高铁动车组长周期高级修计划优化方法

分析了不同类型动车组高级修计划的特点及其关联因素，讨论了高级修计划编制问题的复杂性；基于滚动迭代思想提出了编制动车组长周期高级修计划的方法，通过依次求解规划期内各计划年的动车组高级修轮廓计划，编制了完整的长周期高级修计划；设计了分别表示动车组送修时间以及动车组检修状态的0-1变量，以动车组在2次高级修间隔内走行里程最大化为优化目标，以不同时间段动车组最大检修率限制、承修单位允许的接车以及最大检修能力、计划年度内在高级修上的资金限制、动车组每月高级修允许送修数量、动车组日均控制里程、列车运行图里程等实际要求为约束条件，构建了动车组高级修计划优化的线性0-1整数规划模型；以配属中国铁路北京局集团有限公司的279列动车组历史走行数据以及相关参数为基础，通过Python编程并调用商业求解器对模型进行精确求解，首次实现了对该局所有动车组长周期高级修计划的优化编制。计算结果表明:优化后动车组长周期高级修计划较人工方案减少了19次高级修，节约资金消耗1.505亿元，延长规划期内动车组年均运用时间21 d，增加动车组年均走行里程46 080.21 km；同时避免了人工方案中动车组检修率超标及检修能力超出限制的情况，提高了动车组的运用效率以及计划编制的科学性。 

Optimization method of long cycle high-level maintenance plan for high-speed EMUs

The characteristics of different high-level maintenance plans for electric multiple units (EMUs) and their associated factors were analyzed, and the complexity of high-level maintenance planning problem was discussed. A method for scheduling a long cycle high-level maintenance plan for EMUs was proposed on the basis of rolling iteration method, and a complete long cycle high-level maintenance plan was made after the annual high-level maintenance profile plan was obtained for each planning year in the plan cycle in turn. 0-1 variables representing the repair time and maintenance state of EMUs were designed, and the maximization of the running kilometrage by EMUs in the interval between two adjacent high-level maintenance tasks was taken as the objective. The real-life requirements were used as constraints, including the upper maintenance rate limits of EMUs in different periods, the permitted receiving and the maximum maintenance capacities of the maintenance unit, the capital budget for high-level maintenance in the planning year, the allowed number of EMUs for high-level maintenance tasks per month, the average daily control kilometrage of EMUs, and the kilometrage of the train timetable. A linear 0-1 integer programming model was constructed for the optimization of high-level maintenance plans. Based on the historical running data and relevant parameters of 279 EMUs assigned to China Railway Beijing Group Co., Ltd., the model was accurately solved by Python calling commercial solvers to realize the optimization of the long cycle high-level maintenance plan of all EMUs in the railway group for the first time. Calculation results show that in the optimized long cycle high-level maintenance plan for EMUs, 19 high-level maintenance tasks are reduced compared with the manual plan, and the capital consumption of 150.5 million yuan is saved. In addition, the average annual operating time of EMUs is extended by 21 d during the planning period, and the average annual running kilometrage of EMUs increases by 46 080.21 km. Meanwhile, the exceeded maintenance rate and the maintenance capacity beyond the limit occurring in the manual scheme can be avoided, and the efficiency of EMUs operation improves with more scientific planning under the optimized scheme.