The low probability – high consequence nature of hazardous materials (hazmat) incidents dictate a risk-averse route planning approach. However, preparing routing plans for multiple hazmat shipments between various origin–destination pairs also raises the question of risk-equity, and not just minimization of hazmat risk. Hence, the objective is to plan an equitable routing plan for different rail hazmat shipments while not only ensuring the safety of citizens but also precluding certain population zones from being subjected to intolerable levels of hazmat risk. To this end, we propose an analytical framework that makes use of a conditional value-at-risk (CVaR) measure of risk to generate minimum risk shipment routes while promoting risk-equity in both the arcs and the yards of the railroad network. While the commercial solver, CPLEX, lacks the ability to generate integer solutions for even small problem instances, a Lagrangian relaxation method aimed at being maximized using the Subgradient optimization algorithm is applied to provide a lower bound. The proposed framework is finally used to study several problem instances using the realistic infrastructure of a railroad operator, and to conclude that risk-equity can be achieved by re-routing, and that the design of train services along with the trade-off between yard-risk and arc-risk determine the number of re-routing and the optimal value of CVaR.

危险品（危险品）事故的可能性低-后果严重，决定了规避风险的路线规划方法。但是，为不同目的地对之间的多个危险品运输准备运输计划也提出了风险衡平的问题，而不仅仅是最小化危险品风险。因此，目标是为不同的铁路危险品运输计划一个公平的路线计划，同时不仅要确保公民的安全，而且还要防止某些人口区域遭受不可忍受的危险品风险。为此，我们提出了一个分析框架，该框架利用风险的条件风险值（CVaR）量度来生成最小的风险运输路线，同时在铁路网的弧线和围场中提高风险公平性。商业解决方案CPLEX 由于缺乏针对小问题实例生成整数解的能力，因此应用了旨在使用次梯度优化算法实现最大化的拉格朗日松弛方法来提供下界。所提出的框架最终用于使用铁路运营商的实际基础设施研究几个问题实例，并得出结论，可以通过重新路由来实现风险均等性，并且火车服务的设计以及堆场之间的权衡取舍风险和弧风险确定重新路由的次数和CVaR的最佳值。