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The multi-visit drone-assisted routing problem with soft time windows and stochastic truck travel times

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  • Meng, Shanshan
  • Li, Dong
  • Liu, Jiyin
  • Chen, Yanru

Abstract

We consider a combined truck-drone delivery problem with stochastic truck travel times and soft time windows. A fleet of homogeneous trucks and drones are deployed in pairs to provide delivery services to customers. Each drone can be launched from and retrieved to its truck multiple times, and in each flight, a drone can serve one or more customers. Our objective is to determine the truck routes and drone flights that minimise the total cost, including time window violation penalties. We formulate this problem into a two-stage stochastic model with recourse action in the second stage to optimise the truck waiting time at each node. We approximate the stochastic model with a large-scale mixed-integer program using the sample average approximation (SAA) framework, which is computationally intractable. To this end, we propose a hybrid metaheuristic approach that incorporates SAA. The waiting times of each truck obtained in the planning phase are optimal against the sampled or estimated travel times along the entire route, but the actual values are known only once the truck has returned to the depot. To this end, we reformulate the second-stage model in a rolling-horizon manner, which can be easily implemented and efficiently solved in the execution phase. Extensive numerical experiments demonstrate the strong performance of the proposed metaheuristic approach and rolling-horizon model. The results also highlight the clear benefits of the stochastic modelling approach over its deterministic counterpart, with a pronounced reduction in the total cost in various scenarios.

Suggested Citation

  • Meng, Shanshan & Li, Dong & Liu, Jiyin & Chen, Yanru, 2024. "The multi-visit drone-assisted routing problem with soft time windows and stochastic truck travel times," Transportation Research Part B: Methodological, Elsevier, vol. 190(C).
  • Handle: RePEc:eee:transb:v:190:y:2024:i:c:s019126152400225x
    DOI: 10.1016/j.trb.2024.103101
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    References listed on IDEAS

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    1. Gendreau, Michel & Laporte, Gilbert & Seguin, Rene, 1996. "Stochastic vehicle routing," European Journal of Operational Research, Elsevier, vol. 88(1), pages 3-12, January.
    2. Yang, Weibo & Ke, Liangjun & Wang, David Z.W. & Lam, Jasmine Siu Lee, 2021. "A branch-price-and-cut algorithm for the vehicle routing problem with release and due dates," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    3. Kloster, Konstantin & Moeini, Mahdi & Vigo, Daniele & Wendt, Oliver, 2023. "The multiple traveling salesman problem in presence of drone- and robot-supported packet stations," European Journal of Operational Research, Elsevier, vol. 305(2), pages 630-643.
    4. Lu Zhen & Jiajing Gao & Zheyi Tan & Shuaian Wang & Roberto Baldacci, 2023. "Branch-price-and-cut for trucks and drones cooperative delivery," IISE Transactions, Taylor & Francis Journals, vol. 55(3), pages 271-287, March.
    5. Tamke, Felix & Buscher, Udo, 2021. "A branch-and-cut algorithm for the vehicle routing problem with drones," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 174-203.
    6. Yin, Yunqiang & Li, Dongwei & Wang, Dujuan & Ignatius, Joshua & Cheng, T.C.E. & Wang, Sutong, 2023. "A branch-and-price-and-cut algorithm for the truck-based drone delivery routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1125-1144.
    7. Meng, Shanshan & Chen, Yanru & Li, Dong, 2024. "The multi-visit drone-assisted pickup and delivery problem with time windows," European Journal of Operational Research, Elsevier, vol. 314(2), pages 685-702.
    8. Rave, Alexander & Fontaine, Pirmin & Kuhn, Heinrich, 2023. "Drone location and vehicle fleet planning with trucks and aerial drones," European Journal of Operational Research, Elsevier, vol. 308(1), pages 113-130.
    9. Nguyen, Minh Anh & Dang, Giang Thi-Huong & Hà, Minh Hoàng & Pham, Minh-Trien, 2022. "The min-cost parallel drone scheduling vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 299(3), pages 910-930.
    10. Zhou, Hang & Qin, Hu & Cheng, Chun & Rousseau, Louis-Martin, 2023. "An exact algorithm for the two-echelon vehicle routing problem with drones," Transportation Research Part B: Methodological, Elsevier, vol. 168(C), pages 124-150.
    11. Kitjacharoenchai, Patchara & Min, Byung-Cheol & Lee, Seokcheon, 2020. "Two echelon vehicle routing problem with drones in last mile delivery," International Journal of Production Economics, Elsevier, vol. 225(C).
    12. Li, Hongqi & Wang, Haotian & Chen, Jun & Bai, Ming, 2020. "Two-echelon vehicle routing problem with time windows and mobile satellites," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 179-201.
    13. Amine Masmoudi, M. & Mancini, Simona & Baldacci, Roberto & Kuo, Yong-Hong, 2022. "Vehicle routing problems with drones equipped with multi-package payload compartments," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    14. Yang, Yu & Yan, Chiwei & Cao, Yufeng & Roberti, Roberto, 2023. "Planning robust drone-truck delivery routes under road traffic uncertainty," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1145-1160.
    15. Wang, Zheng & Sheu, Jiuh-Biing, 2019. "Vehicle routing problem with drones," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 350-364.
    16. Liu, Zeyu & Li, Xueping & Khojandi, Anahita, 2022. "The flying sidekick traveling salesman problem with stochastic travel time: A reinforcement learning approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    17. Meng, Shanshan & Guo, Xiuping & Li, Dong & Liu, Guoquan, 2023. "The multi-visit drone routing problem for pickup and delivery services," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 169(C).
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