Abstract: A scheduling system is provided for improving the routing performance of a plurality of objects moving through a transportation network. In one preferred application, a train scheduling system is improved by using an artificial neural network (ANN) to determine the trains' arrival times at various points in the network. Real-time data collection is minimized by training the ANN using stored data regarding historical, previously run train routes. A train's particular physical characteristics are input to the ANN to predict the trains' arrival times at the particular destination within the network. Scheduling and routing functions may then be applied to the ANN output data to determine modified, train arrival times and to make routing changes to optimize the scheduling. Completed route information is continuously fed back to the ANN and the scheduling system to retrain the ANN, assimilate the latest route data and further optimize the system's scheduling performance.