Spectral risk measure minimization in hazardous materials transportation

Due to catastrophic consequences of potential accidents in hazardous materials (hazmat) transportation, a risk-averse approach for routing is necessary. In this article, we consider spectral risk measures, for risk-averse hazmat routing, which overcome challenges posed in the existing approaches such as conditional value-at-risk. In spectral risk measures, one can define the spectrum function precisely to reflect the decision maker’s risk preference. We show that spectral risk measures can provide a unified routing framework for popular existing hazmat routing methods based on expected risk, maximum risk, and conditional value-at-risk. We first consider a special class of spectral risk measures, for which the spectrum function is represented as a step function. We develop a mixed-integer linear programming model in hazmat routing to minimize these special spectral risk measures and propose an efficient search algorithm to solve the problem. For general classes of spectral risk measures, we suggest approximation methods and path-based approaches. We propose an optimization procedure to approximate general spectrum functions using a step function. We illustrate the usage of spectral risk measures and the proposed computational approaches using data from real road networks.