Bayesian Shelf Assortment Optimization
Colgate-Palmolive
The Challenge
Knowing which products cannibalize each other is useful. Knowing what to actually do about it at each retailer is worth considerably more.
After the cannibalization analysis, Colgate wanted to turn those insights into action: given a specific retailer's shelf space, which Colgate products should be there, and in what proportion, to maximize revenue? The system needed to handle three scenarios — predicting sales for the current lineup, forecasting the impact of expanding distribution for an existing product, and estimating what happens when an entirely new product hits the shelf. The bar was high: Colgate already had a commercial assortment optimization tool and wanted to see if we could do better.
Our Approach
From choice modeling to shelf decisions
We extended the choice model from the cannibalization work into a system designed for operational shelf decisions. The model captures how shoppers substitute between products within a brand differently than they substitute across brands — an important distinction when you're deciding whether to add another Colgate variant or make room for it by pulling one.
For products that have never appeared in a given market, the model borrows strength from similar products in the portfolio — sharing information across the brand hierarchy so that a new item gets reasonable predictions even without its own sales history.
Generating recommendations
On top of the statistical model, we built an optimization layer that systematically evaluates add-and-remove decisions across the shelf, scoring each potential change by its predicted revenue impact and surfacing ranked recommendations. We also invested in making the model fast enough to be practical — bringing total computation time down to a few hours so that analysts can run scenarios without planning days ahead.
Results
The system produces concrete, retailer-specific recommendations: add this product, remove that one, here's the expected revenue impact of each change. The model succeeded in markets where simpler approaches failed to converge, particularly for new products with limited history. Colgate received a complete analytical toolkit covering data preparation through final optimization, packaged for their team to run and maintain independently.
The model's predictions compared favorably against their existing commercial solution, validating the approach on Colgate's own benchmarks.
PyMC Labs Team
- Ben Vincent
- Christian
- Luciano
- Ricardo
- Thomas Wiecki
- Adrian
- Tomi
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