Abstract: With the development of the economy, the demand for hazardous material transportation increases rapidly. Due to the advantages of better accessibility and economies of scale, multimodal transportation is widely used in the long-distance transportation of hazardous materials.During multimodal transportation, hazardous materials converge, stay and transit at hubs, which greatly increase the hub’s transportation risk. Therefore, in order to control the risk of multimodal transportation of hazardous materials effectively, it is necessary for government to issue hazardous material transportation permits to proper hubs and optimize the transportation network. We find that studies related to hazmat transportation network design (HTND) problem have the highest relevance to the research of this paper. The existing literatures generally control the transportation risk through a variety of policies and strategies, such as transportation banning, toll setting, flow diverting and speed limiting. These studies mainly focus on a single mode of transportation, especially road transportation, with less research on multimodal transportation. Moreover, the characteristics and constraints of hubs are nearly neglected by most of the research.
Based on the constraints on the location number and maximum tolerable risk of hubs, this paper proposes a risk hierarchical toll setting strategy to minimize the risk of hazardous material multimodal transportation network. Firstly, the strategies of hub location and hierarchical toll setting based on the hub risk level are introduced. Furthermore, according to the ALARP criterion, for each hub, there are three risk levels: acceptable, tolerable and unacceptable. Secondly, a bi-level model is formulated for the hazmat multimodal transport network design. In this model, the upper layer is a hub location and hierarchical toll setting problem for minimizing the total network risk and the total transportation cost, which considers the constraints on both the maximum number and the upper bound risk of hubs. Whereas, the lower layer is a transportation routing problem for minimizing the cost of each transportation event. Thirdly, in this paper, we use KKT conditions to convert the lower layer model to a series of equivalent constraints, linearize the nonlinear constraints in the model, and solve the single-layer bi-objective model after model transformation and simplification with a commercial solver Gurobi. Finally, under the context of road and waterway transportation of hazardous materials in the Chinese Pearl River Delta, numerical experiments are performed and discussed. We first conduct a sensitivity analysis of the maximum number of opening hub. We find that, with an increase in the maximum number of openings of hubs, the total network risk, the total transportation cost, and the average hub risk decrease and gradually stabilize. Second, we present a network design solution based on the hub risk hierarchical toll setting strategy and demonstrate that this strategy can reduce the network risk by regulating the flow of hazardous materials in routes. Third, we compare the network optimal solutions based on four strategies: no government regulation, full government regulation, transportation banning, and hierarchical toll setting based on the hub risk. And we identify the advantages of the hubrisk hierarchical toll setting strategy in balancing the hub risk, controlling the total risk, and reducing the transportation cost.
There are some related topics of this paper deserving further study. For example, it is well worth portraying the relationship between the government regulatory cost and the number of hub locations in the hazmat multimodal transportation network. Meanwhile, in addition to the government and carriers, which are two main participants of the hazardous material transportation in the existing studies, the perspective of the public should be added, and the impact of public’s risk controlling demand on hazmat transportation network design need to be considered.

Key words: hazmat transportation network design, intermodal transportation, toll setting, bi-level optimization

摘要： 近年来,危险品多式联运被广泛应用,而网络中转点由于转运量集聚,导致安全风险较高。为了有效控制危险品多式联运风险,政府可以通过中转点合理选址与分级收费,引导企业合理规划危险品运输路径。首先提出基于中转点风险分级的中转点选址与收费策略,建立危险品多式联运网络设计双层规划模型,上层为网络总风险最小化和总运输成本最小化的中转点选址与分级收费定价问题,下层为各运输事件成本最小化的运输路径规划问题。然后,使用KKT条件转换下层模型为等价约束条件,实现模型单层化,利用Gurobi求解模型。最后,通过算例表明网络风险和运输成本随着中转点数量的增加而降低,证明了中转点分级收费策略可以有效调控危险品多式联运网络风险。

关键词: 危险品运输网络设计, 多式联运, 收费, 双层规划