Modeling a Green Intermodal Routing Problem with Soft Time Window Considering Interval Fuzzy Demand

We discuss an intermodal routing problem that aims to achieve comprehensive improvement in the economics, environmental sustainability, and timeliness of transportation. We formulate the consignee’s uncertain demand for goods to improve the reliability of the planned intermodal route on transportation budget and capacity restriction in practice, in which an interval fuzzy demand is proposed, considering the difficulty of obtaining enough data to precisely evaluate the most likely demand conditions. A soft time window is considered, and its associated interval fuzzy storage and penalty periods are modeled considering timely transportation. A carbon tax regulation is used to reduce the carbon emissions of intermodal transportation. We combine the above settings when modeling the routing problem, establish an interval fuzzy optimization model to address the problem, and further present its equivalent reformulation, which is both crisp and linear. Based on the above modeling, a systematic case analysis reveals the conflicting relationship between the economics and reliability of intermodal transportation and indicates that the consignee should balance the different objectives. Then, a systematic verification of the optimization settings is conducted in a numerical case study. We analyze the carbon emission reduction effect of the carbon tax regulation in different decision-making cases, which provides a complete procedure for the policy maker to test the feasibility of carbon tax regulation in achieving green transportation. Faced with the infeasibility of carbon tax regulation in some decision-making cases, an alternative scheme combining bi-objective optimization and carbon tax regulation is developed for the transportation organizer to effectively reduce carbon emissions when organizing intermodal transportation. Furthermore, the numerical case study demonstrates the advantages of a soft time window in planning a highly reliable intermodal route, which makes the consignee pay attention to its design according to the post-transportation goods processing. Finally, we explore the influence of the uncertainty level of the interval fuzzy demand and the capacity level of the intermodal network on intermodal routing, and we stress that the consignee should take measures to improve the stability of uncertain demand, and the transportation organizer should expand the capacity of the intermodal network to a certain degree.