Robustness analysis of cyber–physical supply chain systems under hybrid cascading failures

With the advancement of Internet of Things (IoT) technology, modern supply chain systems have evolved into cyber–physical systems, known as cyber–physical supply chain systems (CPSCS). The cyber-layer network (CLN) transmits the information flow in CPSCS, while the physical-layer network (PLN) produces and transports the material flow in CPSCS. Considering the functional heterogeneity of enterprises in real-world CPSCS, we divide the nodes in CPSCS into multiple functional groups based on their functions, thereby constructing a new CPSCS model with a multi-group structure. Then, we propose a hybrid cascading failure model incorporating overload failure, underload failure, dependency loss failure, and isolation failure to investigate the robustness of CPSCS. Finally, to more comprehensively evaluate the robustness of CPSCS, we establish a two-dimensional robustness evaluation framework that integrates structural and functional indicators. Based on the CPSCS and hybrid cascading failure models, we investigate the impact of parameters from both models on the robustness of CPSCS under random and intentional disruptions. Simulation results show that, at the micro level, the robustness of CPSCS can be enhanced by increasing the capacity upper bound of nodes in the CLN and decreasing capacity lower bound of nodes in the PLN. At the macro level, robustness can be improved by adjusting the structure of CPSCS, such as expanding system size, increasing the average degree of nodes, optimizing the level-size ratio, and reducing the number of functional groups. The findings of this study can provide valuable insights in building a robust CPSCS.