The Benefits of Delay in Online Decision-Making: Models, Regret Analysis, and Empirical Findings

Background: In many online decision-making contexts, real‑time decisions are irreversible, so a common practice is to intentionally delay decisions to gather more information.

Scenarios: Examples include e‑commerce order fulfillment, ride‑hailing driver matching, and online chess opponent pairing, where waiting can improve matching quality and reduce costs.

Benefits of Delay: Delay can increase market thickness, lower logistics costs by consolidating orders, and provide informational benefits that lead to better decisions. However, excessive waiting incurs negative effects.

Model: The authors propose a resource‑allocation model with multiple warehouses and stochastic customer demand. Decisions are made after a delay of K periods, allowing observation of future orders. The model captures classic problems such as the multisecretary problem, network revenue management, and online matching.

Regret Analysis: Theoretical results show that regret decreases exponentially with the length of the delay, yielding diminishing marginal returns. The bound is of the form ρ^K plus a constant, with ρ < 1.

Empirical Evaluation: Using a public JD.com dataset from March 2018, the algorithm’s gap to the optimal policy drops from about 7.4 % with no delay to 6 % with a one‑hour delay and below 4 % with a four‑hour delay, confirming the practical benefit of modest waiting.

Conclusion: A small amount of delay (e.g., one hour) can substantially reduce transportation costs and improve decision quality, especially when demand forecasts are inaccurate.

Q&A: The authors note that the study focuses on revenue benefits and does not model delay‑induced costs such as customer abandonment, and they discuss the challenges of demand forecasting for long‑tail items.