The joint location-transportation model based on grey bi-level programming for early post-earthquake relief

Yufeng Zhou; Bin Zheng; Jiafu Su; Yufeng Li

doi:10.3934/jimo.2020142

Article Contents

2022, Volume 18, Issue 1: 45-73. Doi: 10.3934/jimo.2020142

This issue Previous Article Statistical mechanics approach for steady-state analysis in M/M/s queueing system with balking Next Article Optimal investment and proportional reinsurance strategy under the mean-reverting Ornstein-Uhlenbeck process and net profit condition

The joint location-transportation model based on grey bi-level programming for early post-earthquake relief

1.
Chongqing Engineering Technology Research Center for Information Management in, Development, Chongqing Technology and Business University, Chongqing, 400067, China
2.
School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610031, China
3.
Research center for economy of upper researches of the Yangtze River, Chongqing Technology, and Business University, Chongqing, 400067, China

^* Corresponding author: Bin Zheng
^* Corresponding author: Bin Zheng

Received: April 30, 2020

Revised: June 30, 2020

Early access: September 2020

Published: January 2022

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Abstract

The initial period after the earthquake is the prime time for disaster relief. During this period, it is of great value to rationally locate the transfer facilities of relief materials and effectively arrange the transportation of relief materials. Considering the characteristics of the two-level emergency logistics system including uncertain demand, uncertain transportation time, multiple varieties of relief materials, shortage of supply, multi-transportation modes and different urgencies of relief material demand, the integrated issue with the concern of transfer facility location and relief material transportation is studied. Then, this problem is formulated as a grey mixed integer bi-level nonlinear programming in which the upper-level aims at the shortest relief material transportation time and the lower-level aims at the maximum fairness of relief material distribution. According to the characteristics of the model, a hybrid genetic algorithm is designed to solve the proposed model. Finally, a numerical simulation is carried out on the background of 5.12 Wenchuan Earthquake. In addition, the validation of the proposed model and algorithm is verified.

Keywords:

Mathematics Subject Classification: Primary: 90B50; Secondary: 90B06.

Citation:

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Figure 1. Schematic Diagram of the Post-Earthquake Emergency Logistics System

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Figure 2. Relief materials from different temporary transfer facilities

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Figure 3. Relief materials from the same temporary transfer facility and do not need waiting

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Figure 4. Relief materials from the same temporary transfer facility and need waiting

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Figure 5. Flow Chart of Genetic Algorithm

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Figure 6. Schematic diagram of chromosome coding

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Figure 7. Operational processes of decision-making in upper-level and lower-level

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Figure 8. Schematic of arithmetic crossover operator

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Figure 9. Schematic diagram of partial matching arithmetic crossover

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Figure 10. Convergence diagram of hybrid genetic algorithm

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Table 1. The amount of relief materials supplied by collection centers

Num.	Collection centers	Food(Units)	Daily necessities(Units)
Ⅰ	Chengdu Military Airport	200000	90000
Ⅱ	Shuangliu Airport	800000	100000
Ⅲ	Chengdu North Railway Station	1200000	130000

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Table 2. The amount of relief materials supplied by collection centers

Candidate temporary transfer facilities	Num	Affected area	$ T{h_j} $(tons)	Candidate temporary transfer facilities	Num.	Affected area	$ T{h_j} $(tons)
Dujiangyan	(1)	①	800	Pingwu	(10)	②	700
Maoxian	(2)	①	800	Jiangyou	(11)	②	800
Pengzhou	(3)	①	800	Deyang	(12)	②	1500
Wenchuan	(4)	①	500	Mianyang	(13)	②	1500
Jiuzhaigou	(5)	①	1000	Guanghan	(14)	②	1300
Chongzhou	(6)	①	800	Guangyuan	(15)	③	1500
Dayi	(7)	①	1200	Qingchuan	(16)	③	1000
Shifang	(8)	②	1000	Wangcang	(17)	③	1000
Beichuan	(9)	②	800	Jiange	(18)	③	1000

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Table 3. The demand for relief materials at affected points

Affected points	Num.	Affected area	Food(units)	Daily necessities(Units)
Dujiangyan	1	①	[224000, 336000]	[22400, 33600]
Guankou	2	①	[42400, 63600]	[4240, 6360]
Qingchengshan	3	①	[38880, 58320]	[3888, 5832]
Zipingpu	4	①	[35200, 52800]	[3520, 5280]
Hongkou	5	①	[38400, 57600]	[3840, 5760]
Maoxian	6	①	[173200, 259800]	[17320, 25980]
Fushun	7	①	[28800, 43200]	[2880, 4320]
Feihong	8	①	[30400, 45600]	[3040, 4560]
Heihu	9	①	[32000, 48000]	[3200, 4800]
Taiping	10	①	[25600, 38400]	[2560, 3840]
Lixian	11	①	[171200, 256800]	[17120, 25680]
Putouxiang	12	①	[25600, 38400]	[2560, 38400]
Mukaxiang	13	①	[16000, 24000]	[1600, 2400]
Tonghuaxiang	14	①	[38400, 57600]	[3840, 5760]
Wenchuan	15	①	[246800, 370200]	[24680, 37020]
Yingxiu	16	①	[32000, 48000]	[3200, 4800]
Shuimo	17	①	[28800, 43200]	[2880, 4320]
Wolong	18	①	[27200, 40800]	[2720, 4080]
Yanmeng	19	①	[27840, 41760]	[2784, 4176]
Sanjiang	20	①	[24640, 36960]	[2464, 3696]
Xiaojin	21	①	[20000, 30000]	[2000, 3000]
Heishui	22	①	[49600, 74400]	[4960, 7440]
Songpan	23	①	[19200, 28800]	[1920, 2880]
Anxian	24	②	[191600, 287400]	[19160, 28740]
Xiushui	25	②	[28480, 42720]	[2848, 4272]
Baolin	26	②	[33600, 50400]	[3360, 5040]
Gaochuan	27	②	[18240, 27360]	[1824, 2736]
Shifang	28	②	[192000, 288000]	[19200, 28800]
Luoshui	29	②	[30400, 45600]	[3040, 4560]
Shuangsheng	30	②	[41600, 62400]	[4160, 6240]
Yinghua	31	②	[38400, 57600]	[3840, 5760]
Mianzhu	32	②	[232400, 348600]	[23240, 34860]
Jiannan	33	②	[28160, 42240]	[2816, 4224]
Mianyuan	34	②	[24960, 37440]	[2496, 3744]
Hanwang	35	②	[21760, 32640]	[2176, 3264]
Beichuan	36	②	[242800, 364200]	[24280, 36420]
Yong'an	37	②	[31040, 46560]	[3104, 4656]
Yongchang	38	②	[33600, 50400]	[3360, 5040]
Kaiping	39	②	[30400, 45600]	[3040, 4560]
Luojiang	40	②	[69600, 104400]	[6960, 10440]
Zhongjiang	41	②	[84800, 127200]	[8480, 12720]
Santai	42	②	[109600, 164400]	[10960, 16440]
Yanting	43	②	[110000, 165000]	[11000, 16500]
Zitong	44	②	[125200, 187800]	[12520, 18780]
Deyang	45	②	[173760, 260640]	[17376, 26064]
Mianyang	46	②	[184000, 276000]	[18400, 27600]
Guangyuan	47	③	[75040, 112560]	[7504, 11256]
Qingchuan	48	③	[216400, 324600]	[21640, 32460]
Walixiang	49	③	[32960, 49440]	[3296, 4944]
Banqiaoxiang	50	③	[39040, 58560]	[3904, 5856]
Qimaxiang	51	③	[36000, 54000]	[3600, 5400]
Yingpanxiang	52	③	[32800, 49200]	[3280, 4920]
Lizhou	53	③	[71200, 106800]	[7120, 10680]
Chaotian	54	③	[66400, 99600]	[6640, 9960]
Cangxi	55	③	[125200, 187800]	[12520, 18780]
Jiange	56	③	[62000, 93000]	[6200, 9300]
Yuanba	57	③	[71200, 106800]	[7120, 10680]

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Table 4. Relevant parameters in upper-level transportation

Num.	Transportation modes	$ T_{ijm}^0 $	Departure point($ i \in SN $)	Destination point($ j \in EN $)	$ {t_{ijm}}( \otimes ) $	$ ca{p_{ijm}} $	$ I{T_{ijm}} $
1	HC	8	2	2	0.15	100	0
2	HC	8	2	4	0.18	100	0
3	HC	8	2	9	0.43	100	0
4	HC	8	2	16	0.47	100	0
5	R	8.2	1	5	0.32	150	6
6	R	9.3	1	13	0.32	150	6
7	R	9	1	14	0.23	170	6
8	R	10.2	1	15	0.42	170	6
9	A	8.2	3	11	3	800	4
10	A	8.8	3	12	0.9	800	4
11	A	9	3	13	1.8	800	4
12	A	8.5	3	14	0.6	800	4
13	A	8.7	3	15	6.6	800	4
14	HC	8	1	1	[1.60, 2.40]	80	0
15	HC	8	1	3	[1.50, 2.26]	80	0
16	HC	8	1	12	[1.95, 2.93]	80	0
17	HC	8	1	13	[3.01, 4.51]	80	0
18	HC	8	1	11	[5.09, 7.63]	80	0
19	HC	8	1	8	[1.95, 2.93]	80	0
20	HC	8	1	14	[2.45, 3.67]	90	0
21	HC	8	1	15	[6.77, 10.15]	90	0
22	HC	8	1	16	[9.92, 14.88]	90	0
23	HC	8	1	18	[6.53, 9.79]	90	0
24	HC	8	1	5	[18.88, 28.32]	90	0
25	HC	8	1	6	[2.08, 3.12]	90	0
26	HC	8	1	7	[2.08, 3.12]	90	0
27	HC	8	1	10	[13.44, 20.16]	90	0
28	HC	8	1	17	[9.68, 14.52]	85	0
29	HC	8	2	1	[1.60, 2.40]	85	0
30	HC	8	2	3	[1.52, 2.28]	85	0
31	HC	8	2	12	[1.92, 2.88]	85	0
32	HC	8	2	13	[3.04, 4.56]	85	0
33	HC	8	2	11	[5.28, 7.92]	85	0
34	HC	8	2	8	[2.27, 3.41]	85	0
35	HC	8	2	14	[2.77, 4.15]	85	0
36	HC	8	2	15	[7.09, 10.63]	85	0
37	HC	8	2	16	[10.24, 15.36]	85	0
38	HC	8	2	18	[6.85, 10.27]	85	0
39	HC	8	2	5	[19.20, 28.80]	80	0
40	HC	8	2	6	[2.40, 3.60]	80	0
41	HC	8	2	7	[2.40, 3.60]	80	0
42	HC	8	2	10	[13.76, 20.64]	80	0
43	HC	8	2	17	[10.00, 15.00]	80	0
44	HC	8	3	1	[1.36, 2.04]	90	0
45	HC	8	3	3	[1.26, 1.90]	90	0
46	HC	8	3	12	[1.71, 2.57]	90	0
47	HC	8	3	13	[2.77, 4.15]	90	0
48	HC	8	3	11	[4.85, 7.27]	90	0
49	HC	8	3	8	[1.71, 2.57]	90	0
50	HC	8	3	14	[2.21, 3.31]	90	0
51	HC	8	3	15	[6.53, 9.79]	90	0
52	HC	8	3	16	[9.68, 14.52]	90	0
53	HC	8	3	18	[6.29, 9.43]	85	0
54	HC	8	3	5	[18.64, 27.96]	85	0
55	HC	8	3	6	[1.84, 2.76]	85	0
56	HC	8	3	7	[1.84, 2.76]	85	0
57	HC	8	3	10	[13.20, 19.80]	85	0
58	HC	8	3	17	[9.44, 14.16]	85	0

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Table 5. Relevant parameters in lower-level transportation

	Depart	Destin				Depart	Destin
	ure	ation				ure	ation
Num.	point	point	$ {t'_{jk}}( \otimes ) $	$ ca{p'_{jk}} $	Num.	point	point	$ {t'_{jk}}( \otimes ) $	$ ca{p'_{jk}} $
	($ j \in $	($ k \in $				($ j \in $	($ k \in $
	$ EN $)	$ DN $)				$ EN $)	$ DN $)
1	1	1	0	40	124	10	45	[9.36, 14.04]	38
2	1	2	[0.32, 0.48]	40	125	10	46	[8.69, 13.03]	38
3	1	3	[0.70, 1.06]	40	126	11	24	[1.89, 2.83]	38
4	1	4	[0.96, 1.44]	40	127	11	25	[2.45, 3.67]	38
5	1	5	[1.41, 2.11]	40	128	11	26	[1.89, 2.83]	39
6	1	21	[10.40, 15.60]	38	129	11	27	[3.81, 5.71]	39
7	2	6	[0.00, 0.00]	38	130	11	28	[2.77, 4.15]	39
8	2	7	[0.22, 0.34]	38	131	11	29	[3.01, 4.51]	39
9	2	8	[0.29, 0.43]	38	132	11	30	[2.64, 3.96]	39
10	2	9	[0.42, 0.62]	38	133	11	31	[3.36, 5.04]	39
11	2	10	[0.18, 0.26]	38	134	11	32	[2.48, 3.72]	39
12	2	11	[6.56, 9.84]	35	135	11	33	[2.56, 3.84]	39
13	2	12	[7.01, 10.51]	35	136	11	34	[2.75, 4.13]	39
14	2	13	[4.96, 7.44]	35	137	11	35	[2.88, 4.32]	39
15	2	14	[4.16, 6.24]	35	138	11	40	[2.40, 3.60]	39
16	2	15	[11.06, 16.58]	35	139	11	41	[4.00, 6.00]	40
17	2	16	[7.86, 11.78]	35	140	11	42	[2.48, 3.72]	40
18	2	17	[9.78, 14.66]	35	141	11	43	[4.19, 6.29]	40
19	2	18	[9.58, 14.38]	43	142	11	44	[3.01, 4.51]	40
20	2	19	[11.38, 17.06]	43	143	11	45	[2.40, 3.60]	40
21	2	20	[10.69, 16.03]	43	144	11	46	[1.65, 2.47]	38
22	2	22	[7.52, 11.28]	43	145	12	24	[1.63, 2.45]	38
23	2	23	[7.22, 10.82]	43	146	12	25	[2.24, 3.36]	38
24	3	1	[1.33, 1.99]	43	147	12	26	[1.63, 2.45]	38
25	3	2	[1.65, 2.47]	43	148	12	27	[3.60, 5.40]	38
26	3	3	[2.13, 3.19]	43	149	12	28	[1.09, 1.63]	38
27	3	4	[2.13, 3.19]	43	150	12	29	[1.60, 2.40]	35
28	3	5	[2.67, 4.01]	43	151	12	30	[1.12, 1.68]	35
29	3	21	[11.36, 17.04]	38	152	12	31	[2.00, 3.00]	35
30	4	6	[2.61, 3.91]	38	153	12	32	[1.44, 2.16]	35
31	4	7	[10.61, 15.91]	38	154	12	33	[1.60, 2.40]	35
32	4	8	[4.16, 6.24]	38	155	12	34	[2.08, 3.12]	35
33	4	9	[4.53, 6.79]	38	156	12	35	[1.84, 2.76]	35
34	4	10	[4.35, 6.53]	38	157	12	40	[0.93, 1.39]	43
35	4	11	[5.04, 7.56]	38	158	12	41	[2.03, 3.05]	43
36	4	12	[5.20, 7.80]	39	159	12	42	[2.85, 4.27]	43
37	4	13	[3.60, 5.40]	39	160	12	43	[4.67, 7.01]	43
38	4	14	[3.76, 5.64]	39	161	12	44	[3.52, 5.28]	43
39	4	15	0	39	162	12	45	0	43
40	4	16	[4.24, 6.36]	39	163	12	46	[1.55, 2.33]	43
41	4	17	[5.12, 7.68]	39	164	13	24	[0.67, 1.01]	43
42	4	18	[5.28, 7.92]	39	165	13	25	[1.23, 1.85]	43
43	4	19	[0.32, 0.48]	39	166	13	26	[1.01, 1.51]	43
44	4	20	[5.76, 8.64]	39	167	13	27	[2.59, 3.89]	38
45	4	22	[9.84, 14.76]	39	168	13	28	[1.81, 2.71]	38
46	4	23	[9.60, 14.40]	39	169	13	29	[2.08, 3.12]	38
47	5	1	[18.61, 27.91]	40	170	13	30	[1.68, 2.52]	38
48	5	2	[18.85, 28.27]	40	171	13	31	[2.40, 3.60]	38
49	5	3	[18.99, 28.49]	40	172	13	32	[1.52, 2.28]	38
50	5	4	[19.73, 29.59]	40	173	13	33	[1.68, 2.52]	38
51	5	5	[19.78, 29.66]	40	174	13	34	[1.52, 2.28]	39
52	5	6	[15.20, 22.80]	38	175	13	35	[1.95, 2.93]	39
53	5	7	[22.21, 33.31]	38	176	13	40	[0.99, 1.49]	39
54	5	8	[13.38, 20.06]	38	177	13	41	[2.88, 4.32]	39
55	5	9	[13.20, 19.80]	38	178	13	42	[2.08, 3.12]	39
56	5	10	[13.14, 19.70]	38	179	13	43	[3.81, 5.71]	39
57	5	11	[21.44, 32.16]	38	180	13	44	[2.56, 3.84]	39
58	5	12	[22.72, 34.08]	35	181	13	45	[1.55, 2.33]	39
59	5	13	[22.56, 33.84]	35	182	13	46	0	39
60	5	14	[22.72, 34.08]	35	183	14	24	[2.08, 3.12]	39
61	5	15	[17.60, 26.40]	35	184	14	25	[2.64, 3.96]	39
62	5	16	[21.12, 31.68]	35	185	14	26	[2.00, 3.00]	40
63	5	17	[22.72, 34.08]	35	186	14	27	[4.00, 6.00]	40
64	5	18	[22.56, 33.84]	35	187	14	28	[1.04, 1.56]	40
65	5	19	[19.04, 28.56]	43	188	14	29	[1.49, 2.23]	40
66	5	20	[24.32, 36.48]	43	189	14	30	[1.15, 1.73]	40
67	5	21	[16.00, 24.00]	43	190	14	31	[1.87, 2.81]	38
68	5	22	[17.92, 26.88]	43	191	14	32	[1.68, 2.52]	38
69	5	23	[8.00, 12.00]	43	192	14	33	[1.84, 2.76]	38
70	6	1	[1.81, 2.71]	43	193	14	34	[2.53, 3.79]	38
71	6	2	[1.92, 2.88]	43	194	14	35	[2.11, 3.17]	38
72	6	3	[1.39, 2.09]	43	195	14	40	[1.55, 2.33]	38
73	6	4	[2.40, 3.60]	43	196	14	41	[2.61, 3.91]	35
74	6	5	[2.99, 4.49]	43	197	14	42	[3.20, 4.80]	35
75	6	21	[11.44, 17.16]	38	198	14	43	[5.04, 7.56]	35
76	6	22	[16.00, 24.00]	38	199	14	44	[3.89, 5.83]	35
77	6	23	[16.00, 24.00]	38	200	14	45	[0.91, 1.37]	35
78	7	1	[2.03, 3.05]	38	201	14	46	[1.92, 2.88]	35
79	7	2	[2.16, 3.24]	38	202	15	47	0	35
80	7	3	[1.60, 2.40]	38	203	15	48	[5.12, 7.68]	43
81	7	4	[2.67, 4.01]	38	204	15	49	[5.39, 8.09]	43
82	7	5	[3.20, 4.80]	39	205	15	50	[4.40, 6.60]	43
83	7	21	[11.68, 17.52]	39	206	15	51	[4.59, 6.89]	43
84	8	24	[1.92, 2.88]	39	207	15	52	[3.63, 5.45]	43
85	8	25	[2.26, 3.38]	39	208	15	53	[0.08, 0.12]	43
86	8	26	[1.33, 1.99]	39	209	15	54	[1.84, 2.76]	43
87	8	27	[3.30, 4.94]	39	210	15	55	[3.57, 5.35]	43
88	8	28	0	39	211	15	56	[1.28, 1.92]	43
89	8	29	[0.83, 1.25]	39	212	15	57	[1.17, 1.75]	43
90	8	30	[0.48, 0.72]	39	213	16	47	[0.37, 0.55]	38
91	8	31	[1.20, 1.80]	39	214	16	48	0	38
92	8	32	[1.01, 1.51]	39	215	16	49	[0.88, 1.32]	38
93	8	33	[1.17, 1.75]	40	216	16	50	[0.72, 1.08]	38
94	8	34	[1.79, 2.69]	40	217	16	51	[1.01, 1.51]	38
95	8	35	[1.41, 2.11]	40	218	16	52	[1.60, 2.40]	38
96	8	40	[1.94, 2.90]	40	219	16	53	[5.09, 7.63]	38
97	8	41	[3.31, 4.97]	40	220	16	54	[6.66, 9.98]	39
98	8	42	[3.07, 4.61]	38	221	16	55	[6.75, 10.13]	39
99	8	43	[4.88, 7.32]	38	222	16	56	[4.53, 6.79]	39
100	8	44	[3.73, 5.59]	38	223	16	57	[5.60, 8.40]	39
101	8	45	[1.36, 2.04]	38	224	17	47	[2.16, 3.24]	39
102	8	46	[1.76, 2.64]	38	225	17	48	[6.48, 9.72]	39
103	9	36	[1.60, 2.40]	38	226	17	49	[6.56, 9.84]	39
104	9	37	[0.93, 1.39]	35	227	17	50	[5.79, 8.69]	39
105	9	38	[1.55, 2.33]	35	228	17	51	[5.97, 8.95]	39
106	9	39	[2.03, 3.05]	35	229	17	52	[5.01, 7.51]	39
107	10	24	[8.67, 13.01]	35	230	17	53	[2.29, 3.43]	39
108	10	25	[9.44, 14.16]	35	231	17	54	[4.00, 6.00]	40
109	10	26	[8.85, 13.27]	35	232	17	55	[3.55, 5.33]	40
110	10	27	[10.80, 16.20]	35	233	17	56	[2.83, 4.25]	40
111	10	28	[9.68, 14.52]	43	234	17	57	[1.20, 1.80]	40
112	10	28	[9.92, 14.88]	43	235	18	47	[1.49, 2.23]	40
113	10	30	[9.55, 14.33]	43	236	18	48	[4.53, 6.79]	38
114	10	31	[10.27, 15.41]	43	237	18	49	[4.40, 6.60]	38
115	10	32	[9.39, 14.09]	43	238	18	50	[4.13, 6.19]	38
116	10	33	[9.52, 14.28]	43	239	18	51	[4.32, 6.48]	38
117	10	34	[9.71, 14.57]	43	240	18	52	[3.36, 5.04]	38
118	10	35	[9.79, 14.69]	43	241	18	53	[1.47, 2.21]	38
119	10	40	[8.80, 13.20]	43	242	18	54	[2.82, 4.22]	35
120	10	41	[11.01, 16.51]	43	243	18	55	[2.69, 4.03]	35
121	10	42	[9.33, 13.99]	38	244	18	56	0	35
122	10	43	[11.15, 16.73]	38	245	18	57	[1.55, 2.33]	35
123	10	44	[9.89, 14.83]	38	-	-	-	-	-

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Table 6. Transportation of relief materials from collection centers to opened temporary transfer facilities

Collection centers	Opened temporary transfer facility	Transportation mode	Food (units)	Collection centers	Opened temporary transfer facility	Transportation mode	Daily necessities (units)
	facility				facility
Ⅱ	(1)	H	54849	Ⅰ	(1)	H	15869
Ⅲ	(1)	H	71647	Ⅱ	(12)	H	13904
Ⅲ	(17)	H	80471	Ⅰ	(16)	H	13037
Ⅲ	(12)	A	384669	Ⅰ	(17)	H	9487
Ⅲ	(13)	A	304150	Ⅲ	(12)	A	49057
Ⅲ	(14)	A	153849	Ⅲ	(13)	A	80943
Ⅲ	(15)	A	205214	Ⅰ	(14)	R	25568
Ⅰ	(13)	R	182926	Ⅰ	(15)	R	26039
Ⅰ	(15)	R	17074	Ⅱ	(2)	HC	12652
Ⅱ	(2)	HC	113786	Ⅱ	(4)	HC	18159
Ⅱ	(4)	HC	80529	Ⅱ	(9)	HC	5805
Ⅱ	(9)	HC	77345	Ⅱ	(16)	HC	11686
Ⅱ	(6)	HC	107638	-	-	-	-

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Table 7. Transportation of relief materials from opened temporary transfer facilities to affected points

Opened temporary transfer facility	Affected point	Food (units)	Opened temporary transfer facility	Affected point	Daily necessities (units)
(1)	1	71036	(1)	1	8753
(1)	2	13446	(1)	2	1657
(1)	3	12330	(1)	3	1519
(1)	4	11163	(1)	4	1376
(1)	5	12178	(1)	5	1501
(2)	6	54926	(2)	6	6768
(2)	7	9133	(2)	7	1126
(2)	8	9641	(2)	8	1188
(2)	9	10148	(2)	9	1251
(2)	10	8119	(2)	10	1001
(4)	11	54292	(4)	11	6690
(4)	12	8119	(4)	12	1001
(4)	13	5074	(4)	13	626
(4)	14	12178	(4)	14	1501
(4)	15	78267	(4)	15	9644
(4)	16	10148	(4)	16	1251
(4)	17	9133	(4)	17	1125
(4)	18	8626	(4)	18	1063
(4)	19	8829	(4)	19	1088
(4)	20	7814	(4)	20	963
(1)	21	6343	(1)	21	1063
(2)	22	15730	(2)	22	1938
(2)	23	6089	(2)	23	719
(13)	24	113026	(13)	24	18783
(13)	25	16801	(13)	25	2792
(13)	26	19821	(13)	26	3294
(13)	27	10760	(13)	27	1789
(14)	28	113262	(14)	28	18822
(14)	29	17934	(14)	29	2981
(12)	30	24541	(12)	30	4078
(14)	31	22653	(14)	31	3765
(12)	32	137095	(12)	32	22782
(12)	33	16612	(12)	33	2761
(13)	34	14725	(13)	34	2447
(12)	35	12837	(12)	35	2134
(9)	36	143230	(9)	36	23802
(9)	37	18311	(9)	37	3043
(9)	38	19821	(9)	38	3294
(9)	39	17934	(9)	39	2981
(12)	40	41058	(12)	40	6643
(12)	41	50024	(12)	41	7529
(13)	42	64654	(13)	42	10744
(13)	43	64890	(13)	43	10783
(13)	44	73856	(13)	44	12273
(12)	45	102502	(12)	45	17034
(13)	46	108543	(13)	46	18038
(15)	47	48232	(15)	47	5687
(16)	48	139090	(16)	48	16399
(16)	49	21185	(16)	49	2498
(16)	50	25093	(16)	50	2959
(16)	51	23139	(16)	51	2728
(16)	52	21082	(16)	52	2486
(15)	53	45764	(15)	53	5396
(15)	54	42678	(15)	54	4862
(17)	55	80471	(17)	55	9487
(15)	56	39850	(15)	56	4698
(15)	57	45764	(15)	57	5396

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Table 8. Transportation of relief materials from opened temporary transfer facilities to affected points

Affected point	$ {\tilde T_{kc}}( \otimes ) $(hours)		Affected point	$ {\tilde T_{kc}}( \otimes ) $(hours)
Affected point	food	Daily necessities	Affected point	food	Daily necessities
1	10	10	30	11.1	11.8
2	10.4	10.4	31	11.44	11.57
3	10.88	10.88	32	22.3	23
4	11.2	11.2	33	11.7	12.4
5	11.76	11.76	34	12.7	12.7
6	8.15	16.3	35	12	12.7
7	8.43	16.58	36	30.86	39.29
8	8.51	16.66	37	18.02	26.45
9	8.67	16.82	38	18.8	27.23
10	8.37	16.52	39	19.4	27.83
11	35.26	22.66	40	10.86	11.56
12	22.86	22.86	41	12.24	12.94
13	20.86	20.86	42	18.6	18.6
14	21.06	21.06	43	25.08	25.08
15	16.36	16.36	44	20.4	20.4
16	21.66	21.66	45	9.7	10.4
17	22.76	22.76	46	10.8	10.8
18	22.96	22.96	47	15.3	10.62
19	16.76	16.76	48	16.94	20.4
20	23.56	23.56	49	18.04	21.5
21	23	23	50	17.84	21.3
22	17.55	25.7	51	18.2	21.66
23	17.17	25.32	52	18.94	22.4
24	15	15	53	15.4	10.72
25	12.34	12.34	54	17.6	12.92
26	12.06	12.06	55	33.12	33.42
27	14.04	14.04	56	16.9	12.22
28	15.6	15.73	57	16.76	12.08
29	10.96	11.09	-	-	-

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Table 9. Sensitivity analysis of $ P $

P	Amount of opened facilities			Opened temporary transfer facilities (the optimal solution)	Objective function value			Running time(s)
P	MIN	MAX	AVG	Opened temporary transfer facilities (the optimal solution)	Optimal	AVG	SD	AVG	minimum	SD
4	4	4	4	(5), (9), (12), (15)	13273776.83	14868939.06	1451416.62	53.48	16.16	42.31
5	5	5	5	(2), (3), (9), (13), (15)	8848462.92	9220754.33	302415.93	207.17	165.37	25.97
6	6	6	6	(1), (4), (9), (12), (13), (15)	6853198.43	7271162.90	290586.68	244.28	183.08	36.24
7	7	7	7	(1), (2), (4), (9), (13), (14), (15)	5781612.49	6227580.83	273625.21	257.40	234.93	12.80
8	8	8	8	(1), (2), (4), (9), (12), (13), (15), (16)	5072974.53	5295173.25	224424.74	244.43	178.19	49.48
9	9	9	9	(1), (2), (4), (9), (13), (14), (15), (16), (17)	4858475.72	5124041.30	150278.08	244.43	178.19	49.48
10	9	10	9.8	(1), (2), (4), (9), (12), (13), (14), (15), (16), (17)	4782950.76	4924828.55	113448.04	233.81	193.92	26.61
11	11	11	11	(1), (2), (3), (4), (9), (12), (13), (14), (15), (16), (17)	4778328.99	4925983.68	107442.10	228.31	213.40	16.51
12	11	12	11.2	(1), (2), (4), (6), (9), (12), (13), (14), (15), (16), (18)	4776395.25	4878544.65	110360.54	232.67	198.17	27.35
13	12	13	12.4	(1), (2), (3), (4), (5), (9), (10), (12), (13), (14), (15), (16), (18)	4783358.20	4892302.40	102522.06	233.92	221.46	7.82
14	11	14	12.5	(1), (2), (4), (6), (9), (12), (13), (14), (15), (16), (17)	4757147.13	4856777.97	106004.73	237.36	224.33	12.72

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Table 10. Performance comparison between genetic algorithm (GA) and immune optimization algorithm (IOA)

$ P $	Algorithm	$ Z_{_1}^* $	$ {\bar Z_1} $	Time(AVG)
9	GA	4858475.72	5124041.30	244.43
9	IOA	4936050.86	5244041.02	250.67
10	GA	4782950.76	4924828.55	233.81
10	IOA	4821963.21	4959828.55	230.14
11	GA	4778328.99	4925983.68	228.31
11	IOA	4790375.49	4965983.68	225.63
12	GA	4776395.25	4878544.65	232.67
12	IOA	4795203.36	4879121.35	229.43
13	GA	4783358.20	4892302.40	233.92
13	IOA	4790522.90	4898580.12	228.45
16	GA	4757147.13	4856777.97	237.36
16	IOA	4767658.14	4848676.16	233.97

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References

[1]	A. Afshar and A. Haghani, Modeling integrated supply chain logistics in real-time large-scale disaster relief operations, Socio-Economic Plan. Sci., 46 (2012), 327-338. doi: 10.1016/j.seps.2011.12.003.
[2]	J. F. Bard, Some properties of the bilevel programming problem, J. Optim. Theory Appl., 68 (1991), 371-378. doi: 10.1007/BF00941574.
[3]	V. Bélanger, A. Ruiz and P. Soriano, Recent optimization models and trends in location, relocation, and dispatching of emergency medical vehicles, European J. Oper. Res., 272 (2019), 1-23. doi: 10.1016/j.ejor.2018.02.055.
[4]	C. Blair, The computational complexity of multi-level linear programs, Ann. Oper. Res., 34 (1992), 13-19. doi: 10.1007/BF02098170.
[5]	A. Bozorgi-Amiri and M. Khorsi, A dynamic multi-objective location-routing model for relief logistic planning under uncertainty on demand, travel time, and cost parameters, The International Journal of Advanced Manufacturing Technology, 85 (2016), 1633-1648.
[6]	C. J. Cao, C. D. Li, Q. Yang, Y. Liu and T. Qu, A novel multi-objective programming model of relief distribution for sustainable disaster supply chain in large-scale natural disasters, J. Cleaner Production, 174 (2018), 1422-1435. doi: 10.1016/j.jclepro.2017.11.037.
[7]	A. Y. Chen and T. Y. Yu, Network based temporary facility location for the Emergency Medical Services considering the disaster induced demand and the transportation infrastructure in disaster response, Transport Res. B. Meth., 91 (2016), 408-423. doi: 10.1016/j.trb.2016.06.004.
[8]	Y. Dai, Z. J. Ma, D. L. Zhu and T. Fang, Fuzzy dynamic location-routing problem in post-earthquake delivery of relief materials, Chinese Journal of Management Science, 15 (2012), 60-70.
[9]	X. T. Deng, Complexity issues in bi-level linear programming, in Multilevel Optimization: Algorithms and Applications, Vol. 20, Kluwer Acad. Publ., Dordrecht, 1998,149–164. doi: 10.1007/978-1-4613-0307-7_6.
[10]	M. Haghi, S. M. T. F. Ghomi and F. Jolai, Developing a robust multi-objective model for pre/post disaster times under uncertainty in demand and resource, J. Cleaner Production, 154 (2017), 188-202. doi: 10.1016/j.jclepro.2017.03.102.
[11]	H. Hu, X. Li, Y. Y. Zhang, C. J. Shang and S. C. Zhang, Multi-objective location-routing model for hazardous material logistics with traffic restriction constraint in inter-city roads, Comput. Ind. Eng., 128 (2019), 861-876. doi: 10.1016/j.cie.2018.10.044.
[12]	J. Jian, Y. Zhang, L. Jiang and J. Su, Coordination of supply chains with competing manufacturers considering fairness concerns, Complexity, 2020 (2020), 4372603. doi: 10.1155/2020/4372603.
[13]	S. Li and K. L. Teo, Post-disaster multi-period road network repair: Work scheduling and relief logistics optimization, Ann. Oper. Res., 283 (2019), 1345-1385. doi: 10.1007/s10479-018-3037-2.
[14]	S. Li, Z. J. Ma and K. L. Teo, A new model for road network repair after natural disaster: Integrating logistics support scheduling with repair crew scheduling and routing activities, Comput. Ind. Eng., 145 (2020), 106506.
[15]	S. L. Li, Z. J. Ma, B. Zheng and Y. Dai, Fuzzy multi-objective location-multimodal transportation problem for relief delivery during the initial post-earthquake period, Chinese Journal of Management Science, 21 (2013), 144-151.
[16]	C. S. Liu, L. Luo, X. C. Zhou and F. H. Huang, Collaborative decision-making of relief allocation-transportation in early post-earthquake: Considering both fairness and efficiency, Control and Decision, 33 (2018), 2057-2063.
[17]	C. S. Liu, G. Kou, Y. Peng and F. E. Alsaadi, Location-routing problem for relief distribution in the early post-earthquake stage from the perspective of fairness, Sustainability, 11 (2019), 3420. doi: 10.3390/su11123420.
[18]	R. Lotfian and M. Najafi, Optimal location of emergency stations in underground mine networks using a multiobjective mathematical model, Injury Prevention, 25 (2019), 264-272. doi: 10.1136/injuryprev-2017-042657.
[19]	H. M. Rizeei, B. Pradhan and M. A. Saharkhiz, Allocation of emergency response centres in response to pluvial flooding-prone demand points using integrated multiple layer perceptron and maximum coverage location problem models, Int. J. Disast. Risk. Red., 38 (2019), 101205. doi: 10.1016/j.ijdrr.2019.101205.
[20]	A. S. Safaei, S. Farsad and M. M. Paydar, Robust bi-level optimization of relief logistics operations, Appl. Math. Model., 56 (2018), 359-380. doi: 10.1016/j.apm.2017.12.003.
[21]	A. S. Safaei, S. Farsad and M. M. Paydar, Emergency logistics planning under supply risk and demand uncertainty, Oper. Res., 20 (2020), 1437-1460. doi: 10.1007/s12351-018-0376-3.
[22]	F. S. Salman and E. Yücel, Emergency facility location under random network damage: Insights from the Istanbul case, Comput. Oper. Res., 62 (2015), 266-281. doi: 10.1016/j.cor.2014.07.015.
[23]	J. Su, Q. Bai, S. Sindakis, X Zhang and T Yang, Vulnerability of multinational corporation knowledge network facing resource loss, Management Decision, 2020. doi: 10.1108/MD-02-2019-0227.
[24]	B. Vahdani, D. Veysmoradi, N. Shekari and S. M. Mousavi, Multi-objective, multi-period location-routing model to distribute relief after earthquake by considering emergency roadway repair, Neural Comput. Appl., 30 (2018), 835-854. doi: 10.1007/s00521-016-2696-7.
[25]	B. Vahdani, D. Veysmoradi, F. Noori and F. Mansour, Two-stage multi-objective location-routing-inventory model for humanitarian logistics network design under uncertainty, Int. J. Disast. Risk. Re., 27 (2018), 290-306.
[26]	H. J. Wang, L. J. Du and S. H. Ma, Multi-objective open location-routing model with split delivery for optimized relief distribution in post-earthquake, Transport Research Part E: Logistics and Transportation Review, 69 (2014), 160-179. doi: 10.1016/j.tre.2014.06.006.
[27]	J. Xu, Z. Wang, M. Zhang and Y. Tu, A new model for a 72-h post-earthquake emergency logistics location-routing problem under a random fuzzy environment, Transportation Letters, 8 (2016), 270-285. doi: 10.1080/19427867.2015.1126064.
[28]	M. Yahyaei and A. Bozorgi-Amiri, Robust reliable humanitarian relief network design: An integration of shelter and supply facility location, Ann. Oper. Res., 283 (2019), 897-916. doi: 10.1007/s10479-018-2758-6.
[29]	W. Yi and L. Özdamar, A dynamic logistics coordination model for evacuation and support in disaster response activities, European J. Oper. Res., 179 (2007), 1177-1193. doi: 10.1016/j.ejor.2005.03.077.
[30]	B. Zeng, M. Tong and X. Ma, A new-structure grey Verhulst model: Development and performance comparison, Appl. Math. Model., 81 (2020), 522-537. doi: 10.1016/j.apm.2020.01.014.
[31]	B. Zeng, M. Zhou, X. Liu and and Z. Zhang, Application of a new grey prediction model and grey average weakening buffer operator to forecast China's shale gas output, Energy Reports, 6 (2020), 1608-1618.
[32]	S. Zhang and H. Yi, Emergency material transportation considering the impact of secondary disasters, in Proceedings of the 2019 10th International Conference on E-business, Management and Economics, 2019,279–285. doi: 10.1145/3345035.3345041.
[33]	S. W. Zhang, H. X. Guo, K. J. Zhu, S. W. Yu and J. L. Li, Multistage assignment optimization for emergency rescue teams in the disaster chain, Knowledge-Based Systems, 137 (2017), 123-137. doi: 10.1016/j.knosys.2017.09.024.
[34]	B. Zheng, Z. J. Ma and Y. F. Zhou, Bi-level model for dynamic location-transportation problem for post earthquake relief distribution, J. Systems & Management, 26 (2017), 326-337.
[35]	Y. Zhou and N. Chen, The LAP under facility disruptions during early post-earthquake rescue using PSO-GA hybrid algorithm, Fresen. Environ. Bull., 28 (2019), 9906-9914.
[36]	Y. F. Zhou, H. X. Yu, Z. Li and J. F. Su, Robust optimization of a distribution network location-routing problem under carbon trading policies, IEEE Access, 8 (2020), 46288-46306. doi: 10.1109/ACCESS.2020.2979259.
[37]	Y. Zhou, L. Yufeng and L. Zhi, A grey target group decision method with dual hesitant fuzzy information considering decision-maker's loss aversion, Sci. Programming, 2020 (2020), 8930387. doi: 10.1155/2020/8930387.