Vehicle routing problem with trucks and drones collaboration: a structured literature review

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Abstract

Coordinated truck-drone delivery has emerged as an important extension of the vehicle routing problem (VRP), offering new opportunities to improve logistics efficiency, accessibility, and sustainability. In this review, we synthesize the literature on truck-drone routing by examining three interrelated themes: Vehicle routing and synchronization models, stochastic and dynamic operational constraints, and payload-energy management. Early studies primarily formulate truck-drone delivery as variants of heterogeneous or two-echelon VRP using mixed-integer linear programming (MILP) to capture coupled routing decisions, drone endurance limits, and launch-retrieval feasibility, often supplemented by heuristic or metaheuristic strategies to address computational scalability. More recent research extends these formulations to stochastic and dynamic VRP settings by incorporating uncertain customer availability, time windows, vehicle delays, and weather disruptions, reflecting a shift toward adaptive routing under incomplete information. Parallel work on payload configuration and energy management investigates modular loading and battery-swapping mechanisms, demonstrating how load heterogeneity and energy constraints fundamentally reshape feasible routing structures. Extensions to multimodal VRP variants, including electric vehicle-drone systems and van-robot hybrids, further broaden applicability in dense and constrained urban environments. Despite these advances, most models remain grounded in static or weakly stochastic assumptions, with limited support for real-time updates or predictive decision-making. In this review, we identified the integration of data-driven prediction and learning-based optimization within dynamic VRP frameworks as a critical direction for advancing truck-drone delivery toward large-scale operational deployment.

Keywords

stochastic / vehicle routing problem (VRP) / urban delivery / machine learning

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References

[1] S. Yu, J. Puchinger, S. Sun, Van-based robot hybrid pickup and delivery routing problem, Eur. J. Oper. Res., 298 (2022), 894-914. https://doi.org/10.1016/j.ejor.2021.06.009

[2] D. Wang, P. Hu, J. Du, P. Zhou, T. Deng, M. Hu, Routing and scheduling for hybrid truck-drone collaborative parcel delivery with independent and truck-carried drones, IEEE Internet Things, 6 (2019), 10483-10495. https://doi.org/10.1109/JIOT.2019.2939397

[3] P. Kitjacharoenchai, B. Min, S. Lee, Two echelon vehicle routing problem with drones in last mile delivery, Int. J. Prod. Econ., 225 (2020), 107598. https://doi.org/10.1016/j.ijpe.2019.107598

[4] A. Anderluh, P. Nolz, V. Hemmelmayr, T. Crainic, Multi-objective optimization of a two-echelon vehicle routing problem with vehicle synchronization and ‘grey zone’ customers arising in urban logistics, Eur. J. Oper. Res., 289 (2021), 940-958. https://doi.org/10.1016/j.ejor.2019.07.049

[5] S. Lichau, R. Sadykov, J. François, R. Dupas, A branch-cut-and-price approach for the two-echelon vehicle routing problem with drones, Comput. Oper. Res., 173 (2025), 106869. https://doi.org/10.1016/j.cor.2024.106869

[6] A. Morim, G. Campuzano, P. Amorim, M. Mes, E. Lalla-Ruiz, The drone-assisted vehicle routing problem with robot stations, Expert Syst. Appl., 238 (2024), 121741. https://doi.org/10.1016/j.eswa.2023.121741

[7] Z. Wang, J. Sheu, Vehicle routing problem with drones, Transport. Res. B-Meth., 122 (2019), 350-364. https://doi.org/10.1016/j.trb.2019.03.005

[8] J. M. Leon-Blanco, P. L. Gonzalez-R, J. L. Andrade-Pineda, D. Canca, M. Calle, A multi-agent approach to the truck multi-drone routing problem, Expert Syst. Appl., 195 (2022), 116604. https://doi.org/10.1016/j.eswa.2022.116604

[9] M. Moshref-Javadi, S. Lee, M. Winkenbach, Design and evaluation of a multi-trip delivery model with truck and drones, Transport. Res. E-Log., 136 (2020), 101887. https://doi.org/10.1016/j.tre.2020.101887

[10] P. L. Gonzalez-R, D. Canca, J. L. Andrade-Pineda, M. Calle, J. M. Leon-Blanco, Truck-drone team logistics: a heuristic approach to multi-drop route planning, Transport. Res. C-Emer., 114 (2020), 657-680. https://doi.org/10.1016/j.trc.2020.02.030

[11] A. Karak, K. Abdelghany, The hybrid vehicle-drone routing problem for pick-up and delivery services, Transport. Res. C-Emer., 102 (2019), 427-449. https://doi.org/10.1016/j.trc.2019.03.021

[12] N. A. Kyriakakis, T. Stamadianos, M. Marinaki, Y. Marinakis, The electric vehicle routing problem with drones: an energy minimization approach for aerial deliveries, Clean. Logist. Suppl. C., 4 (2022), 100041. https://doi.org/10.1016/j.clscn.2022.100041

[13] S. T. W. Mara, R. Sarker, D. Essam, S. Elsayed, Solving electric vehicle-drone routing problem using memetic algorithm, Swarm Evol. Comput., 79 (2023), 101295. https://doi.org/10.1016/j.swevo.2023.101295

[14] N. Sluijk, A. M. Florio, J. Kinable, N. Dellaert, T. Van Woensel, A chance-constrained two-echelon vehicle routing problem with stochastic demands, Transport. Sci., 57 (2022), 252-272. https://doi.org/10.1287/trsc.2022.1162

[15] J. Euchi, A. Sadok, Hybrid genetic-sweep algorithm to solve the vehicle routing problem with drones, Phys. Commun., 44 (2021), 101236. https://doi.org/10.1016/j.phycom.2020.101236

[16] Q. Zhou, J. Wu, M. Zhu, Y. Zhou, F. Xiao, Y. Zhang, LLM-QL: a LLM-enhanced Q-learning approach for scheduling multiple parallel drones, IEEE Trans. Knowl. Data Eng., 37 (2025), 5393-5406. https://doi.org/10.1109/TKDE.2025.3579386

[17] B. Zhou, W. Zeng, H. Yang, Multi-trip UAV-UGV delivery network design with release times, Transport. Res. C-Emer., 181 (2025), 105389. https://doi.org/10.1016/j.trc.2025.105389

[18] E. Teimoury, R. Rashid, The sustainable hybrid truck-drone delivery model with stochastic customer existence, Res. Transp. Econ., 100 (2023), 101325. https://doi.org/10.1016/j.retrec.2023.101325

[19] H. Y. Jeong, B. D. Song, S. Lee, Truck-drone hybrid delivery routing: payload-energy dependency and no-fly zones, Int. J. Prod. Econ., 214 (2019), 220-233. https://doi.org/10.1016/j.ijpe.2019.01.010

[20] M. A. Masmoudi, S. Mancini, R. Baldacci, Y. H. Kuo, Vehicle routing problems with drones equipped with multi-package payload compartments, Transport. Res. E-Log., 164 (2022), 102757. https://doi.org/10.1016/j.tre.2022.102757