Linear, non-approximated models for optimal routing in hazardous environments

A linear optimisation model is presented for the routing of vehicles through hazardous environments or for routing vehicles carrying hazardous materials. The model seeks to find the route with the minimum cost and the minimum probability of accident. As opposed to previously published models, the formulation is linear and no approximations are needed, even in the case of high risk. Several forms of considering risk are presented, as well as a simple method of solution in polynomial time. An example is shown and solved.