Fuzzy Approaches and Simulation-Based Reliability Modeling to Solve a Road–Rail Intermodal Routing Problem with Soft Delivery Time Windows When Demand and Capacity are Uncertain

Abstract

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. Keywords Road-rail intermodal routing Á Demand uncertainty Á Capacity uncertainty Á Soft time windows Á Simulation-based reliability Á Fuzzy programming model Á Fuzzy expected value Á Fuzzy chance-constrained programming Á Fuzzy ranking Electronic supplementary material The online version of this article (

A Fuzzy Multi-Objective Routing Model for Managing Hazardous Materials Door-to-Door Transportation in the Road-Rail Multimodal Network With Uncertain Demand and Improved Service Level

“…The fuzzy membership degree indicated in Figure 5 shows the possibilities of these values appearing in the practical transportation. Although demand fuzziness has not received enough attention from hazardous materials multimodal routing, limited articles on the similar topic for regular goods that consider such a characteristic can be found [6,23,36].…”

“…Equations (6) to (13) ensure the time validity of the planned hazardous materials road-rail multimodal routes, so that the transshipments of hazardous materials between road and rail at the multimodal terminals on the routes can be realized smoothly according to the schedules of rail services. As a result, the coordination of the two transportation modes can be enhanced.…”

“…In the existing literature, there are various studies that employ exact solutions algorithms to solve the multimodal routing problem and demonstrate their feasibility in dealing with empirical cases, e.g., Xie et al [10] and Sun et al [6,21,30,32]. As a result, this study continues to seek for the application of exact solution algorithms in solving the hazardous materials road-rail multimodal routing problem, in which mathematical programming software can be adopted to run the algorithms efficiently.…”

“…By using this method, defuzzification of fuzzy inequality constraints can be also realized. As demonstrated by Sun [6], using this method reduces the flexibility of the fuzzy optimization. Therefore, Jimenez's fuzzy ranking method [40] is employed by this study as an alternative to carry out the defuzzification of Equation (16).…”

“…Compared with road transportation, rail transportation is more cost-efficient and yields better safety, especially in the long-distance bulk transportation settings. Transferring hazardous materials between road and rail can take advantage of the above characteristics of rail transportation and at the same time keep the good mobility of road transportation in goods pickup and delivery to provide door-to-door services [6]. Consequently, hazardous materials road-rail multimodal transportation is being promoted by both governments and transportation industries globally.…”