Structural Measures of Resilience for Supply Chains

TL;DR

This paper studies 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, and empirically calculates the resilience metric and study interventions in a variety of real-world networks.

Abstract

We investigate the structural factors that drive cascading failures in production networks, focusing on quantifying these risks with a topological resilience metric corresponding to the largest exogenous systemic shock that the production network can withstand, such that almost all of the network survives with high probability. We model failures using a node percolation process where systemic shocks cause suppliers to fail, leading to further breakdowns. We classify networks into two categories -- resilient and fragile -- based on their ability to handle shocks as the network grows large, and give bounds on their resilience. We show that the main factors affecting resilience are the number of raw products (primary sector), the number of final goods (final sector), and the source and supply dependencies. Further, we give methods to lower bound resilience based on bounding the cascade size with a linear program that can be efficiently calculated. We establish connections between our model, the independent cascade model, the Risk Exposure Index, and the Eisenberg-Noe contagion model. We give an almost linear-time deterministic algorithm to approximate the cascade size, which matches known lower bounds up to logarithmic factors. Finally, we design intervention algorithms and show that under reasonable assumptions, targeting nodes based on Katz centrality in the edge-reversed network is optimal. Finally, we account for network heterogeneities and validate our findings with real-world data.

Figures (9)

• Figure 1: High-level graphical overview of our main results. Exact bounds are located in \ref{['tab:resiliences']}.
• Figure 2: Supply Chain Instance. Each node in the production network of \ref{['subfig:product_graph']} has a supplier set. The supply chain network between two products is shown in \ref{['subfig:supply_chain']}.
• Figure 3: Production networks of \ref{['sec:motivation']} and \ref{['sec:parallel_products']}. Failures are drawn in pink color.
• Figure 4: (a, b): Backward and Forward Networks. Node failures are drawn in pink. (c): Resilience bounds for a subcritical GW process with branching distribution as a function of $\mu$; note the decreasing trends in both upper and lower bounds, $\mathbb E_{\mathcal{G}}\left [ \overline R_{\mathcal{G}}(\varepsilon) \right ]$ and $\mathbb E_{\mathcal{G}}\left [ \underline R_{\mathcal{G}}(\varepsilon) \right ]$, with increasing $\mu$.
• Figure 5: Resilience estimation and optimal interventions for three networks from willems2008data. We set the number of suppliers for each product to $n = 1$.

Theorems & Definitions (31)

• Theorem 1
• Definition 1
• Lemma 1
• Theorem 2
• Theorem 3
• Theorem 4
• Definition 2
• Theorem 5
• Corollary 1
• Theorem 6