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Research on Cascading Failure of Supply Chain Network Based on Degree and Betweeness
DOI: 10.12677/MOS.2024.131064, PDF, HTML, XML, 下载: 133  浏览: 220

Abstract: In the supply chain network, enterprises can not only undertake the production and manufacturing orders of upstream and downstream enterprises, but also accept logistics transportation, ware-housing, and other tasks in part of the supply chain network. Due to the different locations of busi-nesses in the supply chain network, the amount of additional business that can be developed is also different. With this in mind, this study divides the load of nodes into production load and transpor-tation load, that is, a function of node degree and mediation number, based on the construction of the load-capacity model to study cascading failures in supply chain networks. Simulations are then carried out on classic BA networks and random networks. The influence of relevant parameters on network robustness is studied, and the changing trend of network robustness indicators is analyzed. It is found that when the transport load is increased, the robustness of the scale-free network is first reduced and then improved. The robustness of random networks has been improved.

1. 引言

2. 理论概述

2.1. 图论基础

2.2. 度中心性

2.3. 介数中心性

${B}_{i}=\frac{{\omega }_{j{j}^{\prime }}\left(i\right)}{{\omega }_{j{j}^{\prime }}}$ (1)

2.4.网络模型

2.4.1. BA无标度网络

Step 1：网络中存在m0个节点，节点之间相互连接。

Step 2：每一个时间步，一个新节点加入网络，并选择网络中的m (m < m0)个已经存在的节点建立连接。每个旧节点i被选择的概率为：

${P}_{i}=\frac{{k}_{i}}{\underset{j\in N}{\sum }{k}_{j}}$ (2)

Step 3：重复Step 2，经过一定时间步t后，生成一个具有N = t + m0个节点的BA无标度网络

2.4.2. ER随机网络

3. 级联失效模型

3.1. 节点的初始负载与容量

${L}_{i}\left(0\right)={k}_{i}^{\alpha }+b*{k}_{i}^{{B}_{\text{i}}}$ (3)

${C}_{i}=\left(1+\beta \right){L}_{i}\left(0\right)$ (4)

3.2.负载重分配策略

${\pi }_{j}=\frac{{C}_{\text{j}}}{\underset{j\in {\Gamma }_{i}}{\sum }{C}_{j}}$ (5)

$\Delta {L}_{\text{j}}={L}_{i}*{\pi }_{j}$ (6)

3.3. 鲁棒性指标

$P=\frac{{N}^{\prime }}{N-{N}_{0}}$ (7)

4. 仿真模拟

4.1. 相关参数设置

4.2. BA网络仿真结果分析

Figure 1. The impact of transport load factor b on the robustness S of BA network

Figure 2. The impact of the number of failed nodes n on the robustness S of BA network

4.3. ER网络仿真结果分析

Figure 3. The impact of transport load factor b on the robustness S of ER network

Figure 4. The impact of the number of failed nodes n on the robustness S of ER network

5. 结论

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