A value-at-risk based approach to the routing problem of multi-hazmat railcars

This paper solves a routing problem of multi-hazmat railcars with consolidation operations in order to avoid serious consequences of hazmat accidents. We develop a bi-level optimization model for this problem, and apply a value-at-risk (VaR) approach to generate route choices. By incorporating the consolidation operations performed among different railway shipments, both the risks incurred at yards and on service legs are integratively quantified to evaluate route risks. Due to the inherent complexity of the problem, we propose an exact algorithm as well as a heuristic algorithm to solve the proposed model, and conduct extensive numerical experiments on instances generated from a real railway system in the Midwestern United States. The analysis shows that risk-seeking decision makers will benefit from consolidated transportation due to its potential to significantly reduce total transportation costs. As decision makers become more risk averse, i.e., confidence level increases, increasing the number of train services and reducing the amount of hazmat railcars and consolidation operation has a positive impact on reducing route risk. In addition, the computational results verify the effectiveness of our proposed optimization model and solution approaches, which can generate various routing plans for railway companies under different risk preferences, and our proposed heuristic algorithm gives an optimal or near-optimal solution in 1.41% to 28.22% of the time required by the exact algorithm.