A branch-and-price-and-cut method for train unit scheduling with complex minimum turnround time requirements

We propose a branch-and-price-and-cut method with warm-start for solving the integer fixed-charge multicommodity flow (IFMCF) model for the network flow level of the train unit scheduling problem, in particular with complex minimum turnround time requirements. This problem is regarded to be difficult due to its nature in integer flows and fixed-charge variables. The key components of this method are a warm-start strategy and a dynamic cut generation scheme that will only add certain constraints when needed. We also study the theoretical perspective in finding strong valid inequalities associated with the dynamic cuts for preventing time allowance violations due to coupling/decoupling.