考虑生物危险源扩散的疫区应急物资调配模型

Model of emergency supplies allocation in epidemic areas considering spread of biohazard diffusion

为解决传染性生物危险源扩散后疫区应急物资选址-分配问题,构建多目标优化应急物资调配模型。该模型以最小化配送时间、最小化疫区物资未满足程度为目标函数,结合考虑潜伏期、重复感染率的易感者-潜伏者-感染者-康复者(SEIRS)传染病动力学模型,建立物资需求方程,预测各疫区实时物资需求;针对应急救援过程中疫情扩散对应急物资调配方案的影响,使用改进非支配排序遗传算法(NSGA)-II求解模型。通过k-means算法预选址,实现适用于现有疫区的配送中心选址方案动态更新,进一步联合决策配送中心各类车辆派遣数、各类物资配送量;并以武汉市2020年疫情数据作为算例对比分析。结果表明:该模型计算效率较高,相较于传统NSGA-Ⅱ算法,在收敛性、多样性和稳定性上具有性能优势,所得应急物资调配方案调配时间更短,疫区未满足程度更小,验证了模型的有效性。

In order to solve the problem of location selection and deployment of emergency supplies in epidemic areas after the spread of infectious biohazards,a multi-objective optimal emergency materials allocation model was established.Two kinds of objective functions,the minimization of distribution time and the minimization of the unsatisfied degree of materials,in the epidemic area were applied to this model.The Susceptible-Exposed-Infectious-Recovered-Susceptible(SEIRS)model,considering the incubation period and the repeated infection rate,was combined to establish the material demand equation and predict the real-time material demand in the epidemic area.In view of the impact of the spread of the epidemic on the allocation plan of emergency materials during the emergency rescue process,an impoved NSGA-Ⅱ algorithm solution model was designed.The k-means algorithm was used for pre-location to realize the dynamic update of the location plan of the distribution center applicable to the existing epidemic area.Then,further joint decisions on the dispatch number of various vehicles and the distribution amount of various materials in the distribution center were made.Taking the epidemic data of Wuhan city in 2020 as an example,comparative analysis shows that the model has high computational efficiency,and has performance advantages in convergence,diversity and stability compared with the traditional NSGA-Ⅱ algorithm.The obtained emergency materials allocation plan has a shorter deployment time and less unmet degree in the epidemic area,which verifies the effectiveness of the model.