Layout Planning of Metro-based Underground Logistics System Network Considering Fuzzy Uncertainties

doi:10.16182/j.issn1004731x.joss.21-0206

Abstract

Abstract:

Aming at the network design and optimization of metro-based urban underground logistics under uncertainties, the facility components of two-tier metro-based underground logistics system (M-ULS) are proposed. Focus on the comprehensive costs and system utilization rate, a M-ULS network flow assignment model is established based on the expectation of environmental benefits of underground freight transport. a M-ULS network location-allocation-routing fuzzy random programming model is established, and a crisp linearization method is presented. A solution portfolio combining discrete binary chaos particle swarm optimization-genetic algorithm and exact algorithms is designed for combinatorial optimization. Effectiveness of the presented models and algorithms is verified in real-life cases. Results show that the best M-ULS layout schemes in fuzzy random scenarios are more conservative than those in deterministic scenarios. The external environment benefits of underground logistics can offset 10%~12% of costs in network construction and operations.

Key words: urban underground logistics systems, metro, location and layout, particle swarm optimization algorithm, demand uncertainty

CLC Number:

TP391.9

Wanjie Hu, Jianjun Dong, Rui Ren, Zhilong Chen. Layout Planning of Metro-based Underground Logistics System Network Considering Fuzzy Uncertainties[J]. Journal of System Simulation, 2022, 34(8): 1725-1740.

Figures/Tables 15

Fig. 1

Fig. 2

Fig. 3

Table 1

Representing fuzzy random variables

变量	左边界	右边界	均值	方差
$D ̂ i k$	$m i k 1$	$n i k 1$	$d i k$	$ρ i k$
$R ̂ j$	$m j 2$	$n j 2$	$r j$	—
$E ̂ i$	$m i 3$	$n i 3$	$e i$	—
$C ̂ h$	$m h 4$	$n h 4$	$c h$	—
$U ̂ j$	$m j 5$	$n j 5$	$u j$	—
$V ̂ t$	$m t 6$	$n t 6$	$v t$	—
$P ̂ s$	$m s 7$	$n s 7$	$p s$	—
$Q ̂ h$	$m h 8$	$n h 8$	$q h$	—
$W ̂ j$	$m j 9$	$n j 9$	$w j$	—

Table 1

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Table 2

Theoretical complexity of each algorithm step

算子	时间复杂度	计算量级
总计		×10⁸
选择-交叉-变异	$O (n 2 + 2 n)$	×10⁴
混沌局部搜索	$O (3 n)$	×10²
粒子群状态更新	$O (2 n)$	×10²
选址-分配	$O (n ⋅ \| I \|)$	×10⁴
一级路径优化	$O (n ⋅ \| J ¯ \| ⋅ \| K \| ⋅ \| S \|)$	×10⁵
K-MST	$O (n ⋅ \| I \| ⋅ \| J ¯ \|)$	×10⁵
FWA	$O (n ⋅ \| I \| ⋅ \| J ¯ \| + n ⋅ \| J ¯ \| ⋅ L)$	×10⁶

Table 2

Table 3

Table 4

Parameter values for model simulation

参数	值	参数	值
$σ ˙ j$ /(万件/d)	11	$η$ /%	55
$σ ¨ j$ /(万件/d)	4	$φ$ /(万件/车)	0.02
$H t$ /(万件/d)	60	$ζ C O 2$ /(万元/t)	0.071
$ς$ /(万件/d)	2	$ζ C O$ /(万元/t)	0.359
$r j$ /(亿元)	3	$ζ N O x$ /(万元/t)	10.32
$e i$ /(亿元)	3 000	$ζ P M$ /(万元/t)	26.34
$c h$ /(万元/km)	4 000	$ζ V O C$ /(万元/t)	0.703
$θ$ /d	36 500	$κ$ /(L/km)	0.125
$u j$ /(元/件)	0.1	$ε$ /(万元/L)	7.1×10^-4
$v t$ /(元/件)	0.07	$O C O 2$ /(t/km)	2.8×10^-4
$p s$ /(元/(件·km))	0.006	$O C O$ /(t/km)	1.7×10^-6
$q h$ /(元/(件·km))	0.002 4	$O N O x$ /(t/km)	1.01×10^-6
$w j$ /(元/件)	0.05	$O P M$ /(t/km)	1.2×10^-7
$γ$ /(元/件)	0.5	$O V O C$ /(t/km)	3.4×10^-7

Table 4

Table 5

Distribution of uncertain parameters

变量	左边界控制量	右边界控制量	方差
$R ̂ j$	U(0.126, 0.215)	U(0.225, 0.38)	—
$E ̂ i$	U(0.011, 0.018)	U(0.035, 0.059)	—
$C ̂ h$	U(0.011, 0.018)	U(0.013, 0.022)	—
$U ̂ j$	U(0.027, 0.047)	U(0.045, 0.076)	—
$P ̂ s$	U(0.001, 0.002)	U(0.002, 0.003)	—
$Q ̂ h$	U(0.001, 0.002)	U(0.001, 0.002)	—
$V ̂ t$	U(0.018, 0.031)	U(0.018, 0.03)	—
$W ̂ j$	U(0.011, 0.019)	U(0.01, 0.017)	—
$D ̂ i k k = 1$	U(0.12, 0.32)× $d i k k = 1$	U(0.24, 0.4)× $d i k k = 1$	U(37, 595)
$D ̂ i k k = 2$	U(0.15, 0.48)× $d i k k = 2$	U(0.2, 0.3)× $d i k k = 2$	U(9, 149)
$D ̂ i k k = 3$	U(0.15, 0.25)× $d i k k = 3$	U(0.2, 0.35)× $d i k k = 3$	U(15, 189)
$D ̂ i k k = 4$	U(0.2, 0.4)× $d i k k = 4$	U(0.18, 0.42)× $d i k k = 4$	U(5, 205)

Table 5

Fig. 8

Fig. 9

Table 6

Best configurations of M-ULS network under uncertainties

$δ$ /%	站点数量	一级网络运输成本	二级网络运输成本	站点平均运营成本	站点平均负载率/%	空置惩罚成本	地下转运成本	节点建设成本	管道建设成本	管道里程/km	库存成本	总目标成本
50	10	5.59	1.10	0.99	87.85	0.14	1.86	12.72	8.57	104	1.17	40.04
60	11	6.36	1.34	1.07	92.76	0.08	1.92	15.09	11.78	143	1.87	49.22
70	13	8.16	1.61	1.05	93.60	0.26	3.02	18.67	14.50	177	2.04	60.89
80	16	9.83	1.82	1.04	92.87	0.02	4.02	22.37	14.73	179	2.22	69.55
90	18	10.93	2.11	1.04	92.24	0.78	3.87	26.65	16.19	197	2.83	80.94
100	22	13.67	2.34	0.95	84.07	1.08	5.93	32.88	17.08	208	2.45	93.46

Table 6

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