The Benefits of Delay to Online Decision-Making

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 our proposed online algorithm (called ``delayed Bayesian prophet") 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 data and publicly available real data. 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 where the arrival distribution is independent but non-identical, the setting where the arrival distribution is unknown, and the setting where decisions are made in batches.

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