A dual toll policy for maintaining risk equity in hazardous materials transportation with fuzzy incident rate

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A dual-toll policy, considering a multi-degree fuzzy incident rate, is proposed to mitigate the risk caused by hazardous material (hazmat) transportation in a road network. To address several carriers transporting multiple hazmat types, we use a bi-level programming formulation. The upper and lower levels, respectively, exemplify decision problems faced by the regulators (regional and local governments) and travelers (hazmat and non-hazmat).The contributions of this paper are threefold. •In addition to the total network risk, our model includes risk equity (minimization of the maximum link risk). This makes the spatial distribution of risk closer to homogeneous.•We propose a new definition of risk measurement, based on the integration of a fuzzy incident rate and population exposure, together with the transportation time. This new definition better reflects the uncertain nature of actual transportation situations.•We construct a new real-world transportation network based on data from the City of Nanchang, China. Empirical distances, travel times, population densities, and applicable regulations are incorporated in this network of 32 nodes and 102 arcs. Our model is solved, based upon the preceding figures and toll values that are consistent with Chinese national standards.To solve the model effectively, a genetic-algorithm-based methodology is employed, along with a piecewise linearization method and a Frank-Wolfe approach. Employing both the well-known Sioux-Falls network and the new, larger network, case studies are presented. If distinct hazmat tolls are imposed on differing hazmat types, those case studies enable managerial insights, derived from the dual toll policy, when incident possibilities vary.