Distribution of emergency medical supplies in cities under major public health emergency
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摘要: 为了在发生重大突发公共卫生事件时提高城市医疗物资的应急救援效率, 减少人员伤亡与经济损失, 在分析重大突发公共卫生事件特点与应急物流特征的基础上, 将需求紧迫度作为配送影响因素, 提出以辖区人口、感染确诊及疑似病例、医疗物资需求点规模、医护人员数量和医疗物资缺口率为评价指标的医疗物资需求点需求紧迫度评价指标体系; 针对医疗物资应急物流的特点, 调整医疗物资配送时间窗参数, 建立由车辆行驶成本、配送延误惩罚成本和无配送延误补贴费用组成的总配送费用函数, 并考虑配送车辆载重、配送时间窗、医疗物资需求紧迫度等约束条件, 构建使总配送费用最少与需求紧迫度高的需求点优先配送的双重目标, 优化了医疗物资的配送路径; 依托SPSS、Yaahp和MATLAB软件平台, 结合算例, 利用层次分析法与遗传算法求解考虑与不考虑需求紧迫度的医疗物资应急物流配送路径优化模型。研究结果表明: 重大突发公共卫生事件下, 相对于不考虑需求紧迫度的配送路径, 考虑需求紧迫度的最优配送路径不仅对需求紧迫度较高的医疗物资需求点进行优先配送, 同时还使总配送费用减少了5.8%;需求紧迫度的引入能极大地改善调度的盲目性, 基于配送车辆载重、配送时间窗、医疗物资需求紧迫度等约束条件所构建的双目标优化模型能够有效地提高应急救援效率和减少不必要的调度成本。Abstract: To improve the emergency rescue efficiency of medical supplies and reduce the casualties and economic losses in cities under the major public health emergency, based on the characteristics analyses of major public health emergencies and emergency logistics, the demand urgency was taken as the influencing factor of distribution. The evaluation index system for medical supplies demand points was proposed with the evaluation indexes of population within jurisdictions, confirmed and suspected cases of infection, scale of medical supplies demand point, number of medical staff and gap rate of medical supplies. According to the characteristics of emergency logistics of medical supplies, the time window parameters of medical supplies distribution were adjusted. The total distribution cost function composed of driving cost, penalty cost of distribution delay and subsidy without distribution delay was established. Considering the constraints of vehicle load, distribution time window, and demand urgency of medical supplies, a dual objective of priority distribution for demand points with the minimum total distribution cost and high demand urgency was constructed to optimize the distribution path of medical supplies. Relying on the software platforms of SPSS, Yaahp and MATLAB, and combining with examples, the analytic hierarchy process and genetic algorithm were used to solve the optimization models of emergency logistics distribution path of medical supplies with and without the consideration of demand urgency. Research result shows that under the major public health emergency, the optimal distribution path considering the demand urgency not only gives priority to the medical supplies demand points with higher demand urgency, but also reduces the total distribution cost by 5.8%, comparing with the distribution path without the consideration of demand urgency. The introduction of demand urgency can greatly reduce the blindness of scheduling. The dual objective optimization model restrained by the conditions of vehicle load, distribution time window and demand urgency of medical supplies can effectively improve the emergency rescue efficiency and reduce unnecessary scheduling costs.
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表 1 各医疗物资需求点信息
Table 1. Information of each medical supplies demand point
需求紧迫度评价指标 辖区人口/万人 感染确诊及疑似病例/人 医疗物资需求点规模/m2 医护人员数量/人 医疗物资缺口率/% 需求点1 1 5 417 10 611 67 40 需求点2 64 268 63 739 90 80 需求点3 144 3 417 35 375 77 70 需求点4 155 3 525 88 078 60 60 需求点5 31 5 801 61 251 90 10 需求点6 13 4 275 20 956 76 30 表 2 各医疗物资需求点标准化信息
Table 2. Standardized information of each medical supplies demand point
需求紧迫度评价指标 辖区人口标准化值 感染确诊及疑似病例标准化值 医疗物资需求点规模标准化值 医护人员数量标准化值 医疗物资缺口率标准化值 需求点1 0.00 0.93 0.00 0.21 0.43 需求点2 0.41 0.00 0.69 0.99 1.00 需求点3 0.93 0.57 0.32 0.57 0.86 需求点4 1.00 0.59 1.00 0.00 0.71 需求点5 0.19 1.00 0.65 0.96 0.00 需求点6 0.08 0.72 0.13 0.55 0.29 表 3 指标得分
Table 3. Scores of indexes
评价指标 辖区人口 确诊及疑似病例 医疗物资需求点规模 医护人员数量 医疗物资缺口率 辖区人口 1 1 4 3 1 确诊及疑似病例 1 1 4 3 1 医疗物资需求点规模 1/4 1/4 1 1 1/5 医护人员数量 1/3 1/3 1 1 1/4 医疗物资缺口率 1 1 5 4 1 表 4 医疗物资需求点参数
Table 4. Medical supplies demand points parameters
参数 物资配送中心0 需求点1 需求点2 需求点3 需求点4 需求点5 需求点6 医疗物资需求/单位质量 0.0 4.0 3.0 1.5 4.5 1.5 2.0 最晚配送时间/h 10 000.0 2.3 0.8 2.5 2.0 2.3 2.3 各需求点相对需求紧迫度 1.00 1.10 1.50 2.06 2.00 1.25 1.00 表 5 其他参数设置
Table 5. Other parameter settings
参数 取值 车辆额定载质量/单位质量 8 延误时单位时间惩罚成本/单位费用 60 无配送延误时单位补贴费用/单位费用 120 车辆单位时间的行驶成本/单位费用 200 表 6 各医疗物资需求点最短距离
Table 6. Minimum distances of each medical supplies demand point
h 需求点 0 1 2 3 4 5 6 0 0.00 2.00 1.80 2.00 1.50 1.20 0.80 1 2.00 0.00 1.50 1.40 1.80 1.50 1.50 2 1.80 1.50 0.00 2.00 2.00 2.00 2.00 3 2.00 1.40 2.00 0.00 1.00 2.00 1.00 4 1.50 1.80 2.00 1.00 0.00 1.50 0.80 5 1.20 1.50 2.00 2.00 1.50 0.00 1.30 6 0.80 1.50 2.00 1.00 0.80 1.30 0.00 表 7 考虑与不考虑需求紧迫度的配送路线
Table 7. Distribution routes considering demand urgency or not
求解结果 考虑需求紧迫度 不考虑需求紧迫度 配送路线1 0-2-1-0 0-1-2-0 配送路线2 0-4-3-6-0 0-6-3-4-0 配送路线3 0-5-0 0-5-0 总配送费用/单位费用 1 732.8 1 840.8 -
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