Authors: Jules Désir, Vincent Auriau, Martin Možina, Emmanuel Malherbe
Organizations: Artefact Research Center, Paris, France · MICS, CentraleSupélec Université Paris-Saclay, Gif-sur-Yvette, France · Fortenova Group, Zagreb, Croatia
Brick-and-mortar retailers face many different challenges that involve understanding thoroughly its products catalog and customer preferences. In particular, assortment optimization - proposing the ideal mix of products - and promotion planning hold a pivotal role in their strategy. By leveraging sales data, retailers can make informed decisions on which products to sell and how to manage inventory, based on customer preferences as well as regional and seasonal trends. It is especially crucial to capture interactions between products, in order to minimize the number of items that cannibalize each other's sales and to ensure that complementary products, which are often purchased together, are conjointly available and sold across all stores. In this paper, we propose a model of shopping basket that learns embeddings to represent interactions between products, prices and stores. Our model is built to uncover sales patterns from very large transaction datasets. In particular, the optimization loss is computed with random negative samples in order to overcome the computational bottlenecks that arise with large number of items. Our experiments on synthetic data show the efficiency of drawing such negative samples based on the actual assortment of available products, with better results than approaches from the literature. We also validate our approach by training and evaluating our model on a dataset composed of millions of transactions from Fortenova Group, one of the leading retail company in Southeast Europe. Our model showcases promising applications in the sector of retail, with enriched interfaces to efficiently support category managers.
Retail recommenders rank relevance, but retailers earn contribution margin: an upsell earns the margin difference over the item it replaces, whereas a cross-sell earns its full margin. We introduce joint stochastic basket editing, a formulation in which one policy selects replacement and addition offers for an existing basket, values them by expected incremental contribution margin, and couples them through displayed-offer, accepted-offer, and joint-acceptance response channels. To our knowledge, it is the first formulation in which upsell and cross-sell responses are coupled; prior separable treatments are its zero-coupling special case. In real-data-calibrated simulations on five public basket datasets, StoBasket captures essentially all attainable offer margin: within 0.5% in every default-price setting and within 0.7% when the true response lies outside its model family. Correct economic accounting is the broadest gain: margin-weighted popularity leaves up to 11% of attainable margin unrealized, and a published next-basket recommender leaves 11-52%. Joint selection adds 10.2% of attainable margin on Instacart, where premium tiers and add-ons are strongly linked. When offers pay only together, the best heuristics lose 64% while exact search stays within 0.5%. For a structured subclass, we characterize when staged policies fail and give an exact optimizer that solves every tested real basket in 0.13 ms median and at most 111 ms. Profit saturates long before prediction accuracy: a correctly structured predictor trained on 5,000 randomized sessions comes within 0.06% of perfect prediction, while a signal-free one loses 38%. The same estimates yield a decision-aware market-basket analysis whose cost does not grow with association order.
Transactional basket data can reveal associations among items, but observed co-occurrence conflates item-specific relations with basket-size structure and unmodeled higher-order dependence. We introduce Cardinality-Stratified Interaction Decomposition (CSID), an interpretable framework that decomposes log-odds contrasts stratified by the number of remaining items into item-set-specific and cardinality-common components, without fitting a global joint distribution. CSID uses an information-weighted, gauge-constrained ridge projection to estimate pair and triple components and to diagnose higher-order contributions to pairwise structure. CSID is designed primarily for interpretable decomposition of association structure rather than for full-distribution prediction. In a simulation with zero pair effects, increasingly strong small-basket cardinality potentials drive ordinary Ising couplings spuriously negative, whereas CSID pair estimates remain centered near zero. Detection power rises with the magnitude of planted triple effects, and local deprojection reduces pair-coefficient RMSE from 0.244 to 0.073. Across three grocery datasets, high-information triple components are reproducible over time. In the matched cross-period partial-transfer evaluation, transferred CSID triple components show closer agreement with later-period stratified contrasts than the nodewise-symmetrized cardinality-aware higher-order pseudolikelihood comparator, with gains in weighted Lin's concordance correlation of 0.038--0.122. These results support CSID as an exploratory and interpretable decomposition framework for pairwise and higher-order association structure in transactional data.
AI shopping assistants increasingly influence which products consumers consider. We study retail assortment planning under AI mediation, where a retailer chooses a catalog, an AI intermediary forms a customer-facing shortlist, and the customer chooses from that shortlist according to a multinomial logit model. We consider both deterministic mediation, in which the AI follows a fixed segment-specific ranking, and stochastic mediation based on the Plackett-Luce model. Empirically, we construct a dataset of product rankings from leading AI models, estimate Plackett-Luce ranking models, and evaluate their predictive performance on held-out assortments. Combining these estimates with synthetic customer preferences, we find that accounting for AI mediation can materially change optimal assortments and revenue. Across the tested capacity configurations, ignoring mediation yields mean revenue losses between 2.52% and 11.37% relative to the PL optimum. A much simpler deterministic plug-in, based only on the ordering of fitted AI utilities, performs substantially better, with mean losses of at most 0.53%. Motivated by this performance, we study assortment optimization under deterministic mediation. We characterize its computational complexity and show that, for any fixed number of customer segments, the problem admits a fully polynomial-time approximation scheme.