A robust optimization model for p-median problem with uncertain edge lengths

In this paper, we propose a p-median problem with uncertain edge lengths where uncertainty is characterized by given intervals. The uncertainty in edge lengths may appear in transportation costs or travel times along the edges in any network location problem. Minimax regret approach is a promising tool to cope with uncertainty in network location problems. However, minimax regret algorithms normally suffer from complexity, and they are time consuming. We propose a robust optimization approach to obtain the robust linear counterpart for the same class of the nominal p-median problem. The performance of the proposed model is compared with minimax regret approach through a simple but illustrative example, and results are discussed in more details.