Integrated routing and scheduling of hazmat trucks with stops en route

We consider an integrated routing and scheduling problem in hazardous materials transportation where accident rates, population exposure, and link durations on the network vary with time of day. We minimize risk (accident probability multiplied by exposure) subject to a constraint on the total duration of the trip. We allow for stopping at the nodes of the network. We consider four versions of this problem with increasingly more realistic constraints on driving and waiting periods, and propose pseudopolynomial dynamic programming algorithms for each version. We use a realistic example network to experiment with our algorithms and provide examples of the solutions they generate. The computational effort required for the algorithms is reasonable, making them good candidates for implementation in a decision-support system. Many of the routes generated by our models do not exhibit the circuitous behavior common in risk-minimizing routes. The en route stops allow us to take full advantage of the time-varying nature of accident probabilities and exposure and result in the generation of routes that are associated with much lower levels of risk than those where no waiting is allowed.