Equitable routing of rail hazardous materials shipments using CVaR methodology

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.