Robust Shortest Path Problems with Two Uncertain Multiplicative Cost Coefficients

Abstract

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.