# A Network-Based Method for the EMU Train High-Level Maintenance Planning Problem
[13] developed a method to forecast the maintenance quantity of EMU in an arbitrary time period, accurately and efficiently. Figure 1: The high-level maintenance plan (HMP) process at China Railway Corporation (CR). EMU: electric multiple unit; HM: high-level maintenance. Similar to EMU maintenance scheduling, scheduled maintenance planning problems have been studied in other fields; [PERSON] et al. [14] studied the locomotive operation by constructing a large integer programming model, and they focused on the influence of maintenance for operation. [PERSON] et al. [15] described a model for operational management of locomotive hauled railway cars. They sought for a maximum expected profit schedule that satisfied various constraints, among them maintenance requirements were also included. [PERSON] et al. [16] developed a 0-1 integer programming model to study locomotive operation and maintenance, and applied genetic algorithm to solve the model. However the model ignored the maintenance capacity. [PERSON] and [PERSON] [17; 18] studied the problems of assigning planes to flights and of fleet maintenance operations scheduling. And they also proposed a dynamic approach to cope with the fleet assignment problem and a heuristic technique to solve the embedded maintenance scheduling problem. [PERSON] et al. [18] presented a mathematical formulation for the long-term planning of railway maintenance works. The objective is to minimize the time required for maintenance, expressed as a cost function. Heuristic algorithms computed nearly optimal solutions by combining maintenance activities on each track. [PERSON] and [PERSON] [19] developed integer linear programming model by modifying the connection network representation which provided feasible maintenance routes for each aircraft in the fleet over a weekly planning horizon, with the objective of maximizing the utilization of the total remaining flying time of fleet. The proposed model is solved by using branch-and-bound under different priority settings for variables to branch on. In addition, [PERSON] et al. [20] studied the problem of scheduling maintenance services, and the objective was to find a cyclic maintenance plan of a given length that minimized total operation costs. A branch and price algorithm was applied to solve the model. [PERSON] et al. [21] proposed a novel method to solve the shop scheduling problem featured with uncertain processing times. [PERSON] et al. [22] utilized the Markov property and neural network ensemble to construct an estimated matrix that combines the interaction of the different local factors. Compared to the existing researches, this research includes some highlights as follows. (1) A 0-1 integer programming model and its improvements were proposed to reduce the costs of HM with consideration of all necessary regulations and practical constraints, especially for the passenger transport peak demand; (2) Taking into account the practice constraints, we constructed a time-state network for optimizing HMP; (3) the generation method of the path set was presented to solve the mathematical model effectively and efficiently by controlling the solution space. This paper is organized as follows. Section 2 aims to systematically describe the HMP problem in the CR system. Section 3 constructs a time-state network for optimizing the HMP, then an integer programming model and its improvements were proposed to minimize the HM costs, followed by the path set generation method to solve the mathematical models effectively and efficiently in Section 4. An empirical case and sensitivity analysis using standard optimization solvers are presented in Section 5.