  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.
