A framework for window design in delivery schedules

TL;DR

This paper presents a structured framework for designing and dynamically updating delivery time windows in appointment systems, improving accuracy and efficiency through probabilistic methods and real-time adjustments.

Contribution

It introduces a novel static and dynamic window design framework that adapts in real-time to stochastic service and travel times, enhancing delivery reliability.

Findings

Dynamic window updates improve delivery accuracy.

Probabilistic threshold-based approach reduces scheduling communication.

Numerical experiments show significant performance gains.

Abstract

This paper develops a structured framework for the design and dynamic updating of service time windows in delivery and appointment-based systems. We consider a single-server setting with stochastic service and travel times, where customers are promised a time window in which the provider will arrive. The first part of the paper introduces a static window construction method based on a probabilistic threshold criterion, using an analytical approximation of residual travel and service time distributions. Building on this, we develop a dynamic update mechanism that monitors residual system uncertainty, where time windows are revised during execution only when the remaining time until the window's start falls below a predefined threshold. This threshold-based approach enables communication-efficient scheduling while substantially improving delivery accuracy. Numerical experiments demonstrate significant performance gains of the dynamic approach in both stylized and real-world settings.