关键词: 疫苗流动接种, 同步调度, 可拆分需求, 补给策略, 混合整数规划

Abstract: In recent years, public health events have gained people’s focus and continuous attention, sudden epidemic disasters have affected national economy and national health,and the successful research and development of vaccines has become a key measure to curb the continuous spread of the epidemic. In order to alleviate the congestion of vaccination stations and reduce residents’ travel costs for vaccination, a new smart mobile vaccination vehicle has been put into shopping malls, communities and other places with heavy traffic for mobile vaccination services since April 2021. According to the appointment information of vaccinators on the vaccination platform and the service time window of vaccination points, CDC assigned vaccination tasks to vaccination points, dispatched mobile vaccination vehicles to vaccination points for vaccination services, and in order to solve the inventory limitation problem of mobile vaccination vehicles, dispatched supply vehicles for inventory replenishment, to ensure the sustainability of the service. Under this background, this paper studies the synchronized scheduling optimization for mobile vaccination vehicles and replenishment vehicles with separable demand.
Aiming at the problem of mobile vaccination synchronous scheduling, the existing literature is reviewed from the aspects of public health event decision method, vehicle scheduling optimization problem, synchronization problem, etc., and the reference research ideas and research methods are summarized and refined. For solving the problem, the precise solution of CPLEX and genetic algorithm and their improved methods are studied.
Based on the demand certainty, the spatio-temporal synchronization characteristics of the operation of the inoculation vehicle and the supply vehicle are made clear, that is, the service sequence of the two vehicles is coupled with each other and the inoculation and supply decisions are interdependent. Secondly, the replenishment operation considers the detachable characteristics of replenishment demand and adopts different replenishment strategies. A single objective mixed integer linear programming model is established to determine the service path and service time of the mobile vaccination vehicle, the supply strategy and the supply quantity of the supply vehicle. Since the inoculation vehicle scheduling problem with multiple inoculation points is a NP difficult problem, the precise algorithm is difficult to solve the large-scale example. An evolution algorithm based on greedy strategy is designed to solve the large-scale example. Meanwhile, the experimental comparison with CPLEX precise solution method verifies the effectiveness and feasibility of the model and algorithm. The Solomon dataset is extended to generate examples of different sizes, and the experimental results show that increasing the vaccine consumption speed could significantly reduce the maximum vaccination time, and the flexible replenishment strategy is better than the maximum replenishment strategy, which is more beneficial to saving cost and keeping the stock level stable. Finally, we solve a case on the flow vaccination data of the Shanghai Pudong New Area by which the practical application value of the study has been proved.
The shortcomings of this paper are that it does not fully consider the suddenness and uncertainty of vaccine demand, and the performance of the algorithm designed for the complexity of the model needs to be optimized. The above problems are the directions for future research.

Key words: mobile vaccination, synchronized scheduling, separable demand, replenishment strategy, mixed linear integer programming