Synchronous delivery with different vehicles, as an emerging concept of the delivery network, improves the efficiency of the modern logistics system significantly, which gradually gives birth to a new issue: the traveling salesman problem with drone (TSP-D). In this paper, we propose a one-truck-multiple-drone (OTMD) model on the base of the TSP-D. Compared with the traditional one-truck-one-drone (OTOD) and multiple drones models, our scheme introduces a united objective function into the optimization calculation. In terms of the proposed multiple levels iterative theory, we can compute the optimal synchronous delivery network that takes both the total delivery time and the number of drones into consideration. Four types of customer distributions are employed to investigate the OTMD model and its associated calculation approaches. Comparing the parameters of the optimal network in different delivery models, we study the relationship among the total delivery time, customer distribution and the number of serving drones. These simulation results verify the feasibility and practicality of the OTMD, and demonstrate the features of optimization calculation with different customer distributions, being beneficial to improve the efficiency of the model logistics system.
Efficient PTAS for the maximum traveling salesman problem in a metric space of fixed doubling dimension
