Risk-Averse Network Design with Behavioral Conditional Value-at-Risk for Hazardous Materials Transportation

We consider a road-ban problem in hazardous material (hazmat) transportation. We formulate the problem as a network design problem to select a set of closed road segments for hazmat traffic and obtain a bilevel optimization problem. While modeling probabilistic route choices of hazmat carriers by the random utility model (RUM) in the lower level, we consider a risk-averse measure called conditional value at risk (CVaR) in the upper level, instead of the widely used expected risk measure. Using the RUM and CVaR, we quantify the risk of having hazmat accidents and large consequences and design the network policy for road bans accordingly. Although CVaR has been used in hazmat routing problems, this paper is the first attempt to apply CVaR in risk averse hazmat network design problems considering stochastic route choices of hazmat carriers. The resulting problem is a mixed integer nonlinear programming problem, for which we devise a line search approach combined with Benders decomposition. We demonstrate the efficiency of the proposed computational method with case studies. The average computation time for a network with 105 nodes and 268 arcs is three hours. By applying CVaR to the route-choice behavior of hazmat carriers, we protect the road network from undesirable route choices that may lead to severe consequences. We define the value of RUM-CVaR solutions (VRCS) over the deterministic model based on shortest-path problems and the expected risk measure. Our case study shows that the VRCS can range from 4.9% to 64.1% depending on the probability threshold used in the CVaR measure.