Integrated Optimization of Weekly Scheduling for Urban Rail Transit Vehicles: Task Assignment, Maintenance, Washing, and Parking

Abstract

Efficient weekly scheduling, including task assignments, maintenance, washing, and parking, for urban rail transit vehicles is essential for reducing operational costs and ensuring smooth depot operations. However, optimizing these components separately may cause inefficiencies, conflicts, and suboptimal vehicle utilization, ultimately compromising system performance and reliability. This study presents an integrated optimization model to minimize mileage variance, driving distances, and shunting operations. To address the multiobjective nature of the problem while satisfying operational constraints, a novel utility-balancing simulated annealing (U-SA) algorithm is developed. In this algorithm, the utility-balancing mechanism is embedded in the SA framework and guided by fuzzy programming to coordinate multiple objectives effectively. The algorithm utilizes three distinct operators—mileage-balancing operator, distance-minimization operator, and shunting-optimization operator—to steer the optimization toward an efficient solution. The model and algorithm are validated through a real-world case study of Beijing Subway’s Line 12. Computational results demonstrate that the approach effectively balances objectives, reduces operational costs, and enhances resource utilization. Sensitivity analysis reveals that adding parking tracks reduces shunting operations, while earlier washing windows helps shorten driving distances. This method offers a practical decision-support tool to improve the efficiency of urban rail transit operations.

Keywords

Weekly scheduling / Task assignment / Maintenance / Washing / Parking / Utility-balancing simulated annealing

References

[1] He L, Liang Q, Fang S. Challenges and innovative solutions in urban rail transit network operations and management: China’s Guangzhou Metro experience. Urban Rail Transit, 2016, 2: 33-45

[2] Lu K, Han B, Zhou X. Smart urban transit systems: from integrated framework to interdisciplinary perspective. Urban Rail Transit, 2018, 4(2): 49-67

[3] Cancan D, Barrena E. The integrated rolling stock circulation and depot location problem in railway rapid transit systems. Transp Res Part E Logist Transp Rev, 2018, 109: 115-138

[4] Zhu S, Wang Y, Wei G, Zheng Y, Zhou D, Bes̆inović N. Integrated optimization of energy-efficient train timetable and rolling stock circulation plan with regenerative energy utilization. J Rail Transp Plan Manag, 2025, 33: 100499

[5] Erguido A, Márquez AC, Castellano E, Flores JL, Fernández JFG. Reliability-based advanced maintenance modelling to enhance rolling stock manufacturers’ objectives. Comput Ind Eng, 2020, 144: 106436

[6] Cacchiani V, Caprara A, Toth P. Solving a real-world train-unit assignment problem. Math Program, 2010, 124(1–2): 207-231

[7] Giacco G, D’Ariano A, Pacciarelli D. Rolling stock rostering optimization under maintenance constraints. J Intell Transp Syst, 2014, 18(1): 95-105

[8] Lai Y, Fan D, Huang K. Optimizing rolling stock assignment and maintenance plan for passenger railway operations. Comput Ind Eng, 2015, 85: 284-295

[9] Lusby RM, Haahr JT, Larsen J, Pisinger D. A Branch-and-Price algorithm for railway rolling stock rescheduling. Transp Res B Methodol, 2017, 99: 228-250

[10] Gao Y, Xia J, D’Ariano A, Yang L. Weekly rolling stock planning in Chinese high-speed rail networks. Transp Res Part B Methodol, 2022, 158: 295-322

[11] Zhang C, Gao Y, Yang L, Gao Z, Qi J. Joint optimization of train scheduling and maintenance planning in a railway network: a heuristic algorithm using Lagrangian relaxation. Transp Res Part B Methodol, 2020, 134: 64-92

[12] Zhong Q, Yu Y, Huang Y, Li W, Zhang Y, Yan X. Collaborative optimization of depot location, capacity and rolling stock scheduling considering maintenance requirements. Sci Rep, 2024, 14: 1-18

[13] Liu C, Xu Z, Mei M, Li W. Join optimization method for preventive maintenance and train scheduling of subway vehicles based on a spatiotemporal network graph. Appl Sci, 2025, 15: 4138

[14] Freling R, Lentink R, Kroon L, Huisman D. Shunting of passenger train units in a railway station. Transp Sci, 2002, 39: 261-272

[15] Lentink RM (2006) Algorithmic decision support for shunt planning. PhD thesis, Erasmus University Rotterdam, Netherlands

[16] Haijema R, Duin CW, Van Dijk NM (2006) Train shunting: a practical heuristic inspired by dynamic programming. In: Planning in intelligent systems: aspects, motivations, and methods. Wiley. pp 437–475. https://doi.org/10.1002/0471781266.ch16

[17] Kroon L, Lentink R, Schrijver A. Shunting of passenger train units: an integrated approach. Transp Sci, 2008, 42(4): 436-449

[18] Wang J, Lin B, Jin J. Optimizing the shunting schedule of electric multiple units depot using an enhanced particle swarm optimization algorithm. Comput Intell Neurosci, 2016, 2016: 1-11

[19] Haahr JT, Lusby RM, Wagenaar JC. Optimization methods for the train unit shunting problem. Eur J Oper Res, 2017, 262(3): 981-995

[20] Kamenga F, Pellegrini P, Rodriguez J, Merabet B, Houzel B (2019) Train unit shunting: integrating rolling stock maintenance and capacity management in passenger railway stations. In: International conference on railway operations modelling and analysis (ICROMA). Norrköping, Sweden. pp 1–10

[21] Wang J, Zhao Y, Gronalt M, Lin B, Wu J. Synchronized optimization for service scheduling, train parking and routing at high-speed rail maintenance depot. IEEE Trans Intell Transp Syst, 2022, 23: 4525-4540

[22] van den Broek R, Hoogeveen H, van den Akker M, Huisman B. A local search algorithm for train unit shunting with service scheduling. Transp Sci, 2022, 56(1): 141-161

[23] Shi J, Li H, Wang D, Vansteenwegen P. Reschedule the shunting and service scheduling plan after disturbances at a Chinese high-speed railway depot. IEEE Access, 2024, 12: 38615-38630

[24] Wang F, Wang P, Zhu Z, Xu R, Pan H, Besinovic N. Robust optimization of train timetables with short-length and full-length services considering uncertain passenger volume and service choice behavior. Transp Res Part C Emerg Technol, 2024, 169: 104855

[25] Cui Z, Yang Y, Hu S, Liu X, Chen L. The decoupling effect analysis of meteorological comfort on urban rail transit ridership. Urban Rail Transit, 2026

[26] Li C, Tang J, Zhang J, Zhao Q, Wang L, Li J. Integrated optimization of urban rail transit line planning, timetabling and rolling stock scheduling. PLoS ONE, 2023, 18(5 e0285932

[27] Zimmermann H. Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst, 1978, 1: 45-55

[28] Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput, 2002, 6(2): 182-197

[29] Xiu C, Pan J, D’Ariano A, Zhan S, Feng T, Peng Q. Integrated train rescheduling and speed management in a railway network: a meso-micro approach based on direct multiple shooting and alternating direction method of multipliers. Transp Res Part C Emerg Technol, 2025, 174: 105076

[30] Ding X, Hu H, Liu Z, Mu Q. The spatiotemporal evolution mechanism of urban rail transit fault propagation in networked operation modes. Urban Rail Transit, 2024, 10: 65-88

[31] Yin J, Tang T, Yang L, Xun J, Su S, Wang Y (2018) A two-stage stochastic optimization model for passenger-oriented metro rescheduling with backup trains. International Conference on Intelligent Transportation Systems (ITSC), Maui, Hawaii, USA. pp 2315–2320

[32] Su B, D’Ariano A, Su S, Wang Z, Tessitore ML, Tang T. A risk-averse two-stage stochastic programming approach for backup rolling stock allocation and metro train rescheduling under uncertain disturbances. Transp Res Part B Methodol, 2025, 196: 103233

Funding

National Key Research and Development Program of China(2024YFA1012904)

National Natural Science Foundation of China(72471023)

Fundamental Research Funds of CRSC(KYRW-2025-01)

RIGHTS & PERMISSIONS

The Author(s)

Just Accepted

This article has successfully passed peer review and final editorial review, and will soon enter typesetting, proofreading and other publishing processes. The currently displayed version is the accepted final manuscript. The officially published version will be updated with format, DOI and citation information upon launch. We recommend that you pay attention to subsequent journal notifications and preferentially cite the officially published version. Thank you for your support and cooperation.