Route Optimization of Cross-Border Intermodal Transport for Multi-Category Engineering Materials in International Railway Construction Projects Under Time Uncertainty

Cross-border transport of engineering materials for international railway construction projects is characterized by substantial heterogeneity among material categories, complex intermodal networks, and considerable variability in customs-clearance and cross-gauge transshipment times at border crossings. Route optimization that focuses solely on minimizing deterministic transportation costs is therefore insufficient to ensure continuous operations at overseas construction sites. Unlike existing intermodal-routing models, which generally assume homogeneous cargo and do not represent competition among heterogeneous material categories for shared cross-border capacity under uncertain clearance and transshipment times, the proposed model explicitly incorporates these features. This study develops a route-optimization model for the cross-border intermodal transport of multiple categories of engineering materials under time uncertainty. The model has two objectives—minimizing total transportation cost and minimizing total transportation time—and includes constraints on supply–demand balance, flow continuity, the shared capacities of arcs, border ports, and transshipment nodes, category-specific capacity use, material–mode compatibility, and maximum delivery times. Triangular fuzzy numbers characterize uncertainty in arc travel, transshipment, and customs-clearance times. The α-cut method transforms the fuzzy time constraints into deterministic equivalents, and the augmented ε-constraint method (AUGMECON2) generates the cost–robust-time Pareto frontier. A case study of the China–Thailand Railway corridor on the Central Route of the Pan-Asia Railway validates the proposed model. Moving from the cost-optimal to the time-optimal solution reduces robust transportation time by 23.13% while increasing total cost by 13.74%. The cost–time trade-off also exhibits increasing marginal costs. The cross-gauge transshipment station is the only shared hub operating near full capacity, whereas maritime travel time is the most sensitive source of uncertainty affecting robust transportation time. Tightening the delivery-time limit for rails has the greatest effect on both total cost and network resilience. These findings support differentiated route planning for cross-border engineering materials, capacity expansion at critical hubs, and decisions that balance transportation budgets with project-schedule requirements.