考虑不确定性的多情景应急车辆综合调度模型

doi:10.16265/j.cnki.issn1003-3033.2023.11.1061

摘要/Abstract

摘要：

为提升不同应急情景下各救援力量的联合应急救援效率,降低救援风险,减少财产损失,采用情景分析的方法对应急状态不确定性进行参数估计,引入风险厌恶水平,构建一种以总调度成本和风险最小化为目标的应急车辆综合调度模型;运用非支配排序遗传算法(NSGA-II)求解目标函数值,通过仿真案例对比分析考虑情景与不考虑情景2种情况下的求解结果;利用模型分析不同情景下惩罚成本与风险厌恶水平的关系,给出合理风险厌恶水平值,选定最终调度方案。结果表明:该模型与方案能够有效满足不同应急情景下需求点的需求,提高救援效率,解决在情景与风险共同作用下的应急车辆综合调度问题。

关键词: 不确定性, 应急情景, 应急车辆, 综合调度模型, 调度方案, 风险厌恶水平, 救援效率

Abstract:

In order to improve the joint emergency rescue efficiency of rescue forces under different emergency scenarios, and to reduce rescue risk and property losses, a scenario analysis method was used to estimate the parameters of emergency state uncertainty, and an integrated emergency vehicle scheduling model aimed at minimizing the total scheduling cost and risk was established by introducing risk aversion level. Secondly, Non-dominated Sorting Genetic Algorithms(NSGA-II) was used to solve the objective function value, and the simulation case was used to compare and analyze the solution results under the consideration of the scenario and without consideration of the scenario. Finally, the relationship between penalty cost and risk aversion level in different scenarios was analyzed, the reasonable risk aversion level value was given, and the final scheduling scheme was selected. The results show that the model and scheme can effectively meet the needs of different emergency situations, improve rescue efficiency, and solve the comprehensive scheduling problem of emergency vehicles under the combined effects of scenarios and risk.

Key words: emergency rescue, scenario analysis, scheduling scheme, risk aversion level, rescue efficiency

许钧, 李筱, 王修来. 考虑不确定性的多情景应急车辆综合调度模型[J]. 中国安全科学学报, 2023, 33(11): 156-164.

XU Jun, LI Xiao, WANG Xiulai. Multi-scenario integrated scheduling model of emergency vehicles considering uncertainty[J]. China Safety Science Journal, 2023, 33(11): 156-164.

图/表 11

图1

表1

参数符号说明

符号	符号说明	符号	符号说明
O	应急指挥中心	$d m n s$	在情景s下受灾点n对任务资源m的需求量
R	救援中心集合;R={1,2,…,r}〗	$d m p s$	在情景s下人员安置点p对任务资源m的需求量
E	应急物资储备库集合;E={1,2,…,e}〗	$l r m$	救援中心r储备任务资源m的最低储备量
M	任务资源集合,M={1,2,…,m}〗。其中,1伤员救援,2救援物资,3生活物资	$L r m$	救援中心r储备任务资源m的最高储备量
N	受灾点集合,N={1,2,…,n}〗	g_em	应急物资储备库e储备任务资源m的储备容量
P	人员安置点集合,P={1,2,…,p}〗	$r e m n$	运输任务资源m至受灾点n的车辆的容量限制
S	情景集合,S={1,2,…,s}〗。其中,s=1,2,3分别代表乐观、一般、悲观情景	$r e m p$	运输任务资源m至人员安置点p的车辆的容量限制
$x r m n s$	0-1变量;在情景s下承担了从救援中心r运输资源m到受灾点n的任务	f_r	救援中心r的固定成本
$x e m n s$	0-1变量;在情景s下承担了从应急物资储备库e运输资源m到受灾点n的任务	f_e	应急物资储备库e的固定成本
$x e m p s$	0-1变量;在情景s下承担了从应急物资储备库e运输资源m到人员安置点p的任务	$f r m n$	从救援中心r运输任务资源m到受灾点n的车辆固定成本;r换为e时,表示从应急物资储备库出发
$q r m n s$	在情景s下从救援中心r运输资源m到受灾点n的运输量	$h r m n s$	从救援中心r运输任务资源m到受灾点n的单位运输成本,r换为e时表示从应急物资储备库出发
$q e m n s$	在情景s下从应急物资储备库e运输资源m到受灾点n的运输量	$f e m p$	应急物资储备库e运输任务资源m到人员安置点p的车辆固定成本
$q e m p s$	在情景s下从应急物资储备库e运输资源m到人员安置点p的运输量	$h e m p s$	应急物资储备库e运输任务资源m到人员安置点p的单位运输成本
$i e m s$	应急物资储备库e对资源m的储存成本	$w m p s$	人员安置点p的未满足量
$w m n s$	受灾点n的未满足量	$u m n s$	受灾点n因未满足导致的惩罚成本
$u m p s$	人员安置点p因未满足导致的惩罚成本	c_pc	单位时间延迟服务的惩罚成本
c_ac	单位时间提前服务的等待成本	t_n	受灾点的服务时间窗;n换为p表示人员安置点
$t e m n s$	受灾点到达时间;n换为p表示人员安置点	$j e n$	e到受灾点n的距离;e换为p同理
$v e n s$	到n或p的运输速度 (n换为p时)	μ	决策者的风险厌恶水平;范围是[0,1]

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表4

图3

表5

图4

表6

表7

参考文献 16

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情景 s	概率	资源需求/件	运输成本/ (元·km^-1)	惩罚成本/ (元·h^-1)	运输速度/ (km·h^-1)
乐观	0.3	-20%	-10%	-15%	+20%
一般	0.4	名义值	名义值	名义值	名义值
悲观	0.3	+20%	+10%	+15%	-20%

需求点	伤员救援/人	救援物资/件	生活物资/件	运输成本/ (元·km^-1)	惩罚成本/ (元·h^-1)	运输速度/ (km·h^-1)
受灾点	6	500	—	15	10	50
人员安置点	—	—	500	6.48	8	50

μ	平均总成本(期望)	风险 (方差)	μ	平均总成本(期望)	风险 (方差)
0	29 854.37	5.241 3	0.6	31 547.25	1.957 2
0.1	29 962.18	5.112 6	0.7	31 710.49	1.378 3
0.2	30 126.54	4.876 5	0.8	32 032.27	0.293 2
0.3	30 352.83	4.237 1	0.9	32 143.51	0.135 7
0.4	30 684.04	3.512 5	1	32 208.16	0.000 1
0.5	31 236.78	2.494 1	—	—	—

情景	风险厌恶水平μ
情景	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
乐观	5 532.17	5 552.20	5 578.92	5 670.17	5 802.30	5 858.07	5 901.92	6 066.34	6 169.38	6 207.39	6 249.33
一般	5 831.35	5 862.15	5 889.38	5 920.91	5 960.13	5 959.52	5 994.73	6 155.67	6 249.75	6 280.73	6 298.97
悲观	6 171.98	6 161.32	6 148.10	6 130.63	6 171.21	6 138.25	6 160.45	6 267.06	6 298.19	6 331.14	6 347.44
平均	5 845.17	5 858.56	5 872.13	5 907.24	5 977.88	5 985.28	6 019.03	6 163.02	6 239.11	6 273.09	6 298.58

出发点	运输路径	任务资源	救援效率
R1	R1→N2→N4→N6→N9→R1	伤员救援	N10、N14的伤员救援需求量未被全部满足;救援效率为90%
R2	R1→N1→N3→N8→N5→R1	伤员救援
R3	R2→N11→N6→R2	伤员救援
	R2→N20→N18→N16→R2
	R2→N17→N10→N14→R2
	R3→N7→N9→R3	伤员救援
	R3→N12→N15→R3
	R3→N19→N13→N8→R3
E1	E1→N4→N11→N9→E1 ︙ E1→P8→P14→P7→P2→E1	救援物资 ︙ 生活物资	N7的救援物资需求量未被全部满足;救援效率为95% P11的生活物资需求量未被全部满足;救援效率为93.75%
E2	E2→N6→N13→N14→E2 ︙ E2→P7→P1→P3→P10→E2	救援物资 ︙ 生活物资
︙	︙	︙
E7	E7→N12→N19→E7 ︙ E7→P13→P9→P6→E7	救援物资 ︙ 生活物资
E8	E8→N18→N20→N15→E8 ︙ E8→P16→P15→P6→P10→E8	救援物资 ︙ 生活物资