越览（147）——精读博士论文的4.3仿真设计

摘要：This issue of tweets will introduce 4.3 Simulation design of indicators for supply chain network resilience under random and targe

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“越览（147）——精读博士论文

《供应链网络结构视角下的产业链韧性研究》

的4.3 仿真设计

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Today, the editor brings you

4.3 Simulation design

of "Yuelan (147)—— Intensive reading of

the doctoral dissertation

‘Research on the resilience of

the supply chain from the perspective of

supply chain network structure’".

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一、内容摘要（Summary of content）

本期推文将从思维导图、精读内容、知识补充三个方面介绍博士论文《供应链网络结构视角下的产业链韧性研究》的4.3仿真设计。

This issue of tweets will introduce 4.3 Simulation design of indicators for supply chain network resilience under random and targeted disruptions of the doctoral thesis "Research on Industrial Chain Resilience from the Perspective of Supply Chain Network Structure" from three aspects: mind mapping, intensive reading content, and knowledge supplement.

二、思维导图（Mind mapping）

三、精读内容（Intensive reading content）

（一）仿真步骤（Simulation steps）

本研究参考 Law 与 Kelton（2000）提出的离散事件模拟方法，围绕复杂网络中断情景下的供应链韧性开展仿真实验。模拟流程包括构建概念模型、开发模拟程序、设计中断实验与输出结果分析。以真实汽车产业供应链网络为基础，构建三类网络结构：真实供应链网络、随机网络和无标度网络，并通过度分布特征确认无标度网络的幂律性质。中断模拟涵盖两种类型：一是模拟自然灾害、事故等情形的随机中断，通过等概率移除节点实现，每轮删除总节点数的5%；二是模拟恐怖袭击、军事打击等针对性破坏的目标中断，按节点重要性递减顺序删除每轮1%的节点，逐轮更新节点指标。

This study refers to the discrete event simulation method proposed by Law and Kelton (2000) and conducts simulation experiments on supply chain resilience under complex network disruption scenarios. The simulation process includes building a conceptual model, developing a simulation program, designing disruption experiments, and analyzing output results. Based on the real automotive industry supply chain network, three types of network structures are constructed: real supply chain network, random network, and scale-free network, and the power-law properties of scale-free networks are confirmed through degree distribution characteristics. Disruption simulation covers two types: one is to simulate random disruptions in situations such as natural disasters and accidents, which is achieved by removing nodes with equal probability, and deleting 5% of the total number of nodes in each round; the other is to simulate targeted disruptions such as terrorist attacks and military strikes, and delete 1% of the nodes in each round in descending order of node importance, and update node indicators round by round.

不同于以往仅采用点度中心性衡量节点重要性，本文引入包括点度中心性、介数中心性、离心度、接近中心性、特征向量中心性与聚类系数在内的六类指标，全面反映节点在网络中的结构地位。在模拟过程中，节点及其连接边一并移除，记录网络拓扑结构的韧性变化，以比较不同类型网络在面对中断冲击时的恢复能力和结构稳定性。尽管节点移除的模拟简化了现实中部分能力丧失的情形，但该方法已广泛用于复杂网络韧性研究，能有效刻画网络受扰后的系统脆弱性与鲁棒性特征。

Different from the previous method of measuring node importance only by degree centrality, this paper introduces six indicators including degree centrality, betweenness centrality, eccentricity, closeness centrality, eigenvector centrality and clustering coefficient to comprehensively reflect the structural status of nodes in the network. During the simulation, nodes and their connecting edges are removed together, and the changes in the resilience of the network topology are recorded to compare the recovery ability and structural stability of different types of networks in the face of interruption shocks. Although the simulation of node removal simplifies the situation of partial capacity loss in reality, this method has been widely used in the study of complex network resilience and can effectively characterize the system vulnerability and robustness characteristics after the network is disturbed.

（二）随机中断的仿真结果（Simulation results of random interruption）

本文采用 Python 实现节点随机移除模拟，并借助 Gephi 计算四类网络在随机中断情景下的供应链韧性指标，所得结果为 100 次独立实验的平均值。从可用性指标来看，随着节点移除比例上升，四类网络均保持较高稳定性，其中无标度网络可用性最高，真实网络在中断前即表现出相对较低的可用性（70.51%），反映出其结构性脆弱性。

This paper uses Python to implement random node removal simulation, and uses Gephi to calculate the supply chain resilience indicators of four types of networks under random interruption scenarios. The results are the average of 100 independent experiments. From the availability index, as the proportion of node removal increases, the four types of networks maintain a high stability, among which the scale-free network has the highest availability. The real network shows a relatively low availability (70.51%) before the interruption, reflecting its structural fragility.

连通性指标显示真实网络具有显著的产业聚集效应，即便在20%节点被移除后仍维持较高连通性，优于其他网络。平均路径长度和最大路径长度分析表明，真实网络中断后可达性有所下降，而随机网络与无标度网络则因外围节点被移除导致平均路径缩短，传递效率反而提升。

The connectivity index shows that the real network has a significant industrial agglomeration effect, and even after 20% of the nodes are removed, it still maintains a high connectivity, which is better than other networks. The analysis of average path length and maximum path length shows that the accessibility of the real network decreases after the interruption, while the average path of the random network and the scale-free network is shortened due to the removal of peripheral nodes, and the transmission efficiency is improved.

真实网络最长路径在中断比例达到15%时出现峰值，随后下降，反映出网络碎片化导致部分难以到达的节点脱离最大子图，从而减小整体路径长度。结果揭示当前汽车产业供应链网络具备一定韧性，可承受一般性随机冲击，但在提升可用性与优化节点结构方面仍具提升空间。

The longest path in the real network peaks when the interruption rate reaches 15%, and then decreases, reflecting that network fragmentation causes some difficult-to-reach nodes to be out of the largest subgraph, thereby reducing the overall path length. The results show that the current automotive industry supply chain network has a certain degree of resilience and can withstand general random shocks, but there is still room for improvement in terms of improving availability and optimizing node structure.

（三）目标中断的仿真结果（Simulation results of target interruption）

1. 点度中心性中断（Degree centrality discontinuity）

在点度中心性中断下，四类供应链网络韧性显著下降，尤其真实网络最为脆弱，仅中断1%节点，其可用性即降至37.2%，4%时几乎瘫痪；相比之下，无标度网络仍保持较高可用性。连通性方面，真实与无标度网络在中断1%节点时即下降超过50%，4%时真实网络连通性几乎消失。可达性指标显示，真实网络在中断2%时路径最长，效率最低，超过该比例则整体网络功能崩溃。总体来看，定向攻击远比随机中断破坏更强，无标度网络具备更强韧性。

Under the interruption of point degree centrality, the resilience of the four types of supply chain networks decreased significantly, especially the real network, which was the most vulnerable. When only 1% of the nodes were interrupted, its availability dropped to 37.2%, and it was almost paralyzed at 4%. In contrast, the scale-free network still maintained a high availability. In terms of connectivity, the real and scale-free networks dropped by more than 50% when 1% of the nodes were interrupted, and the connectivity of the real network almost disappeared at 4%. The accessibility index shows that the real network has the longest path and the lowest efficiency when 2% of the nodes are interrupted. If this ratio is exceeded, the overall network function will collapse. Overall, targeted attacks are far more destructive than random interruptions, and scale-free networks have greater resilience.

2. 介数中心性中断（Betweenness centrality disruption）

在介数中心性中断下，四类网络的供应链韧性均下降，但整体破坏程度弱于点度中心性中断。真实网络最为脆弱，1%节点移除时可用性降至38.28%，4%时仅为11.84%。连通性方面，各网络均有下降，真实网络降幅最大。可达性上，真实网络在移除2%节点时路径最长，随后下降。总体来看，无标度网络（r=3）表现最稳健，说明其结构对定向攻击更具韧性。相比之下，点度中心性高的节点更关键，攻击其对网络破坏更严重，建议以核心企业为中心构建汽车产业集群以增强韧性。

Under the interruption of betweenness centrality, the supply chain resilience of the four types of networks all decreased, but the overall degree of damage was weaker than that of degree centrality interruption. The real network is the most vulnerable, with availability dropping to 38.28% when 1% of the nodes are removed and only 11.84% when 4%. In terms of connectivity, all networks have declined, with the real network having the largest decline. In terms of accessibility, the real network has the longest path when 2% of the nodes are removed, and then declines. Overall, the scale-free network (r=3) performs the most robustly, indicating that its structure is more resilient to targeted attacks. In contrast, nodes with high degree centrality are more critical, and attacks on them cause more serious damage to the network. It is recommended to build an automotive industry cluster centered on core enterprises to enhance resilience.

3. 离心度中断（Centrifugal interruption）

离心度中断对供应链网络的破坏较弱，真实网络的韧性指标变化不明显，始终优于其他网络。可用性在节点移除过程中基本保持稳定，连通性虽略有下降，但仍高于其他网络，表明真实网络内形成了较稳定的产业集群。平均路径和最大路径长度变化也较小，维持在较低水平。相比之下，随机网和无标度网的韧性指标持续下降，表明其结构更易受离心度中断影响。总体而言，离心度对供应链韧性影响较小，重要性低于点度和介数中心性。

The disruption of eccentricity has a weak impact on the supply chain network, and the resilience index of the real network has not changed significantly, and it is always better than other networks. Availability remains basically stable during the node removal process. Although connectivity has slightly decreased, it is still higher than other networks, indicating that a relatively stable industrial cluster has been formed in the real network. The average path and maximum path length also change slightly and remain at a low level. In contrast, the resilience index of random networks and scale-free networks continues to decline, indicating that their structures are more susceptible to eccentricity disruptions. Overall, eccentricity has little effect on supply chain resilience and is less important than point degree and betweenness centrality.

4. 接近中心性中断（Proximity to centrality interruption）

基于接近中心性的节点中断对供应链韧性的破坏较轻，真实网络的可用性虽下降但幅度较小，连通性下降速度也低于点度和介数中心性中断。平均路径长度和最大路径长度在真实网络中持续上升，表明接近中心性高的企业有助于缩短资源传递距离，提高传递效率，增强供应链韧性。无标度网络在可达性方面表现更优，整体显示接近中心性对提升供应链稳定性作用有限但积极。

Node disruptions based on proximity centrality have less damage to supply chain resilience. The availability of the real network has decreased but to a lesser extent, and the rate of connectivity decline is also lower than that of point degree and betweenness centrality disruptions. The average path length and maximum path length continue to rise in the real network, indicating that companies with high proximity centrality can help shorten the distance of resource transfer, improve transfer efficiency, and enhance supply chain resilience. The scale-free network performs better in terms of accessibility, and overall shows that proximity centrality has a limited but positive effect on improving supply chain stability.

5. 特征向量中心性中断（Eigenvector centrality breaks）

特征向量中心性中断对供应链韧性的影响与接近中心性中断相似。真实网络的可用性和连通性均呈下降趋势，但下降幅度较小，无标度网络表现最佳。节点移除导致真实网络的平均路径长度和最大路径长度上升，表明供应链需绕开受影响节点，采用更远路径维持运行。随机网和无标度网的路径长度变化较小，结构更稳定，说明特征向量中心性较高节点的中断对整体供应链破坏较弱。

The impact of eigenvector centrality disruption on supply chain resilience is similar to that of proximity centrality disruption. The availability and connectivity of real networks both show a downward trend, but the decline is small, and scale-free networks perform best. Node removal leads to an increase in the average path length and maximum path length of real networks, indicating that the supply chain needs to bypass the affected nodes and use longer paths to maintain operation. The path length of random networks and scale-free networks changes less and the structure is more stable, indicating that the disruption of nodes with higher eigenvector centrality has less damage to the overall supply chain.

6. 聚类系数中断（Clustering coefficient cutoff）

聚类系数中断对供应链韧性影响较小。节点移除比例增加时，四个网络的可用性基本稳定，真实网络维持约70%。连通性方面，随机网和真实网变化不大，无标度网稍有下降。平均路径长度和最大路径长度基本保持不变，说明聚类系数中断对资源传递效率影响有限，且对真实网和随机网破坏微弱，对无标度网络有一定影响。

The interruption of clustering coefficient has little impact on supply chain resilience. When the proportion of node removal increases, the availability of the four networks is basically stable, and the real network maintains about 70%. In terms of connectivity, the random network and the real network have little change, and the scale-free network has a slight decrease. The average path length and the maximum path length remain basically unchanged, indicating that the interruption of clustering coefficient has limited impact on resource transfer efficiency, and has little damage to the real network and random network, and has a certain impact on the scale-free network.

（四）供应链网络重构（Supply chain network reconstruction）

网络中节点连接方式影响网络结构，无标度网络通过优先连接高节点度节点形成，随机网络则通过随机连接节点生成。研究表明，点度中心性、介数中心性、特征向量中心性和接近中心性均影响供应链韧性，点度中心性和介数中心性影响最大。目前供应链韧性改善多聚焦于点度中心性，本文结合三种中心性指标，考虑节点度数、距离和资源控制，提出一种新的连接方式，对真实汽车五级供应链网络进行重构以提升韧性。

The way nodes are connected in the network affects the network structure. Scale-free networks are formed by preferentially connecting nodes with high node degrees, while random networks are generated by randomly connecting nodes. Studies have shown that degree centrality, betweenness centrality, eigenvector centrality, and proximity centrality all affect supply chain resilience, with degree centrality and betweenness centrality having the greatest impact. Currently, supply chain resilience improvement focuses on degree centrality. This paper combines the three centrality indicators, considers node degree, distance, and resource control, and proposes a new connection method to reconstruct the real five-level automotive supply chain network to improve resilience.

重构模型设定重构概率（rate=0.25）和最大重构半径（max R=2），控制边的重新连接数量和范围。具体操作为：随机选取需重构边，断开点度中心性较高一端节点，计算另一端节点半径范围内节点介数中心性，选择介数中心性最高节点重新连接。完成所有重构边后形成新的网络。

The reconstruction model sets the reconstruction probability (rate=0.25) and the maximum reconstruction radius (max R=2) to control the number and range of edge reconnections. The specific operation is: randomly select the edge to be reconstructed, disconnect the node with higher degree centrality, calculate the node betweenness centrality within the radius of the other node, and select the node with the highest betweenness centrality to reconnect. After completing all the reconstructed edges, a new network is formed.

实验结果表明，重构后的汽车产业供应链网络在随机和目标中断下均表现出良好韧性，虽非所有中断类型的最优，但为无法预测风险时提供了有效的折衷方案。该重构方法是一种简单有效的启发式策略，有助构建具有平衡韧性的帕累托最优供应链网络。

The experimental results show that the reconstructed automotive industry supply chain network shows good resilience under both random and targeted disruptions. Although it is not optimal for all types of disruptions, it provides an effective compromise when risks cannot be predicted. This reconstruction method is a simple and effective heuristic strategy that helps to build a Pareto optimal supply chain network with balanced resilience.

四、知识补充（Knowledge supplement）

帕累托最优，又称帕累托效率，是一种经济学和决策理论中的概念，用来描述资源配置或方案的最优状态。具体含义是：

Pareto optimality, also known as Pareto efficiency, is a concept in economics and decision theory that is used to describe the optimal state of resource allocation or solutions. The specific meaning is:

在一个多目标或多参与者的系统中，若无法通过改变当前状态使某个个体或目标变得更好，而不使至少另一个个体或目标变得更差，则该状态被称为帕累托最优。

In a multi-objective or multi-participant system, if it is impossible to make an individual or objective better by changing the current state without making at least another individual or objective worse, the state is called Pareto optimal.

简单来说，帕累托最优意味着资源已经达到一种平衡状态，任何改进都会导致至少一方受损，无法再“无损”地改进。举例：在供应链网络中，若网络结构达到帕累托最优，意味着在提升某一方面（如韧性、成本、效率）的同时，不会导致其他方面（如稳定性、连接性）恶化。

Simply put, Pareto optimality means that resources have reached a state of equilibrium, and any improvement will cause damage to at least one party, and it is no longer possible to improve "without loss". For example: in a supply chain network, if the network structure reaches Pareto optimality, it means that while improving one aspect (such as resilience, cost, efficiency), it will not cause other aspects (such as stability, connectivity) to deteriorate.

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