retail merchandisers

Abstract: Retailers can learn customer preferences by experimenting with different assortments. However, the cost of each experiment and the operational burden of repeatedly changing product offerings can make extensive experimentation impractical. We study how much a retailer can improve its final assortment decision using customer observations from one (or a very small number of) fixed experimental assortments. We consider the multinomial logit model, where product revenues are known but customer preferences are unknown. In this setting, we jointly design the experimental assortment and the rule for selecting a final assortment from observed customer choices to minimize worst-case regret: the expected revenue loss of the final assortment relative to an optimal assortment under the true preferences, maximized over possible customer preferences. We first characterize exactly the minimax regret and an optimal assortment when no experimentation is possible. We then show, surprisingly, that offering a single experimental assortment to just one customer can already substantially reduce regret, depending on how the products' revenues compare. We derive the exact minimax regret and an optimal experimental policy in this setting. When a single fixed experimental assortment is offered to many customers, we give a geometric characterization of the limiting minimax regret and construct an asymptotically optimal policy. Depending on product revenues, this single experiment can yield no improvement over no experimentation or nearly complete regret reduction. Finally, we extend our analysis to multiple experimental assortments chosen in advance, characterizing the limiting minimax regret, constructing asymptotically optimal policies, and identifying which collections of assortments allow worst-case regret to vanish as the number of customer observations grows.

Abstract: 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.