Hybrid truck–drone delivery under aerial traffic congestion

This paper focuses on a hybrid truck–drone delivery system, in which a truck carries goods and a fleet of drones around the neighborhoods of customers, while the drones are dispatched from the truck to perform the last-mile delivery. We formulate a continuous traffic equilibrium model in the form of partial differential equations (PDEs) to describe the optimal drone routing and truck–drone synchronization strategies when low-altitude aerial traffic congestion arises in large-scale steady-state operations. A customized solution algorithm is then developed, using a physics-informed neural network framework and various enhancement techniques, to efficiently solve the PDEs. The PDE solution is then used to evaluate the operational cost of a truck–drone delivery system, through a dimensionless surrogate model, which further provides the basis for optimizing several service design decisions, such as truck speed, truck routing plan and delivery headway. Numerical experiments are conducted to show the applicability of the proposed modeling framework, and to draw managerial insights for logistics carriers.