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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

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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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