This paper presents an optimal routing algorithm (ORA) for maximizing voltage stability as well as for minimizing power loss in radial power systems. In the proposed ORA, a novel voltage stability index (VSI) for real-time assessment is newly introduced based on the conventional critical transmission path framework. In addition, the suggested algorithm can automatically detect the critical transmission paths resulting in voltage collapse when additional real or reactive loads are added. To implement an effective ORA, we have developed an improved branch exchange (IBE) method based on a loss calculation index and tie-branch power flow equations, which are suggested for real-time applications. The proposed algorithm has been tested with IEEE test systems as well as a large-scale power system in Korea to demonstrate its effectiveness and efficiency.