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摘要: 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。Abstract: 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.
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图 5 2021~2025年长周期高级修计划
Figure 5. Long cycle high-level maintenance plans for 2021-2025
表 1 不同时间段允许的检修率
Table 1. Permissible maintenance rates in different time periods
时期 时段 允许检修率 春运 每年正月初一前15天及后25天 3.1%(最大松弛4.1%) 春暑运之间时段 每年春运结束~ 当年6月30日 7.1%(最大松弛8.1%) 暑运 每年7月1日~ 当年8月31日 6.1%(最大松弛7.1%) 国庆 每年10月1日~ 当年10月7日 2.1%(最大松弛4.1%) 平时 其余时间 12.1% 
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表 2 每月允许的最大送修列数
Table 2. Numbers of permissible maintenance in each month
月份 四级修/列次 五级修/列次 月份 四级修/列次 五级修/列次 1 6 6 7 8 8 2 6 6 8 8 8 3 6 6 9 10 10 4 8 8 10 10 10 5 8 8 11 10 10 6 8 8 12 8 8
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表 3 部分动车组参数
Table 3. Parameters of some EMUs
序号 本次修程 时间窗下限/d 时间窗上限/d 日均里程/ km 控制里程下限/km 控制里程上限/km 1 三 278 423 3 091 2 000 3 300 2 三 287 432 3 091 2 000 3 300 3 三 296 441 3 091 2 000 3 300 4 三 275 420 3 091 2 000 3 300 5 三 282 427 3 091 2 000 3 300 6 四 273 447 2 576 2 000 3 300 7 五 290 339 2 010 1 600 3 000 8 三 338 387 2 010 1 600 3 000 9 三 407 456 2 010 1 600 3 000 10 三 289 338 2 010 1 600 3 000 11 三 288 337 2 010 1 600 3 000 12 三 474 523 2 010 1 600 3 000 13 三 452 501 2 010 1 600 3 000 14 三 576 625 2 010 1 600 3 000 15 四 389 574 2 423 2 000 3 300 16 四 389 574 2 423 2 000 3 300 17 四 347 532 2 423 2 000 3 300 18 三 1 107 2 423 2 000 3 300 19 四 379 564 2 423 2 000 3 300 20 四 395 580 2 423 2 000 3 300
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表 4 人工方案高级修发生量
Table 4. Numbers of high-level maintenance tasks in manual plan
列次 年份 2021年 2022年 2023年 2024年 2025年 总计 三级修 70 85 49 65 80 349 四级修 20 52 67 61 37 237 五级修 23 18 20 5 30 96 总计 113 155 136 131 147 682
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表 5 优化方案高级修发生量情况
Table 5. Numbers of high-level maintenance tasks in optimized plan
列次 年份 2021年 2022年 2023年 2024年 2025年 总计 三级修 70(0) 89(4) 46(-3) 49(-16) 79(-1) 333(-16) 四级修 24(4) 46(-6) 60(-7) 56(-5) 52(15) 238(1) 五级修 23(0) 15(-3) 21(1) 3(-2) 30(0) 92(-4) 总计 117(4) 150(-5) 127(-9) 108(-23) 161(14) 663 (-19)
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表 6 送修时间与累计里程对比
Table 6. Comparison of maintenance times and accumulated kilometrages
年度 人工方案 优化方案 送修时间差/d 累计里程差/km 2021 2022-01-28 2022-01-31 3 16 675.36 2022 2022-12-02 2023-01-02 31 74 905.41 2023 2024-02-20 2024-03-25 34 47 721.86 2024 2025-01-26 2025-03-04 37 87 682.56 2025 2025-12-28 2025-12-28 0 3 415.86
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表 7 人工方案与优化方案对比
Table 7. Comparison of manual plan and optimized plan
方案 检修率超标天数/d 三级修检修能力超标天数/d 三级修接车能力超标天数/d 人工方案 174 22 21 优化方案 0 0 0
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[1] LIN Bo-liang, WU Jian-ping, LIN Rui-xi, et al. Optimization of high-level preventive maintenance scheduling for high-speed trains[J]. Reliability Engineering and System Safety, 2019, 183: 261-275. doi: 10.1016/j.ress.2018.11.028 [2] 武建平, 何君礼, 林柏梁, 等. 动车组高级修计划优化模型及算法研究[J]. 铁道学报, 2019, 41(7): 1-9. https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB201907003.htmWU Jian-ping, HE Jun-li, LIN Bo-liang, et al. An optimization model and algorithm for EMU train high-level maintenance planning[J]. Journal of the China Railway Society, 2019, 41(7): 1-9. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB201907003.htm [3] WU Jian-ping, LIN Bo-liang, WANG Jia-xi, et al. A network-based method for the EMU train high-level maintenance planning problem[J]. Applied Sciences, 2017, 8(2): 1-18. [4] 王忠凯, 史天运, 林柏梁, 等. 动车组高级检修车间调度问题的优化模型及算法[J]. 中国铁道科学, 2016, 37(6): 82-89. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201606012.htmWANG Zhong-kai, SHI Tian-yun, LIN Bo-liang, et al. Optimization model and algorithm for overhaul job shop scheduling of electric multiple unit[J]. China Railway Science, 2016, 37(6): 82-89. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201606012.htm [5] 赵晓明. 动车组高级修检修停时优化研究[J]. 中国铁路, 2020(10): 62-65. https://www.cnki.com.cn/Article/CJFDTOTAL-TLZG202010011.htmZHAO Xiao-ming. Study of optimization of stopping time for high-level maintenance and inspection of EMUs[J]. China Railway, 2020(10): 62-65. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TLZG202010011.htm [6] 王利锋. 大规模动车组高级修工艺设计研究[J]. 高速铁路技术, 2018, 9(6): 49-52. https://www.cnki.com.cn/Article/CJFDTOTAL-GSTL201806010.htmWANG Li-feng. Research on advanced maintenance technology design for large-scale EMUs[J]. High Speed Railway Technology, 2018, 9(6): 49-52. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GSTL201806010.htm [7] 吴晨恺, 陈进, 林凤涛. 基于等效锥度的动车组三级修间隔周期研究[J]. 城市轨道交通研究, 2018, 21(10): 48-51. https://www.cnki.com.cn/Article/CJFDTOTAL-GDJT201810014.htmWU Chen-kai, CHEN Jin, LIN Feng-tao. On interval extension in third degree repair of CRH based on equivalent conicity[J]. Urban Mass Transit, 2018, 21(10): 48-51. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GDJT201810014.htm [8] 王忠凯. 动车组运用检修计划优化方法的研究[D]. 北京: 中国铁道科学研究院, 2012.WANG Zhong-kai. Research on the optimization of operation and maintenance schemes of EMUs[D]. Beijing: China Academy of Railway Sciences Co., Ltd., 2012. (in Chinese) [9] 李建. 动车组运用与检修计划综合优化方法研究[D]. 北京: 北京交通大学, 2017.LI Jian. Research on integrated method for optimizing the assignment and maintenance plan of electrical multiple units[D]. Beijing: Beijing Jiaotong University, 2017. (in Chinese) [10] 王家喜. 动车所检修作业计划优化方法研究[D]. 北京: 北京交通大学, 2018.WANG Jia-xi. A study on the optimization method of maintenance operation plan in depots of electric multiple units[D]. Beijing: Beijing Jiaotong University, 2018. (in Chinese) [11] MARÓTI G, KROON L. Maintenance routing for train units: the transition model[J]. Transportation Science, 2005, 39(4): 518-525. doi: 10.1287/trsc.1050.0116 [12] MARÓTI G, KROON L. Maintenance routing for train units: the interchange model[J]. Computers and Operations Research, 2007, 34(4): 1121-1140. doi: 10.1016/j.cor.2005.05.026 [13] CADARSO L, MARÍN A. Improving robustness of rolling stock circulations in rapid transit networks[J]. Computer and Operation Research, 2014, 51(3): 146-159. [14] ALBERTI A R, CAVALCANTE C, SCARF P, et al. Modelling inspection and replacement quality for a protection system[J]. Reliability Engineering and System Safety, 2018, 176: 145-153. [15] BERRADE M, SCARF P, CAVALCANTE C, et al. Imperfect inspection and replacement of a system with a defective state: a cost and reliability analysis[J]. Reliability Engineering and System Safety, 2013, 120: 80-87. doi: 10.1016/j.ress.2013.02.024 [16] WANG Xiao-lin, HE Kang-zhe, HE Zhen, et al. Cost analysis of a piece-wise renewing free replacement warranty policy[J]. Computers and Industrial Engineering, 2019, 135: 1047-1062. [17] WANG Jin-ting, ZHU Sheng, DU Si-miao. Analysis of a two-dimensional stair-case warranty policy with preventive maintenance[J]. IMA Journal of Management Mathematics, 2020(1): 1-17. [18] CAVALCANTE C, SCARF P, BERRADE M. Imperfect inspection of a system with unrevealed failure and an unrevealed defective state[J]. IEEE Transactions on Reliability, 2019, 68(2): 764-775. [19] DRIESSEN J, PENG H, VAN HOUTUM G. Maintenance optimization under non-constant probabilities of imperfect inspections[J]. Reliability Engineeringand System Safety, 2017, 165: 115-123. [20] ALBERTI A R, CAVALCANTE C. A two-scale maintenance policy for protection systems subject to shocks when meeting demands[J]. Reliability Engineering and System Safety, 2020, 204: 107118. [21] WANG Xiao-lin, LI Li-shuai, XIE Min. An unpunctual preventive maintenance policy under two-dimensional warranty[J]. European Journal of Operational Research, 2020, 282(1): 304-318. [22] SU Chun, WANG Xiao-lin. A two-stage preventive maintenance optimization model incorporating two-dimensional extended warranty[J]. Reliability Engineering and System Safety, 2016, 155: 169-178. [23] PENG Shi-zhe, JIANG Wei, ZHAO Wen-hui. A preventive maintenance policy with usage-dependent failure rate thresholds under two-dimensional warranties[J]. ⅡSE Transactions, 2021, 53(11): 1231-1243. [24] YANG Li, YE Zhi-sheng, LEE C G, et al. A two-phase preventive maintenance policy considering imperfect repair and postponed replacement[J]. European Journal of Operational Research, 2019, 274(3): 966-977. [25] GRIGORIEV A, KLUNDERT J, SPIEKSMA F. Modeling and solving the periodic maintenance problem[J]. European Journal of Operational Research, 2006, 172(3): 783-797. [26] MOUDANI W E, MORA-CAMINO F. A dynamic approach for aircraft assignment and maintenance scheduling by airlines[J]. Journal of Air Transport Management, 2000, 6(4): 233-237. [27] SRIRAM C, HAGHANI A. An optimization model for aircraft maintenance scheduling and re-assignment[J]. Transportation Research Part A: Policy and Practice, 2003, 37(1): 29-48. [28] KEYSAN G, NEMHAUSER G L, SAVELSBERGH M W. Tactical and operational planning of scheduled maintenance for per-seat, on-demand air transportation[J]. Transportation Science, 2010, 44(3): 291-306. [29] DERIS S, OMATU S, OHTA H, et al. Ship maintenance scheduling by genetic algorithm and constraint-based reasoning[J]. European Journal of Operational Research, 1999, 112(3): 489-502. [30] GO H, KIM J, LEE D. Operation and preventive maintenance scheduling for containerships: mathematical model and solution algorithm[J]. European Journal of Operational Research, 2013, 229(3): 626-636. [31] 于毅, 刘红, 阮继华. 基于层次分析法优化船舶维修计划[J]. 江苏船舶, 2001, 18(4): 14-16. https://www.cnki.com.cn/Article/CJFDTOTAL-JSCB200104003.htmYU Yi, LIU Hong, RUAN Ji-hua. Optimizing ship maintenance plans based on analytic hierarchy process method[J]. Jiangsu Ship, 2001, 18(4): 14-16. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSCB200104003.htm [32] HAGHANI A, SHAFAHI Y. Bus maintenance systems and maintenance scheduling: model formulations and solutions[J]. Transportation Research Part A: Policy and Practice, 2002, 36(5): 453-482. -
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