Minmax regret 1-center problem on a network with a discrete set of scenarios

We consider the minmax regret 1-center problem on a general network with uncertainty on demands. Unlike other papers which considered the problem under interval uncertainty, we assume here that demand uncertainty is modelled by a finite number of discrete scenarios. We develop a solution approach based on the decomposition of the network into basic intervals and present a polynomial algorithm for the problem. Finally, we illustrate our approach with an example.ou