A framework for window design in delivery schedules
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.
Cite
@article{arxiv.2601.19601,
title = {A framework for window design in delivery schedules},
author = {Bharti Bharti and René Bekker and Nikki Levering and Michel Mandjes},
journal= {arXiv preprint arXiv:2601.19601},
year = {2026}
}