za1and Za2

as the locations ofassortments a1 and a2 respectively, Equation 1 can be rewritten as:

PðYa1;a2¼ ya1;a2

jb; jZa12 Za2

jÞ ¼ f ð ya1;a2jEðYa1;a2

jb; jZa12 Za2

jÞÞ ð2Þ

with the conditional mean, E, given by:

EðYa1;a2jb; jZa1

2 Za2jÞ ¼ g21ðha1;a2

ðb; jZa12 Za2

jÞÞ ð3Þ

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that has a link function g and a predictor function ha1;a2of the following form:

ha1;a2ðb; jZa1

2 Za2jÞ ¼ b2 jZa1

2 Za2j ð4Þ

We use the attractiveness of the assortment brand composition and the pricing structureas covariates. We specifically use the customer evaluation of the most preferred brand inthe configuration as a measure of the assortment’s product attractiveness. We also useweighted price discount (WPD), computed as the following, as a second covariate:

WPD ¼

XK

k¼1

pdkbpk

XK

k¼1

bpk

ð5Þ

where pd ¼ the level of price discount for brand k present in the assortment, bp ¼ theaverage brand evaluation for brand k, where k ¼ 1; :::K are the total number of brandspresent in the assortment. As Y ¼[ya1a2

] is dichotomous in nature, we use a logisticregression model where the probability of a tie depends on the distance in space betweenZa1

andZa2. Therefore:

log oddsð ya1;a2¼ 1jZa1

; Za2;bÞ ¼ b2 jZa1

2 Za2j ð6Þ

We estimate Equation 6 using a Bayesian approach (Handcock et al., 2007). Thisestimation method is more appropriate for our application than the alternative two-stagemaximum likelihood procedure (Fraley and Raftery, 1998, 2002, 2006) using theexpectation maximizing algorithm (Dempster et al., 1977) because it estimates the latentpositions of the assortments using their clustering information. Therefore, we use theBayesian estimation approach using MCMC sampling for determining the location andmembership of assortment clusters (see Appendix 1 for details of the estimation process).

DataBecause the unit of analysis for the proposed model is an assortment, the approach canbe applied to any set of alternative assortments within a category without restrictionson the number of brands within each or their respective price levels. For purposes ofillustration, we estimate the category vulnerability clusters using data fromassortments constructed from three brands of soft drinks available at regular or saleprices. We selected the three well-known brands Coke, Pepsi, and Dr. Pepper for thisstudy. We conducted the analysis separately for two sets of data, one with relativelyshallow discounts and another with relatively deep discounts whenever a brand wason sale. We then replicated the analysis with enhanced water as the category of interestand three brands (Propel, Vitamin Water, Smart Water) within it. As noted, our modelcan be estimated easily if the observed set of assortments in the market is a subset ofthose we use or contain greater variation in either price or the number of brands thanwhat is used in our illustrative studies.

In each of our two studies with soda brands, we first constructed assortmentconfigurations with all combinations of the three brands in groups of two or three. Ineach case, the available brands had a regular price of $1. Then, we made additional

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versions of each assortment by changing the prices of one or more of the brandspresent to a discounted sale price that was 25 per cent less than the regular price. Theresult was all possible combinations of brands and price levels in assortments of sizetwo or three (see Appendix 2, Table AI). The entire process was repeated, for a secondstudy, to construct a similar portfolio of assortments with the same regular price but adeep price discount of 50 per cent. A total of 160 adults who were individually recruitedto participate in the study provided the data for estimating the models. One half of thesample saw assortments where each of the present brands was available either at itsregular price of $1 or at a discounted price that was 25 per cent lower. The other halfsaw assortments where the products were on the same regular price but the discountedprice was 50 per cent lower.

During the course of each study, which was conducted on personal computers,participants first reported their evaluation of each of the selected brands on a ten-pointscale. Thereafter, they were sequentially presented with the assortment combinations ofthe three brands and the pricing levels, each including a “no-purchase” option, in randomorder. Within each assortment configuration, the number of brands on price promotionwas varied from none to the maximum number of brands present. For every assortment,the participants reported which brand they would buy if they were in the market and theonly available brands were the ones that were presented at the prices shown. Within ourstudy both the regular and diet versions of a brand were available whenever a brand waspresent in an assortment. Participants were allowed to select a “no-purchase” option ifthey would not choose any brand from within a configuration presented. For this study,we assume that each purchase consisted of a unit quantity. However, the extension of ourapproach to incorporate the purchase of multiple units is straightforward.

ResultsCategory vulnerabilityWe begin by discussing the results for the data from the study with shallow discountsand then for the second data set with deep discounts. For each set, we selected theoptimal cluster solution based on the posterior probabilities of cluster memberships forrespondents. We find that a one-cluster[1] solution was optimal for those who saw ashallow discount, but a three-cluster solution was optimal for respondents who sawbrands on deep discount (Table I).

The location of the various assortment and pricing combinations for the shallowdiscount condition is depicted in Figure 1. The average category vulnerability, asdefined by the share of the “no-purchase option” in these data was 20 per cent. The

Price promotion Number of vulnerability clusters Posterior probability

Category with shallow discount 2 0.72153 0.58444 0.58635 0.6028

Category with deep discount 2 0.68093 0.74074 0.72915 0.7099

Table I.Selection of the number ofvulnerability clusters

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boundary of the cluster in this figure is illustrated as a circle and the cluster centre isdepicted as a “ þ ” sign. While the solution corresponds to a single cluster, we find thatthe cluster variance is somewhat high. There are several assortment and pricingconfigurations that are close to the cluster centre and similar to each other in terms ofcategory vulnerability, while there are others that are dispersed far from the centre.The average vulnerability of the assortments within the cluster boundary was 14.8 percent, whereas that of the assortments outside the boundary was 23 per cent.

A general pattern of results is that the assortments close to the centre tend to containall the configurations with three brands and a couple of two-brand configurations withthe Coke brand available at a discounted price. All the three-brand assortments are invery close proximity, suggesting that once all the brands from this set were offered, ashallow discount on one or more of them did not change the category vulnerabilitysubstantially. Among the two-brand assortments, vulnerability was low when the Cokebrand was on sale and the second brand in the assortment was Pepsi. However, whetherPepsi was also on sale at the same time did not affect category vulnerability because theassortments “cP” and “cp” are located close to each other. An examination of the locationof the assortments outside the cluster boundary shows that pairs of two-brandconfigurations were located in close proximity. The relative locations of theseassortments provide insights into the effects of price discounting on categoryvulnerability. For example, assortments “CD” and “Cd” are almost overlapping implyingthat if Coke and Dr. Pepper were the only two brands available and the former was onregular price, discounting the latter did not change category vulnerability. The relativeproximity of other pairs can be interpreted similarly. For example, we find thatconfigurations “CP” and “Cp” are located close to each other. This suggests that if Cokeand Pepsi were the only two brands available, and Coke was on regular price, a shallowdiscount on Pepsi did not reduce category vulnerability.

Figure 1.Vulnerability cluster for

shallow price discount(soda)

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The results from the model estimation for the deep discount condition are shown inFigure 2. In contrast to the shallow discount condition, we find that the assortmentconfigurations form three clusters implying that a deep discount resulted in astructural change in the market and in the relationships among the alternativeassortments. The average vulnerability across the three clusters in this condition was16 per cent, 8 per cent, and 21 per cent (see Table II). The first cluster containscombinations of Coke and Dr. Pepper at regular and sale prices and has the highestvariance among the three clusters. The second is the lowest vulnerability cluster thatalso has the lowest variance. In other words, the vulnerability across the variousassortments in this cluster is highly comparable. This cluster contains assortmentswith three brands that contain most of the price combinations of the three brandassortments as well as two brand clusters containing Coke and Pepsi on sale. The thirdcluster which contains two-brand assortments of Pepsi and Dr. Pepper results in thehighest level category of average vulnerability among the respondents.

These results provide a parsimonious view of the vulnerability of the categorycontaining the three soda brands for the markets represented by the sample ofparticipants used in the study. The analysis can easily be extended to both a largernumber of brands and to data available from other sources including scannerpanels. These results can help retail category managers assess the impact of makingchanges in the assortment of brands to carry and their prices on category

Price promotion Cluster 1 Cluster 2 Cluster 3

Category with shallow discount 0.20Category with deep discount 0.16 0.08 0.21

Table II.Category vulnerability bydiscount level

Figure 2.Vulnerability clusters fordeep price discount (soda)

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vulnerability. Configurations that vary in terms of their brand composition andprices but have a similar effect on category vulnerability can be treatedinterchangeably for category planning purposes. For example, we find that in ourdata, once all three brands were offered, discounting one or more brands did notresult in a major change in category vulnerability. Similarly, in many cases, once apair of brands was selected, discounting one of them did not influence categoryvulnerability in a significant way. Findings such as these can bring efficiency to thecategory management process by demonstrating the effects of multiple alternativeconfigurations in a single view[2].

ReplicationWe replicated the study using enhanced water as the focal category. The three brandsthat we selected included Propel, Vitamin Water, and Smart Water. The rest of thedesign of the study remained the same as in first study and the data were analyzedusing the same approach. A total of 140 adults participated in the study. The resultsfrom the analysis are presented in Tables III and IV and the plots of the clustersolutions are presented in Figures 3 and 4. We find that a three-cluster solution wasoptimal for the shallow discount case and the average vulnerability levels varied from17 per cent to 22 per cent across the clusters. A four-cluster solution was optimal for thedeep discount case and the category vulnerability varied from 12 per cent to 20 per centacross the clusters.

The mean level of vulnerability in the shallow discount condition was the highest inCluster 1. The radius of this cluster was moderate as compared to that for theremaining two clusters. The cluster tended to contain smart water on sale. There wereonly a couple of assortments with Vitamin Water in this cluster and a couple withPropel. The second cluster was very small and tight and tended to contain assortmentof two brands at regular price. The third cluster, with the lowest level of vulnerabilitywas dominated Vitamin water at both regular and sale prices and Propel to a lesserextent. In the deep discount condition, Cluster 1, with the lowest average vulnerabilitytended to contain Vitamin Water and a few with Propel. The second cluster, tended to

Price promotion Number of vulnerability clusters Posterior probability

Category with shallow discount 2 0.62613 0.73624 0.67285 0.5936

Category with deep discount 2 0.63713 0.74924 0.79455 0.7423

Table III.Selection of the number of

vulnerability clusters(water)

Price promotion Cluster 1 Cluster 2 Cluster 3 Cluster 4

Category with shallow discount 0.17 0.19 0.22Category with deep discount 0.12 0.16 0.18 0.20

Table IV.Category vulnerability by

discount level (water)

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contain assortment of two brands, predominantly with Propel and Vitamin Water. Thethird cluster was a tight one with assortments of two brands containing Vitamin Waterat regular price. And finally, the fourth cluster contained Propel and Smart Watercombinations.

Figure 3.Vulnerability clusters forshallow discount(enhanced water)

Figure 4.Vulnerability clusters fordeep discount (enhancedwater)

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General discussionThe widespread availability of transactions-level data has improved retailers’ ability torationalize their product portfolios and bring efficiency to their operations. However, asthey optimize their product lines, retailers have to be mindful of the impact thatvariations in assortments may have on category demand. In other words, they have tomanage the tradeoffs between an efficient utilization of their shelf-space and meetingcustomer demand for a wide range of preference structures and price sensitivities. And,as the number of permutations of brands on and off promotions becomes large, itbecomes increasingly difficult for retailers to assess the consequences of all the productand pricing scenarios for each category in order to decide on their optimal productportfolio mix.

In this paper, we addressed this problem by proposing a new approach to thinkabout, measure, and utilize information on category vulnerability. This approach helpsthe assortment planning and pricing problem transcend from a brand level to anassortment level, and offers the potential for conceptual, methodological, and strategicefficiencies. From a conceptual perspective, our method provides a contrast totraditional category management approaches that tend to focus at a brand level andaim to drop slow moving items from a category (Broniarczyk and Hoyer, 2005), orreduce items that share common but undesirable attributes (Boatwright and Nunes,2001). In contrast, our approach focuses at an assortment level and further aggregatesthem into clusters rather than disaggregate them into brands. This is especially usefulin categories that consist of multiple potential items where the number of possiblecombinations of assortments that can be constructed is extremely large. Under thesecircumstances, instead of investigating the differences across assortments, ourapproach looks for commonalities in the levels of category vulnerability irrespective ofthe assortment composition. It helps discover alternative assortment configurationsthat might otherwise vary significantly in terms of the brands and price levels butwhich might overall be equally unattractive from a category vulnerability perspective.

Retailers can achieve parsimony in their assortment planning decisions using ourapproach by grouping alternative assortment configurations into clusters based on theextent of the category’s vulnerability. They can be relatively insensitive to thevariations among the assortments within each cluster and can choose from amongthem based on other considerations such as fewer numbers of brands or theavailability of trade promotions. The model therefore helps simplify the demand side ofthe retailers’ category management problem so that they can focus more on operationalefficiency. The resulting gains in efficiency are useful because retailers do not have toestimate new brand choice models to assess the demand impact of all alternativeproduct and pricing configurations.

Our model is scalable and can accommodate categories with large number of SKUs.This is because the model is estimated at an assortment level, not at a brand level, andis relatively insensitive to the size and composition of the assortments. And, theproposed vertex clustering-based approach is flexible enough to accommodate a largenumber of entities that would correspond to the alternative assortment configurations.We believe that this methodological approach can help reduce the complexity of theassortment planning problem by an order of magnitude by enabling categorymanagers to work with a relatively small numbers of clusters of assortments. They canbe insensitive to variations of assortments within clusters especially if the clusters are

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“tight” with small variance in vulnerability across them. The impact of the approach islikely to be significantly high for retailers who carry large number of categories andnumerous SKUs at variable price points within each. Retailers can also employ ourmodel using other metrics. While in our illustrative example, we used category volumeor demand as the metric of interest, the model itself is flexible enough to accommodatealternative metrics.

An additional benefit of our approach is that it provides insights into thevulnerability of a category without explicitly needing to model the brand choiceprocess within it. While it does consider the observable and unobservablecharacteristics of the various assortments and the relationships among them ascovariates, it does not need to rely on the full understanding of the dynamics of theconsumers’ choice process. This is a significant advantage in light of the fact that thebrand choice process is often complex and difficult to capture under different pricingand assortment combinations.

The proposed model can help retailers improve category management in severalways. First, it brings to light the asymmetry in the effect of price promotions from acategory perspective. This is in contrast to traditional approaches that viewasymmetry from a brand share perspective. Our approach can illustrate theasymmetric effects of the price promotions or of adding or subtracting different brandsto the assortment on category volume. Second, the category vulnerability analysis canhelp retailers negotiate with individual brand marketers regarding stocking andpricing decisions. Knowing the sensitivity of the vulnerability of the category to bothchanges in the price as well the addition versus removal of a brand from theassortment will equip retailers with information about whether they stand to gain orlose if the brand marketer does not agree to their conditions regarding stocking andpricing policies. And third, the approach will sensitize retailers to the fact that depthsof discount impact the structure of a product category, and improve theirsophistication in the use of price promotions and the acceptance of trade promotions.

While the approach is designed specifically for retailers, it also offers key strategicinsights to brand marketers who participate in these category markets. Specifically, theresults from our analysis can help marketers assess the vulnerability of their brand toretailers’ stocking decisions. In particular, if the category vulnerability with andwithout a brand is comparable across many assortment and pricing configurations, thebrand might be at risk of being eliminated by the retailer. Second, marketers can alsogain from knowing the asymmetric effects of their price promotions versus those ofothers on category volume. They can use the information to negotiate terms of tradepromotions with retailers. To that extent, our model will be able to bring efficiency tonot only the retailer’s assortment selection process but also to the brand managers’pricing and promotion planning process.

Limitations and directions for future researchThe proposed approach is an initial attempt to conceptualize categories in terms ofalternative assortments, rather than explicitly in terms of the individual brandscontained therein, and assesses category vulnerability to alternative configurations.While we believe that the approach is novel and provides insights that are differentfrom those provided by market partitioning models and brand choice models, it is notwithout limitations that could be addressed in future research. First, the model does not

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explicitly consider time-based dynamics. To that extent, it does not fully account forany carryover effects of the product assortment and pricing regime in previous periodson the vulnerability in the current period. Second, the model considers only the actualproducts and prices that are used and does not allow for estimating vulnerability byinterpolation or extrapolation to new values. We expect that as retailers learn aboutcategory vulnerability from successive implementations of the model, the number ofalternative assortments under consideration will evolve and ultimately shrink andstabilize to a much smaller number than currently observed. However, the model onlyhelps assess vulnerability at any given stage of the evolution rather than provideinsights into its dynamics over time. And finally, while it does control for observedcharacteristics of assortments, it does not draw causal linkages between them and theobserved vulnerabilities. However, despite these limitations, it is a novel and robustmethodology that can help bring parsimony to the category planning process.

Notes

1. The distribution of posterior probability suggested that a cluster solution with 2 or fewerassortments was appropriate. We accepted the 1the cluster solution based on the observeddistribution of assortments (Figure 1).

2. A split-half reliability test using two random halves of the data, showed high correlations incategory vulnerability across the two halves (f ¼ 0:891, p , 0:0001) for the shallowdiscount condition and the deep discount condition(f ¼ 0:891, p , 0:0001). The number ofclusters and cluster memberships were similar in the two halves.

References

Amine, A. and Cadenat, S. (2003), “Efficient retailer assortment: a consumer choice evaluationperspective”, International Journal of Retail & Distribution Management, Vol. 31 No. 10,pp. 486-97.

Berry, L.L. (1969), “The Components of department store image: a theoretical and empiricalanalysis”, Journal of Retailing, Vol. 45 No. 1, pp. 3-20.

Boatwright, P. and Nunes, J.C. (2001), “Reducing assortment: an attribute-based approach”,Journal of Marketing, Vol. 65 No. 3, pp. 50-63.

Borges, A., Cliquet, G. and Fady, A. (2005), “Buying association and its impact on promotionalutility”, International Journal of Retail & Distribution Management, Vol. 33 No. 5,pp. 343-52.

Briesch, R.A., Chintagunta, P.K. and Fox, E.J. (2009), “How does assortment affect grocery storechoice?”, Journal of Marketing Research, Vol. 46 No. 2, pp. 176-89.

Boyd, E.D. and Bahn, K.D. (2009), “When do large assortments benefit consumers?An information processing perspective”, Journal of Retailing, Vol. 85 No. 3, pp. 288-97.

Bradlow, E.T., Bronnenberg, B., Russell, G.R., Arora, N., Bell, D.R., Duvvuri, S.D., Hofstede, F.T.,Sismeiro, C., Thomadsen, R. and Yang, S. (2005), “Spatial models in marketing”, MarketingLetters, Vol. 16 Nos 3/4, pp. 267-78.

Brijs, T., Swinnen, G., Vanhoof, K. and Wets, G. (2004), “Building an association rules frameworkto improve product assortment decisions”, Data Mining and Knowledge Discovery, Vol. 8No. 1, pp. 7-23.

Broniarczyk, S.M. and Hoyer, W.D. (2005), “Retail assortment: more – better”, in Krafft, M. andMantrala, M.K. (Eds), Retailing in the 21st Century: Current and Future Trends, Springer,Heidelberg, pp. 225-38.

Assessingcategory

vulnerability

77

Bultez, A., Gijsbrechts, E., Naert, P. and Abeele, P.V. (1989), “Asymmetric cannibalism in retailassortments”, Journal of Retailing, Vol. 65 No. 2, pp. 153-92.

Cachon, G.P. and Kok, A.G. (2007), “Category management and coordination in retail assortmentplanning in the presence of basket shopping consumers”, Management Science, Vol. 53No. 6, pp. 934-51.

Carpenter, J.M. and Moore, M. (2006), “Consumer demographics, store attributes, and retailformat choice in the US grocery market”, International Journal of Retail & DistributionManagement, Vol. 34 No. 6, pp. 434-52.

Chernev, A. (2003), “When more is less and less is more: the role of ideal point availability andassortment in consumer choice”, Journal of Consumer Research, Vol. 30 No. 2, pp. 170-83.

Chernev, A. and Hamilton, R. (2009), “Assortment size and option attractiveness in consumerchoice among retailers”, Journal of Marketing Research, Vol. 46 No. 3, pp. 410-20.

Chong, J.K., Ho, T. and Tang, C.S. (2001), “A modeling framework for category assortmentplanning”, Manufacturing and Service Operations Management, Vol. 3 No. 3, pp. 191-210.

CNN (2010), Dumped! Brand names fight to stay in store, available at: http://money.cnn.com/2010/02/15/news/companies/walmart_dropping_brands/index.htm

Deng, X. and Kahn, B.E. (2009), “Is your product on the right side? The ‘location effect’ onperceived product heaviness and package evaluation”, Journal of Marketing Research,Vol. 46 No. 6, pp. 725-38.

Dempster, A.P., Laird, N.M. and Rubin, D.B. (1977), “Maximum likelihood from incomplete datavia the EM algorithm”, Journal of the Royal Statistical Society. Series B (Methodological),Vol. 39 No. 1, pp. 1-38.

Fraley, C. and Raftery, A.E. (1998), “How many clusters? Which clustering methods? Answersvia model-based cluster analysis”, Computer Journal, Vol. 41 No. 8, pp. 578-88.

Fraley, C. and Raftery, A.E. (2002), “Model-based clustering, discriminant analysis, and densityestimation”, Journal of the American Statistical Association, Vol. 97 No. 458, pp. 611-31.

Fraley, C. and Raftery, A.E. (2006), MCLUST Version 3: An R Package for normal mixtureModeling and Model-based Clustering, Technical Report 504, Department of Statistics,University of Washington, Seattle, WA.

Gordon, A.D. (1973), “Classification in the Presence of Constraints”, Biometrics, Vol. 29 No. 4,pp. 821-7.

Gourville, J. and Soman, D. (2005), “Overchoice and assortment type; when and why varietybackfires”, Marketing Science, Vol. 24 No. 3, pp. 382-95.

Grewal, D., Levy, M., Mehrotra, A. and Sharma, A. (1999), “Planning merchandizing decisions toaccount for regional and product assortment differences”, Journal of Retailing, Vol. 75No. 3, pp. 405-24.

Handcock, M.S., Raftery, A.E. and Tantrum, J.M. (2007), “Model-based Clustering for socialnetworks”, Journal of the Royal Statistical Society A, Vol. 170 No. 2, pp. 201-354.

Hoch, S., Dreze, X. and Purk, M.E. (1994), “EDLP, Hi-Lo, and Margin Arithmetic”, Journal ofMarketing, Vol. 58 No. 4, pp. 16-27.

Huffman, C. and Kahn, B.E. (1998), “Variety for sale: mass customization or mass confusion?”,Journal of Retailing, Vol. 74 No. 4, pp. 491-513.

Iyengar, S.S. and Lepper, M.R. (2000), “When choice is demotivating: can one desire too much of agood thing?”, Journal of Personality and Social Psychology, Vol. 79 No. 6, pp. 995-1006.

Kahn, B.E. (1999), “Introduction to the special issue: assortment planning”, Journal of Retailing,Vol. 75 No. 3, pp. 289-94.

IJRDM40,1

78

Kahn, B.E. and Lehmann, D.R. (1991), “Modeling choice among assortment”, Journal of Retailing,Vol. 67 No. 3, pp. 274-99.

Krivitsky, P.N. and Handcock, M.S. (2008), “Fitting position latent cluster models for socialnetworks with latentnet”, Journal of Statistical Software, Vol. 24 No. 5, pp. 1-23.

Mcintyre, S.H. and Miller, C.M. (1999), “The selection and pricing of retail assortments:an empirical approach”, Journal of Retailing, Vol. 75 No. 3, pp. 295-318.

Mantrala, M.K., Levy, M., Kahn, B.E., Fox, E.J., Gaidarev, P., Dankworth, B. and Shah, D. (2009),“Why is assortment planning so difficult for retailers? A framework and research agenda”,Journal of Retailing, Vol. 85 No. 1, pp. 71-83.

Miller, M.M., Smith, S.A., Mcintyre, S.H. and Achabal, D.D. (2010), “Optimizing and evaluatingretail assortments for infrequently purchased products”, Journal of Retailing, Vol. 86 No. 2,pp. 159-71.

Monni, S. and Li, H. (2008), “Vertex clustering in random graphs via reversible jump MarkovMonte Carlo”, Journal of Computational and Graphical Statistics, Vol. 17 No. 2, pp. 388-409.

Moore, M. and Carpenter, J.M. (2008), “An examination of consumer price cue usage in USdiscount formats”, International Journal of Retail & Distribution Management, Vol. 36No. 5, pp. 345-59.

Morales, A., Kahn, B.E., McAlister, L. and Broniarczyk, S.M. (2005), “Perceptions of assortmentvariety: the effects of congruency between consumers’ internal and retailers’ externalorganization”, Journal of Retailing, Vol. 81 No. 2, pp. 159-69.

MSNBC (2009), Costco stops carrying Coca-Cola products”, available at: www.msnbc.msn.com/id/33987167/ (accessed 22 July 2010).

Martınez-Ruiz, M.P. and Molla-Descals, A. (2008), “Retail price promotion influences for productvarieties in grocery stores: evidence from Spain”, International Journal of Retail& Distribution Management, Vol. 36 No. 6, pp. 494-517.

Simonson, I. (1999), “The effect of product assortment on buyer preferences”, Journal of Retailing,Vol. 75 No. 3, pp. 347-70.

Gomez Suarez, M. (2005), “Shelf space assigned to store and national brands: a neural networksanalysis”, International Journal of Retail & Distribution Management, Vol. 33 Nos 11/12,pp. 858-78.

Urban, T.L. (1998), “An inventory-theoretic approach to product assortment and shelf-spaceallocation”, Journal of Retailing, Vol. 74 No. 1, pp. 15-35.

Zhaolin, L. (2007), “A single-period assortment optimization model”, Product and OperationsManagement, Vol. 16 No. 3, pp. 369-80.

Further reading

Churchill, G.A. Jr (1979), “A paradigm for developing better measures of marketing constructs”,Journal of Marketing Research, Vol. 16 No. 1, pp. 64-73.

Roedder-John, D., Loken, B., Kim, K. and Monga, A.B. (2006), “Brand concept maps:a methodology for identifying brand association networks”, Journal of Marketing, Vol. 43No. 4, pp. 549-63.

Appendix 1As a first step to the estimation process, for a given number of groups G, prior distributions forthe parameters b ¼ bT

0 ; l ¼ ðl1; :::; lGÞ;s2g and mg are specified as follows:

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bkiid,N ðjk;c

2kÞ and k ¼ 1 ðA1Þ

Z iiid,XG

g¼1

lgMVNdðmg ;s2gI dÞ i ¼ 1; :::n ðA2Þ

mgiid,MNVNdð0;v

2I dÞ g ¼ 1; :::G ðA3Þ

s 2giid,s 2

0Invx2a g ¼ 1; :::G ðA4Þ

ðl1; :::;lGÞ , Dirichletðn1; :::; nGÞ ðA5Þ

The hyper parameters j ¼ 0; c ¼ 2I; s 20 ¼ 0:103;a ¼ 2, and v ¼

p2 are used in the above

equations in accordance with Handcock et al. (2007). We use these values for C and v becausethey allow for a wide range for the values of b. The values for a and s0

2 control the clusteridentification sensitivity in order to group assortments even when the deviations among themare very low. The MCMC algorithm iterates over the above priors, latent positions zi of theassortment configurations, and the group membership, Fa1, where Fa1 captures the clustermembership of assortment a1.

We draw the positions of the assortments from a mixture of Gaussians. The components ofthe mixture symbolize different assortment groups, and the positions of the assortments form acluster within the latent space (Krivitsky and Handcock, 2008). Finally an MCMC process withMetropolis-Hastings was used to estimate Fi;mg;s

2gandlg .

The following MCMC algorithm is used to estimate the above equations.Step 1. Use Metropolis-Hastings steps to sample Ztþ1, thus updating each assortment in

random order.(a) Propose

~Z*

i MVNdðZ it; d2Z ; I dÞ

(b) With probability equal to:

PðY jZ*;X ;btÞfdðZ

*

i ;mFi;s2KiIdÞ

PðY jZt;X ;btÞfdðZit ;mFi;s2KiI dÞ

and set i th element of Ztþ1 to Z*

i . Else set it to Zit.Step 2. Use Metropolis-Hastings steps to sample btþ1.(a) Propose b ~*MVNdðbt; d

2bI pÞ

(b) With probability equal to:

PðY jZtþ1;X ;b*Þfpðb

*; j;CÞ

PðY jZtþ1;X ;btÞfpðbt ; j;CÞ;

Set btþ1 ¼ b*. Else set btþ1 ¼ bt

(c) Finally, update Fi;mg;s2gandlgfrom equation (A3) to equation (A5).

For the full posterior distributions, please see Handcock et al. (2007). We estimated the aboveequations for different number of clusters (G) starting from 2 through 5 and selected theclustering model with highest posterior probability as the optimal cluster solution. Throughout,we maintained the number of dimensions as two in order to facilitate a pictorial representation ofthe vulnerability structure for ease of decision-making.

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Appendix 2

About the authorsMayukh Dass is Assistant Professor of Marketing at the Rawls College of Business, Texas TechUniversity, USA. He holds a PhD in Business Administration, an MS in Statistics, an MS inArtificial Intelligence from the University of Georgia and a B.Engg in Electronics and PowerEngineering from Nagpur University, India. His research focuses on statistical and analyticalmethods with applications to valuation issues in dynamic economies and brand management. Heis a member of the INFORMS and the Academy of Marketing Science.

Piyush Kumar is Associate Professor of Marketing at the Terry College of Business,University of Georgia, USA. His research interests include web analytics, internet-basedbusiness models, brand management and analytics, and service management. He has previouslypublished in Marketing Science, Journal of Marketing Research, Journal of Marketing, Journal ofRetailing and other journals. He holds a B.Tech in Mechanical Engineering from the IndianInstitute of Technology, Kanpur, an MBA from the Indian Institute of Management,Ahmedabad, and a PhD from Purdue University. Piyush Kumar is the corresponding author andcan be contacted at: pkumar@terry.uga.edu

Soda Enhanced water

CP PVCp PvCD PSCd PscP pVcp pvcD pScd psPD VSPd VspD vSpd vsCPD PVSCPd PVsCpD PvSCpd PvscPD pVScPd pVscpD pvScpd pvs

Notes: C: Coke/Diet Coke at regular price; c: Coke/Diet Coke at sale price; P: Pepsi/Diet Pepsi at regularprice; p: Pepsi/Diet Pepsi at sale price; D: Dr Pepper/Diet Dr Pepper at regular price; d: Dr Pepper/DietDr Pepper at sale price; P: Propel at regular price; p: Propel at sale price; V: Vitamin Water at regularprice; v: Vitamin Water at sale price; S: Smart Water at regular price; s: Smart Water at sale price

Table AI.Assortment

configurations used ineach study

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