A Time-Dependent Fuzzy Programming Approach for the Green Multimodal Routing Problem with Rail Service Capacity Uncertainty and Road Traffic Congestion

This study explores an operational-level container routing problem in the road-rail multimodal service network. In response to
the demand for an environmentally friendly transportation, we extend the problem into a green version by using both
emission charging method and bi-objective optimization to optimize the CO2 emissions in the routing. Two uncertain
factors, including capacity uncertainty of rail services and travel time uncertainty of road services, are formulated in order
to improve the reliability of the routes. By using the triangular fuzzy numbers and time-dependent travel time to separately
model the capacity uncertainty and travel time uncertainty, we establish a fuzzy chance-constrained mixed integer nonlinear
programming model. A linearization-based exact solution strategy is designed, so that the problem can be effectively solved
by any exact solution algorithm on any mathematical programming software. An empirical case is presented to demonstrate
the feasibility of the proposed methods. In the case discussion, sensitivity analysis and bi-objective optimization analysis are
used to find that the bi-objective optimization method is more effective than the emission charging method in lowering the
CO2 emissions for the given case. Then, we combine sensitivity analysis and fuzzy simulation to identify the best
confidence value in the fuzzy chance constraint. All the discussion will help decision makers to better organize the green
multimodal transportation.