A minmax regret version of the time-dependent shortest path problem

We consider a shortest path problem where the arc costs depend on their relative position on the given path and there exist uncertain cost parameters. We study a minmax regret version of the problem under different types of uncertainty of the involved parameters. First, we provide a Mixed Integer Linear Programming (MILP) formulation by using strong duality in the uncertainty interval case. Second, we develop three algorithms based on Benders decomposition for general polyhedral sets of uncertainty. In order to make the algorithms faster we use constant factor approximations to initialize them. Finally, we report some computational experiments for different uncertainty sets in order to compare the behavior of the proposed algorithms.