Assortment Planning for Recommendations at Checkout under Inventory Constraints

29 Pages Posted: 17 Oct 2016 Last revised: 20 Aug 2018

Xi Chen

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

Will Ma

Massachusetts Institute of Technology (MIT)

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Linwei Xin

University of Chicago - Booth School of Business

Date Written: October 16, 2016

Abstract

In this paper, we consider a dynamic personalized assortment planning problem under inventory constraints. In particular, each arriving customer is defined by a primary item of interest (which can be interpreted as her type). As long as the item is available, the decision-maker can then offer the customer a personalized assortment of add-on items based on her type, at potentially discounted prices. This problem, which is motivated by a new checkout recommendation system at Walmart’s online grocery, not only finds practical applications but also serves as a general framework that incorporates many operations problems as special cases (e.g., personalized assortment planning [12], single-leg booking [2, 15], and online matching with stochastic rewards [21, 23]). In our personalized assortment planning problem, multiple item prices (discounted or not), combined with customer withdrawal when their initially selected items stock out, pose additional challenges for the development of an online policy with performance guarantees. We overcome these challenges by introducing the notion of an inventory protection level in expectation, and derive an algorithm with a 1/4−ε competitive ratio guarantee under adversarial arrivals, unifying the existing results.

Keywords: revenue management, personalized recommendation, assortment planning, online algorithms, competitive ratio, protection level

Suggested Citation

Chen, Xi and Ma, Will and Simchi-Levi, David and Xin, Linwei, Assortment Planning for Recommendations at Checkout under Inventory Constraints (October 16, 2016). 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
New York, NY NY 10012
United States

Will Ma (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

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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