Worst-Case Conditional Value-at-Risk Minimization for Hazardous Materials Transportation

Despite significant advances in risk management, routing hazardous materials (hazmat) has relied on relatively simpler methods. In this paper, we formally introduce an advanced risk measure, called conditional valueat-risk (CVaR), applied to truck routing problems for hazmat transportation. We find that CVaR offers a flexible, risk-averse, and computationally tractable routing method that is adequate to mitigate hazmat accidents. We further extend CVaR to consider the worst-case CVaR (WCVaR) under data uncertainty. The two important data types in hazmat transportation are accident probabilities and accident consequences, both of which are subject to many ambiguous factors. In addition, historical data are usually insufficient to construct probability distribution of accident probabilities and consequences. This motivates a new robust optimization approach to consider and compute WCVaR. Important axioms are studied for both CVaR and WCVaR risk measures to be coherent and appropriate in the context of hazmat transportation, and computational methods are proposed. We demonstrate the proposed notions of CVaR and WCVaR through a case study in a realistic road network.