Data-driven optimization for drone-truck delivery network design under stochastic demand and semi-open queuing network

The rapid growth of e-commerce and urban logistics has driven the need for efficient and cost-effective last-mile delivery solutions. In this paper, we design a delivery network that uses a mixed fleet of trucks and drones, leveraging automated battery swapping machines (ABSMs) for drones. We study the long-term location and capacity design (i.e., the number of chargers and batteries) of ABSMs, as well as the routing of drones visiting intermediate ABSMs to swap their batteries before reaching customers. Each ABSM is modeled as a semi-open queuing network, and we adopted the matrix geometric method to evaluate an ABSM’s performance under a given combination of arrival rate, service rates, and the number of servers and batteries. We used a machine learning method to estimate a closed-form formulation representing the relationship between ABSM design factors and its performance in the network design model. To solve this computationally challenging problem, we propose distinct solution approaches, including a customized Genetic algorithm, an exact cutting-plane algorithm, and a stepwise linear approximation mixed-integer linear programming model. The computational performance of the algorithms is evaluated based on actual prepared food delivery data from the San Francisco Bay Area, United States, and drone data. Results demonstrate that increasing the maximum allowable number of batteries and chargers in each ABSM from one to 21 reduces the required number of trucks by 99%, which decreases the total system cost by 79.7%.