With the emergence of innovations associated with public transport (PT) services, such as Mobility-as-a-Service, demand responsive transit, and autonomous vehicles, the door-to-door PT journey is achievable via multiple transfers between and within different PT modes. As such, seamless transfers between different modes of public transportation become an increasingly important factor for the attractiveness of PT services. At the same time, recent developments in travel time prediction methodologies offer new, reliable data sources for the optimization of PT operations. This work, with the consideration of these two elements, develops a mixed integer linear programming model for the PT schedule synchronization problem. The novelty is threefold. First, a novel concept of path-oriented scheduling is proposed. The path transfer time is explicitly formulated and minimized to provide a seamless travel experience considering that the emerging multimodal mobility inevitably induces multiple transfers. Second, time-dependent travel time data is also utilized in the model, which allows us to harness new and more representative data sources for improving PT services. Third, in order to complement the increase in computational complexity as a result of the utilization of time-dependent travel time data, three novel valid inequalities (VIs) are derived. Numerical studies show that the use of time-dependent travel time data is beneficial in terms of reducing path transfer times, when compared to using the mean historical travel times. The numerical study also reveals a tradeoff between the maximum allowable path transfer time and trip time. Using simulation studies on three bus lines in Copenhagen, we demonstrate that the valid inequalities could reduce the computation time by 8.5% on average, where the maximum reduction of computation time could reach 54.0%. The proposed valid inequalities are benchmarked against two classes of valid inequalities in the literature. It is found that the proposed valid inequalities could outperform those in the literature. We also found that further improvement in computational performance can be attained by using a combination of the proposed valid inequalities.