Discovery of a phase transition behavior for supply chains against disruptive events

In today's global economy, supply chain (SC) entities have become increasingly interconnected with demand and supply relationships due to the need for strategic outsourcing. Such interdependence among firms not only increases efficiency, but also creates more vulnerabilities in the system. Natural and human-made disasters such as floods and transport accidents may halt operations and lead to tremendous economic losses. Due to the interdependence among firms, the adverse effects of any disruption can be amplified and spread throughout the systems. This paper aims at understanding the systemic behaviors of SC systems against cascading failures. Considering the upper and lower bound load constraints, i.e., surplus inventory and cost, we examine the fraction of failed entities under load decrease and load fluctuation scenarios through numerical simulations. We also provide analytic results through mean-field theory. Results indicate the occurrence of a first-order phase transition, and such systemic risk failures need to be considered in the future by policymakers in conjunction with SC risk management strategies to improve system resilience. With respect to the lower bound parameter, i.e., cost per output, the system is more robust under power law distributions than uniform distributions, for the studied scenarios.