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The optimal delivery route problem for truck–drone delivery is defined as a traveling salesman problem with drone (TSP-D), which has been studied in a wide range of previous literature. However, most of the existing studies ignore truck waiting time at rendezvous points. To fill this gap, this paper builds a mixed integer nonlinear programming model subject to time constraints and route constraints, aiming to minimize the total delivery time. Since the TSP-D is non-deterministic polynomial-time hard (NP-hard), the proposed model is solved by the variable neighborhood tabu search algorithm, where the neighborhood structure is changed by point exchange and link exchange to expand the tabu search range. A delivery network with 1 warehouse and 23 customer points are employed as a case study to verify the effectiveness of the model and algorithm. The 23 customer points are visited by three truck–drones. The results indicate that truck–drone delivery can effectively reduce the total delivery time by 20.1% compared with traditional pure-truck delivery. Sensitivity analysis of different parameters shows that increasing the number of truck–drones can effectively save the total delivery time, but gradually reduce the marginal benefits. Only increasing either the truck speed or drone speed can reduce the total delivery time, but not to the greatest extent. Bilateral increase of truck speed and drone speed can minimize the delivery time. It can clearly be seen that the proposed method can effectively optimize the truck–drone delivery route and improve the delivery efficiency.

Optimal Route Planning for Truck–Drone Delivery Using Variable Neighborhood Tabu Search Algorithm