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Multi-Trip Time-Dependent Vehicle Routing Problem with Split Delivery

Author

Listed:
  • Jie Zhang

    (College of Systems Engineering, National University of Defense Technology, Changsha 410073, China)

  • Yifan Zhu

    (College of Systems Engineering, National University of Defense Technology, Changsha 410073, China)

  • Xiaobo Li

    (College of Systems Engineering, National University of Defense Technology, Changsha 410073, China)

  • Mengjun Ming

    (College of Systems Engineering, National University of Defense Technology, Changsha 410073, China)

  • Weiping Wang

    (College of Systems Engineering, National University of Defense Technology, Changsha 410073, China)

  • Tao Wang

    (College of Systems Engineering, National University of Defense Technology, Changsha 410073, China)

Abstract

Motivated by some practical applications of post-disaster supply delivery, we study a multi-trip time-dependent vehicle routing problem with split delivery (MTTDVRP-SD) with an unmanned aerial vehicle (UAV). This is a variant of the VRP that allows the UAV to travel multiple times; the task nodes’ demands are splittable, and the information is time-dependent. We propose a mathematical formulation of the MTTDVRP-SD and analyze the pattern of the solution, including the delivery routing and delivery quantity. We developed an algorithm based on the simulation anneal (SA) framework. First, the initial solution is generated by an improved intelligent auction algorithm; then, the stochastic neighborhood of the delivery route is generated based on the SA algorithm. Based on this, the model is simplified to a mixed-integer linear programming model (MILP), and the CPLEX optimizer is used to solve for the delivery quantity. The proposed algorithm is compared with random–simulation anneal–CPLEX (R-SA-CPLEX), auction–genetic algorithm–CPLEX (A-GA-CPLEX), and auction–simulation anneal–CPLEX (A-SA) on 30 instances at three scales, and its effectiveness and efficiency are statistically verified. The proposed algorithm significantly differs from R-SA-CPLEX at a 99% confidence level and outperforms R-SA-CPLEX by about 30%. In the large-scale case, the computation time of the proposed algorithm is about 30 min shorter than that of A-SA. Compared to the A-GA-CPLEX algorithm, the performance and efficiency of the proposed algorithm are improved. Furthermore, compared to a model that does not allow split delivery, the objective function values of the solution of the MTTDVRP-SD model are reduced by 52.67%, 48.22%, and 34.11% for the three scaled instances, respectively.

Suggested Citation

  • Jie Zhang & Yifan Zhu & Xiaobo Li & Mengjun Ming & Weiping Wang & Tao Wang, 2022. "Multi-Trip Time-Dependent Vehicle Routing Problem with Split Delivery," Mathematics, MDPI, vol. 10(19), pages 1-24, September.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3527-:d:927212
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    References listed on IDEAS

    as
    1. Bortfeldt, Andreas & Yi, Junmin, 2020. "The Split Delivery Vehicle Routing Problem with three-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 282(2), pages 545-558.
    2. Sun, Peng & Veelenturf, Lucas P. & Hewitt, Mike & Van Woensel, Tom, 2018. "The time-dependent pickup and delivery problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 116(C), pages 1-24.
    3. Diego Cattaruzza & Nabil Absi & Dominique Feillet, 2016. "Vehicle routing problems with multiple trips," 4OR, Springer, vol. 14(3), pages 223-259, September.
    4. Rosario Paradiso & Roberto Roberti & Demetrio Laganá & Wout Dullaert, 2020. "An Exact Solution Framework for Multitrip Vehicle-Routing Problems with Time Windows," Operations Research, INFORMS, vol. 68(1), pages 180-198, January.
    5. Liu, Shixin & Qin, Shujin & Zhang, Ruiyou, 2018. "A branch-and-price algorithm for the multi-trip multi-repairman problem with time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 116(C), pages 25-41.
    6. Nguyen, Phuong Khanh & Crainic, Teodor Gabriel & Toulouse, Michel, 2013. "A tabu search for Time-dependent Multi-zone Multi-trip Vehicle Routing Problem with Time Windows," European Journal of Operational Research, Elsevier, vol. 231(1), pages 43-56.
    7. Said Dabia & Stefan Ropke & Tom van Woensel & Ton De Kok, 2013. "Branch and Price for the Time-Dependent Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 47(3), pages 380-396, August.
    8. Azi, Nabila & Gendreau, Michel & Potvin, Jean-Yves, 2007. "An exact algorithm for a single-vehicle routing problem with time windows and multiple routes," European Journal of Operational Research, Elsevier, vol. 178(3), pages 755-766, May.
    9. Donati, Alberto V. & Montemanni, Roberto & Casagrande, Norman & Rizzoli, Andrea E. & Gambardella, Luca M., 2008. "Time dependent vehicle routing problem with a multi ant colony system," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1174-1191, March.
    10. J. Molina & A. D. López-Sánchez & A. G. Hernández-Díaz & I. Martínez-Salazar, 2018. "A Multi-start Algorithm with Intelligent Neighborhood Selection for solving multi-objective humanitarian vehicle routing problems," Journal of Heuristics, Springer, vol. 24(2), pages 111-133, April.
    11. Maciek Nowak & Özlem Ergun & Chelsea C. White, 2008. "Pickup and Delivery with Split Loads," Transportation Science, INFORMS, vol. 42(1), pages 32-43, February.
    12. Ju Myung Song & Weiwei Chen & Lei Lei, 2018. "Supply chain flexibility and operations optimisation under demand uncertainty: a case in disaster relief," International Journal of Production Research, Taylor & Francis Journals, vol. 56(10), pages 3699-3713, May.
    13. Ichoua, Soumia & Gendreau, Michel & Potvin, Jean-Yves, 2003. "Vehicle dispatching with time-dependent travel times," European Journal of Operational Research, Elsevier, vol. 144(2), pages 379-396, January.
    14. Zongyi Chen & Mingkang Yang & Yijun Guo & Yu Liang & Yifan Ding & Li Wang, 2020. "The Split Delivery Vehicle Routing Problem with Three-Dimensional Loading and Time Windows Constraints," Sustainability, MDPI, vol. 12(17), pages 1-21, August.
    15. Phuong Khanh Nguyen & Teodor Gabriel Crainic & Michel Toulouse, 2017. "Multi-trip pickup and delivery problem with time windows and synchronization," Annals of Operations Research, Springer, vol. 253(2), pages 899-934, June.
    16. Aristide Mingozzi & Roberto Roberti & Paolo Toth, 2013. "An Exact Algorithm for the Multitrip Vehicle Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 193-207, May.
    17. Moshe Dror & Pierre Trudeau, 1989. "Savings by Split Delivery Routing," Transportation Science, INFORMS, vol. 23(2), pages 141-145, May.
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    5. Frey, Christian M.M. & Jungwirth, Alexander & Frey, Markus & Kolisch, Rainer, 2023. "The vehicle routing problem with time windows and flexible delivery locations," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1142-1159.
    6. Ji, Bin & Zhang, Zheng & Yu, Samson S. & Zhou, Saiqi & Wu, Guohua, 2023. "Modelling and heuristically solving many-to-many heterogeneous vehicle routing problem with cross-docking and two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1219-1235.

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