Simultaneous train rerouting and rescheduling on an N-track network: A model reformulation with network-based cumulative flow variables

Train dispatching is critical for the punctuality and reliability of rail operations, especially for a complex rail network. This paper develops an innovative integer programming model for the problem of train dispatching on an N-track network by means of simultaneously rerouting and rescheduling trains. Based on a time–space network modeling framework, we first adapt a commonly used big-M method to represent complex “if-then” conditions for train safety headways in a multi-track context. The track occupancy consideration on typical single and double tracks is then reformulated using a vector of cumulative flow variables. This new reformulation technique can provide an efficient decomposition mechanism through modeling track capacities as side constraints which are further dualized through a proposed Lagrangian relaxation solution framework. We further decompose the original complex rerouting and rescheduling problem into a sequence of single train optimization subproblems. For each subproblem, a standard label correcting algorithm is embedded for finding the time dependent least cost path on a time–space network. The resulting dual solutions can be transformed to feasible solutions through priority rules. We present a set of numerical experiments to demonstrate the system-wide performance benefits of simultaneous train rerouting and rescheduling, compared to commonly-used sequential train rerouting and rescheduling approaches.