随机需求下多种应急医疗物资联合储备与分配问题研究  

Research on Joint Reserve and Allocation of Multiple Emergency Medical Materials under Uncertain Demands

作　　者：张瑶 张煜炜 李珍萍[1,2] 吴玉文 Zhang Yao;Zhang Yuwei;Li Zhenping;Wu Yuwen(School of Statistics and Data Science,Beijing Wuzi University,Beijing 101149,China;School of Management and Engineering,Capital University of Economics and Business,Beijing 100070,China)

机构地区：[1]北京物资学院统计与数据科学学院,北京101149 [2]首都经济贸易大学管理工程学院,北京100070

出　　处：《中国管理科学》2024年第7期129-137,共9页Chinese Journal of Management Science

基　　金：北京市自然科学基金项目(9212004,Z180005);国家自然科学基金项目(71771028);北京市属高校高水平创新团队支持计划项目(IDHT20180510)。

摘　　要：针对突发公共卫生事件发生后每个需求点对各种医疗物资的需求具有不确定性,在储备库容量有限的情况下,研究了各需求点对每种医疗物资需求量服从独立均匀分布情况下的多种应急医疗物资联合储备与分配问题。考虑各种物资占用的储备空间、存储成本以及各个需求点的缺货成本等,以物资存储成本和期望缺货成本之和最小化为目标,建立了多种医疗物资联合储备与分配问题的两阶段随机规划模型。在需求量概率分布参数已知的情况下,将两阶段随机规划模型转化为确定型凸二次规划模型,证明了最优解满足的性质并给出了最优解的解析表达式。进一步分析了储备库容量变化对最优储备策略的影响,通过数值实验验证了本文方法的有效性。Considering the uncertain demands for medical materials at each demand point after the public health emergencies,the joint reserve and allocation problem of multiple kinds of emergency medical materials is studied with limited reserve capacity based on the condition that the demand for each kind of medical materials at each demand point obeys the independent and uniform distribution.A two-stage stochastic programming model for the joint reserve and allocation of multiple medical materials is established,the objective function is to minimize the total cost including the inventory cost of the reserve medical materials and the total expected shortage cost at each demand point.Given the parameters of demand probability distribution,the two-stage stochastic programming model is transformed into a deterministic convex quadratic programming model.The properties of the optimal solution are proposed and proved,then the optimal solution is analytical expressed.Finally,the influence of the reserve capacity change on the optimal reserve and allocation solution is analyzed,and the effectiveness of the proposed method is verified by simulation on an example generated from practical data.It provides a decision-making basis for solving the practical multiple medical materials joint reserve and allocation problem in this paper.

关 键 词：随机需求 医疗物资 储备与分配 两阶段随机规划 凸二次规划 

分 类 号：O221.5[理学—运筹学与控制论] F259.21[理学—数学]