Abstract
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.
Highlights
Introduction published maps and institutional affilThe new concept of Logistics 4.0 requires higher quality standards of demand, distribution, and inventory management [1]
This study focused on the optimal route problem for truck–drone delivery, which is a classic flying sidekick traveling salesman problem (FSTSP)
We considered the scenario that the drones may arrive at rendezvous points later than the trucks
Summary
The new concept of Logistics 4.0 requires higher quality standards of demand, distribution, and inventory management [1]. The prosperity of e-commerce and mobile business requires more efficient logistics [2]. With the rapid development of drone technology, drones have been widely applied in health care, agriculture, aerial photography, mapping, etc. In the last few years, some e-commerce and logistics companies started to adopt drones in deliveries, which greatly reduces delivery costs and improves delivery efficiency. DHL company reported in 2015 that it successfully delivered medicals and other goods considered as urgent on a small island in northern Germany using drones. Amazon carried out its first drone delivery practice in 2017. Drone-only delivery has limitations in delivery coverage and carrying capacity due to the drones’ endurance
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