Integrated Optimisation of Train Timetables and Maintenance Windows under Mixed Passenger and Freight Train Operation Mode

The train timetable and maintenance windows are closely interrelated and mutually constrained, creating a coupled relationship. Optimising the train timetable can greatly enhance the operational efficiency of trains. This study focuses on the mixed passenger-freight train operation mode and investigates the integrated optimisation of train timetables and maintenance windows in this context. The problem is modelled as a multi-objective mixed-integer programming problem. The model’s objectives are twofold: to minimise the total travel time of all trains and to maximise the density of train paths. Several constraints are incorporated, including those related to train stopping, train safety intervals, passenger train departure time windows and maintenance windows. These constraints ensure that the model reflects practical operational requirements while achieving optimal efficiency. The model places particular emphasis on station capacity constraints. To facilitate solving, these constraints are linearised. A case study is conducted to compare scenarios with and without considering station capacity constraints. The results demonstrate the effectiveness of the proposed model. This study provides theoretical support for the integrated optimisation of train timetables and maintenance windows under mixed passenger-freight train operation mode and offers valuable insights for improving the efficiency of railway transportation.