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Drone-based last-mile delivery is an emerging technology that uses drones loaded onto a truck to deliver parcels to customers. In this paper, we introduce a fully automated system for drone-based last-mile delivery through incorporation of autonomous vehicles (AVs). A novel problem called the autonomous vehicle routing problem with drones (A-VRPD) is defined. A-VRPD is to select AVs from a pool of available AVs based on crowd sourcing, assign selected AVs to customer groups, and schedule routes for selected AVs to optimize the total operational cost. We formulate A-VRPD as a Mixed Integer Linear Program (MILP) and propose an optimization framework to solve the problem. A greedy algorithm is also developed to significantly improve the running time for large-scale delivery scenarios. Extensive simulations were conducted taking into account real-world operational costs for different types of AVs, traveled distances calculated considering the real-time traffic conditions using Google Map API, and varying load capacities of AVs. We evaluated the performance in comparison with two different state-of-the-art solutions: an algorithm designed to address the traditional vehicle routing problem with drones (VRP-D), which involves human-operated trucks working in tandem with drones to deliver parcels, and an algorithm for the two echelon vehicle routing problem (2E-VRP), wherein parcels are first transported to satellite locations and subsequently delivered from those satellites to the customers. The results indicate a substantial increase in profits for both the delivery company and vehicle owners compared with the state-of-the-art algorithms.
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This content will become publicly available on May 1, 2026
Modular vehicle routing problem: Applications in logistics
Recent studies and industry advancements indicate that modular vehicles (MVs) have the potential to enhance transportation systems through their ability to dock and split during a trip. Although various applications of MVs have been explored across different domains, their application in logistics remains underexplored. This study examines the use of MVs in cargo delivery to reduce total delivery costs. We model the delivery problem for MVs as a variant of the Vehicle Routing Problem, referred to as the Modular Vehicle Routing Problem (MVRP). In the MVRP, MVs can either serve customers independently or dock with other MVs to form a platoon, thereby reducing the average cost per unit. In this study, we mainly focus on two fundamental types of MVRPs, namely the capacitated MVRP (CMVRP) and the MVRP with time windows (MVRPTW). To address these problems, we first developed mixed-integer linear programming (MILP) models, which can be solved using commercial optimization solvers. Given the NP-hardness of this problem, we also designed a Tabu Search (TS) algorithm with a solution representation based on Gantt charts and a neighborhood structure tailored for the MVRP. Multi-start and shaking strategies were incorporated into the TS algorithm to escape local optima. Additionally, we explored other potential applications in logistics and discussed problem settings for three MVRP variants. Results from numerical experiments indicate that the proposed algorithm successfully identifies nearly all optimal solutions found by the MILP model in small-size benchmark instances, while also demonstrating good convergence speed in large-size benchmark instances. Comparative experiments show that the MVRP approach can reduce costs by approximately 5.6% compared to traditional delivery methods. Sensitivity analyses reveal that improving the cost-saving capability of MV platooning can enhance overall benefits.
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- PAR ID:
- 10578303
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Transportation Research Part E: Logistics and Transportation Review
- Volume:
- 197
- Issue:
- C
- ISSN:
- 1366-5545
- Page Range / eLocation ID:
- 104022
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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