To ride or to fly: Optimal freight-on-transit operations using drones

With the rapid growth of e-commerce, urban areas are facing increasing congestion, particularly from last-mile deliveries. This challenge has prompted the exploration of innovative solutions. One such promising approach is freight-on-transit (FoT) operations, which utilize existing high-capacity urban transit networks to transport goods to designated transit stations, where more energy-efficient and flexible modes complete the last-mile delivery. This paper proposes a modeling framework for optimizing FoT operations using drones. The proposed mixed-integer linear program formulation accounts for fixed transit vehicle schedules, capacity constraints, and drone battery limitations. The problem is decomposed into a min-cost flow and drone vehicle routing problem with time windows, and a Lagrangian relaxation with a column generation algorithm is proposed as the solution method. Numerical experiments on hypothetical networks demonstrate the system’s effectiveness, highlighting the importance of buffer capacity in transit vehicles and extended drone battery life. A real-world case study in Chicago’s Metra system reveals significant cost savings and operational benefits compared to traditional truck-based or drone-only delivery methods.