Mixed route strategies for the risk-averse shipment of hazardous materials

Previous work on the risk-averse routing of hazardous materials has focussed on ways of finding the safest route between a pair of points. For repeated shipments where the arc incident probabilities are unknown, it is shown that the safest strategy is in general to use a mix of routes. Starting with a simple two-route example, it is shown that exposure can be significantly reduced by sharing shipments between routes. In order to determine the safest set of routes and the safest share of traffic between these routes, a minmax problem is formulated. The properties of the optimality conditions are explored. A simple solution heuristic based on a shortest path algorithm and the method of successive averages is proposed. Connections to game theory provide useful insights into the nature of the solution.