A novel mixed integer programming model for freight train travel time estimation

Travel time estimation is a crucial problem in the field of transportation. While this problem has been extensively studied for over-the-road and air travel modes of transportation and researchers have accomplished substantial advancements in improving the accuracy of the related models, we still observe a significant lack of accurate methods for estimating the travel time of freight trains. The planned train schedule is often dramatically affected by the delays that occur in complex networks due to various reasons such as train movement conflicts, resource unavailability, and unforeseen conditions. We develop a novel mixed integer programming model to address this problem. Considering the current train schedule, characteristics of the railroads, availability of resources, operational restrictions, different types of delay, and congestion-related factors, the proposed model obtains the estimated travel time of trains by minimizing the total amount of deviation from the planned timetable. This optimization scheme enables us to impose all business constraints and network restrictions on the model. Our proposed formulation is generic and can be utilized for other railway networks with minor modifications. To evaluate our model, we use the network characteristics and planned trains movement data of Prorail in Netherlands. The model is implemented in Julia and solved with Gurobi solver efficiently which demonstrates the superiority of our approach.