Anticipating the forthcoming integration of shared autonomous vehicles (SAVs) into urban networks, the imperative of devising an efficient real-time scheduling and routing strategy for these vehicles becomes evident if one is to maximize their potential in enhancing travel efficiency. In this study, we address the problem of jointly scheduling and routing SAVs across an urban network with the possibility of platooning the vehicles at intersections to reduce their travel time. We argue that this is especially useful in large urban areas. We introduce a novel vehicle scheduling and routing method that allows a specific number of SAVs to converge at the intersections of urban corridors within designated time intervals, facilitating the formation of SAV platoons. Dedicated lanes and signal priority control are activated to ensure that these platoons go through the corridors efficiently. Based on the above concept, we propose a linear integer programming model to minimize the total travel time of SAVs and the delays experienced by the conventional vehicles due to SAV priority, thereby optimizing the overall performance of the road network. For large instances, we develop a two-stage heuristic algorithm to solve it faster. In the first stage, leveraging an evaluation index that manifests the compatibility of each vehicle-to-request combination, we allocate passenger requests to a fleet of SAVs. In the second stage, a customized genetic algorithm is designed to coordinate the paths of various SAVs, thus achieving the desired vehicle platooning effect. The optimization method is tested on a real-world road network in Shanghai, China. The results display a remarkable reduction of 15.76 % in the total travel time of the SAVs that formed platoons. The overall performance of the road network could be improved with the total travel time increase of conventional vehicles significantly smaller than the reduction observed in SAVs’ total travel time.