Optimizing multimodal deliveries with synergistic drone network design
研究卡车与无人机协同配送网络设计，通过排队论模型最小化无人机投资成本并满足最长路线配送时间目标，案例显示可提升配送时间17.17%。
Drone-based deliveries offer significant potential to improve delivery times due to rapid deployment and independence from road conditions. However, pure drone-based cargo deliveries are expensive and restricted by drone’s limited cruising range. On the other hand, pure truck freight services are efficient in well-developed road networks. To address the issue of inefficient delivery times in remote areas, we study a synergistic truck-drone network design problem that improves service performance at minimal cost. We propose an optimization model that minimizes drone investment cost while meeting delivery-time targets for the longest routes. Our model uses an M/G/ k queueing system to account for the waiting time during drone transportation, with the general service time distribution stemming from the heterogeneous travel time between the drone station and the discharging locations. To handle the nonlinearity of waiting time, we apply discretization and power-function approximations. The resulting nonlinear model remains tractable for solvers such as Gurobi. Through a case study conducted with order information data from a major e-commerce platform in Shaanxi, China, we find that our drone network design has the potential to improve the delivery time performance by 17.17% at an economical price. Furthermore, extending the cruising range from 80 km to 120 km improves delivery time by 36.33%. We also discuss managerial insights on infrastructure design, truck-drone synergy, drone technology, and how prioritizing different portions of the longest deliveries alters the resulting design. • Design truck–drone delivery networks to improve delivery times in remote areas at minimal cost. • Formulate a drone network design model targeting worst-case delivery-time performance. • Model drone waiting times using an M/G/k queue with heterogeneous station-to-destination travel times. • Apply discretization and power-function approximations to obtain a tractable model solvable by commercial solvers. • A case study shows 17.17% delivery-time improvement; extending range to 120 km yields 36.33%.