In this thesis, we apply the reliability-based backup 2-center model proposed by Wang, where each facility may fail with a given probability. Once a facility fails, the other has to be responsible for all the services. We assume that two facilities do not fail at the same time. In the weighted backup 2-center problem on paths, we want to locate two
facilities on vertex-weighted paths such that the expected weighted distance is minimized. We construct an O(n)-time algorithm, where n is the number of vertices in the given path.
