Optimal routing of hazardous materials considering risk of spill

The diffusion of gases over wide areas from possible spills during transport of hazardous materials is considered when determining the least risk path through a network. Spills could occur through improper operation of vehicle or container or through a collision. Relationships for minimum risk paths are developed for these cases: specific wind directions, uniform average wind direction, maximum concentration wind directions, wind-rose averaged wind directions and speeds, and multiday routing with uncertain weather conditions. The relationships are illustrated for a full-sized urban network. This paper illustrates, how a Geographical Information System approach coupled with elementary principles of optimization theory can be used to solve such complex routing problems. The mathematics developed also reveals some consistent properties of all routing problems that are generalizable. For short trips the least risk path is invariant with the assumed wind speed, the size of spill, and the toxicity of the material. It is also invariant with the selection between uniform average wind direction and maximum risk direction criteria. A hybrid between numerical and analytical methods was adopted to reduce computation requirements which are still large but acceptable.