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Scheduling trucks and drones for cooperative deliveries

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  • Gao, Jiajing
  • Zhen, Lu
  • Laporte, Gilbert
  • He, Xueting

Abstract

Truck and drone based cooperative delivery system is an emerging instant delivery mode for transporting packages in a more timely and efficient way than traditional delivery mode. This paper studies the scheduling of a fleet of truck groups, each of which can carry multiple drones. We formulate a mixed integer programming model for truck groups routes, and for the timing of the drones’ launching and return to their dedicated truck. The model objective is to minimize the total operational cost, including truck travel cost, drone travel cost, using truck groups fixed cost, and potential penalty for late delivery at customer locations. Column generation-based heuristic algorithm and some acceleration techniques are designed for solving the model efficiently. We carry out numerical experiments for validating the effectiveness of the mathematical model, algorithm, and acceleration techniques. In addition, sensitivity analyses are performed to derive some managerial implications.

Suggested Citation

  • Gao, Jiajing & Zhen, Lu & Laporte, Gilbert & He, Xueting, 2023. "Scheduling trucks and drones for cooperative deliveries," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:transe:v:178:y:2023:i:c:s1366554523002557
    DOI: 10.1016/j.tre.2023.103267
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    References listed on IDEAS

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    1. Yan, Rui & Zhu, Xiaoping & Zhu, Xiaoning & Peng, Rui, 2022. "Optimal routes and aborting strategies of trucks and drones under random attacks," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    2. 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.
    3. John Gunnar Carlsson & Siyuan Song, 2018. "Coordinated Logistics with a Truck and a Drone," Management Science, INFORMS, vol. 64(9), pages 4052-4069, September.
    4. Chen, Cheng & Demir, Emrah & Huang, Yuan, 2021. "An adaptive large neighborhood search heuristic for the vehicle routing problem with time windows and delivery robots," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1164-1180.
    5. Yu, Shaohua & Puchinger, Jakob & Sun, Shudong, 2022. "Van-based robot hybrid pickup and delivery routing problem," European Journal of Operational Research, Elsevier, vol. 298(3), pages 894-914.
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    Cited by:

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    2. Ghoniem, Ahmed & Boz, Semih & El-Adle, Amro M., 2025. "Parcel delivery by vehicle and drone in ordered customer neighborhoods," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 197(C).
    3. Zhao, Shuaiqi & Yang, Hualong & Zheng, Jianfeng & Li, Dechang, 2024. "A two-step approach for deploying heterogeneous vessels and designing reliable schedule in liner shipping services," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 182(C).
    4. Chen, Enming & Zhou, Zhongbao & Li, Ruiyang & Chang, Zhongxiang & Shi, Jianmai, 2024. "The multi-fleet delivery problem combined with trucks, tricycles, and drones for last-mile logistics efficiency requirements under multiple budget constraints," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 187(C).
    5. Gao, Jiajing & Zhao, Jianyi & Zhao, Zheng & Cheng, Junkai & Zhen, Lu, 2025. "Cooperative game based heterogeneous tasks planning for UAV swarms in edge environments," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 197(C).
    6. Cui, Haipeng & Li, Keyu & Jia, Shuai & Meng, Qiang, 2024. "Dynamic collaborative truck-drone delivery with en-route synchronization and random requests," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 192(C).
    7. Mulumba, Timothy & Diabat, Ali, 2024. "Optimization of the drone-assisted pickup and delivery problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 181(C).

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