Estimating Hierarchical Demand in Retail Operations

Abstract

A hierarchical structure over product attributes is a central input to many product assortment and inventory optimization models, yet no existing method can recover such structures from the aggregate sales data that retailers routinely collect. We introduce HASTERAD (hierarchical attribute substitution tree estimation via recursive attribute discovery), which recovers a substitution tree from standard SKU–store–week scanner data. Leveraging variation in prices and promotions, HASTERAD compares attribute‐based substitution patterns and then recursively partitions the product space to recover a candidate hierarchy of attribute‐level substitution. Applied to the IRI Marketing Data Set, it recovers a stable and economically interpretable tree. To quantify its economic value, we execute a three‐step optimization process on synthetic data with known ground truth: we recover a tree with HASTERAD, estimate demand parameters on that tree, and optimize assortments. HASTERAD's chosen assortments forgo less than 11% of the profit available to a clairvoyant planner, even in demanding settings where a traditional flat demand model forgoes almost 100%. Performance remains strong whether the method is applied to a multi‐store panel, where stockouts are unobservable, or to a single store's internal records, where data are sparse but stockouts are observed. These findings are robust across several alternative specifications. Our central empirical finding concerns model selection. A tree chosen by best in‐sample fit, from an exhaustive search over simple hierarchies, fits the observed sales nearly as well as HASTERAD's recovered tree, yet prescribes assortments whose expected profits are substantially lower. Fit evaluates observed purchases, but assortment optimization depends on predicting demand under assortments not yet observed.