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

**Authors:** Marios Papachristou, M. Amin Rahimian  
**arXiv:** [2303.12660](https://arxiv.org/abs/2303.12660)  
**Date:** 2023-03-22  
**Summary page:** https://www.summarizepaper.com/en/paper/2303.12660v1/

## Key points

- The paper studies the resilience of supply chain networks in the face of systemic shocks that cause product suppliers to fail independently.
- Cascading failures in supply chains follow a power law distribution in random directed acyclic graphs.
- The authors define a supply chain resilience metric 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.
- The authors present their model for why supply chain networks are prone to catastrophic failures and why a measure of resilience is needed to distinguish different supply chain architectures.
- They study various network architectures and classify them as resilient or fragile based on their ability to avoid large cascading failures almost surely.
- Networks become more resilient when multi-sourcing increases but less resilient when interdependencies among products increase.
- They provide a general computational framework for lower-bounding the proposed metric in general graphs and make additional connections to financial networks, financial contagions, centrality measures, as well as propose algorithms for optimal interventions in supply chains.
- They validate their theoretical results by empirically calculating the resilience metric and studying interventions in real-world networks.
- The paper makes several contributions including identifying topological risk factors that contribute to increased risk of cascading failures in production networks; proposing a novel theory-informed resilience metric that complements existing measures; and providing interventions for improving resilience with theoretical guarantees.

## Summary

This paper focuses on studying the resilience of supply chain networks in the face of systemic shocks that cause product suppliers to fail independently. The authors begin by showing that cascading failures in supply chains follow a power law distribution in random directed acyclic graphs, which encode the natural ordering of products from raw materials to complex products. To address the need for a supply chain resilience metric, they define it 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. In Section 2, the authors present their model for why supply chain networks are prone to catastrophic failures and why a measure of resilience is needed to distinguish different supply chain architectures. They use a node percolation process where possible suppliers of a product fail independently with probability x, and a product can be produced when its requirements are met and its suppliers do not fail. In Section 3, they study various network architectures and classify them as resilient or fragile based on their ability to avoid large cascading failures almost surely. They also introduce their new resilience metric formally and present their main results for different architectures in Table 1. They show that networks become more resilient when multi-sourcing increases but less resilient when interdependencies among products increase. In Section 4, they provide a general computational framework for lower-bounding the proposed metric in general graphs and make additional connections to financial networks, financial contagions, centrality measures, as well as propose algorithms for optimal interventions in supply chains. In Section 5, they validate their theoretical results by empirically calculating the resilience metric and studying interventions in real-world networks. Finally, in Section 6, they summarize their main insights and conclusions and provide potential avenues for future work. Overall, this paper makes several contributions including identifying topological risk factors that contribute to increased risk of cascading failures in production networks; proposing a novel theory-informed resilience metric that complements existing measures; and providing interventions for improving resilience with theoretical guarantees.