Mixed-Integer Programming for Railway Capacity Analysis and Cyclic, Combined Train Timetabling and Platforming

We present the literature’s first mixed-integer linear programming model of a cyclic, combined train timetabling and platforming problem. The model’s objectives are to minimize (1) the cycle length and (2) the total journey time of all trains dispatched during one cycle. The model falls outside the framework of the well-known periodic event scheduling problem and explicitly considers the minimization of cycle length using linear constraints and a linear objective function. We define the model, propose methods for obtaining bounds on the optimal objective value, and describe preprocessing techniques for reducing the number of variables and constraints. Numerous life-size problem instances are solved to optimality using IBM ILOG CPLEX. Results show the model’s effectiveness in pursuing objectives 1 and 2, the benefits of deciding the cyclic train order versus assuming a given order, and the model’s ability to calculate railway capacity without bias.