Modeling equity of risk in the transportation of hazardous materials

We develop and analyze a model to generate an equitable set of routes for hazardous material shipments. The objective is to determine a set of routes that will minimize the total risk of travel and spread the risk equitably among the zones of the geographical region in which the transportation network is embedded, when several trips are necessary from origin to destination. An integer programming formulation for the problem is proposed. We develop and test a heuristic that repeatedly solves single-trip problems, a Lagrangian dual approach with a gap-closing procedure is used to optimally solve single-trip problems. We report a sampling of our computational experience, based on a real-life routing scenario in the Albany district of New York State. Our findings indicate that one can achieve a high degree of equity by modestly increasing the total risk and by embarking on different routes to evenly spread the risk among the zones. Furthermore, it appears that our heuristic procedure is excellent in terms of computational requirements as well as solution quality. We also suggest some directions for future research.