A Material Allocation Model for Public Health Emergency under a Multimodal Transportation Network by Considering the Demand Priority and Psychological Pain

In a public health emergency, residents urgently require a large number of rescue materials for treatment or protection. These rescue materials are usually located far from the emergency area. The government must organize rescue materials transportation by selecting suitable transport modes. Thus, we propose a material allocation model for public health emergencies under a multimodal transportation network to determine the best rescue material supply route. In this model, we set the demand priorities according to the emergency degrees to decide the transportation sequence. Meanwhile, we introduce the psychological pain cost brought by the rescue material shortage into the proposed model to trade off the priority and fairness of demand. Having compared it to the research literature, this is the first study that considers multiple categories of materials, absolute pain costs, relative pain costs and demand priority under multimodal transportation. The research problem is formulated into an integer programming model, and we develop a modified genetic algorithm to solve it. A set of numerical examples are conducted to test the performance of the proposed algorithm, and to investigate features and applications of the proposed model. The results indicate that the modified genetic algorithm performs better in the calculation examples at different scales. For small-scale instances, the algorithm produces consistent results with Gurobi. As the instance size increases, Gurobi fails to find the optimal solution within 1800 s, while this algorithm is able to find the optimal solution within an acceptable time frame. Additionally, when dealing with large-scale instances, the algorithm exhibits a significant advantage in terms of runtime. Sensitivity analysis of key factors indicate that (1) Adjusting the relative pain cost coefficient can make the best trade-off between fairness, economy and timeliness; (2) Compared with a single mode of transport, multimodal transport can reduce the psychological pain cost and the logistics cost; (3) Improving the loading and unloading capacity of nodes can reduce the delivery time of materials and the psychological pain cost of residents, but the influence of other factors and cost-effectiveness need to be considered.