Structural Measures of Resilience for Supply Chains

A team of researchers—Marios Papachristou, M. Amin Rahimian, and Arash Azadegan—has published a paper titled 'Structural Measures of Resilience for Supply Chains' on arXiv, proposing a new, theoretically-grounded framework to quantify supply chain robustness. The core of their work is a novel resilience metric defined as the maximum supplier failure rate a network can sustain while still maintaining a target aggregate production level. To develop this, they apply concepts from node percolation theory and branching processes to model how localized disruptions cascade through complex, multi-tier sourcing dependencies.

Their analysis identifies four critical structural determinants of a supply chain's resilience: the number of raw materials, the number of finished goods, sourcing requirements, and sourcing influence. This reveals two distinct architectural regimes. 'Top hat' structures, characterized by excessive raw materials and high centralization, are inherently fragile. In contrast, 'rolling pin' structures, which maintain controlled input/output widths and sparsity, can absorb significant shocks. The researchers formulate the resilience computation as a scalable linear program capable of approximating cascading failure sizes in large, real-world networks with cycles and heterogeneous suppliers.

Furthermore, the framework is extended to account for exogenous failure correlations, such as those caused by geographic or geopolitical factors, which can undermine traditional diversification strategies. This addresses a key weakness in current risk management approaches. The theoretical results are validated using multi-echelon supply chain data, providing a practical tool to inform network design, supplier diversification, and inventory planning. This moves supply chain risk management from a reactive to a proactive, design-focused discipline.