Mixed Routing Strategies for Hazardous Materials: Decision-Making Under Complete Uncertainty

Previous work on the risk-averse routing of hazardous materials has focused on ways of finding a single safest route between a pair of points. For repeated shipments where there is complete uncertainty about link incident probabilities, 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 maximum 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 which considers both the loss in the event of an incident and shipment (travel) cost. Connections to game theory provide useful insights into the nature of the solution. The properties of the optimality conditions are explored leading to the formulation of an equivalent linear programming problem.