The Benefits of Delay to Online Decision-Making

30 Pages Posted: 20 Oct 2022 Last revised: 11 Nov 2022

See all articles by Yaqi Xie

Yaqi Xie

University of Chicago - Booth School of Business

Will Ma

Graduate School of Business

Linwei Xin

University of Chicago - Booth School of Business

Date Written: November 10, 2022

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 such 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 suggest that a little delay is all we need.

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 (November 10, 2022). 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

Graduate School of Business ( email )

3022 Broadway
New York, NY 10027
United States

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

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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