Carbon Shadow Pricing and Efficiency in Multimodal Freight Transport Networks: A Z-number DEA Analysis

We integrate a $50/ton CO₂ shadow price into a Z-number Data Envelopment Analysis (DEA) framework to evaluate carbon cost internalization across 59 logistics centers in Iran’s freight transport network. Reflecting the transport sector’s key role in emissions and energy use across multimodal freight corridors, rail-intensive sites show score increases up to +9.4% and rank improvements, while road-dependent hubs show score decreases down to −15.8% and rank declines. A strong negative correlation (r = −0.94) links rail share to rank improvement. Internalizing carbon externalities reshapes infrastructure priorities toward low-carbon modal configurations, offering a replicable tool for climate-responsive freight analysis under uncertainty