The transportation of hazardous materials (hazmat) has drawn significant attention from various stakeholders due to the undesirable impacts on the environment and public health. Focusing on the connection between the traffic and the risk associated with the hazmat shipments, the present research aims to assist the regulator in designing a policy of dual tolls, imposed on both hazmat and non-hazmat shipments, to mitigate the hazmat risk in a road network.
A bi-objective bi-level programming formulation is constructed. To be specific, the upper level model indicates the regulator’s decision problem, minimizing the maximum link risk and the total network risk by imposing a dual-toll policy on any carrier. The lower level jointly considers the decisions of multiple hazmat carriers and non-hazmat travelers, minimizing the total transportation cost, including the toll cost. (By “nonhazmat traveler”, we mean both people who carry and do not carry products.) Given the bi-level structure and the non-linear nature, a solution procedure with two parts is designed. First, we develop two alternative linearization approaches. One is piecewise linearization, transforming the non-linear terms into linear ones. The other applies the Frank-Wolfe algorithm, an iterative first-order optimization algorithm. Then a genetic-algorithm-based methodology will integrate both levels. Computational experiments on different sizes of networks are performed to demonstrate the effectiveness of the model. Various analyses, involving trade-offs, sensitivities, and examination of convergence, are conducted to provide additional managerial insights. These can be used to facilitate stakeholders’ decision making.
200 University Avenue West
Waterloo, ON N2L 3G1