考虑时间窗与公平性的应急物资调配多目标动态规划模型

doi:10.16265/j.cnki.issn1003-3033.2025.03.0667

摘要/Abstract

摘要：

突发公共卫生事件后隔离社区的物资调配需求激增,面对总供给不足、分配公平性以及特殊分配需求等问题,采用“物资供应点-分配中心-隔离社区”逐级调配模式,研究多周期、多物资种类、跨区域的应急物资动态调度问题。通过需求时间窗来表征隔离社区对应急物资送达时间的现实要求;以老龄人口为例,着重考虑弱势群体的紧急需求,综合经济性、物资分配满足率和分配公平性3个层面,建立非线性多目标动态规划模型;采用Epsilon约束算法求解模型,以上海市突发公共卫生事件封控期的物资调配为案例研究,给出最优解的Pareto前沿面,并对模型中的关键参数进行灵敏度分析。结果表明:在有限的应急物资供给限制下,考虑老龄人口占比情况的物资分配方案有助于优先保障弱势群体的物资供给,但也导致了隔离社区整体的分配不公平率增加;考虑时间窗需求的物资分配方案中,跨区域调配网络运营总成本以及隔离社区的物资需求未满足率较高,但此时系统整体的物资分配相对公平,且能够满足各隔离社区对物资送达时间窗的需求,为决策者权衡个体需求与整体利益提供有益参考。

关键词: 时间窗, 公平性, 应急物资调配, 多目标动态规划模型, 突发公共卫生事件

Abstract:

During the attack of public health emergencies, the surge in material demand in isolated communities leads to a series of problems, i.e., serious shortfalls in supply, fairness of distribution and special distributional needs. To address this issue, a multi-period, multi-type, cross-regional emergency material dynamic allocation problem was studied based on a hierarchical distribution network of "material supply point-distribution center-isolated community". Especially, the demand time windows were applied to characterize the realistic requirements of isolated communities for the delivery time, and the special needs of some vulnerable groups, e.g., aging populations, were considered. Thus, a multi-objective non-linear dynamic program was developed by integrating the three dimensions of considerations: economy, material distribution satisfaction rate and distribution equity. In view of the multi-objective structure, the Epsilon constraint algorithm was used to solve the proposed model, and the material allocation during the attack of public health emergencies in Shanghai was taken as a case study to analyze the Pareto front of the optimal solutions and conduct the sensitivity analysis on some key parameters in the model. The results show that, under the constraint of limited emergency material supply, the material allocation strategy considering the aging populations helps to prioritize the material supply of vulnerable groups. However, it also contributes to an increase in the unfairness rate of the isolated communities as a whole. For the material allocation strategy considering the delivery time windows of isolated communities, the total operation cost of the cross-regional distribution network and the unmet rate of the material demand in the isolated communities are high, but the overall distribution of supplies in the system is relatively fair, and it could better meet the needs of isolated communities in terms of delivery of supplies, which provides a useful reference for the decision makers to balance the individual demand and the overall interests.

Key words: time windows, fairness, emergency supplies scheduling, multi-objective dynamic programming model, public health emergency

中图分类号:

X951交通运输安全

宋晗, 崔娜, 张艳萍. 考虑时间窗与公平性的应急物资调配多目标动态规划模型[J]. 中国安全科学学报, 2025, 35(3): 242-252.

SONG Han, CUI Na, ZHANG Yanping. Multi-objective dynamic program for emergency material allocation considering time window and fairness[J]. China Safety Science Journal, 2025, 35(3): 242-252.

图/表 13

图1

图2

图3

表1

图4

表2

图5

图6

图7

表3

是否考虑弱势群体情况下各目标函数值对比

是否优先考虑弱势群体占比较高的社区	$f 1$ 总成本/元	$f 2$ 未满足率之和	$f 3$ 不公平率之和
是	1.082 1×10⁷	2 125.11	170.26
否	1.084 9×10⁷	1 393.63	114.25

表3

图8

图9

表4

是否考虑时间窗下各目标数值对比

是否优先考虑时间窗需求	$f 1$ 总成本/元	$f 2$ 未满足率之和	$f 3$ 不公平率之和
是	1.082 1×10⁷	2 125.11	170.26
否	4.836 1×10⁵	1 238.31	2 007.65

表4

参考文献 16

[1]	NIKOO N, BABAEI M, MOHAYMANY A S. Emergency transportation network design problem: identification and evaluation of disaster response routes[J]. International Journal of Disaster Risk Reduction, 2018, 27: 7-20.
[2]	CHAI Gan, CAO Jinde, HUANG Wei, et al. Optimized traffic emergency resource scheduling using time varying rescue route travel time[J]. Neurocomputing, 2018, 275: 1567-1575.
[3]	曹源, 温佳坤, 马连川. 重大疫情下的列车动态编组与调度[J]. 交通运输工程学报, 2020, 20(3): 120-128.
	CAO Yuan, WEN Jiakun, MA Lianchuan. Dynamic marshalling and scheduling of trains in major epidemics[J]. Journal of Traffic and Transportion Engineering, 2020, 20(3): 120-128.
[4]	李文莉, 李昆鹏, 田倩南, 等. 突发疫情环境下考虑订单释放时间的零售物流配送路径优化研究[J]. 中国管理科学, 2022, 30(9): 195-205.
	LI Wenli, LI Kunpeng, TIAN Qiannan, et al. The research on retail logistics distribution routing optimization considering order release dates in epidemic outbreak environment[J]. Chinese Journal of Management Science, 2022, 30(9): 195-205.
[5]	冯春, 向阳, 薛坤, 等. 多周期多品种应急物资配送多目标优化模型[J]. 中国管理科学, 2017, 25(4): 124-132.
	FENG Chun, XIANG Yang, XUE Kun, et al. Multi-objective optimization model of the emergency logistics distribution with multicycle and multi-item[J]. Chinese Journal of Management Science, 2017, 25(4): 124-132.
[6]	宋英华, 白明轩, 马亚萍, 等. 考虑区域灾情分级的应急物资公平调度优化模型[J]. 中国安全科学学报, 2022, 32(1): 172-179. doi: 10.16265/j.cnki.issn1003-3033.2022.01.023
	SONG Yinghua, BAI Mingxuan, MA Yaping, et al. Optimal model for fair dispatch of emergency materials considering regional disaster classification[J]. China Safety Science Journal, 2022, 32(1): 172-179. doi: 10.16265/j.cnki.issn1003-3033.2022.01.023
[7]	WANG Shulin, SUN Baiqing. Model of multi-period emergency material allocation for large-scale sudden natural disasters in humanitarian logistics: efficiency, effectiveness and equity[J]. International Journal of Disaster Risk Reduction, 2023, 85: DOI:10.1016/j.ijdrr.2023.103530.
[8]	HUANG Kai, JIANG Yiping, YUAN Yufei, et al. Modeling multiple humanitarian objectives in emergency response to large-scale disasters[J]. Transportation Research Part E: Logistics and Transportation Review, 2015, 75: 1-17.
[9]	赵建有, 韩万里, 郑文捷, 等. 重大突发公共卫生事件下城市应急医疗物资配送[J]. 交通运输工程学报, 2020, 20(3): 168-177.
	ZHAO Jianyou, HAN Wanli, ZHENG Wenjie, et al. Distribution of emergency medical supplies in cities under major public health emergency[J]. Journal of Traffic and Transportation Engineering, 2020, 20(3): 168-177.
[10]	吕伟, 李志红, 冯满满, 等. 考虑资源和时间窗约束的应急物资调配模型[J]. 中国安全科学学报, 2019, 29(12): 137-143. doi: 10.16265/j.cnki.issn1003-3033.2019.12.022
	LYU Wei, LI Zhihong, FENG Manman, et al. Emergency material allocation in consideration of resource and time window constraints[J]. China Safety Science Journal, 2019, 29(12): 137-143. doi: 10.16265/j.cnki.issn1003-3033.2019.12.022
[11]	LIU Haishi, SUN Yuxuan, PAN Nan, et al. Study on the optimization of urban emergency supplies distribution paths for epidemic outbreaks[J]. Computers & Operations Research, 2022, 146: DOI:10.1016/j.cor.2022.105912.
[12]	HAGHANI A, OH S. Formulation and solution of a multi-commodity, multi-modal network flow model for disaster relief operations[J]. Transportation Research Part A: Policy and Practice, 1996, 30(3): 231-250.
[13]	柴获, 何瑞春, 韩伟, 等. 带时间窗的危险货物车辆路径问题2阶段优化[J]. 中国安全科学学报, 2023, 33(12): 160-166. doi: 10.16265/j.cnki.issn1003-3033.2023.12.2080
	CHAI Huo, HE Ruichun, HAN Wei, et al. Two-stage optimization of vehicle routing problem for hazardous materials with time windows[J]. China Safety Science Journal, 2023, 33(12): 160-166. doi: 10.16265/j.cnki.issn1003-3033.2023.12.2080
[14]	CAO Cejun, LIU Yang, TANG Ou, et al. A fuzzy bi-level optimization model for multi-period post-disaster relief distribution in sustainable humanitarian supply chains[J]. International Journal of Production Economics, 2021, 235: DOI:10.1016/j.ijpe.2021.108081.
[15]	单子丹, 盛晨辉, 王晓燕, 等. 突发事件下应急物资多目标优化调度模型与算法研究:以新冠肺炎疫情为例[J]. 运筹与管理, 2023, 32(1): 34-40. doi: 10.12005/orms.2023.0006
	SHAN Zidan, SHENG Chenhui, WANG Xiaoyan, et al. Research on the multi-objective optimization dispatching model and algorithm of emergency supplies under emergency events: a case of COVID-19[J]. Operations Research and Management Science, 2023, 32(1): 34-40. doi: 10.12005/orms.2023.0006
[16]	MOSALLANEZHAD B, CHOUHAN V K, PAYDAR M M, et al. Disaster relief supply chain design for personal protection equipment during the COVID-19 pandemic[J]. Applied Soft Computing, 2021, 112: DOI:10.1016/j.asoc.2021.107809.

路网节点数	总成本/10⁷元	利益损失效用值	运行时间/s
24	1.08	2 295.38	252.53
50	8.06	5 201.88	291.93
77	30.96	7 105.97	2 641.94
100	—	—	10 000