Model of emergency supplies allocation in epidemic areas considering spread of biohazard diffusion

doi:10.16265/j.cnki.issn1003-3033.2023.11.0434

Abstract

Abstract:

In order to solve the problem of location selection and deployment of emergency supplies in epidemic areas after the spread of infectious biohazards, a multi-objective optimal emergency materials allocation model was established. Two kinds of objective functions, the minimization of distribution time and the minimization of the unsatisfied degree of materials, in the epidemic area were applied to this model. The Susceptible-Exposed-Infectious-Recovered-Susceptible(SEIRS) model, considering the incubation period and the repeated infection rate, was combined to establish the material demand equation and predict the real-time material demand in the epidemic area. In view of the impact of the spread of the epidemic on the allocation plan of emergency materials during the emergency rescue process, an impoved NSGA-II algorithm solution model was designed. The k-means algorithm was used for pre-location to realize the dynamic update of the location plan of the distribution center applicable to the existing epidemic area. Then, further joint decisions on the dispatch number of various vehicles and the distribution amount of various materials in the distribution center were made. Taking the epidemic data of Wuhan city in 2020 as an example, comparative analysis shows that the model has high computational efficiency, and has performance advantages in convergence, diversity and stability compared with the traditional NSGA-II algorithm. The obtained emergency materials allocation plan has a shorter deployment time and less unmet degree in the epidemic area, which verifies the effectiveness of the model.

Key words: biohazard diffusion, emergency supplies in epidemic areas, allocation model, multi-objective optimization, emergency rescue, improved non-dominated sorting genetic algorithm(NSGA)-II

ZHANG Minbo, ZHONG Ziyi, YAN Jin, WANG Cuiling, WANG Zichao, LI Chunxin. Model of emergency supplies allocation in epidemic areas considering spread of biohazard diffusion[J]. China Safety Science Journal, 2023, 33(11): 206-213.

Figures/Tables 10

Fig.1

Fig.2

Tab.1

Alternative distribution center

B	城市名	地理坐标	S_ik/件			$E i v$ /辆
B	城市名	地理坐标	k₁	k₂	k₃	v₁	v₂	v₃
b₁	天门	(60°39'N,113°10'E)	4 692	898	1 832	10	10	10
b₂	孝感	(30°56'N,113°54'E)	3 867	1 204	2 512	6	15	13
b₃	黄石	(30°12'N,115°06'E)	4 521	559	1 934	10	10	11
b₄	赤壁	(113°88'N,29°72'E)	2 899	956	2 484	8	9	7
b₅	信阳	(32°13'N,114°07'E)	3 078	854	2 388	7	12	9
b₆	钟祥	(31°10'N,112°34'E)	2 983	736	2 096	9	11	13
b₇	荆州	(112°24'N,30°33'E)	4 581	951	1 873	10	15	9
b₈	荆门	(31°02'N,112°12'E)	3 260	1 026	2 144	11	9	12
b₉	洪湖	(29°48'N,113°27'E)	6 125	653	2 065	7	12	11
b₁₀	咸宁	(29°53'N,114°17'E)	4 862	987	2 254	11	9	15
b₁₁	庐山	(29°42'N,116°26'E)	3 228	688	2 317	7	9	10
b₁₂	抚州	(27°95'N,116°36'E)	4 120	856	2 057	10	10	11
b₁₃	黄冈	(30°27'N,114°52'E)	4 934	1 089	3 048	15	10	14
b₁₄	麻城	(31°10'N,115°01'E)	4 057	1 109	2 138	9	10	8
b₁₅	景德镇	(29°17'N,117°13'E)	3 545	837	2 067	8	9	9
b₁₆	婺源	(29°25'N,117°85'E)	3 659	964	2 218	9	11	12
b₁₇	宜昌	(30°42'N,111°17'E)	4 122	1 046	1 849	12	8	9
b₁₈	南昌	(28°40'N,115°55'E)	5 879	1 264	2 403	10	12	17
b₁₉	安庆	(30°53'N,117°05'E)	3 477	1 187	2 123	9	13	10
b₂₀	随州	(31°42'N,113°22'E)	2 954	983	2 377	10	10	10
b₂₁	黄山	(30°01'N,118°01'E)	3 255	874	2 050	8	16	12
b₂₂	上饶	(25°27'N,117°58'E)	3 843	1 033	1 963	10	9	11
b₂₃	鄂州	(30°23'N,114°52'E)	6 089	922	3 089	11	14	13
b₂₄	岳阳	(29°22'N,113°06'E)	4 229	1 127	987	10	11	9

Tab.1

Fig.3

Fig.4

Tab.2

Tab.3

Tab.4

Emergency materials dispatching plan

配送中心	疫区	$e i k 1$ /辆			$e i k 2$ /辆			$e i k 3$ /辆			$Q i j k 1$ / 件	$Q i j k 2$ / 件	$Q i j k 3$ / 件
配送中心	疫区	v₁	v₂	v₃	v₁	v₂	v₃	v₁	v₂	v₃	$Q i j k 1$ / 件	$Q i j k 2$ / 件	$Q i j k 3$ / 件
b₁₄	j₁	3	5	2	1	2	1	1	0	2	3750	850	1800
b₁	j₁	3	5	4	2	0	1	1	1	0	4 250	750	1 400
b₉	j₁	4	5	5	0	1	1	0	3	0	5 000	350	1 800
b₄	j₁	1	2	4	2	0	0	1	2	0	2 200	600	2 000
b₂	j₁	2	3	5	0	2	3	0	3	1	3 300	850	2 300
b₂₃	j₁	4	5	7	1	1	1	1	2	1	5 500	650	2500
b₁₃	j₁	3	4	5	2	0	1	2	0	2	4 150	750	2 600
b₁₀	j₁	4	2	7	1	1	1	1	1	1	4 450	650	1 900
b₁₁	j₂	1	2	6	0	2	0	1	1	1	2 700	400	1 900
b₁₈	j₂	2	3	7	1	0	2	0	2	0	3 800	600	1 200
b₁₅	j₂	3	2	2	1	1	1	0	3	0	2 700	650	1 800
b₃	j₂	2	4	4	1	1	1	1	1	0	3 400	450	1400

Tab.4

Fig.5

Fig.6

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J	城市	d_jk/件
J	城市	k₁	k₂	k₃
j₁	武汉	32 538	5 423	16 269
j₂	九江	12 534	2 089	6 267