This article was originally published in the Spring 2012 edition of OnAnalytics, published by the Institute for Business Analytics at Indiana University’s Kelley School of Business.
This article focuses on insights from Venkat Venkataramanan a professor of Decision Sciences and Vice Provost for Finance and Strategy. Find more information about this research in the article, “Managing Variety on the Retail Shelf: Using Household Scanner Panel Data to Rationalize Assortments“.
As the variety of products on the market continues to expand, retailers are faced with difficult decisions about their stock assortments. The fear of failing to stock customers’ preferred brands can cause retailers to fill their shelves with an overwhelming assortment of products, a potentially costly strategy that doesn’t always yield returns. Taking into account the heterogeneity of customer preferences, customer’s willingness to substitute a second or third choice if their first choice is unavailable, and the dissatisfaction customers experience when they cannot purchase their preferred brands, the researchers propose and test a model for retail category assortment that allows managers to balance customer satisfaction with short-term profit.
Statement of the Problem
Retailers face assortment decisions for each category of goods, balancing the attempt to stock as many preferred brands as possible with the constraints of limited shelf space and the administrative and warehouse costs of carrying each item. In order to make informed assortment decisions, managers need a means of quantifying the relative merit of custom-er satisfaction and cost savings. The researchers propose a systematic assessment tool that takes into account both the possibility of substitution and the “disutility” incurred when customers cannot purchase their preferred items.
Data Sources Used
In order to test the optimization model, the researchers used household scanner panel data available from the AC Nielsen Company, collected from supermarkets in a specified city. The researchers selected the category of canned tuna for the case study. Purchasing data was provided for 1097 households and the eight largest canned-tuna brands, which collectively represented 90% of purchases in the category. In addition to purchasing information, the data provided information on prices, in-store displays, and feature advertising.
Analytic Techniques
The assortment question is framed as an integer programming problem. The researchers used a multinomial probit model to serve as a discrete choice framework for modeling demand. To capture customer heterogeneity, they place a distributional assumption on the utility function parameters. They employ a diagonal covariance structure to simplify the calculation of choice probabilities.
Although the customer demand model contains both a deterministic and a stochastic component of utility, the researchers focus exclusively on the deterministic component when applying the model to avoid confounding the impact of heterogeneity and probabilistic choice on the assortment decision.
The researchers begin with a basic formulation for assortments and stocking that incorporates profits and disutility. They create a measurement of disutility equal to the reduction in price necessary to make the customer indifferent between the preferred and less-preferred items. The model also addresses the likelihood that certain products serve as “traffic generators” that have a high impact on store choice. Because scanner data does not capture no-purchase decisions, the researchers offer a formulation to reflect this disutility.
The problem has an embedded uncapacitated plant location model, which has been shown to be NP-hard. For the small problem sizes of interest to this study, the solution is easily obtained, but larger-scale models will call for heuristics.
The assortment decision will be affected by the depth of no-purchase (d, number of substitutions the customer is willing to make before choosing not to purchase) and the weight the retailer places on profit and customer disutility.
For the computational study, the researchers used the scanner data to obtain Bayesian posterior estimates of the model parameters and calculate coefficients of price, display, and feature. They created a cross-classification table of first and second preference brands for the sample, and computed optimal assortments at both d = 2 (substituting only if second choice was available) and d = 3 (substituting if second or third choice was available).
The linear programming package LINDO was used to solve the models. The program, written in C, allows the decision maker to vary the depth of no-purchase and weight placed on consumer disutility and profit. The researchers solved 80 instances of the problem at varying weights of disutility vs. profit (from 0.0 to 0.99).
An additional three-product, three-customer data set was also evaluated to provide a counterexample of the computational study’s results.
Results
The researchers first solved the model with the canned tuna data with d = 2 (one substitution) and fixed costs set at $1 per brand per re-stocking period. (Retail contribution margins were assumed to be 30% of purchase price.) The results vary according to the relative weight assigned to customer utility and profit: a “myopic retailer” concerned only with immediate profit will benefit most from carrying only four items – brands numbered 1, 3, 5, and 7 – while those who weight disutility at 0.3 or above would carry brands 1, 3, 4, 5, 7, and 8. Brands 2 and 6 were dropped because they did not appear among the preferences revealed by the scanner data.
Interestingly, as the weight on disutility increases, the optimal assortment first grows to include brand 4 and then shrinks again – dropping 1, 4, and 5 but adding 8 – before adding back in first 4, then 5, and eventually 1 into the assortment. Also noteworthy are the significant drops in disutility accompanied by comparatively minimal drops in profit: changing the assortment from 1,3,4,5,7 to 3,7,8 causes a drop from 34.17 to 32.64 in profit but yields a decrease in disutility from 69.62 to 20.38.
Predictably, higher fixed costs result in smaller assortments when disutility is given less weight in relation to profit. With the fixed costs set at $5 per item per stocking period, a myopic retailer need carry only two items – 3 and 7 – and the weight placed on disutil-ity would need to reach 0.7 in order to merit the full assortment of the six items identified among customer preferences. In this case, the number of items in the assortment only increases with increasing weight on disutility. Like the first case, however, a steep drop
in utility can be achieved with a minimal loss in terms of profit: adding item 8 to the assortment of 3 and 7 yields a drop from 95.92 to 20.38 in disutility, while the profit decrease is only from 22.72 to 20.64.
Analysis of the d = 3 case (substituting second or third preference) yielded similar results. Both profits and disutility were at least as large as for d = 2, and the optimal assortment changed non-monotonically (increasing then decreasing in size) with fixed costs set at $1 and monotonically (increasing) with fixed costs set at $5.
The three-product, three-customer instance revealed that the pat-terns observed in the computational study did not hold, indicating the difficulty of predicting the structure of optimal assortment.
Business Implications
This model can be used to assist retailers in determining optimal assortments within a product category, allowing retailers to weight their inputs to reflect the relative importance they place on customer satisfaction in relation to immediate profits.
Retailers should take note that, surprisingly, an incremental increase in the weight placed on customer satisfaction does not always yield a larger optimal assortment. Taking into account customers’ willingness to (reluctantly) substitute for a less-preferred brand creates a more subtle and complex picture of optimal selection.
Additionally, the computational study reveals that a relatively small decrease in profits can yield a large drop in disutility, suggesting that a long-term strategy of customer retention may require only a small loss in immediate profits.
This study serves as an example of how analytics can be used not only to model profit maximization, but also to develop a means of addressing retailers’ interest in satisfying customers. Such analyses help to guide sound businesses decisions over both the short and long-term horizons.