Production Networks Resilience : Cascading Failures, Power Laws and Optimal Interventions

Problem definition: The pandemic crisis made apparent the need to take a holistic view of production networks to understand risk factors that arise due to their many interdependent units. We investigate the structural factors contributing to the severity of cascading failures in production networks, how to quantify the effect of these risk factors with resilience metrics, and how to design and evaluate interventions to improve resilience. Methodology/Results: We propose a node percolation process on production networks that model product suppliers failing independently due to exogenous, systemic shocks and causing other products to fail as their production requirements are unmet. We first show that the size of the cascading failures 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 resilience metric, which we define as the maximum magnitude shock the production network can withstand with only a small fraction of products failing. Next, we study the resilience of several architectures, such as trees, parallel products, and random trellis, and classify them as resilient or fragile depending on their topological attributes. In the next step, we give general lower bounds and optimal interventions for improving resilience as a function of Katz centralities. Finally, we empirically calculate the resilience metric and study interventions in various real-world networks to validate our theoretical results.Managerial implications: We offer new thoughts and theories on reasoning about supply chain resilience based on topological attributes such as source dependency and product complexity and propose novel, theory-informed metrics that we evaluate empirically on real-world networks. Our theories also inform intervention designs for improving resilience, not just from a firm’s perspective but also on a national scale