The Benefits of Delay to Online Decision-Making

43 Pages Posted: 20 Oct 2022 Last revised: 21 Feb 2023

See all articles by Yaqi Xie

Yaqi Xie

University of Chicago - Booth School of Business

Will Ma

Columbia University - Columbia Business School, Decision Risk and Operations

Linwei Xin

University of Chicago - Booth School of Business

Date Written: February 18, 2023

Abstract

Real-time decisions are usually irrevocable in many contexts of online decision-making. One common practice is delaying real-time decisions so that the decision-maker can gather more information to make better decisions (for example, in online retailing, there is typically a time delay between when an online order is received and when it gets picked and assembled for shipping). However, decisions cannot be delayed forever. In this paper, we study this fundamental trade-off and aim to theoretically characterize the benefits of delaying real-time decisions. We provide a theoretical foundation for a broad family of online decision- making problems by proving that the gap between the proposed online algorithm with delay and the offline optimal hindsight policy decays exponentially fast in the length of delay. We also conduct extensive numerical experiments on the benefits of delay, using both synthetic and real data that is publicly available. Both our theoretical and empirical results demonstrate an important managerial insight: a little delay is all we need. Finally, we extend our analysis and results to the setting with unknown demand distribution and the setting in which decisions are made in batches.

Keywords: online decision-making, resource allocation, delay, batching, multisecretary problem, order fulfillment, multi-item order

Suggested Citation

Xie, Yaqi and Ma, Will and Xin, Linwei, The Benefits of Delay to Online Decision-Making (February 18, 2023). Available at SSRN: https://ssrn.com/abstract=4248326 or http://dx.doi.org/10.2139/ssrn.4248326

Yaqi Xie

University of Chicago - Booth School of Business ( email )

5807 S Woodlawn Ave
Chicago, IL 60637
United States

Will Ma

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

New York, NY
United States

Linwei Xin (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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