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Managing Variety on the Retail Shelf: Using Household Scanner Panel Data to Rationalize Assortments

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Part of the International Series in Operations Research & Management Science book series (ISOR,volume 223)

Abstract

We propose a model for the rationalization of retail assortment and stocking decisions for retail category management. We assume that consumers are heterogenous in their intrinsic preferences for items and are willing to substitute less preferred items to a limited extent if their preferred items are not available. We propose that the appropriate objective function for a far-sighted retailer includes not only short-term profits but also a penalty for disutility incurred by consumers who do not find their preferred items in the available assortment. The retailer problem is formulated as a constrained integer programming problem. We demonstrate an empirical application of our proposed model using household scanner panel data for eight items in the canned tuna category. Our results indicate that the inclusion of the penalty for disutility in the retailer’s objective function is informative in terms of choosing an assortment to carry. We find that customer disutility can be significantly reduced at the cost of a small reduction in short term profits. We also find that the optimal assortment behaves non-monotonically as the weight on customer disutility in the retailer’s objective function is increased.

Keywords

  • Retail assortment
  • Substitution
  • Heterogeneity
  • Scanner data
  • Integer programming
  • Optimization

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Notes

  1. 1.

    Part of the increase is attributed to enhanced utility due to reduced clutter in the category. Our model does not allow for such an effect.

  2. 2.

    In Sect. 6 of the chapter, as future research, we discuss the possibility of extending the model to determine optimal prices as well.

  3. 3.

    The transformation of utilities by dividing by the price coefficient also serves to remove the influence of the unidentified scale factor that confounds the vector of parameter estimates (Swait and Louviere 1993).

  4. 4.

    The consumer model in Sect. 3 was developed assuming each consumer is a separate segment, i.e., the number of consumers in each segment is one. Other models of brand choice that provide estimates for “segments” of consumers could be employed, such as formulations of Kamakura and Russell (1989) and Chintagunta et al. (1991).

  5. 5.

    We assume, for simplification, that each consumer buys exactly one unit in each restocking period. This assumption can be relaxed by weighting each consumer by the number of units bought. In general, the number of units bought by a consumer within any stocking period may be uncertain. Incorporating this uncertainty will result in a stochastic programming formulation. We elaborate upon this idea in the discussion of future work in Sect. 6.

  6. 6.

    In the optimization model, the item “assigned” to a consumer will be the one that maximizes the consumer’s utility. Thus, consumers will in effect self-select their best alternative from the available assortment.

  7. 7.

    Notice that this disutility is due to non-stocking of items and not due to stock-out of an item.

  8. 8.

    Dissatisfaction measured as sum across segments of the differences in utilities implies that a large number of small disutilities is equivalent to a small number of large disutilities; e.g., two segments with one unit of disutility each is equivalent to one segment (of same size) with two units of disutility. This may not be desirable since larger differences in utilities signify consumers loyal to certain brands, and smaller differences in utilities signify switchers. A non-linear (say, e.g., exponential) function of difference in utilities will allow us to distinguish between loyals and switchers.

  9. 9.

    A similar objective function (weighted combination of profits and consumer utility) was also considered by Little and Shapiro (1980) in the context of pricing nonfeatured products in supermarkets. Similarly, there is extensive literature on bi-criterion optimization problems; see, for example, French and Ruiz-Diaz (1983).

  10. 10.

    Category purchase incidence is frequently modeled using scanner data (e.g. Bucklin and Gupta 1992). However, the consumers’ decision is considered to be one of choosing to buy one of the items in the assortment at today’s prices and promotions, versus postponing the purchase decision to a future occasion when prices may be better, and relying meanwhile on available household inventory for consumption. Thus, the impact of assortment unavailability is not modeled.

  11. 11.

    Note that only the rank ordering of preferences is used to construct Table 10.3 to illustrate the nature of substitution between items. The retailer optimization problem uses interval-scaled values of preferences.

  12. 12.

    For the illustration here we assume that the total market consists of the 1,097 consumers in our sample.

References

  • Adams, P. W., & Sherali, H. D. (1990). Linearization strategies for a class of zero–one mixed integer programming problems. Operations Research, 38, 217–226.

    CrossRef  Google Scholar 

  • Arrow, K., Karlin, S., & Scarf, H. (1958). Studies in the mathematical theory of inventory and production. Stanford: Stanford University Press.

    Google Scholar 

  • Bassok, Y., Anupindi, R., & Akella, R. (1997). Single period multi–product inventory models with substitution. Operations Research, 47, 632–642.

    CrossRef  Google Scholar 

  • Bawa, K., & Shoemaker, R. W. (1987). The effects of a direct mail coupon on brand choice behavior. Journal of Marketing Research, 24, 370–376.

    CrossRef  Google Scholar 

  • Boatwright, P., & Nunes, J. C. (2001). Reducing assortment: An attribute based approach. Journal of Marketing, 65, 50–63.

    CrossRef  Google Scholar 

  • Borin, N., Farris, P., & Freeland, J. (1994). A model for determining retail product category assortment and shelf space allocation. Decision Sciences, 25(3), 359–384.

    CrossRef  Google Scholar 

  • Borle, S., Boatwright, P., Kadane, J. B., Nunes, J. C., & Shmueli, G. (2005). Effect of product assortment changes on customer retention. Marketing Science, 24(4), 612–622.

    CrossRef  Google Scholar 

  • Broniarczyk, S. M., Hoyer, W. D., & McAlister, L. (1998). Consumers’ perceptions of the assortment offered in a grocery category: The impact of item reduction. Journal of Marketing Research, 35, 166–176.

    CrossRef  Google Scholar 

  • Bucklin, R. E., & Gupta, S. (1992). Brand choice, purchase incidence, and segmentation: An integrated modeling approach. Journal of Marketing Research, 29(9), 201–215.

    CrossRef  Google Scholar 

  • Bultez, A., Gijsbrechts, E., Naert, P., & Vanden Abeele, P. (1989). Asymmetric cannibalism in retail assortments. Journal of Retailing, 65(2), 153–192.

    Google Scholar 

  • Bultez, A., & Naert, P. (1988). S.H.A.R.P.: Shelf allocation for retailer’s profit. Marketing Science, 7(3), 211–231.

    Google Scholar 

  • Carpenter, G., & Lehmann, D. R. (1985). A model of marketing mix, brand switching and competition. Journal of Marketing Research, 22, 318–329.

    CrossRef  Google Scholar 

  • Chintagunta, P., Jain, D. C., & Vilcassim, N. J. (1991). Investigating heterogeneity in brand preferences in logit models for panel data. Journal of Marketing Research, 28, 417–428.

    CrossRef  Google Scholar 

  • Chong, J., Ho, T.-H., & Tang, C. (2001). A modeling framework for category assortment planning. Journal of Manufacturing and Service Operations Management, 3(3), 191–210.

    CrossRef  Google Scholar 

  • Cornuejols, G., Fisher, M., & Nemhauser, G. (1977). Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms. Management Science, 23(8), 789–810.

    CrossRef  Google Scholar 

  • Corstjens, M., & Doyle, P. (1981). A model for optimizing retail space allocations. Management Science, 27(7), 822–833.

    CrossRef  Google Scholar 

  • Coughlan, A. T., Anderson, E., Stern, L. W., & El-Ansary, A. I. (2006). Marketing channels. Englewood Cliffs, NJ: Prentice Hall.

    Google Scholar 

  • Dobson, G., & Kalish, S. (1988). Positioning and pricing a product line. Marketing Science, 7(2), 107–125.

    CrossRef  Google Scholar 

  • Dobson, G., & Kalish, S. (1993). Heuristics for pricing and positioning a product–line using conjoint and cost data. Management Science, 39, 160–175.

    CrossRef  Google Scholar 

  • Emmelhainz, M. A., Stock, J. R., & Emmelhainz, L. W. (1991). Consumer responses to retail stockouts. Journal of Retailing, 67(2), 139–147.

    Google Scholar 

  • Erlenkotter, D. (1978). A dual-based procedure for uncapacitated facility location. Operations Research, 26(6), 992–1009.

    CrossRef  Google Scholar 

  • Food Marketing Institute. (1993). Variety or duplication: A process to know where you stand. Washington, D.C.: The Research Department, Food Marketing Institute.

    Google Scholar 

  • French, S., & Ruiz-Diaz, F. (1983). A Survey of multi–objective combinatorial scheduling. In S. French, et al. (Eds.), Multi–objective decision making. New York: Academic.

    Google Scholar 

  • Gaur, V., & Honhon, D. (2006). Assortment planning and inventory decisions under a locational choice model. Management Science, 52(10), 1528–1543.

    CrossRef  Google Scholar 

  • Gruen, T., Cortsen, D. S., & Bharadwaj, S. (2002). Retail out-of-stocks: A worldwide examination of extent, causes and consumer responses. Grocery Manufacturers of America.

    Google Scholar 

  • Harris, B., & McPartland, M. (1993). Category management defined: What it is and why it works. Progressive Grocer, 72(9), 5–8.

    Google Scholar 

  • Imai, K., & van Dyck, D. A. (2005). A Bayesian analysis of the multinomial probit model using the marginal data augmentation. Journal of Econometrics, 124(2), 311–334.

    CrossRef  Google Scholar 

  • Kalish, S., & Nelson, P. (1991). A comparision of ranking, rating, and reservation price measurement in conjoint analysis. Marketing Letters, 2(4), 327–335.

    CrossRef  Google Scholar 

  • Kamakura, W. A., & Russell, G. (1989). A probabilistic choice model for market segmentation and elasticity structure. Journal of Marketing Research, 26, 379–390.

    CrossRef  Google Scholar 

  • Kok, A., & Fisher, M. L. (2004). Demand estimation and assortment optimization under substitution: Methodology and application. Operations Research, 55(6), 1001–1021.

    Google Scholar 

  • Krishna, A. (1992). The normative impact of consumer price expectations for multiple brands on consumer purchase behavior. Marketing Science, 11(3), 266–286.

    CrossRef  Google Scholar 

  • Lee, H. L., & Nahmias, S. (1994). Single product single location models. In S. Graves, A. R. Kan, & P. Zipkin (Eds.), Logistics of production and inventory. Handbook in operations research and management science. Amsterdam: North–Holland.

    Google Scholar 

  • Little, J. D., & Shapiro, J. (1980). A theory for pricing nonfeatured products in supermarkets. Journal of Business, 53(3), S199–S209.

    CrossRef  Google Scholar 

  • Mahajan, S., & van Ryzin, G. (2001). Stocking retail assortments under dynamic consumer substitution. Operations Research, 49, 334–351.

    CrossRef  Google Scholar 

  • McBride, R., & Zufryden, F. S. (1988). An integer programming approach to optimal product line selection. Marketing Science, 7, 126–140.

    CrossRef  Google Scholar 

  • McCullogh, R., & Rossi, P. E. (1994). An exact likelihood analysis of the multinomial probit model. Journal of Econometrics, 64, 207–240.

    CrossRef  Google Scholar 

  • Miller, C., Smith, S. A., McIntyre, S. H., & Achabal, D. D. (2006). Optimizing retail assortments for infrequently purchased products. Working Paper, Retail Management Institute, Santa Clara University.

    Google Scholar 

  • Morgan, L. O., Daniels, R. L., & Kouvelis, P. (2001). Marketing/manufacturing trade-offs in product line management. IIE Transactions, 33, 949–962.

    Google Scholar 

  • Nielsen Marketing Research (1992). Category management: Positioning your organization to win. Lincolnwood, IL: NTC Business Books.

    Google Scholar 

  • Pentico, D. (1974). The assortment problem with probabilistic demands. Management Science, 21, 286–290.

    CrossRef  Google Scholar 

  • Pentico, D. (1988). A discrete two-dimensional assortment problem. Operations Research, 36(2), 324–332.

    CrossRef  Google Scholar 

  • Schiller, Z., Burns, G., & Miller K. L., (1996). Marketing: Making it simple. Business Week, 9 September.

    Google Scholar 

  • Sloot, L., Fok, D., & Verhoff, P. C. (2006). The short- and long-term impact of an assortment reduction on category sales. Journal of Marketing Research, XLIII, 536–548.

    Google Scholar 

  • Smith, S., & Agrawal, N. (2000). Management of multi–item retail inventory systems with demand substitution. Operations Research, 48, 50–64.

    CrossRef  Google Scholar 

  • Swait, J., & Louviere, J. (1993). The role of the scale factor in the estimation and comparision of multinomial logit models. Journal of Marketing Research, 30, 305–314.

    CrossRef  Google Scholar 

  • Urban, G. L., Johnson, P. L., & Hauser, J. R. (1984). Testing competitive market structures. Marketing Science, 3(2), 83–112.

    Google Scholar 

  • van Dijk, A., van Heerde, H. J., Leeflang, P. S. H., & Wittink, D. R. (2004). Similarity based spatial methods to estimate shelf-space elasticities. Quantitative Marketing and Economics, 2, 257–277.

    CrossRef  Google Scholar 

  • van Ryzin, G., & Mahajan, S. (1999). On the relationship between inventory costs and variety benefits in retail assortments. Management Science,45, 1496–1509.

    Google Scholar 

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Acknowledgements

We are grateful to the A.C. Nielsen Company for generously providing the data used in this paper, to Edward Malthouse for his help with setting up the data, to Qiang Liu for help with data analysis, and to Pradeep Chintagunta, Maqbool Dada and Yehuda Bassok for valuable comments on an earlier version of the paper.

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Appendix

Appendix

Proof of Proposition 4.1.

Without loss of generality, we will illustrate this for the general case rather than the special case of fixed depth of search d.

First consider the constraint (10. 6a′′ ). The constraint for j = 1 will be

$$ 1-\left({x}_{s2}+{x}_{s3}+\dots +{x}_{sK}+{x}_{s0}\right)\ge {y}_1 $$

However, from (10.6c) we know that

$$ {x}_{s1}+{x}_{s2}+\dots +{x}_{jK}+{x}_{s0}\le 1 $$

Actually, given a “no purchase” option, the above is an equality; i.e.,

$$ {x}_{s1}+{x}_{s2}+\dots +{x}_{jK}+{x}_{s0}=1 $$

Using this we rewrite \( 1-\left({x}_{s2}+{x}_{s3}+\dots +{x}_{sK}+{x}_{s0}\right)\ge {y}_1 \) as simply x 1 ≥ y 1. Similarly, we can write (10. 6a″) for j = k as

$$ {x}_{s1}+{x}_{s2}+\dots +{x}_{sk}\ge {y}_k. $$

Using this, for any arbitrary customer segment s that prefers K products in the ordinal order (without loss of generality) the constraint sets (10. 6a′) and (10. 6a″) are

Table 7

Consider normalized constraint (1′) and (1″):

$$ {x}_{s1}+\left(\frac{V_{s2}}{V_{s1}}\right){x}_{s2}+\cdots \left(\frac{V_{sk}}{V_{s1}}\right){x}_{sk}\kern2em \mathrm{and}\kern2em {x}_{s1}\ge {y}_1. $$

Since (1′′) and (1) are identical in x s1 dimension and (1) has k − 1 extra variables (degrees of freedom), constraint (1′′) is tighter than constraint (1). Using similar arguments one can show that constraints (2′′) to ((k − 1)′′) will be tighter than (2) to ((k − 1)). Constraint (k ′′) may be identical to (k ). The argument can be repeated for other segments. Thus problem (P1) with (10. 6a′′ ) is a tighter formulation than (P1) with (10. 6a ).

To see that relaxation of x sj still leads to an integer solution, first consider (1′′). If y 1 = 0, then x s1 = 0 using (10.6c). If y 1 = 1, then x s1 = 1. Now consider (2′′). Suppose y 1 = 0. If y 2 = 0 then x s2 = 0; otherwise (y 2 = 1), x s2 = 1. However, if y 1 = 1, then (10.6b) ensures that x s2 = 0. Following this argument, we can show that x sj is integer. ■ 

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Anupindi, R., Gupta, S., Venkataramanan, M.A. (2015). Managing Variety on the Retail Shelf: Using Household Scanner Panel Data to Rationalize Assortments. In: Agrawal, N., Smith, S. (eds) Retail Supply Chain Management. International Series in Operations Research & Management Science, vol 223. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7562-1_10

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