Spectral Risk Measure Minimization in Hazardous Materials Transportation

Due to catastrophic consequences of accidents by hazardous materials (hazmat) transportation, a risk-averse approach for routing is appropriate for risk mitigation. In this paper, we consider spectral risk measures, which are coherent and more general than 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 first consider a special class of spectral risk measures, for which the spectrum function is represented as a weighted sum of step functions. We develop a mixed integer 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 weighted sum of step functions. We illustrate the usage of spectral risk measures and the proposed computational approaches via a case study in the real road network of Ravenna, Italy.