Truck–drone hybrid routing problem with time-dependent road travel time

• A truck-drone hybrid routing problem with time-dependent travel time is studied. • A mixed-integer programming model is developed for TDHRP-TDRTT. • An iterated local search heuristic combing multi-phase approaches is devised. • The model and algorithm are tested by a case study in a terrain-constraint network. • A sensitivity analysis is implemented with four road congestion indices. Combining trucks and drones in package delivery provides a promising venue for a future logistics system that is more efficient and sustainable than the existing one. However, how to coordinate trucks and drones, particularly under uncertain traffic conditions (thus, travel time), remains a critical question in this field. To address this challenge, this study proposes and solves a truck–drone hybrid routing problem with time-dependent road travel time (TDHRP-TDRTT) to address the truck–drone cooperation issue. TDHRP-TDRTT is formulated as a cost minimization problem with constraints associated with logistics demand and supply. An iterative local search heuristic algorithm based on intra-pair and inter-pair customer exchanges and link re-optimization is developed to solve TDHRP-TDRTT. Our results on small-scale and benchmark instances show that the proposed algorithm has better computational performance than CPLEX solver, the adaptive large neighborhood search, hybrid genetic-sweep algorithm, and variable neighborhood search. A case study using traffic data from Chongqing, China shows that the truck–drone solution improves the timeliness of delivery, undertakes sensitivity analysis considering four road congestion states, significantly reduces trucking mileage, and facilitates overcoming terrain limitations. Therefore, the proposed model and algorithm are of practical significance in reducing operating cost, improving transportation efficiency, and facilitating a smart and sustainable urban logistics distribution system.