A Bi-Objective Fuzzy Credibilistic Chance-Constrained Programming Approach for the Hazardous Materials Road-Rail Multimodal Routing Problem under Uncertainty and Sustainability

Abstract

Hazardous materials transportation involves extensive risk and cannot be avoided in practice. An advanced routing, however, can help to reduce the risk by planning the best transportation routes for hazardous materials that can make effective tradeoffs between the risk objective and the economic objective. In this study, we explore the hazardous materials routing problem in the road-rail multimodal transportation network with a hub-and-spoke structure, in which the risk is measured by the multiplication of population exposure and the associated volume of hazardous materials, and minimizing the total risk of all the transportation orders of hazardous materials is set as the risk objective. It is difficult to estimate the population exposure exactly during the routing decision-making process, which results in its uncertainty. In this study, we formulate the uncertain population exposure from a fuzzy programming perspective by using triangular fuzzy numbers. Moreover, the carbon dioxide emission constraint is formulated to realize the sustainable transportation of hazardous materials. To optimize the problem under the above framework, we first establish a bi-objective fuzzy mixed integer nonlinear programming model, and then develop a three-stage exact solution strategy that the combines fuzzy credibilistic chance constraint, linearization technique, and the normalized weighting method. Finally, a computational experiment is carried out to verify the feasibility of the proposed method in dealing with the problem. The experimental results indicate that tradeoffs between the two conflicting objectives can be effectively made by using the Pareto frontier to the hazardous materials routing problem. Furthermore, the credibility level and carbon dioxide emission cap significantly influence the hazardous materials routing optimization. Their effects on the optimization result are quantified by using sensitivity analysis, which can draw some useful insights to help decision makers to better organize the hazardous materials road-rail multimodal transportation under uncertainty and sustainability.

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

“…Lowering costs reflects the customer demand on improving transportation economy and is always the most important objective of intermodal routing optimization. Even in the multi-objective optimization on the intermodal routing problem, for example, the hazardous materials routing problem [29,30] and fresh food routing problem [31], the economic objective plays an important role in the optimization. A few studies on the intermodal routing problem, e.g., Chang [8] and Moccia et al [32], adopt a piecewise linear cost function that shows the effect of economies of scale to calculate the economic objective.…”

“…Therefore, it is not completely applicable to use the piecewise linear cost function to represent the economic objective function. Currently, the majority of the existing studies employ generalized costs to formulate the charges for accomplishing the transportation orders, e.g., Sun et al [1,18,25,30], Ayar and Yaman [31], Hrušovský et al [2] and Demir et al [3]. Generalized costs have a structure shown as Figure 2 [30,33,34] and thus cover all the payment created in the activities of the intermodal transportation.…”

“…Mathematics 2019, 7, x FOR PEER REVIEW 5 of 40 the transportation orders, e.g., Sun et al [1,18,25,30], Ayar and Yaman [31], Hrušovský et al [2] and Demir et al [3]. Generalized costs have a structure shown as Figure 2 [30,33,34] and thus cover all the payment created in the activities of the intermodal transportation. In this study, we continue to use generalized costs to formulate the economic objective of road-rail intermodal routing problem.…”

“…Under this situation, soft time windows receive a lot of attention from the intermodal routing literature when discussing the formulation of due dates. Sun et al [1,18,30] and Fazayeli et al [46] explore the intermodal location-routing problem with due dates denoted by soft time windows. In Fazayeli et al's study, the penalty cost strategy that is the same as that of Hrušovský et al [2] and Demir et al [3] is used to optimize the timeliness of the intermodal transportation.…”

“…The hub-and-spoke network is widely acknowledged to be the most suitable consolidation network to construct the road-rail intermodal transportation system [18]. The superiority of the road-rail intermodal hub-and-spoke network is its systematic integration of the different advantages of the time-flexible road transportation and scheduled rail transportation in the pre haul-long haul-end haul transportation chain, which is stressed by Wang et al [19] and Sun et al [1,18,30].…”