An iterative conditional dispatch algorithm for the dynamic dispatch waves problem

A challenge in same-day delivery operations is that delivery requests are typically not known beforehand, but are instead revealed dynamically during the day. This uncertainty introduces a trade-off between dispatching vehicles to serve requests as soon as they are revealed to ensure timely delivery, and delaying the dispatching decision to consolidate routing decisions with future, currently unknown requests. In this paper we study the dynamic dispatch waves problem, a same-day delivery problem in which vehicles are dispatched at fixed decision moments. At each decision moment, the system operator must decide which of the known requests to dispatch, and how to route these dispatched requests. The operator's goal is to minimize the total routing cost while ensuring all requests are served on time. We propose iterative conditional dispatch (ICD), an iterative solution construction procedure based on a sample scenario approach. ICD iteratively solves sample scenarios to classify requests to be dispatched, postponed, or undecided. The set of undecided requests shrinks in each iteration until a final dispatching decision is made in the last iteration We develop two variants of ICD: one variant based on thresholds, and another variant based on similarity. A significant strength of ICD is that it is conceptually simple and easy to implement. This simplicity does not harm performance: through rigorous numerical experiments, we show that both variants efficiently navigate the large state and action spaces of the dynamic dispatch waves problem and quickly converge to a high-quality solution. In particular, the threshold-based ICD variant improves over a greedy myopic strategy by 27.2% on average, and outperforms methods from the literature by 0.8% on average, and up to 1.5% in several cases