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When is Assortment Optimization Optimal? 2022-05-23

Subject:When is Assortment Optimization Optimal?

Guest:Will Ma, Assistant Professor, Columbia University

HostCao Yufeng, Assistant Professor, ACEM-SJTU

Time:Wednesday, May 25, 2022, 10:00-11:30

Venue: Tencent Meeting

(Please send email to by 18:00 May. 24th for meeting number and password.)


Assortment optimization concerns the problem of selling fixed-price items to a buyer who wants at most one of them. Despite being faced whenever retailers are deciding which brands/variants of a good to offer, the best method for selling these items with fixed prices is not well understood. Academic work has focused on the specific selling method of making a subset ("assortment") of items immediately available, while selling methods involving randomization have begun appearing in practice.

In this paper we analyze the revenue possible from any selling method, given that the buyer's preference is private but randomly drawn from a known distribution. In particular, we introduce a Bayesian mechanism design problem where the items have fixed prices, the buyer has a random ranking over the items given these prices (and an outside option), and the seller optimizes a (randomized) allocation of up to one item. We show that assortment-based allocations are suboptimal in general, but under many commonly-studied Bayesian priors for buyer rankings such as the Multi-Nomial Logit (MNL) and Markov Chain choice models, assortments are in fact optimal. Therefore, this large literature on assortment optimization has much greater significance than appreciated before — it is not only computing optimal assortments; it is computing the economic limit of the seller's revenue for selling these fixed-price substitute items.

We derive several further results — a more general sufficient condition for assortments being optimal that captures choice models beyond Markov Chain, a proof that Nested Logit choice models cannot be captured by Markov Chain but can to some extent be captured by our condition, and suboptimality gaps for assortments when our condition does not hold. Finally, we show that our mechanism design problem provides the tightest-known Linear Programming relaxation for assortment optimization under explicit ranking distributions.

Guest Bio:

Will Ma is an Assistant Professor of Decision, Risk, and Operations at Columbia Business School. His research interests include the analysis of online algorithms, data-driven modeling, and optimization theory, applied to revenue and supply chain management. His research is partially funded by Amazon. Previously, he had been a postdoctoral researcher at Google, and received his Ph.D. from the MIT Operations Research Center. Will has also had experience as a video game start-up founder and a professional poker player, designing the poker class that is taught annually at MIT.