In this study, a freight routing problem considering both soft delivery time windows and demand and capacity uncertainty in a road–rail intermodal transportation system is investigated. According to fuzzy set theory, uncertain demands and capacities are formulated as trapezoidal fuzzy numbers. Soft delivery time windows under a fuzzy environment is established, in which fuzzy periods caused by early and late deliveries that lead to penalty are modeled based on maximum functions. To solve the routing problem yielding the above characteristics, this study designs a fuzzy mixed-integer nonlinear programming model whose objective is to minimize the total costs created in the road–rail intermodal transportation activities. After using the fuzzy expected value method to address the fuzzy objective, two fuzzy approaches, i.e., fuzzy chance-constrained programming method and fuzzy ranking method, are separately adopted to undertake the defuzzification of the fuzzy constraints. Improved linear formulations of the model are then produced to make it easier to solve. A simulation-based reliability modeling is developed to quantify the reliability of the optimization results given by different fuzzy approaches under different parameter settings in a simulation environment. Finally, an empirical case is presented to verify the feasibility of the proposed methods. The effects of demand and capacity fuzziness on the routing optimization are revealed, and an optimization procedure that helps decision-makers to select a more suitable fuzzy approach and determine the best parameter setting for a given case is demonstrated. Some insights that are helpful for organizing a reliable transportation are also drawn.

在这项研究中，研究了同时考虑软交付时间窗口和路轨联运系统中需求和容量不确定性的货运路线问题。根据模糊集理论，不确定需求和能力被表述为梯形模糊数。建立了在模糊环境下的软交货时间窗口，其中基于最大功能对由提前交货和延迟交货导致罚款的模糊时间段进行建模。为了解决产生上述特征的路径问题，本研究设计了一个模糊混合整数非线性规划模型，其目标是使路轨联运运输活动中产生的总成本最小化。在使用模糊期望值方法解决模糊目标之后，有两种模糊方法，即 分别采用模糊机会约束规划法和模糊排序法对模糊约束进行去模糊化。然后生成改进的模型线性公式，使其更易于求解。建立了基于仿真的可靠性建模，以量化仿真环境中不同参数设置下不同模糊方法给出的优化结果的可靠性。最后，以经验为例，验证了所提方法的可行性。揭示了需求和容量模糊性对路由优化的影响，并演示了一种优化过程，该过程可帮助决策者选择更适合的模糊方法并确定给定情况下的最佳参数设置。