Facility location of material reserve bases for large railway projects under uncertainty

doi:10.16265/j.cnki.issn1003-3033.2024.06.0814

Abstract

Abstract:

In order to improve the reliability of the logistics facility network of railway construction projects in complex environments, scenario reduction techniques were used to generate a minimum subset of disruption scenarios and their disruption probabilities to describe the disruption scenarios of transport channels. The polyhedral uncertainty sets were used to describe the uncertainty of logistics demand. To minimize the combined costs of transport, construction, operation and penalty costs, a two-stage stochastic and robust optimisation technique was applied to construct an uncertainty optimisation model for the location of material reserves bases. The model was solved based on a C&CG algorithm. The validity of the model and the algorithm was verified by taking a C railway construction project in a complex environment as an example. The results show that the cost variation coefficient of the model-acquired solutions is 4.3% of the traditional model in the random disruption scenario, and the cost fluctuation of the model-acquired solutions can be up to 38% of that of the traditional model in the extreme demand fluctuation. The two-stage uncertainty optimisation model given in this paper can effectively reduce the cost variation of the logistics facility network resulting from the disruption of transport channels and demand fluctuations.

Key words: railway projects, material reserve bases, facility location, engineering logistics, scenario reduction, robust optimization, column and constraint generation (C&CG) algorithm

CLC Number:

X948

ZHANG Jin, YANG Wenguang, SUN Wenjie, SHEN Hao, HONG Zhichao, LI Guoqi. Facility location of material reserve bases for large railway projects under uncertainty[J]. China Safety Science Journal, 2024, 34(6): 197-206.

Figures/Tables 10

Fig.1

Table 1

Description of parameters

类型	符号	含义
变量	$x p t$	t阶段内经运输通道p运输至施工点的物资量
	$H t i$	是否在t阶段内使用物资集散中心i,若使用为1,否则为0
	$W t j$	是否在t阶段内使用物资储备点j,若使用为1,否则为0
	$δ t k$	施工点k在t阶段内未满足的需求量
参数	$B p s$	在中断情景s下,运输通道p是否中断,若中断则为0,否则为1
	$q s$	情景s发生的概率
	$d t k$	t阶段内施工点k的需求量
	cap_j	物资储备点j的容量
	$c p$	p路经的运输费用
	$f j$	j点修建物资储备基地的固定费用
	$c δ$	施工点未满足需求量的惩罚成本
	$c j$	物资储备基地j的单位时间运营成本
	$r t$	t阶段包含的单位时间数量
集合	$i ∈ I$	物流网络中可用的所有物资集散中心的集合
	$j ∈ J$	物流网络中可用的所有的物资储备基地集合
	$k ∈ K$	施工点的集合
	$s ∈ S$	中断情景的集合
	$t ∈ T$	施工阶段的集合
	$p ∈ P$	运输路径的集合
	$P k$	运输至k施工点的所有运输路径集合
	$P j$	经过j物资储备基地的所有运输路径集合
	$P i$	由i物资集散中心发出的所有运输路径集合

Table 1

Table 2

Parameter distribution information

参数	随机分布	参数	随机分布
$d ¯ t k$	$U (0,100)$	cap_j	$U (200,100)$
$d ⌢ t k$	$d ¯ t k / 2$	$f j$	$U (1000,5000)$
$c p$	$U (20,30)$	$c j$	$U (500,1000)$

Table 2

Table 3

Table 4

Table 5

Different model sitting schemes

阶段	模型
阶段	$P (Ⅰ)$	$P (Ⅱ)$	$P (Ⅳ) (θ = 0.1)$	$P (Ⅳ) (θ = 0.3)$	$P (Ⅳ) (θ = 0.5)$
1	j₃, j₁₁	j₂,j₅,j₁₁	j₂,j₅, $j 1 0$	j₂,j₅,j₁₁	j₂,j₄,j₅,j₁₁
2	j₃, j₁₁	j₂,j₅,j₁₁	j₂,j₅, $j 1 0$	j₂,j₅,j₁₁	j₂,j₄,j₅, $j 1 0$ ,j₁₁
3	j₃, j₁₁	j₂,j₅,j₁₁	j₂,j₅, $j 1 0$	j₂,j₅, $j 1 0$ ,j₁₁	j₂,j₄,j₅, $j 1 0$ ,j₁₁
4	j₃,j₉,j₁₁	j₂,j₅,j₁₁	j₂,j₅, $j 1 0$	j₂,j₅, $j 1 0$ ,j₁₁	j₂,j₄,j₅, $j 1 0$ ,j₁₁
5	j₃,j₉,j₁₁	j₂,j₅,j₁₁	j₂,j₅, $j 1 0$	j₂,j₅, $j 1 0$ ,j₁₁	j₂,j₄,j₅, $j 1 0$ ,j₁₁
目标函数值/万元	$1.58 × 104$	$1.75 × 104$	$1.93 × 104$	$2.14 × 104$	$2.33 × 104$

Table 5

Fig.2

Fig.3

Fig.4

Fig.5

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中断情景	1	2	3	4	5	6
发生概率	0.03	0.06	0.14	0.04	0.26	0.47
中断路径数量	47	98	27	27	58	0

物资储备基地备选点	1	2	3	4	5	6	7	8	9	10	11
最大容量/万t	2.5	0.8	2.5	1	1.1	2.5	1.6	1.6	1.6	1.5	1.5
建设成本/万元	572	870	850	617	604	605	599	575	550	525	500
运营成本/万元	17	17	15	12	10	10	8	6	5	3	2