How Uncertain Information on Service Capacity Influences the Intermodal Routing Decision: A Fuzzy Programming Perspective

Abstract

Capacity uncertainty is a common issue in the transportation planning field. However, few studies discuss the intermodal routing problem with service capacity uncertainty. Based on our previous study on the intermodal routing under deterministic capacity consideration, we systematically explore how service capacity uncertainty influences the intermodal routing decision. First of all, we adopt trapezoidal fuzzy numbers to describe the uncertain information of the service capacity, and further transform the deterministic capacity constraint into a fuzzy chance constraint based on fuzzy credibility measure. We then integrate such fuzzy chance constraint into the mixed-integer linear programming (MILP) model proposed in our previous study to develop a fuzzy chance-constrained programming model. To enable the improved model to be effectively programmed in the standard mathematical programming software and solved by exact solution algorithms, a crisp equivalent linear reformulation of the fuzzy chance constraint is generated. Finally, we modify the empirical case presented in our previous study by replacing the deterministic service capacities with trapezoidal fuzzy ones. Using the modified empirical case, we utilize sensitivity analysis and fuzzy simulation to analyze the influence of service capacity uncertainty on the intermodal routing decision, and summarize some interesting insights that are helpful for decision makers.

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

“…In the majority of the existing studies on the intermodal routing problem, travel time and loading/unloading time are treated as deterministic parameters. Sun et al [50] pointed out that both overestimation and underestimation might exist if uncertain parameters are valued in a deterministic way, which will reduce the reliability of the intermodal routing.…”

“…Based on the fuzzy set theory introduced by Zadeh [55], fuzzy programming has been widely considered as a useful tool to deal with uncertainty [56]. In the fuzzy programming, the uncertain parameters or variables can be effectively valued by the pessimistic, optimistic and most likely estimations from experts and decision makers based on their knowledge and experience [50]. Consequently, compared with the rest three methods, fuzzy programming does not rely on the size of the existing data or the real-time information of a system and is hence more flexible in practical decision making.…”

“…To realize the defuzzification of Equation (18), fuzzy chance-constrained programming is applied in this study to reformulate the fuzzy constraint. Compared with the fuzzy possibility and fuzzy necessity measures, the fuzzy credibility measure is self-dual and can ensure that a fuzzy event must hold if its credibility equals 1 while it must fail if its credibility equals 0 [27,50]. Therefore, fuzzy credibility is more suitable than the other two measures to be used to construct a fuzzy chance constraint.…”

“…Then we can obtain 10 deterministic cases that can be used to test the performances of different confidence levels and the two MILP models. The fuzzy simulation is run according to Figure 15 [1,50].…”

Green and Reliable Freight Routing Problem in the Road-Rail Intermodal Transportation Network with Uncertain Parameters: A Fuzzy Goal Programming Approach

“…Uncertainty is the primary factor that influences the reliability of intermodal transportation [27][28][29]. Although a short-term planning [8], the routing optimization should be undertaken before the actual transportation starts [30]. However, the operations of the transportation network are easily disrupted by various factors, such as bad weather, traffic congestion, accidents, breakdown or shortage of transportation facilities, and so on [26].…”