Vulnerability analysis of multimodal freight transportation networks considering carbon price and ship energy choices

The evolution of transport-energy integration and carbon emission policies influences transport structures, thereby altering the vulnerability of multimodal freight networks. Based on a complex network methodology that accounts for heterogeneous ship energy types, carbon cost is incorporated into the path utility function to determine link weights. Critical nodes are identified using a gravity model, and a capacity-load model is employed to simulate cascading failures, enabling analysis of how carbon pricing and ship energy choices affect network vulnerability. The results indicate that under targeted attacks, the waterway transport network displays the most pronounced vulnerability, whereas the railway network exhibits superior reliability. Under random attacks, the three transport layers show no statistically significant performance variation. As carbon prices rise, network efficiency initially improves but declines beyond an optimal threshold. Multimodal networks employing electric ships demonstrate superior stability, with significantly lower sensitivity to carbon price fluctuations in connectivity and efficiency compared to their diesel and LNG counterparts, which exhibit marked variability. Energy price volatility exclusively affects diesel ships, substantially disrupting network connectivity and efficiency. Within the context of transport-energy integration, it is imperative to enhance risk management at hub ports, strengthen cross-layer connectivity, and implement coordinated regulation of carbon prices and new energy ships to improve overall network resilience.