Assortment Planning for Recommendations at Checkout Under Inventory Constraints

In this paper, we consider a personalized assortment planning problem under inventory constraints, where each arriving customer type is defined by a primary item of interest. As long as that item is in stock, the customer adds it to the shopping cart, at which point the retailer can recommend to the customer an assortment of add-ons to go along with the primary item. This problem is motivated by the new “recommendation at checkout” systems that have been deployed at many online retailers, and it also serves as a framework that unifies many existing problems in online algorithms (e.g., personalized assortment planning, single-leg booking, and online matching with stochastic rewards). In our problem, add-on recommendation opportunities are eluded when primary items go out of stock, which poses additional challenges for the development of an online policy. We overcome these challenges by introducing the notion of an inventory protection level in expectation and derive an algorithm with a 1/4-competitive ratio guarantee under adversarial arrivals. Funding: This work was supported by the Adobe Data Science Research Award and the Alibaba Innovation Research Award. L. Xin was partly supported by the National Science Foundation (NSF) [Award CMMI-1635160], X. Chen was supported by the NSF [CAREER Award IIS-1845444]. W. Ma and D. Simchi-Levi were supported by the Accenture and MIT Alliance in Business Analytics.