Optimization Study on the Hybrid Scheduling of Truck–Drone Delivery System

The exigency to curtail last-mile delivery expenses is an intricate issue within the logistics industry. Owing to their flexibility, portability, and low cost, drones have great potential in the application of logistics and distribution. Drones also have short cruising ranges and small load capacity. To overcome their shortcomings, a hybrid delivery model of truck-carried drones is proposed to achieve logistics distribution. This paper comprehensively addresses pertinent constraints, including drone load capacity, flight distance, and time window, and formulates a mathematical model aimed at minimizing transportation costs. The model determines the optimal allocation between trucks and drones, the optimal path sequence for trucks to travel, and the optimal launch of drones on the truck path and recovery points. Simultaneously, we developed an improved equilibrium optimizer simulated annealing (IEOSA) algorithm to address the issue, employing both Solomon standard calculation instances and real distribution scenarios from Shanghai, China, for simulation analysis. Experimental findings demonstrate that IEOSA exhibits superior efficiency and solution quality in tackling hybrid distribution problems. Furthermore, the truck–drone hybrid distribution model proves to be more efficient in completing distribution tasks compared to relying solely on truck distribution.