Fast Bi-Level Task Assignment and Routing for Truck-Drone Collaborative Delivery

Abstract

The emerging use of drones in last-mile delivery (e.g., for e-commerce and emergency services) creates a need to optimize collaborative operations among trucks, drones, and supporting facilities. In this paper, we focus on the Cumulative Vehicle Routing Problem with Drone Stations (CumVRP-DS), which jointly optimizes customer (task) assignment and vehicle routing in the context of drone-station-assisted last-mile delivery. The objective is to minimize the total customer waiting time. To solve this problem, we first formulate it as a Mixed Integer Linear Programming (MILP) model, which extends the multi-level network (MLN) formulation to incorporate drone-stations. Second, we propose an improved bi-level meta-heuristic algorithm, designed to reduce the search effort required at the inner routing layer. Computational experiments show that the proposed MILP formulation is able to produce theoretically-guaranteed optimal results for instances with up to 100 customers with Gurobi, and the improved bi-level meta-heuristic achieves significantly better solutions on large instances (over 100 customers) with an average 4.4% reduction in objective values. Furthermore, our analysis provides key operational insights: it demonstrates that (1) similar task assignments often lead to similar (near-)optimal truck routes, justifying the route-reconstruction strategy, and (2) inner-layer routing can be effectively handled by reconstruction alone, suggesting computational resources should be prioritized for the task-assignment sub-problem. These insights offer an effective solution framework and practical guidelines for similar drone-assisted delivery optimization problems.