Generalized route planning model for hazardous material transportation with VaR and equity considerations

Recently, the Value-at-Risk (VaR) framework was introduced for the routing problem of a single hazmat trip. In this paper, we extend the VaR framework in two important ways. First, we show how to apply the VaR concept to a more realistic multi-trip multi-hazmat type framework, which determines routes that minimize the global VaR value while satisfying equity constraints. Second, we show how to embed the algorithm for the single hazmat trip problem into a Lagrangian relaxation framework to obtain an efficient solution method for this general case. We test our computational experience based on a real-life hazmat routing scenario in the Albany district of New York State. Our results indicate that one can achieve a high degree of risk dispersion while controlling the VaR value within the desired confidence level.