Comparing Models for the Vehicle Routing Problem with Drones Across Different Operational Patterns

Modeling the vehicle routing problem with drones (VRPD) is a key focus in drone delivery research. Existing VRPD models can be categorized into three distinct operational patterns based on drone–truck coordination rules: the collaborative pattern, the parallel pattern, and the hybrid pattern. This study establishes multi-objective VRPD models for each pattern under dynamic demand, aiming to investigate their fundamental characteristics. A solution framework integrating a quadrant shrinking heuristic (QSH) with an improved tabu search (TS) algorithm is developed to solve the models, while a rolling horizon approach is employed to address the dynamic demand. Through a series of numerical experiments, we conduct sensitivity tests on a key parameter and the recharging time for drones, as well as a comparative analysis of the properties of VRPD models across different patterns, providing practical recommendations regarding their respective application scenarios and operational management.