The method is based on an approach in which sequences are designed once the timetable and the rolling stock assignment have been done.

As for the particular EMU circulation plan in China, it is mainly based on a condition of the utilization of the EMU on one railway sector or within several interacting sectors, which is generally viewed as a more reasonable mode for the EMU operation (see, e.g., Zhao et al. Although the scheduling of the EMU shares something in common with the scheduling of other kinds of transportation tools, especially the scheduling of locomotive in ordinary railway, it has its own characteristics.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper is concerned with the scheduling of Electrical Multiple Units (EMUs) under the condition of their utilization on one sector or within several interacting sectors.

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.The algorithm is based on the graph theory and could be able to deal with the problems of practical size within a reasonable time. In Section 2, we describe the details of the EMU circulation scheduling problem we study.Furthermore, we propose a heuristic, which shares the characteristics with the existing methods and is based on local search strategy. In Section 3, we introduce the concept of the train connection graph, based on which the model of EMU circulation scheduling in high-speed railway network is constructed.The EMU operation plan in each country differs in small points.In China, the EMU operation plan defines the arranging of the train trips and maintenance tasks of each level to each EMU within a certain period of time according to the given train timetable, the configuration of EMU, the condition of EMU maintenance facilities, and the rules of the operation of the stations.Based on the introduction of the train connection graph which describes the possible connection relationship between trains, the integer programming model of EMU circulation planning is constructed.In order to analyzing the resolution of the model, a heuristic which shares the characteristics with the existing methods is introduced first.Some realistic problems such as the unit coupling or uncoupling when scheduling the EMU are also considered. [1] designed an effective heuristic procedure for the train unit assignment problem that were able to find solutions significantly better than the “manual” solutions found by practitioners. [2] proposed a heuristic which is based on the natural Lagrangian relaxation of a natural integer linear programming of the train unit assignment problem which turns out to be much faster in practice and still providing solutions of good quality. [3] deal with the tactical problem of finding the most effective allocation of the train types, subtypes, and units of rolling stock to the train series, such that as many people as possible can be transported with a seat, especially during the rush hours.Lin and Kwan [4] proposed a two-phase approach for the train unit scheduling problem; the first phase assigns and sequences train trips to train units considering some real-world scenarios and the second phase focuses on satisfying the remaining station detailed requirements.Due to the complexity, the lower bound is computed through a polynomial approximation algorithm which is a modification from the one solving the degree constraint minimum 1-tree problem.Then, a branching strategy is designed to cope with the maintenance constraints.

## Comments Branch And Bound Assignment Problem

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