Population-based risk equilibration for the multimode hazmat transport network design problem

The shipment of hazardous materials is important and many of these products are flammable, explosive or radioactive. Despite high security standards, accidents still happen and the transportation of hazmat causes fear among the population. Therefore, the society expects authorities to distribute the risk fairly. To support such a fair distribution, we propose a new population-based risk definition that evaluates the risk for the population in any given area with respect to its multimodal transportation network. Moreover, we propose different objective functions for equilibrating the risk and extend the bilevel Hazmat Transport Network Design Problem by considering several transportation modes. In this problem, the government wants to equilibrate the risk among the population centers by restricting links to the shipment of hazardous goods. When taking that decision, the government has to anticipate the reaction of the carriers who want to minimize the transportation costs. This bilevel problem is transformed into a single-level mixed-integer linear program. The numerical results give insights to authorities (1) on how to evaluate risk for a fair distribution, and (2) that there is a positive convex relation between risk minimization and risk equilibration. The zones with high risk will initially benefit from the risk redistribution. However, pure equality just penalizes zones with low risk. Therefore, a significant improvement in risk distribution can be achieved at the cost of just a small increase in total risk. Moreover, compared to classical approaches in the literature, we achieve a better risk distribution among the population without increasing the total risk.