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Int. J. Environ. Res. Public Health 2016, 13(8), 762; doi:10.3390/ijerph13080762

Bi-Objective Modelling for Hazardous Materials Road–Rail Multimodal Routing Problem with Railway Schedule-Based Space–Time Constraints

1
School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China
2
Ministry of Education Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing 100044, China
3
Transportation and Economics Research Institute, China Academy of Railway Sciences, Beijing 100081, China
*
Author to whom correspondence should be addressed.
Academic Editor: Jason K. Levy
Received: 12 June 2016 / Revised: 19 July 2016 / Accepted: 22 July 2016 / Published: 28 July 2016
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Abstract

The transportation of hazardous materials is always accompanied by considerable risk that will impact public and environment security. As an efficient and reliable transportation organization, a multimodal service should participate in the transportation of hazardous materials. In this study, we focus on transporting hazardous materials through the multimodal service network and explore the hazardous materials multimodal routing problem from the operational level of network planning. To formulate this problem more practicably, minimizing the total generalized costs of transporting the hazardous materials and the social risk along the planned routes are set as the optimization objectives. Meanwhile, the following formulation characteristics will be comprehensively modelled: (1) specific customer demands; (2) multiple hazardous material flows; (3) capacitated schedule-based rail service and uncapacitated time-flexible road service; and (4) environmental risk constraint. A bi-objective mixed integer nonlinear programming model is first built to formulate the routing problem that combines the formulation characteristics above. Then linear reformations are developed to linearize and improve the initial model so that it can be effectively solved by exact solution algorithms on standard mathematical programming software. By utilizing the normalized weighted sum method, we can generate the Pareto solutions to the bi-objective optimization problem for a specific case. Finally, a large-scale empirical case study from the Beijing–Tianjin–Hebei Region in China is presented to demonstrate the feasibility of the proposed methods in dealing with the practical problem. Various scenarios are also discussed in the case study. View Full-Text
Keywords: hazardous materials; multimodal routing; risk evaluation; bi-objective optimization; linear reformulation hazardous materials; multimodal routing; risk evaluation; bi-objective optimization; linear reformulation
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MDPI and ACS Style

Sun, Y.; Lang, M.; Wang, D. Bi-Objective Modelling for Hazardous Materials Road–Rail Multimodal Routing Problem with Railway Schedule-Based Space–Time Constraints. Int. J. Environ. Res. Public Health 2016, 13, 762.

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