IDEAS home Printed from
   My bibliography  Save this article

Designing optimal railroad operating plans: Lagrangian relaxation and heuristic approaches


  • Keaton, Mark H.


Railroad managers must determine (1) which pairs of terminals are to be provided with direct train connections, (2) the frequency of service, (3) how the individual cars are routed through the available configuration of trains and intermediate terminals, and (4) how cars are physically grouped or "blocked" within trains. The objective is to minimize the sum of train costs, car time costs, and classification yard costs, while not exceeding limits on train size and yard volumes. These decisions are modeled as a mixed-integer programming problem, where the decision to operate a given train connection corresponds to 0-1 variable. With no limits on train size, the model can be solved very efficiently using Lagrangian relaxation. If the solution contains some overloaded trains, which is likely, heuristic adjustments are necessary to obtain a feasible operating plan.

Suggested Citation

  • Keaton, Mark H., 1989. "Designing optimal railroad operating plans: Lagrangian relaxation and heuristic approaches," Transportation Research Part B: Methodological, Elsevier, vol. 23(6), pages 415-431, December.
  • Handle: RePEc:eee:transb:v:23:y:1989:i:6:p:415-431

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Jin, Jian Gang & Zhao, Jun & Lee, Der-Horng, 2013. "A column generation based approach for the Train Network Design Optimization problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 50(C), pages 1-17.
    2. Nozick, Linda K. & Morlok, Edward K., 1997. "A model for medium-term operations planning in an intermodal rail-truck service," Transportation Research Part A: Policy and Practice, Elsevier, vol. 31(2), pages 91-107, March.
    3. Crainic, Teodor Gabriel, 2000. "Service network design in freight transportation," European Journal of Operational Research, Elsevier, vol. 122(2), pages 272-288, April.
    4. repec:pal:jorsoc:v:68:y:2017:i:12:d:10.1057_s41274-017-0187-6 is not listed on IDEAS
    5. Marin, Angel & Salmeron, Javier, 1996. "Tactical design of rail freight networks. Part I: Exact and heuristic methods," European Journal of Operational Research, Elsevier, vol. 90(1), pages 26-44, April.
    6. Khaled, Abdullah A. & Jin, Mingzhou & Clarke, David B. & Hoque, Mohammad A., 2015. "Train design and routing optimization for evaluating criticality of freight railroad infrastructures," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 71-84.
    7. Crainic, Teodor Gabriel & Laporte, Gilbert, 1997. "Planning models for freight transportation," European Journal of Operational Research, Elsevier, vol. 97(3), pages 409-438, March.
    8. Lin, Bo-Liang & Wang, Zhi-Mei & Ji, Li-Jun & Tian, Ya-Ming & Zhou, Guo-Qing, 2012. "Optimizing the freight train connection service network of a large-scale rail system," Transportation Research Part B: Methodological, Elsevier, vol. 46(5), pages 649-667.
    9. Alena Otto & Erwin Pesch, 2017. "Operation of shunting yards: train-to-yard assignment problem," Journal of Business Economics, Springer, vol. 87(4), pages 465-486, May.
    10. KePing Li & ZiYou Gao & BaoHua Mao & ChengXuan Cao, 2011. "Optimizing Train Network Routing Using Deterministic Search," Networks and Spatial Economics, Springer, vol. 11(2), pages 193-205, June.
    11. repec:pal:jorsoc:v:59:y:2008:i:7:d:10.1057_palgrave.jors.2602403 is not listed on IDEAS

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:23:y:1989:i:6:p:415-431. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.