Locomotives are often scheduled on a fixed sector and could be viewed as an assignment problem which could be solved by Hungarian algorithm.  formulated the locomotive-scheduling problem as a multicommodity flow problem with side constraints on a weekly space-time network.
Each locomotive type defines a commodity in the network.
Empty movements and shunting operations are considered and the robustness is introduced by selectively avoiding empty train movements and these operations.
Cadarso and Marín  presents a model to study the robust determining of the best sequence for each rolling stock in the train network.
However, the EMUs are scheduled within several linked sectors and some complicated constraints such as the EMU maintenance constraints must be taken into account; therefore, more applicable methods should be developed for solving the construction of the EMU circulation plan.
Zhao and Tomii  transformed the original problem into the Traveling Salesperson Problem and introduced a probability based local search algorithm, whose key points are about the connection of the trains and the generation of the maintenance arcs.  transformed the original problem into a multiple Traveling Salesperson Problem with replenishment and designed a hierarchical optimization heuristic algorithm.  designed a simulated annealing algorithm by introducing the penalty function and 3-opt neighborhood structure, which is based on the circular permutation of all trains.  introduces the optimized EMU connection graph, based on which the improved particle swarm optimization algorithm is designed for solving the problem.
The scheduling of EMU falls in the category of rolling stock circulation problems and the operation plan of them determines the concrete activities they need to perform when the system is running.
In order not to result in the waste of the precious resources, they need to be operated as reasonably as possible.
In Section 4, we design the neighbor structure of the solution of the problem and the local search method is illustrated.
In Section 5, the exact branch and bound algorithm for solving the problem is outlined, and the details of the algorithm such as the calculation of the approximate lower bound and the branching strategy is illustrated.