We consider a robust shortest path problem when the cost coefficient is the product of two uncertain factors. We first show that the robust problem can be solved in polynomial time by a dual variable enumeration with shortest path problems as subproblems. We also propose a path enumeration approach using a $K$-shortest paths finding algorithm that may be efficient in many real cases. An application in hazardous materials transportation is discussed and the solution methods are illustrated by numerical examples.
http://dx.doi.org/10.1002/nav.21540 accepted in Naval Research Logistics.