Dynamic truck–drone routing problem for scheduled deliveries and on-demand pickups with time-related constraints

The on-demand logistics services have risen continuously with the expansion of e-commerce. Logistics companies face challenges to meet customers’ expectations with high efficiency and reliability at a low cost. Hence, this paper investigates the dynamic truck–drone routing problem with scheduled deliveries and on-demand pickups (D-TDRP-SDOP) for an on-demand logistics system. Trucks and drones are deployed to serve a batch of deterministic deliveries and an uncertain set of pickup requests with deadlines subject to maximum working hour constraints. The drones can serve multiple requests per trip subject to load constraints and endurance capacity restrictions. The service provider aims to maximize the total profits by dynamic reassignment and recourse of the vehicles. We formulate the D-TDRP-SDOP problem as a Markov decision process (MDP) and propose a heuristic solution approach framework, consisting of an offline enhanced construction algorithm (OECA) and a segment-based heuristic, to solve the MDP. The comprehensive numerical experiments demonstrate the effectiveness of the proposed solution approach and the benefits of the model. Our model improves the total profits by 15% by considering on-demand requests, and the drone operations contribute to a 50% improvement in the acceptance rate of dynamic customer requests. Improved drone technology, such as a higher drone speed and a higher battery capacity, can enable the system to serve more on-demand requests and increase the final profits. However, the benefit diminishes when the drone capability reaches a certain threshold.