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In this study, we systematically investigate a road-rail intermodal routing problem the optimization of which is oriented on the customer demands on transportation economy, timeliness and reliability. The road-rail intermodal transportation system is modelled as a hub-and-spoke network that contains time-flexible container truck services and scheduled container train services. The transportation timeliness is optimized by using fuzzy soft time windows associated with the service level of the transportation. Reliability is enhanced by considering multiple sources of time uncertainty, including road travel time and loading/unloading time. Such uncertainty is modelled by using fuzzy set theory. Triangular fuzzy numbers are adopted to represent the uncertain time. Under the above consideration, we first establish a fuzzy mixed integer nonlinear programming model with a weighted objective that includes minimizing the costs and maximizing the service level for accomplishing transportation orders. Then we use the fuzzy expected value model and fuzzy chance-constrained programming separately to realize the defuzzification of the fuzzy objective and use fuzzy chance-constrained programming to deal with the fuzzy constraint. After defuzzification and linearization, an equivalent mixed integer linear programming (MILP) model is generated to enable the problem to be solved by mathematical programming software. Finally, a numerical case modified from our previous study is presented to demonstrate the feasibility of the proposed fuzzy programming approaches. Sensitivity analysis and fuzzy simulation are comprehensively utilized to discuss the effects of the fuzzy soft time windows and time uncertainty on the routing optimization and help decision makers to better design a crisp transportation plan that can effectively make tradeoffs among economy, timeliness and reliability.

mathematics

Fuzzy Programming Approaches for Modeling a Customer-Centred Freight Routing Problem in the Road-Rail Intermodal Hub-and-Spoke Network with Fuzzy Soft Time Windows and Multiple Sources of Time Uncertainty