Optimising last-mile delivery network through locker–drone logistics system design under uncertain demand

With the rapid growth of e-commerce, urban logistics systems are facing increasing pressure due to escalating logistics demands. Concurrently, online shopping has emerged as the predominant mode of consumer purchasing, leading to frequent deliveries of small parcels to diverse locations. This trend has introduced significant challenges for traditional last-mile delivery methods, complicating the process and driving up costs. In response, the locker–drone system has been investigated as a promising solution for prompt and efficient delivery within the logistics chain, particularly for last-mile operations. To establish an efficient locker–drone-based last-mile logistics system, this paper explores the Locker–Drone Logistics System Planning Problem (LDLSPP). LDLSPP is formulated as a mixed-integer linear programme that involves joint decisions at both strategic and operational levels while addressing the unique characteristics of the locker–drone system and the inherent uncertainty of demand. At the strategic level, decisions focus on the layout and location of lockers, the deployment of drones to lockers and their allocation to demand points, as well as the inventory quantities of commodity parcels. At the operational level, the problem addresses parcel distribution quantities. In the LDLSPP framework, various types of modules are assembled within lockers, with the total number of modules constrained by geographical space, manufacturing technology limitations, and system stability. To address demand uncertainty, a two-stage stochastic programming model is proposed, incorporating different demand scenarios in the second stage. To enhance the efficiency of the logistics systems, unsatisfied penalties for different types of commodities are introduced. The LDLSPP aims to minimise the total cost as its primary objective. An enhanced Benders-Based Branch-and-Cut Method with a warm start is employed to solve the problem efficiently. The performance of the proposed model and algorithm is evaluated through a simulated example and further validated using a real-world case study. The algorithm achieves significant performance improvements compared to Gurobi. Finally, managerial implications and insights are provided to managers to support decision-making processes for implementing locker–drone logistics systems.