Skip to main content
Log in

Joint optimization model for train scheduling and train stop planning with passengers distribution on railway corridors

  • Published:
Journal of the Operational Research Society

Abstract

Aiming to provide a more practical modeling framework for railway optimization problem, this paper investigates the joint optimization model for train scheduling, train stop planning and passengers distributing by considering the passenger demands over each origin and destination (OD) pair on a high-speed railway corridor. Specifically, through introducing new decision variables associated with the number of passengers distributed in each train over each OD pair and formulating the connection constraints between the train stop plan and passenger distributions, the total travel time of all the trains is firstly adopted as the objective function to optimize the train stop plan and timetable with the passenger demands being guaranteed. Then, based on the generated train stop plan and timetable, the passenger distribution plan is further optimized with the purpose of minimizing the total travel time of all the passengers. Finally, the effectiveness and efficiency of the proposed approaches are verified by the obtained train stop plans, timetables and passenger distribution plans for a sample railway corridor and Wuhan–Guangzhou high-speed railway corridor. The computational results showed that the proposed methods can effectively obtain the train stop plan, timetable and passenger distribution plan at the same time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figue 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6

Similar content being viewed by others

References

  • Amit I and Goldfarb D (1971). The timetable problem for railways. Developments in Operations Research 2(1):379–387.

    Google Scholar 

  • Cacchiani V, Caprara A, and Melchiorri C (2006). Models and Algorithms for Combinatorial Optimization Problems arising in Railway Applications. PhD thesis, University of Bologna.

  • Cacchiani V, Caprara A, and Toth P (2008). A column generation approach to train timetabling on a corridor. 4OR: A Quarterly Journal of Operations Research 6(2):125–142.

    Article  Google Scholar 

  • Cacchiani V, Caprara A, and Fischetti M (2012). A Lagrangian heuristic for robustness, with an application to train timetabling. Transportation Science 46(1):124–133.

    Article  Google Scholar 

  • Cai X and Goh C (1994). A fast heuristic for the train scheduling problem. Computers & Operations Research 21(5):499–510.

    Article  Google Scholar 

  • Cai X, Goh C, and Mees A (1998). Greedy heuristics for rapid scheduling of trains on a single track. IIE Transactions 30(5):481–493.

    Article  Google Scholar 

  • Caprara A, Fischetti M, and Toth P (2002). Modeling and solving the train timetabling problem. Operations Research 50(5):851–861.

    Article  Google Scholar 

  • Caprara A, Monaci M, Toth P, and Guidac P (2006). A Lagrangian heuristic algorithm for a real-world train timetabling problem. Discrete Applied Mathematics 154(5):738–753.

    Article  Google Scholar 

  • Chang YH, Yeh CH, and Shen CC (2000). A multi-objective model for passenger train services planning application to Taiwan’s high-speed rail line. Transportation Research Part B 34(2):91–106.

    Article  Google Scholar 

  • Cheng J and Peng Q (2014). Combined stop optimal schedule for urban rail transit with elastic demand. Application Research of Computers 31(11):3361–3364.

    Google Scholar 

  • Corman F, D’Ariano A, and Hansen IA (2014). Evaluating disturbance robustness of railway schedules. Journal of Intelligent Transport Systems: Technology, Planning, and Operations 18(1):106–120.

    Article  Google Scholar 

  • Corman F, D’Ariano A, Marra AD, Pacciarelli D, and Sam M (2016). Integrating train scheduling and delay management in real-time railway traffic control. Transportation Research Part E. DOI:10.1016/j.tre.2016.04.007.

    Google Scholar 

  • D’Ariano A, Pacciarelli D, and Pranzo M (2007). A branch and bound algorithm for scheduling trains in a railway network. European Journal of Operational Research 183(2):643–657.

    Article  Google Scholar 

  • Dollevoet T, Corman F, D’Ariano A, and Huisman D (2014). An iterative optimization framework for delay management and train scheduling. Flexible Services and Manufacturing 26(4):490–515.

    Article  Google Scholar 

  • Feng X, Sun Q, Feng J, and Wu K (2013). Optimization model of existing stop schedule for high-speed railway. Journal of Traffic and Transportation Engineering 13(1):84–90.

    Google Scholar 

  • Fu H, Sperry BR, and Nie L (2013). Operational impacts of using restricted passenger flow assignment in high-speed train stop scheduling problem. Mathematical Problems in Engineering 78(70):143–175.

    Google Scholar 

  • Ghoneim NSA and Wirasinghe SC (1986). Optimal zone structure during peak periods for existing urban rail lines. Transportation Research Part B 20(1):7–18.

    Article  Google Scholar 

  • Ghoseiri K, Szidarovszky F, and Asgharpour MJ (2004). A multi-objective train scheduling model and solution. Transportation Research Part B 38(10):927–952.

    Article  Google Scholar 

  • Goossens JW, Hoesel SV, and Kroon L (2005). On solving multi-type railway line planning problems. European Journal of Operational Research 168(2):403–424.

    Article  Google Scholar 

  • Goverde RMP, Corman F, and D’Ariano A (2013). Railway line capacity consumption of different railway signalling systems under scheduled and disturbed conditions. Journal of Rail Transport Planning & Management 3(3):78–94.

    Article  Google Scholar 

  • Higgins A, Kozan E, and Ferreira L (1996). Optimal scheduling of trains on a single line track. Transportation Research Part B: Methodological 30(2):147–161.

    Article  Google Scholar 

  • Higgins A, Kozan E, and Ferreira L (1997). Heuristic techniques for single line train scheduling. Journal of Heuristics 3(1):43–62.

    Article  Google Scholar 

  • Huang J and Peng Q (2012). Two-stage optimization algorithm for stop schedule plan of high-speed train. Journal of Southwest Jiaotong University 47(3):484–489.

    Google Scholar 

  • Huang Y, Yang L, Tang T, Cao F, and Gao Z (2016). Saving energy and improving service quality: bicriteria train scheduling in urban rail transit systems. IEEE Transactions on Intelligent Transportation Systems 17(12):3364–3379.

    Article  Google Scholar 

  • Huisman D, Kroon L, Lentink RM, and Vromans MJCM (2005). Operations research in passenger railway transportation. Statistica Neerlandica 59(7):467–497

    Article  Google Scholar 

  • Iida Y (1998). Timetable preparation by A.I. approach. In Proceeding of European Simulation Multiconference, Nice France, pp. 163–168.

  • Kroon L, Maróti G, Helmrich MR, Vromans M, and Dekker R (2008). Stochastic improvement of cyclic railway timetables. Transportation Research Part B 42(6):553–570.

    Article  Google Scholar 

  • Larsen R, Pranzo M, D’Ariano A, Corman F, and Pacciarelli D (2014). Susceptibility of optimal train schedules to stochastic disturbances of process times. Flexible Services and Manufacturing Journal 26(4):466–489.

    Article  Google Scholar 

  • Li F, Gao Z, Li K, and Yang L (2008). Efficient scheduling of railway traffic based on global information of train. Transportation Research Part B 42(10):1008–1030.

    Article  Google Scholar 

  • Li D, Han B, Li X, and Zhang H (2013). High-speed railway stopping schedule optimization model based on node service. Journal of the China Railway Society 35(6):1–5.

    Google Scholar 

  • Lusby RM, Larsen J, Ehrgott M, and Ryan D (2011). Railway track allocation: models and methods. OR Spectrum 33(4):843-883.

    Article  Google Scholar 

  • Meng L and Zhou X (2011). Robust single-track train dispatching model under a dynamic and stochastic environment: a scenario-based rolling horizon solution approach. Transportation Research Part B 45(7):1080–1102.

    Article  Google Scholar 

  • Meng L and Zhou X (2014). Simultaneous train rerouting and rescheduling on an N-track network: a model reformulation with network-based cumulative flow variables. Transportation Research Part B 67(3):208–234.

    Article  Google Scholar 

  • Niu H, Zhou X, and Gao R (2015). Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: nonlinear integer programming models with linear constraints. Transportation Research Part B 76:117–135.

    Article  Google Scholar 

  • Pouryousef H, Lautala P, and Watkins D (2016). Development of hybrid optimization of train schedules model for N-track rail corridors. Transportation Research Part C 67:169–192.

    Article  Google Scholar 

  • Qi J, Yang L, Gao Y, and Li S (2015). Robust train timetabling problem with optimized train stop plan. In 2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD’15), Zhangjiajie, China, pp. 936–940.

  • Samà M, Pellegrini P, D’Ariano A, Rodriguez J, and Pacciarelli D (2016). Ant colony optimization for the real-time train routing selection problem. Transportation Research Part B 85(1):89–108.

    Article  Google Scholar 

  • Samà M, D’Ariano A, Corman F, and Pacciarelli D (2017). A variable neighborhood search for fast train scheduling and routing during disturbed railway traffic situations. Computers & Operations Research 78:480–499.

    Article  Google Scholar 

  • Xiong Y (2012). Research on the Express/Slow Train of the Regional Rail Line. Chengdu: Southwest Jiaotong University, pp. 32–40.

    Google Scholar 

  • Xu B (2012). Study on Stop Schedule Plan of High Speed Railway. Beijing: Beijing Jiaotong University, pp. 66–72.

    Google Scholar 

  • Xu X, Li K, and Yang L (2015). Scheduling heterogeneous train traffic on double tracks with efficient dispatching rules. Transportation Research Part B 78:364–384.

    Article  Google Scholar 

  • Yang L, Li K, and Gao Z (2009). Train timetable problem on a single-line railway with fuzzy passenger demand. IEEE Transactions on Fuzzy Systems 17(3):617–629.

    Article  Google Scholar 

  • Yang L, Gao Z, and Li K (2010). Passenger train scheduling on a single-track or partially double-track railway with stochastic information. Engineering Optimization 42(11):1003–1022.

    Article  Google Scholar 

  • Yang L, Li K, Gao Z, and Li X (2012). Optimizing trains movement on a railway network. Omega 40(5):619–633.

    Article  Google Scholar 

  • Yang L, Zhou X, and Gao Z (2013) Rescheduling trains with scenario-based fuzzy recovery time representation on two-way double-track railways. Soft Computing 17(4):605–616.

    Article  Google Scholar 

  • Yang L, Zhou X, and Gao Z (2014) Credibility-based rescheduling model in a double-track railway network: a fuzzy reliable optimization approach. Omega 48(10):75–93.

    Article  Google Scholar 

  • Yang L, Qi J, Li S, and Gao Y (2016). Collaborative optimization for train scheduling and train stop planning on high-speed railways. Omega 64:57–76.

    Article  Google Scholar 

  • Yin J, Tang T, Yang L, Gao Z, and Ran B (2016). Energy-efficient metro train rescheduling with uncertain time-variant passenger demands: an approximated dynamic programming approach. Transportation Research Part B 91:178–210.

    Article  Google Scholar 

  • Yin J, Yang L, Tang T, Gao Z, and Ran B (2017). Dynamic passenger demand oriented metro train scheduling with energy-efficiency and waiting time minimization: mixed-integer linear programming approaches. Transportation Research Part B 97:182–213.

    Article  Google Scholar 

  • Zhang Y, Ren M, and Du W (1998). Optimization of high speed train operation. Journal of Southwest Jiaotong University 33(4):400–404.

    Google Scholar 

  • Zhou X and Zhong M (2005). Bicriteria train scheduling for high-speed passenger railroad planning applications. European Journal of Operational Research 167(3):752–771.

    Article  Google Scholar 

  • Zhou X and Zhong M (2007). Single-track train timetabling with guaranteed optimality: branch and bound algorithms with enhanced lower bounds. Transportation Research Part B 41(3):320–341.

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Nos. 71422002, 71401007, 71401008), the Fundamental Research Funds for the Central Universities (No. 2016YJS082) and the State Key Laboratory of Rail Traffic Control and Safety (No. RCS2017ZZ001), Beijing Jiaotong University.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shukai Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qi, J., Li, S., Gao, Y. et al. Joint optimization model for train scheduling and train stop planning with passengers distribution on railway corridors. J Oper Res Soc (2017). https://doi.org/10.1057/s41274-017-0248-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1057/s41274-017-0248-x

Keywords

Navigation