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.

Emergency material delivery is vital to disaster emergency rescue. Herein, the framework of the emergency material delivery system (EMDS) with the unmanned aerial vehicle (UAV) as the vehicle is proposed, and the problem is modeled into a multi-trip time-dependent dynamic vehicle routing problem with split-delivery (MTTDDVRP-SD) in combination with the rescue reality, which provides decision support for planning disaster relief material. Due to the universality of dynamic interference in the process of material delivery, an optimization algorithm based on the traditional intelligent auction mechanism is proposed to avoid system performance degradation or even collapse. The algorithm adds pre-authorization and sequential auction mechanisms to the traditional auction mechanism, where the pre-authorization mechanism improves the capability performance of the system when there is no interference during the rescue process and the sequential auction mechanism improves the resilience performance of the system when it faces interferences. Finally, considering three types of interference comprehensively, which includes new task generations, task unexpected changes and UAV’s number decreases, the proposed algorithm is compared with DTAP (DTA based on sequential single item auctions) and CBBA-PR (consensus-based bundle algorithms-partial replanning) algorithms under different dynamic interference intensity scenarios for simulation experimental from two perspectives of the capability performance and resilience performance. The results of Friedman’s test with 99% confidence interval indicate that the proposed algorithm can effectively improve the capability performance and resilience performance of EMDS.