In this paper, we study the severity of cascading failures in supply chain networks defined by a node percolation process corresponding to product suppliers failing independently due to systemic shocks. We first show that the size of the cascades follows a power law in random directed acyclic graphs, whose topology encodes the natural ordering of products from simple raw materials to complex products. This motivates the need for a supply chain resilience metric, which we define as the maximum magnitude shock that the production network can withstand such that at least $(1 - \varepsilon)$-fraction of the products are produced with high probability as the size of the production network grows to infinity. Next, we study the resilience of many network architectures and classify them as resilient, where large cascading failures can be avoided almost surely, and as fragile, where large cascades are inevitable. In the next step, we give bounds on the expected size of cascading failures in a given production network graph as the solution to a linear program and show that extending the node percolation process to a joint percolation process that affects the nodes and the links of the production network becomes a special instance of the well-studied financial contagion model of Eisenberg and Noe. We show that under certain assumptions, the Katz centrality of each node can be used as a measure of their vulnerability and give general lower bounds as well as optimal interventions for improving resilience as a function of Katz centralities. Finally, to validate our theoretical results, we empirically calculate the resilience metric and study interventions in a variety of real-world networks.

翻译：本文研究供应链网络中由节点渗流过程导致的级联失效严重程度，该过程对应于产品供应商因系统性冲击而独立失效。我们首先证明，在随机有向无环图中，级联规模服从幂律分布，其拓扑结构编码了从简单原材料到复杂产品的自然产品顺序。这促使我们定义供应链韧性指标：生产网络能承受的最大冲击幅度，使得当生产网络规模趋于无穷时，至少$(1 - \varepsilon)$比例的产品以高概率被生产。随后，我们分析多种网络架构的韧性，将其分类为韧性（可几乎确定避免大规模级联失效）与脆弱（大规模级联不可避免）两类。下一步，我们给出给定生产网络图中级联失效期望规模的界限（作为线性规划的解），并证明将节点渗流过程扩展为同时影响生产网络节点与边的联合渗流过程，将归结为Eisenberg和Noe已充分研究的金融传染模型的特殊实例。我们证明，在特定假设下，各节点的Katz中心性可作为其脆弱性的度量，并基于Katz中心性给出韧性改进的通用下界及最优干预策略。最后，为验证理论结果，我们在多种真实世界网络中经验性地计算韧性指标并研究干预措施。