Collaborative Last-Mile Delivery: A Multi-Platform Vehicle Routing Problem With En-route Charging

TL;DR

The paper addresses last-mile delivery by introducing a collaborative multi-platform VRP-DR framework that coordinates $\oldsymbol{M}$ trucks, $\\boldsymbol{N}$ drones, and $\\boldsymbol{K}$ robots with en-route charging. It formulates a MILP to minimize a weighted sum of total operational costs and makespan and develops FINDER, a scalable heuristic that decomposes the problem into truck routing, synchronized drone/robot assignment, and energy-aware insertions. Key contributions include the first triple-platform VRP-DR model, a dual-objective optimization, and extensive experiments showing that collaboration reduces makespan with modest cost increases, while en-route charging and flexible docking offer meaningful efficiency gains. The results have practical implications for urban logistics, enabling faster deliveries through coordinated fleet usage, energy-aware planning, and dynamic docking strategies; future work aims to extend to pickups, multiple depots, and dynamic conditions.

Abstract

The rapid growth of e-commerce and the increasing demand for timely, cost-effective last-mile delivery have increased interest in collaborative logistics. This research introduces a novel collaborative synchronized multi-platform vehicle routing problem with drones and robots (VRP-DR), where a fleet of $\mathcal{M}$ trucks, $\mathcal{N}$ drones and $\mathcal{K}$ robots, cooperatively delivers parcels. Trucks serve as mobile platforms, enabling the launching, retrieving, and en-route charging of drones and robots, thereby addressing critical limitations such as restricted payload capacities, limited range, and battery constraints. The VRP-DR incorporates five realistic features: (1) multi-visit service per trip, (2) multi-trip operations, (3) flexible docking, allowing returns to the same or different trucks (4) cyclic and acyclic operations, enabling return to the same or different nodes; and (5) en-route charging, enabling drones and robots to recharge while being transported on the truck, maximizing operational efficiency by utilizing idle transit time. The VRP-DR is formulated as a mixed-integer linear program (MILP) to minimize both operational costs and makespan. To overcome the computational challenges of solving large-scale instances, a scalable heuristic algorithm, FINDER (Flexible INtegrated Delivery with Energy Recharge), is developed, to provide efficient, near-optimal solutions. Numerical experiments across various instance sizes evaluate the performance of the MILP and heuristic approaches in terms of solution quality and computation time. The results demonstrate significant time savings of the combined delivery mode over the truck-only mode and substantial cost reductions from enabling multi-visits. The study also provides insights into the effects of en-route charging, docking flexibility, drone count, speed, and payload capacity on system performance.

Figures (13)

• Figure 1: Schematic illustration of the proposed VRP-DR
• Figure 2: Illustration of multiple scenarios for drone and robot launch and recovery operations
• Figure 3: Objective values: exact vs heuristic (small/medium instances)
• Figure 4: Computation times: exact vs heuristic (small/medium instances)
• Figure 5: Graphical representation of the objective values and computation time of the heuristic solution for large-scale instances