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					OPERATIONS RESEARCH (ONLINE FORUM COMMENTARY)
Vol. 57, No. 1, May–June 2009, online commentary issn 0030-364X | eissn 1526-5463 | 09

INFORMS

Determining Optimal Assortment: Forecasting Demand of New Products and Estimating Substitution Pattern
Comment on “Rocket Science Retailing” by Marshall Fisher
Juin-Kuan Chong
Associate Professor of Marketing NUS Business School National University of Singapore Singapore bizcjk@nus.edu.sg

Tek-Hua Ho
William Halford Jr. Family Professor of Marketing Haas School of Business University of California Berkeley Berkeley, CA USA hoteck@haas.berkeley.edu

To deliver the right products to the right customers profitably requires a fundamental shift in retail decision making from art to science; and from one that is based on human intuition to one that is driven by customer data. Marshall Fisher and his collaborators pioneered this transformation by developing many rigorous and practical statistical and operations research methods for the retailing industry. This “Rocket Science” approach brings retail decision making to a whole new level of efficiency and sophistication. Retail decision making begins with assortment planning and assortment drives pricing and inventory sizing decisions. It is thus apt for Fisher to begin his lecture on assortment planning. This commentary focuses on the excellent works of Fisher and collaborators in assortment planning and aims to achieve 2 goals. First, we will describe other research for demand forecasting (including new products that have new attribute levels and lost sale due to imperfect demand substitution) that may be better suited in some industries (e.g., frequently purchased consumer products). Second, we highlight the importance of using alternative sources of data to validate their method of estimating demand substitution, which uses managerial judgment. Our suggestions and approaches may be added to the existing toolbox for effective retail decision making. The key to determining an optimal assortment at a store lies in the correct characterization of demand for each product and the substitution patterns across products. This characterization is challenging because there are often a large number of products in a category and an even larger number of substitution patterns. For example, if there are N products at a store, one must estimate (N*(N-1))/2 substitution patterns even with the assumption of symmetry in substitution. The estimation complexity for SKU demand can be substantially reduced if one represents products
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: Commentary on Marshall Fisher Operations Research (Online Forum Commentary) 57(1), 2009 INFORMS

as a bundle of attribute levels (e.g., brand, warranty, and size). By estimating demands for each attribute level that SKU has, one can then derive a SKU demand from these attribute level demands by a multiplicative model (see Table 4 in Fisher, 2009). See Fader and Hardie (1996) and Ho and Chong (2003) for an alternative attribute-level modeling approach that uses panel level data. Let us use an example to demonstrate how this reduction in complexity works. If there are 37 brands, 9 sizes, and 145 flavors in an ice-cream category, there are a total of 37 x 9 x 145 = 48,285 possible SKUs. Instead of estimating 48,285 product demands, one only needs to estimate 37+9+145 = 191 attribute level values. We further reduced the dimensionality burden by replacing the attribute level values with behavioral equations that captured historical demand and substitution patterns (see Ho and Chong, 2003). Our approach requires only 6 parameter estimates for each attribute and hence a total of 18 parameter values for a product category that has 3 attributes. Despite this parsimony, our approach fits the data well. There is however a barrier in implementing the Fader and Hardie (1996)’s and Ho and Chong (2003)’s approaches. Both approaches use customer panel level data which may not be possible in some product categories either because such data cannot be captured or because the inter-purchase time is long. However, the key advantage of both approaches is that it allows for correlation in demand at both the product and attribute levels by allowing their values to evolve as new purchases are observed. (Fisher’s approach allows for correlation at the product but not at the attribute level since it invokes the independence assumption in deriving SKU demand from attribute level demands.) The correlation at the attribute level can sometimes be important. For example, Mary may prefer chocolate flavor but only from Ben & Jerry’s (in this case, demand are correlated across brand and flavor). In addition, our approach allows one to forecast demand for a new product (with attribute levels that were previously not available in the category). For example, a store may introduce a new flavor to the ice-cream category. Our approach automatically imputes a starting value for a new attribute level and uses it to forecast demand for any new product with that specific attribute level. (The starting values capture the customer’s response to past introduction of new attribute levels). As more purchase data come in, the approach will revise the starting value and produce more accurate forecasts of the new attribute level value. Fisher and colleagues simplify the number of substitution pairs by incorporating managerial judgment. Store managers were asked to rule out unlikely substitution patterns and classify possible patterns into distinct classes of substitution probabilities. A potential problem of managerial judgment is that store managers may exhibit systematic biases in classifying these substitution patterns. Hence it may be important to validate human judgments using customer level data. Specifically, one may use the consideration set formed by customers to validate. Consideration set is the set of products that customers consider before their choice. One can determine consideration set by eliciting it directly from customers via a survey or estimating it indirectly using a panel data set. In an indirect estimation, a consideration set is frequently defined as the set of products that deliver utilities above an empirically determined threshold (see Roberts and Lattin, 1991). Thus, only products that are above the threshold are included for substitution. As long as a customer who wishes to purchase a product cannot find a perfect product substitute (i.e., the substitution probability is strictly less than 1), a sale may be lost. Under the Fisher’s approach, lost sale is defined as 1 - substitution probability summed over all possible substitutes. An alternative approach to estimate lost sale is to explicitly incorporate a purchase incidence model, commonly used in marketing. Chong, Ho and Tang (2001) develop such a model and use the assortment and household’s expected inventory level as predictors for the purchase incidence probability. Lost sale is then estimated to be the difference between a target assortment and the actual assortment. This alternative method may work better with a panel level data set. References

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Chong, Juin-Kuan, Teck-Hua Ho and Chris Tang (2001), “A Modeling Framework for Category Assortment Planning,” Manufacturing & Service Operations Management, 3(3), pp. 191-210. Fader, Peter S. and Bruce G. S. Hardie (1996), “Modeling Consumer Choice among SKUs,” Journal of Marketing Research, 33(4), pp. 442-452. Fisher, Marshall (2009), “Rocket Science Retailing: The 2006 Philip McCord Morse Lecture,” Operations Research, 57(3), pp. 527-540. Ho, Teck-Hua and Juin-Kuan Chong (2003), “A Parsimonious Model of Stockkeeping-Unit Choice,”‘ Journal of Marketing Research, 40(3), pp. 351-365. Roberts, J. H. and James M. Lattin (1991), “Development and Testing of A Model of Consideration Set Composition,” Journal of Marketing Research, 28(4), pp. 429-440.