Quadratic scheduling of emergency materials considering horizontal transportation under natural disasters

doi:10.16265/j.cnki.issn1003-3033.2023.08.1527

Abstract

Abstract:

In view of the abruptness of natural disasters and their secondary disasters, which make the information transmission at the disaster-affected points lag and fuzzy, resulting in the shortage of emergency supplies at the disaster-affected points, horizontal transportation had been introduced for coordinated scheduling of emergency materials between disaster sites in this paper. The WRSR comprehensive evaluation method was used to calculate the urgency of material as a basis for material scheduling orders in disaster-affected points that were insufficient. The random road traffic rate coefficient was introduced to address the impact of post-disaster road damage on scheduling time and cost. With the goal of minimizing time and cost, a quadratic scheduling model for emergency materials considering lateral transportation was constructed. The genetic algorithm was used to solve the model, and the results were compared with those of no horizontal transfer scheduling. The results show that the introduction of horizontal transfer between disaster-affected points effectively reduces the scheduling time and cost, shortens the "empty window period" of emergency materials at disaster-affected points, and improves the efficiency of emergency logistics and the resilience of the emergency materials distribution network.

Key words: natural disasters, horizontal transfer, emergency logistics, quadratic scheduling, weight rank-sum ratio(WRSR)

CHEN Weijiong, ZHAN Weiwei, KANG Yutao, ZHANG Shanjie, ZHANG Yang, HAN Weijia. Quadratic scheduling of emergency materials considering horizontal transportation under natural disasters[J]. China Safety Science Journal, 2023, 33(8): 212-218.

Figures/Tables 11

Fig.1

Fig.2

Fig.3

Fig.4

Tab.1

Symbols involved in the model

符号	说明
I	$I = (0,1, …, i)$ 受灾点集合,0为配送中心
K	受灾点物资紧迫程度指标,K $= {1,2, …, k)$
$x i j$	变量。1表示物资从受灾点i运输到j,否则为0
$a i k$	受灾点i物资紧迫程度的第k个评价指标
$ω k$	受灾点评价指标的权重, $k ∈ K$
$σ i$	受灾点i物资紧迫程度
$d i$	受灾点物资需求量, $i ∈ I$
$r i$	受灾点i满足度
C	固定单位成本
M	单位库存成本
$w i$	当前转运前或第一次调度后受灾点i库存
$w i ⌢$	当前转运后受灾点i库存
$b i$	受灾点i二次调度需求量
$p i$	受灾点i需求未满足时单位处罚成本, $i ∈ I$
$c i j$	受灾点i到受灾点j的单位运输成本
c	车辆单位运输成本
$t i j$	从受灾点i到受灾点j的转运时间, $i, j ∈ I$
v	运输车辆行驶速度
$s i j$	受灾点i到受灾点j的距离
$ε i j$	受灾点i与受灾点j间可通行率系数, $i, j ∈ I, i ≠ j, 0 < ε i j < 1$
$q i j$	受灾点i到受灾点j转运物资量

Tab.1

Tab.2

Fig.5

Fig.6

Tab.3

Fig.7

Tab.4

References 13

[1]	YU Lina, ZHANG Canrong, JIANG Jingyan, et al. Reinforcement learning approach for resource allocation in humanitarian logistics[J]. Expert Systems with Applications, 2021, 173:DOI:10.1016/j.eswa.2021.114663.
[2]	ZHANG Jianghua, LIU Haiyue, YU Guodong, et al. A three-stage and multi-objective stochastic programming model to improve the sustainable rescue ability by considering secondary disasters in emergency logistics[J]. Computers & Industrial Engineering, 2019, 135: 1145-1154. doi: 10.1016/j.cie.2019.02.003
[3]	MOHAMMADI R, GHOMI S M T F, JOLAI F. Prepositioning emergency earthquake response supplies: a new multi-objective particle swarm optimization algorithm[J]. Applied Mathematical Modelling, 2016, 40(9/10): 5183-5199. doi: 10.1016/j.apm.2015.10.022
[4]	WIDENER M J, HORNER M W. A hierarchical approach to modeling hurricane disaster relief goods distribution[J]. Journal of Transport Geography, 2011, 19(4): 821-828. doi: 10.1016/j.jtrangeo.2010.10.006
[5]	FIEDRICH F, GEHBAUER F, RICKERS U. Optimized resource allocation for emergency response after earthquake disasters[J]. Safety Science, 2000, 35(7): 41-57. doi: 10.1016/S0925-7535(00)00021-7
[6]	孙昌玖, 裴虹, 刘丹, 等. 考虑横向转运的震后应急物资协同调度研究[J]. 武汉理工大学学报:信息与管理工程版, 2018, 40(4):389-395.
	SUN Changjiu, PEI Hong, LIU Dan, et al. Research on post-earthquake relief cooperative dispatching considering lateral transshipment policies[J]. Journal of Wuhan University of Technology:Information & Management Engineering, 2018, 40(4): 389-395.
[7]	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 diapatch of emergency materials considering regional disaster classification[J]. China Safety Science Joural, 2022, 32(1):172-179.
[8]	BURTON J, BANERJEE A. Cost-parametric analysis of lateral transshipment policies in two-echelon supply chains[J]. International Journal of Production Economics, 2005, 93/94: 169-178. doi: 10.1016/j.ijpe.2004.06.015
[9]	FIROUZ M, KESKIN B B, MELOUK S H. An integrated supplier selection and inventory problem with multi-sourcing and lateral transshipments[J]. Omega, 2017, 70: 77-93. doi: 10.1016/j.omega.2016.09.003
[10]	HUO Jiazhen, LI Hu. Batch ordering policy of multi-location spare parts inventory system with emergency lateral transshipments[J]. Systems Engineering-Theory & Practice, 2007, 27(12): 62-67.
[11]	ÖZDAMAR L, EKINCI E, KÜÇÜKYAZICI B. Emergency logistics planning in natural disasters[J]. Annals of Operations Research, 2004, 129(1): 217-245. doi: 10.1023/B:ANOR.0000030690.27939.39
[12]	SHEU J B. An emergency logistics distribution approach for quick response to urgent relief demand in disasters[J]. Transportation Research Part E: Logistics and Transportation Review, 2007, 43(6): 687-709. doi: 10.1016/j.tre.2006.04.004
[13]	林勇, 肖骅, 张立, 等. 震灾应急物资分配-运输优化模型及算法研究[J]. 中国安全科学学报, 2020, 30(10): 171-178. doi: 10.16265/j.cnki.issn 1003-3033.2020.10.024
	LIN Yong, XIAO Hua, ZHANG Li, et al. Optimization model and algorithm of emergency supplies allocation-transportation in earthquake disater[J]. China Safety Science Journal, 2020, 30(10): 171-178. doi: 10.16265/j.cnki.issn 1003-3033.2020.10.024

受灾点	1	5	14	16	22	28	30
WRSR值	0.28	0.41	0.45	0.57	0.38	0.31	0.65
排序	26	20	18	10	22	25	6
受灾点	31	32	38	39	47	48	49
WRSR值	0.51	0.40	0.54	0.55	0.63	0.70	0.74
排序	14	21	12	11	7	4	3
受灾点	53	59	65	66	67	68	72
WRSR值	0.34	0.48	0.80	0.52	0.67	0.59	0.36
排序	24	16	2	13	5	9	23
受灾点	79	85	86	87	94	95	97
WRSR值	0.43	0.49	1.21	0.61	0.46	0.19	0.24
排序	19	15	1	8	17	28	27

调度路线	转运量	时间	成本
91→14	7	0.38	261.54
37→16	12	1.27	1 014.03
74→22	9	0.53	384.60
76→28	9	1.02	650.73
90→30	18	1.50	1 720.25
90→32	2	0.31	137.27
70→31	17	0.28	382.90
25→39	7	0.87	466.88
55→39	5	0.75	325.03
60→48	23	2.23	3 177.74
84→49	11	4.24	2 900.22
26→53	11	7.08	4 775.51
96→59	11	0.23	253.46
34→65	14	1.26	1 159.72
51→66	11	0.64	519.49
55→67	14	1.25	1 146.54
80→68	18	0.08	183.08
74→72	10	0.13	176.51
29→79	10	0.56	437.30
98→85	11	0.13	184.16
17→86	17	0.44	551.56
100→86	14	2.50	2 200.00
2→87	19	0.65	846.39
52→94	11	0.65	526.64
42→97	7	0.63	364.12
0→31→49→32→65→1→0	370	15.21	16 176.07
0→72→39→68→28→0	311	12.27	8 560.77
0→59→14→16→85→5→0	394	10.15	8 933.38
0→95→94→0	153	9.16	3 454.64
合计	1526	76.40	62 008.52

调度路线	调度量	时间	成本
0→5→16→85→97→0	304	10.88	11 917.66
0→86→38→14→87→0	300	10.92	18 636.10
0→79→68→28→0	219	13.08	13 342.58
0→53→94→59→95→0	305	8.37	8 685.09
0→48→47→49→31→0	330	14.79	19 757.10
0→30→32→66→65→1→0	351	15.28	18 392.68
0→72→22→67→39→0	299	12.19	15 687.48
合计	2108	85.52	106 418.69