The robust path centdian problem with interval vertex weights on tree networks

In this paper the robust path centdian problem is investigated on tree networks with the same interval vertex weights for the both path center and path median problems. The used objective function in this paper is the simple sum of path median and path center problems. In the past research works the vertex weights for the both path median and path center location problems are disjoint. The used approach to compute the robust solution is the minmax regret criterion. In this method for any selected path on the tree, the maximum value of regret is minimized for all possible events of vertex weights. Using the minmax regret criterion, an algorithm with O(n^5) time complexity is presented to obtain a robust solution of the robust path centdian problem on tree networks. In this paper using the worst case scenarios for the path median and path center we obtain the worst case scenarios of robust centdian problem. Then we obtain a robust solution for this problem.