Train Scheduling

  • Carl Van DykeEmail author
  • Marc Meketon
  • Problem Solving Competition Committee
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 222)


Train schedule design is a critical element of the overall railroad operating plan design problem. It determines the utilization of the network, the train driver or crew requirements, the service received by customers, impacts locomotive requirements, and is a large determinant of network efficiency. This chapter focuses on the role of the train schedules, and describes the data elements making up a train schedule, the process of designing the train schedules, and managing these schedules on a real-time basis. This chapter provides the definitions for the following core OR train design problems:
  • Train routing: how best to generate the routes of each train such that all traffic will be moved, and total train miles will be minimized. Minimizing total train miles also tends to maximize train size subject to a requirement that minimum train frequencies be observed.

  • Block-to-train assignments: which blocks (groups of railcars) will be placed on each train, minimizing overall train complexity and the need to swap blocks en-route from one train to another.

  • Train timing and connections: setting the timing of each train such that the overall transit times for all shipments will be minimized, taking into account the connections of railcars from one train to another, and the associated minimum processing times for such connections. Timing must also take into account the effective numbers of trains per hour that can be processed at each yard and can travel over each line segment.


Dwell Time Schedule Algorithm Locomotive Requirement Work Event Train Schedule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Assad AA (1980a) Modelling of rail networks: toward a routing/makeup model. Transport Res Part B 14(1–2):101–114CrossRefGoogle Scholar
  2. Assad AA (1980b) Models for rail transportation. Transport Res 14A:205–220CrossRefGoogle Scholar
  3. Carpara A, Fischetti M, Toth P (2002) Modeling and solving the train timetabling problem. Oper Res 50:851–861CrossRefGoogle Scholar
  4. Crainic TG, Rousseau JM (1986) Multicommodity, multimode freight transportation: a general modeling and algorithmic framework for the service network design problem. Transport Res 208:225–242CrossRefGoogle Scholar
  5. Dorfman M, Medanic J (2004) Scheduling trains on a railway network using a discrete event model of railway traffic. Transport Res B 38:81–98CrossRefGoogle Scholar
  6. Gorman MF (1998a) The freight railroad operating plan problem. Ann Oper Res 78:51–69CrossRefGoogle Scholar
  7. Gorman MF (1998b) An operating plan model improves service design at santa fe railway. Interfaces 28(4):1–12CrossRefGoogle Scholar
  8. Haghani AE (1987) Rail freight transportation: a review of recent optimization models for train routing and empty car distribution. J Adv Transport 21:147–172CrossRefGoogle Scholar
  9. Haghani AE (1989) Formulation and solution of a combined train routing and makeup, and empty car distribution model. Transport Res 23B:433–452CrossRefGoogle Scholar
  10. Huntley CL, Brown DE, Sappington DE, Markowicz BP (1995) Freight routing and scheduling at CSX transportation. Interfaces 25(3):58–71CrossRefGoogle Scholar
  11. Ireland P, Case R, Fallis J, Van Dyke C, Kuehn J, Meketon M (2004) The Canadian pacific railway transforms operations by using models to develop its operating plans. Interfaces 34(1):5–14CrossRefGoogle Scholar
  12. Jha KC, Ahuja RK, Sahin G (2008) New approaches for solving the block-to-train assignment problem. Networks 51:48–62CrossRefGoogle Scholar
  13. Keaton MH (1989) Designing optimal railroad operating plans: Lagrangian relaxation and heuristic approaches. Transport Res 23B:415–431CrossRefGoogle Scholar
  14. Keaton MH (1992) Designing optimal railroad operating plans: a dual adjustment method for implementing Lagrangian relaxation. Transport Sci 26:262–279CrossRefGoogle Scholar
  15. Kraft ER (2000) Implementation strategies for railroad dynamic freight car scheduling. J Transport Res Forum 39(3):119–137, jointly with Transportation QuarterlyGoogle Scholar
  16. Kraft ER (1998) A reservations-based railway network operations management system, Ph. D. Dissertation, Department of Systems Engineering, University of Pennsylvania, Philadelphia, PA, UMI Order # 9829930Google Scholar
  17. Newman AM, Yano Candace A (2000) Direct and indirect trains and containers in an intermodal setting. Transport Sci 34:256–270CrossRefGoogle Scholar
  18. Newman AM, Yano Candice A (2001) Scheduling trains and containers with due dates and dynamic arrivals. Transport Sci 35:181–191CrossRefGoogle Scholar
  19. Railroad Applications Section (2012) 2011 RAS Problem Solving Competition, Train Design Optimization, INFORMS.

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Carl Van Dyke
    • 1
    Email author
  • Marc Meketon
    • 2
  • Problem Solving Competition Committee
    • 3
  1. 1.TransNetOptPrincetonUSA
  2. 2.Oliver WymanPrincetonUSA
  3. 3.Railway Applications Section, INFORMSPrincetonUSA

Personalised recommendations