Assortment Planning for Recommendations at Checkout under Inventory Constraints

34 Pages Posted: 17 Oct 2016 Last revised: 16 Oct 2021

See all articles by Xi Chen

Xi Chen

New York University (NYU) - Leonard N. Stern School of Business

Will Ma

Graduate School of Business

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Linwei Xin

University of Chicago - Booth School of Business

Date Written: November 2, 2020

Abstract

In this paper, we consider a personalized assortment planning problem under inventory constraints, where the type of each arriving customer is defined by a primary item of interest. As long as that item is in stock, the customer adds it to her shopping cart, at which point the retailer can recommend to the customer an assortment of add-ons to go along with her primary item. This problem is motivated by the new "recommendation at checkout'' systems that have been deployed at many online retailers, and also serves as a framework which unifies many existing problems in online algorithms (personalized assortment planning, single-leg booking, 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.

Keywords: revenue management; assortment optimization; personalized recommendation; online algorithms; competitive ratio

Suggested Citation

Chen, Xi and Ma, Will and Simchi-Levi, David and Xin, Linwei, Assortment Planning for Recommendations at Checkout under Inventory Constraints (November 2, 2020). Available at SSRN: https://ssrn.com/abstract=2853093 or http://dx.doi.org/10.2139/ssrn.2853093

Xi Chen

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

Will Ma (Contact Author)

Graduate School of Business ( email )

3022 Broadway
New York, NY 10027
United States

HOME PAGE: http://www.columbia.edu/~wm2428/

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering ( email )

MA
United States

Linwei Xin

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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