Multimodal transport has emerged as an effective solution for improving freight efficiency and promoting sustainable logistics, reducing environmental impacts; however, route choice remains challenging under uncertain demand and dynamic transshipment time. This study addresses this problem by developing a bi-objective route-choice model that minimises total transport cost and total transport time while explicitly capturing the correlation between freight demand and transshipment time. The model is transformed into a deterministic equivalent using chance-constrained programming, enabling rigorous optimisation under predefined confidence levels and solved by a simulated annealing-based genetic algorithm (SAGA), which combines the global exploration capability of genetic algorithms with the local search efficiency of simulated annealing to improve convergence and solution quality. By incorporating carbon emission costs into the objective functions, the model supports environmentally and economically sustainable transport strategies. A numerical case study is conducted to validate the proposed approach. The results show that when freight demand is significantly below the capacity threshold, the optimal solution tends to adopt a single-mode transport scheme with stable route structure, whereas higher demand necessitates multimodal strategies, with cost–time trade-offs clearly observed. Sensitivity analysis further reveals a clear trade-off between cost and time: a time-oriented strategy dominated by rail transport reduces total transport time by approximately 20%, whereas a cost-oriented strategy relying on waterway transport decreases total cost by about 73%. These findings demonstrate the effectiveness of the proposed model and provide decision support for efficient and sustainable multimodal transport planning under demand uncertainty.
Hu et al. (Mon,) studied this question.