A Linear Approach to Node-restricted Minmax Regret Robust 1-median on a Tree

In this paper, we consider the node-restricted minmax regret 1-median problem on a tree network where node weights are deterministic and edge lengths are subject to uncertainty with unknown symmetric distribution. There have been proposed some complicated and time-consuming algorithms to obtain robust solutions for robust 1-median problem. We formulate the robust regret function as a mixed integer problem and extend the linear counterpart such that the complexity of our proposed model is the same as the traditional 1-median problem. We use a numerical example to demonstrate the performance of our proposed method.