Plug-In Hybrid Electric Vehicle Traveling-Salesman Problem with Drone

Abstract

Drones and electric vehicles (EVs) represent promising technologies for enhancing the efficiency and sustainability of last-mile delivery services. This paper focuses on the optimization of customer deliveries through the integration of a plug-in hybrid electric vehicle (PHEV) and a drone. Our model, named the plug-in hybrid electric vehicle traveling-salesman problem with drone (PHEVTSPD), assumes the PHEV can be recharged, either fully or partially, at charging stations, while the drone can be launched or retrieved from the EV. Both the EV and drone are capable of independently serving the customer. In comparison with traditional truck-only or drone-only delivery models, the hybrid EV–drone model overcomes the limitations of drone payload capacity and EV service area, thereby significantly improving delivery efficiency and reducing greenhouse-gas emissions. This research presents a three-index mixed-integer linear program (MILP) formulation of PHEVTSPD. Additionally, a linear or piecewise linear approximation of the concave time–state-of-charge (SoC) function is adopted in the model. To solve the proposed problem, we introduce an adaptive large-neighborhood search (ALNS) metaheuristic. Numerical analysis results reveal that the proposed ALNS method outperforms variable neighborhood search (VNS) with an average optimality gap of approximately 3% when solving instances with 10 nodes. Furthermore, a piecewise linear function with a six-line-segment approximation demonstrates an average of 10.8% lower cost compared with a linear approximation.