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Assortment Optimization for General Multi-purchase Choice Models


The static assortment optimization problem is a classical and well-studied problem where customers choose a single item while behaving according to some customer choice model like the ubiquitous random utility model. However, the variant where customers choose multiple items has received less attention, primarily due to the added complexity of modeling utility-maximizing behavior over sets of items, even when considering natural extensions of the standard MNL choice model. In this paper, we propose a general multi-purchase choice model that can be viewed as a natural extension of the single-purchase utility choice models. We also study the respective assortment optimization problem without making specific distributional assumptions on the random utilities. We propose a computationally efficient algorithmic framework that is based on an asymptotic regime referred to as the large-offering regime, where the number of items available to the retailer grows large. Through this asymptotic lens, we develop an efficient approximation algorithm with corresponding asymptotic optimality guarantees under general utility distributions. Our numerical results demonstrate that our algorithm is very competitive even when the number of items available to the retailer is modest and even when the customers choose a single item.


Working Paper


Tarek Abdallah, Anton Braverman, Wenhao Gu

Date Published



Abdallah, Tarek, Anton Braverman, and Wenhao Gu. 2024. Assortment Optimization for General Multi-purchase Choice Models.


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