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.
Citation
http://dx.doi.org/10.1002/nav.21540 accepted in Naval Research Logistics.