4/7/22 | 4:15pm | E25-111
Abstract: Assortment optimization concerns the problem of selling items with fixed prices to a unit-demand buyer with private utilities. Despite being a commonly-faced problem for retailers selling different, exogenously-priced brands of the same good, the best method for doing so is not well understood. Academic work has focused on the specific method of making a subset (``assortment") of brands immediately available, while practitioners have deployed selling methods involving randomization for increasing revenue.
In this paper we characterize the space of all possible selling methods given the buyer's private information and unaligned incentives, using mechanism design. In particular, we introduce a Bayesian mechanism design problem where the items have fixed prices and the seller optimizes over (randomized) allocations of up to one item. We show that assortment-based allocations are suboptimal in general, but under many commonly-studied Bayesian priors for buyer preferences 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 just computing optimal assortments; it is computing the economic limit of the seller's revenue in the fixed-price, unit-demand environment.
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.
Bio: Will Ma is an Assistant Professor of Decision, Risk, and Operations at Columbia Business School. He received his Ph.D. in 2018 from the MIT Operations Research Center, advised by David Simchi-Levi. His research interests include the analysis of online algorithms, data-driven modeling, and optimization theory, applied to revenue and supply chain management. Will has been a postdoctoral researcher at Google and his research is partially funded by Amazon. Previously, Will has also been a start-up founder for video games and a professional poker player, designing the poker class that is taught annually at MIT.