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Article Excerpt
Assortment planning is both extremely important and challenging for retailers. No assortment planning process is capable of accounting for all of the marketing and operational implications of its decisions due to limited data and the complexity of the task. Organizational forms such as category management (CM) (ACNielsen 1998) and assortment planning models in the literature (e.g., Kok and Fisher 2004) focus on the selection of products in a single category assuming store traffic is exogenous, i.e., prices and variety within a category influence demand conditional on a store visit, but does not influence store choice. For example, many retailers are adopting an "efficient assortment" strategy, which primarily seeks to find the profit maximizing level of variety by eliminating low-selling products (Kurt Salmon Associates 1993). However, if a retailer reduces variety in all categories based on single-category analyses, then the store becomes less attractive and some customers are likely to defect to other retailers, reducing store traffic. This concern is particularly relevant with respect to basket shoppers--consumers who desire to purchase from multiple categories. If a basket shopper does not find an item that she wants in one category, she may purchase her entire basket from another retailer (Bell and Lattin 1998). Although retailers are well aware of this interdependence across categories, there is little research on what can be done to address it.
This paper develops a stylized model to evaluate CM at two competing retailers in the presence of basket shopping consumers. Each retailer offers two merchandise categories. Retailers determine prices and variety level in each category. Single-category shoppers and basket shoppers choose between the two retailers or a no-purchase option, depending on their utilities in each category at each retailer. A retailer can manage its merchandise categories with a centralized or a decentralized regime. The common practice of CM is an example of a decentralized regime for controlling assortment because each category manager is charged with maximizing profit for his or her assigned category. Because basket shoppers' store choice decision depends on the prices and variety levels of other categories, one category's optimal decisions depends on the decisions of the other categories. Hence, a game-theoretic situation arises. CM can be interpreted as an explicit noncooperative game between the category managers because each category manager is responsible exclusively for the profits of her own category. Alternatively, it can be interpreted as an iterative application of single-category planning where each category's variety level is optimized assuming all other assortment decisions for the retailer are fixed. Decentralized regimes such as CM are analytically manageable but they ignore (in their pure form) the impact of cross-category interactions. Centralized regimes account for these effects, but actually only in theory because they are not implementable in practice: it is extremely difficult to design a model to account for all cross-category effects, to estimate its parameters with available data, and solve it. Chen et al. (1999) also emphasize the need for models that are solvable with parameters that can be estimated from available data. As CM and centralization are two extremes, merchandising managers often create an intermediate approach by adding constraints to the planning process based on their own knowledge about the store's categories and customers: for example, include a particular product, have at least two brands in a subgroup, and ensure that the timing and depth of promotions are coordinated across obviously complementary products such as chips and salsa or beer and pretzels. It is not clear, however, if the appropriate constraints are implemented (e.g., whether there should be two brands or five brands) or whether all of the necessary interactions are accounted for with this ad-hoc approach.
Previous research shows that CM resulted in a more profitable pricing structure by eliminating the competitive pricing between brands. Zenor (1994) and Basuroy et al. (2001) compare brand management (i.e., decentralized management of competing products) to CM (centralized management of a category) in a single category and find that CM leads to higher prices. Our paper attempts to shift the discussion one level higher by comparing CM with centralized store management. It is expected that decentralization will perform worse than centralization, so the question is whether it performs well under certain conditions. It is also important to assess whether the loss due to decentralization is significant and whether decentralized solutions have a consistent bias (too much or too little variety, too high or too low prices). Finally, is there a way to have the best of both worlds, i.e., are there easily solvable management regimes, based on readily available data, that lead to nearly optimal assortments?
We characterize the assortment chosen in a decentralized regime, which we refer to as CM, as well as the assortment in a centralized solution (OPT). We show that if there are any basket shoppers, CM provides less variety and higher prices than OPT. CM can lead to poor decisions because the category manager does not sufficiently account for how his or her decisions influence total store traffic. With numerical examples, we demonstrate that the profit loss due to CM can be significant. More importantly, the performance worsens as the number of categories and proportion of basket shoppers increase. These results hold both for a single retailer and in duopoly competition. The dominant strategy for each retailer is to switch to centralized management (OPT). Our point is that decentralization can be costly if there are basket shopping consumers and the interactions among categories is not explicitly modeled. To address the potential problem with a decentralized approach to assortment planning, we propose a simple heuristic that retains decentralized decision making (category managers optimize their own categories' profit) but adjusts how profits are measured. To be specific, instead of using an accounting measure of a category's profit, we define a new measure called basket profits. Basket profits can be estimated using point-of-sale data. It enables CM to approximately measure the true marginal benefits of merchandising decisions and lead to near-optimal profits. We believe that this analytical approach is an attractive alternative relative to ad-hoc coordination across category managers.
We review the related literature in the next section. We introduce our model in [section]2. We present the analysis of the variety competition case (where prices are exogenous) in [section]3, followed by the price and variety competition case in [section]4. We present a brief numerical study in [section]5, discuss alternative demand models in [section]6, and conclude in [section]7. Appendix A presents a replenishment system with convex costs. All proofs are presented in Appendix B.
1. Related Literature
Our consumer choice model is built on the random utility approach (see Anderson et al. 1992). Each consumer receives a random utility from each item in the choice set and the highest utility item is chosen. As a result, increasing the breadth and depth of the assortment in our model increases total demand. The findings in Dhar et al. (2001) are generally consistent with that assumption. However, we recognize that our model does not explicitly account for other possible factors that influence the relationship between assortment variety and demand: the space devoted to a category and the presence or absence of a favorite item influence the perception of variety (Kahn and Lehmann 1991, Broniarczyk et al. 1998) as well as the arrangement, complexity, and presence of repeated items in an assortment (Hoch et al. 1999, Huffman and Kahn 1998, Simonson 1999).
Although research has primarily focused on single-category choice decisions, there is recent research that examines multiple category purchases in a single-shopping occasion by modeling the dependency across multicategory items explicitly (see Russell et al. 1997 for a review). Manchanda et al. (1999) find that two categories may co-occur in a consumer basket, either due to their complementary nature (e.g., cake mix and frosting) or due to coincidence (e.g., similar purchase cycles or unobserved factors). Bell and Lattin (1998) show that consumers make their store choice based on the total basket utility. Bodapati and Srinivasan (1999) relates feature advertising to store traffic effects using a nested logit framework. In these papers and in ours, consumers first assign a utility to an anticipated market basket and subsequently use this utility to determine store choice.
Fixed costs for each store visit (e.g., search and travel costs) provide an intuitive explanation for why consumers basket shop. Bell et al. (1998) use market basket data to analyze consumer store choices and explicitly consider the roles of fixed and variable costs of shopping. We do not explicitly derive optimal baskets. We take them as given; however, consumers make optimal store choice given their baskets. Some consumers distribute their shopping across stores to take advantage of discounts and different selections, a behavior known as cherry-picking. Fox and Hoch (2005) compare cherry-picking consumers with single-store shoppers and find that consumers with lower income and larger shopping baskets are more likely to engage in cherry-picking.
Price competition across multiple categories has been studied by several researchers using Hotelling type models in which consumers travel and search costs impact retailers' strategies and whether or not consumers cherry-pick. Lal and Rao (1997) show that in equilibrium one firm will adapt every day low pricing, whereas the other firm adapts promotional pricing strategy. The loss-leader literature suggests offering promotions in one category to increase store traffic and overall profit (see, for example, Lal and Matutes 1989). From an empirical perspective, Walters and Mackenzie (1988) report that loss-leader pricing produced only a small increase in store traffic. Recent empirical research in marketing (e.g., Bayus and Putsis 1999, Draganska and Jain 2005) examines the relation of prices with product variety and other marketing mix variables that are endogenously determined by firms and their impact on market shares.
Chen et al. (1999) also study the impact of basket shopping consumers. They show that merchandising decisions should not be governed by accounting profits, but rather by a new construct they develop called marketing profits. Like us, they argue that simple techniques, based on readily available data, are needed to guide decision making. However, there are some significant differences between their work and ours. In their model, each consumer type bases its store choice decision on the variety of a single category, what they call the lead category. Hence, expanding variety in category B has no influence on the store choice decision of category A lead customers. In contrast, our consumers base their decisions on the utility of multiple categories. As a result, there are minimal strategic interactions among categories in their model. A second key difference is how they improve decision making. They assume that a store makes optimal shelf space decisions and infer marketing profit parameters that would imply those decisions are optimal. They then use those marketing profit estimates to guide other merchandising decisions, such as advertising allocation. We use point-of-sales data to estimate basket profits and then derive optimal assortment decisions.
Assortment planning has attracted researchers from both operations and marketing fields. See Kok et al. (2006) for a recent review of this literature. van Ryzin and Mahajan (1999), Smith and Agrawal (2000), and Kok and Fisher (2004) study assortment selection and stocking decisions for a group of substitutable products in a single category assuming that store traffic is exogenous. Agrawal and Smith (2003) extend this work to the case with basket shopping consumers. Cachon et al. (2005) partially relaxes the exogenous store traffic assumption by considering consumer search behavior. The customers can choose to purchase an item at the store or to continue to search, which means that the fraction of "no-purchase" customers depends on the assortment. Chong et al. (2001) present an empirically-based modeling framework for managers to assess the revenue and lost sales implication of alternative assortments. Dreze et al. (1994) study the impact of shelf space on sales and Boatwright and Nunes (2001) study assortment reduction by making sure that certain attributes are represented in the assortment. Hopp and Xu (2005) study the impact of product modularity in the optimal product line length from a manufacturer's perspective. Hopp and Xu (2006) study price, service, and assortment competition in a single category between two retailers and find that the retailers provide less variety and lower prices in competition.
We use game theory to study competitive interactions in the decentralized regime and between the retailers. Gruca and Sudharshan (1991) and Basuroy and Nguyen (1998) study a market share game based on the multinomial logit (MNL) model and demonstrate that certain conditions are needed for equilibrium to exist. Karnani (1985) studies a multiplicative competitive interactions (MCI) model with several firms that compete in a single market through several marketing decisions. Existence of equilibria is not guaranteed in his model because the profit function of a single firm is not jointly concave in the marketing variables. Our model has multiple customer types which may be considered as multiple markets. Monahan (1987) studies a model in which two firms compete with each other in several markets with an MCI model with a single marketing variable. Our model also has several markets, but the retailer's shares in different markets (customer types) are interdependent and multiple marketing variables (i.e., price and variety levels in all categories) play a role in each market.
2. Model Basics
Consider two retailers X and Y that carry two categories of goods. The set of products in category j is {1, 2,..., I} for j = 1, 2, where I is a large number. Let subscript r denote retailer r, r = x, y. Retailer r offers [n.sub.rj] products and sets its margin [p.sub.rj] in category j. The unit procurement cost for product i...
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