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Scheduling trucks and drones for cooperative deliveries

Author

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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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    Full references (including those not matched with items on IDEAS)

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    2. Yang, Hongtai & Wu, Jianzhang & Zhang, Zhaolin & Liu, Xiaobo & D’Ariano, Andrea, 2025. "Optimal design for an urban truck-drone collaborative delivery system enhanced with relay points," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 204(C).
    3. Deng, Menghua & Li, Yuanbo & Ding, Jianpeng & Zhou, Yanlin & Zhang, Lianming, 2024. "Stochastic and robust truck-and-drone routing problems with deadlines: A Benders decomposition approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 190(C).
    4. 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).
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    6. 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).
    7. 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).
    8. Yang, Kai & Zhang, Zhenzhen & Zhao, Jingyi & Liang, Zhe, 2025. "A neighborhood-based matheuristic for the vehicle routing problem with delivery options," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 203(C).
    9. 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).
    10. Zeng, Jialu & Hu, Yi & Pei, Mingyang, 2026. "Optimizing bidirectional delivery with multiple drones and trucks: a mixed-integer nonlinear model to addressing no-fly zone constraints," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 205(C).
    11. Campuzano, Giovanni & Lalla-Ruiz, Eduardo & Mes, Martijn, 2025. "Optimizing autonomous multimodal last-mile delivery systems with time windows: Analyzing trade-offs between drones, robots, and trucks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 204(C).
    12. 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).
    13. Ge, Xianlong & Yin, Qiushuang & Moktadir, Md. Abdul & Ren, Jingzheng, 2025. "Multi-objective optimization of truck-drone cooperative routing problem based on customer classification and fuzzy time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 203(C).

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