Publications

A retailer deciding which products to offer must reason about substitution and multipurchase behavior simultaneously. Both effects are interactions between pairs of products, and deciding how to model them involves a trade-off between expressiveness and tractability. Real catalogs are very large and, therefore, model estimation and optimization are even more difficult. Indeed, pairwise parameters grow quadratically in the number of products while transactions grow only linearly, leaving most of them unidentified, and the decision problem grows with the catalog. This work proposes a model that supports estimation and optimization at real catalog scales, with more than 70,000 items.

We introduce the K-Stage Markov Chain Model (KSMC), which treats substitution and co-purchase (up to size K) as separate primitives on a single set of products, and give an expectation–maximization (EM) algorithm for general K. Since n products carry on the order of n² transition parameters, more than the actual transaction data can identify, we estimate them in feature space rather than item space. This also lets a fitted model make predictions for products it has never seen. This generality has a price: its cardinality-constrained assortment problem admits no constant-factor polynomial-time approximation under the Exponential Time Hypothesis.

Our main contribution is a two-level KSMC, structured around the retailer's existing category taxonomy, that separates the multipurchase mechanism at the category level from substitution that occurs within each category. Its complete-data log-likelihood decomposes additively into independent EM problems, one for each category and one more at the category level. The expected revenue is also additively separable by category. This reduces the constrained assortment optimization problem with a shared assortment budget to one revenue curve per category plus a category-level allocation across them. We give an exact allocation rule on arbitrary curves and prove that the full problem inherits the per-category oracle's approximation ratio.

We evaluate our framework on two real catalogs from fast-fashion retailers: H&M across 132 categories and 72,969 articles and the Italian retailer Nuna Lie across 21 categories and 5,336 articles. With the same shelf space, the optimized assortments are worth around 70% to 75% more than the retailers realized, and on realized assortments the fitted models reproduce revenue within 0.3% in aggregate.

Modeling multiple-item purchases is important for retail decisions, but challenging because the number of possible baskets grows exponentially with the number of items, and item interactions may depend on both the offered assortment and the partially formed basket. We introduce Cross-Effects Transformer (XTra), a sequential choice model that decomposes item utility into intrinsic utility, assortment context interactions, and basket interactions. XTra derives explicit item-to-item interaction scores from contextualized representations, allowing pairwise relationships to vary with the surrounding assortment and basket. On the Visuelle 2.0 retail dataset, XTra improves test unordered basket negative log-likelihood from 11.039 for the closest Transformer baseline to 10.243 and a smaller XTra model achieves 10.267 with approximately half as many parameters as the baseline. XTra can utilize pretrained multimodal item representations to generalize to infrequently observed items, and its learned interaction rankings are stable across training runs and correlate with held-out co-purchase associations. These results provide a predictive foundation for studying context-dependent assortment and basket decisions.

This paper studies the product replacement problem. In this problem, the retailer's headquarters needs to decide which and how much inventory of new items to send to each store from a large set of potential new products. Once the new items arrive at the store, the store manager then needs to decide which items to remove from the store floor to make room for these new items, as they need to be displayed immediately.

We first address misaligned incentives for the different decision-makers (headquarters and store managers). This is because decision-makers focus on specific areas: headquarters concentrates on global operations, considering production, transportation, and other costs beyond revenue, while store managers prioritize store revenue and customer demand. We then address settings where store managers deviate from pure incentive-based behavior by modeling preferences and including uncertainty. A key contribution of this work, as a result, is that we incorporate important elements that make the problem bilevel and NP-hard.

For both decision-makers, namely, headquarters and store managers, we develop efficient and robust policies that address those elements. In collaboration with Zara, the fashion retailer, we show the impact of our recommended policies first using synthetic data and then with their data. In particular, compared to the current practice, we show using real data an up to 5% improvement in revenue when store managers use our proposed strategies and an overall 2-6% profit improvement for headquarters even when store managers exhibit suboptimal behavior based on their preferences.