Abstract: The rapid growths of international trade and freight transportation have brought multimodal transportation into a new stage. Meanwhile, several countries are planning to or have already carried out low-carbon policies to reduce CO₂ emissions released from transportation industry, including China.Route selection problem in multimodal transportation under the cap and trade policy is investigated in this paper, which takes the uncertainties of transport time and fright rate into consideration, and their probability distributions are also unknown.
Robust optimization is introduced to deal with the uncertainty of parameters, which allows us to conduct mixed integer linear programming models immune to data uncertainty. Firstly, the box uncertainty set is applied to capture uncertainties of time and fright rate, and then a robust optimization model offering the flexibility of adjusting the budget of uncertainties is constructed based on the deterministic model for route selection problem in multimodal transportation under cap and trade policy. The robust model is finally transformed into a tractable robust equivalent model by dualization.
Numerical experiments are conducted according to a real multimodal transportation system in southern China, and related data are collected from logistics companies, websites of local transportation sectors and annals of relevant departments.Results of experiments show that the proposed robust models could deal with route selection problems in multimodal transportation under uncertainty, in which the unknown parameters'probability distributions are not given.Those models allow decision makers to make decisions by adjusting the budget parameters of uncertainty according to their preferences. Moreover, it is found that either transportation time uncertainty or fright rate uncertainty has influences on multimodal transportation routing decisions, but the influences are carried out in different ways.Furthermore, after expanding the above models under the cap and trade policy to other low-carbon policies, it is advised that a combination of different low-carbon policies is better for emission reduction in multimodal transportation.
A new idea about solving route selection problem is provided in multimodal transportation under the cap and trade policy and uncertainty.

Key words: route selection problem, multimodal transportation, robust optimization, the cap and trade policy, MIP