Near-Optimal Bayesian Online Assortment of Reusable Resources

50 Pages Posted: 21 Oct 2020 Last revised: 10 May 2022

See all articles by Yiding Feng

Yiding Feng

Microsoft Corporation - Microsoft Research New England

Rad Niazadeh

University of Chicago - Booth School of Business

Amin Saberi

Stanford University - Department of Management Science & Engineering

Date Written: September 24, 2020

Abstract

Motivated by the applications of rental services in e-commerce, we consider revenue maximization in online assortment of reusable resources for a stream of arriving consumers with different types. We design competitive online algorithms with respect to the optimum online policy in the Bayesian setting, in which types are drawn independently from known heterogeneous distributions over time. In the regime where all the initial inventories are no less than c_min, our main result is a near-optimal 1-min(1/2,\sqrt{log(c_min)/c_min}) competitive algorithm for the general case of reusable resources. As a side result, by leveraging techniques from the literature on prophet inequality, we further show an improved near-optimal 1-1/\sqrt{c_min+3} competitive algorithm for the special case of non-reusable resources.

Our algorithm relies on an expected LP benchmark for the problem, solves this LP, and simulates the solution through an independent randomized rounding. The main challenge is obtaining point-wise inventory feasibility in a computationally efficient fashion from these simulation-based algorithms. To this end, we use several technical ingredients to design "discarding policies" -- one for each resource. These policies handle the trade-off between the inventory feasibility under reusability and the revenue loss of each of the resources. However, discarding a unit of a resource changes the future consumption of other resources. To handle this new challenge, we also introduce "post-processing" assortment procedures that help with designing and analyzing our discarding policies as they run in parallel, which might be of independent interest. We finally evaluate the performance of our algorithms using the numerical simulations on the synthetic data.

Keywords: Assortment optimization, Online assortment, Reusable resources, Competitive analysis, Online algorithms

Suggested Citation

Feng, Yiding and Niazadeh, Rad and Saberi, Amin, Near-Optimal Bayesian Online Assortment of Reusable Resources (September 24, 2020). Chicago Booth Research Paper No. 20-40, Available at SSRN: https://ssrn.com/abstract=3714338 or http://dx.doi.org/10.2139/ssrn.3714338

Yiding Feng

Microsoft Corporation - Microsoft Research New England ( email )

One Memorial Drive, 14th Floor
Cambridge, MA 02142
United States

Rad Niazadeh (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S Woodlawn Ave
Chicago, IL 60637

HOME PAGE: http://radniazadeh.github.io/

Amin Saberi

Stanford University - Department of Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

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