Multipurchase Assortment Optimization Under a General Random Utility Model

The static assortment optimization problem, where customers select a single item according to some choice model such as a random utility model, is a classical and well-studied setting. In contrast, the multipurchase variant, where customers may choose multiple items, has received far less attention because modeling utility-maximizing behavior over sets of items is substantially more complex, even under natural extensions of the Multinomial Logit model. In this paper, we propose a general multipurchase choice model that extends the classical single-purchase framework without relying on specific distributional assumptions for the random utilities. We study the associated assortment optimization problem and address its computational intractability by introducing a tractable surrogate problem (SP). The SP arises naturally from an asymptotic regime where the number of items offered grows without bound. It can be solved efficiently, and its solutions perform remarkably well in numerical experiments compared with the true optimum. Beyond proving the asymptotic optimality of the SP solution, we derive nonasymptotic bounds that quantify its approximation error and provide explicit convergence rates. We further establish the identifiability of the surrogate choice model, provided there is sufficient variation in the offered assortments, and we also develop a maximum likelihood estimation procedure for the model parameters that remains valid, even when purchases of outside options are unobserved.

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2025.1702.