Heterogeneous mean-field approximation and simulation models for dynamic risk propagation in complex supply chain networks

Risk management is vital for effectively operating supply chains under ubiquitous uncertainties. In this paper, we investigate dynamic risk propagation using compartmental model, combined with the time-varying and heterogeneous characteristics of risks, to construct a time-varying heterogeneous mean-field approximation (THMA) model. Through the THMA framework, we derive the Risk Dissipation Index (RDI) as a real-time stability monitor and rigorously prove that this model serves as a conservative upper bound for the exact model. Additionally, we delineate the applicability conditions of the THMA model, identifying specific regimes where it holds validity. To address limitations of the THMA model in capturing stochastic fluctuations and to cover scenarios beyond its theoretical scope, we develop a complementary discrete-event simulation model. Within this simulation, we propose the Recovery Potential Index (RPI) to quantify the probability of system restoration. To resolve the computational inefficiency in estimating the RPI for rare recovery events, we implement the Importance Splitting (IS) algorithm to accelerate the simulation. Numerical examples illustrate the effectiveness of our proposed models.