Computational Optimization and Applications

, Volume 31, Issue 3, pp 295–308 | Cite as

Shunting Minimal Rail Car Allocation

  • Marco E. LübbeckeEmail author
  • Uwe T. Zimmermann


We consider the rail car management at industrial in-plant railroads. Demands for loaded or empty cars are characterized by a track, a car type, and the desired quantity. If available, we assign cars from the stock, possibly substituting types, otherwise we rent additional cars. Transportation requests are fulfilled as a short sequence of pieces of work, the so-called blocks. Their design at a minimal total transportation cost is the planning task considered in this paper. It decomposes into the rough distribution of cars among regions, and the NP-hard shunting minimal allocation of cars per region. We present mixed integer programming formulations for the two problem levels. Our computational experience from practical data encourages an installation in practice.


Mixed integer programming shunting minimization decomposition rail transport 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W.P. Allman, “An optimization approach to freight car allocation under time-mileage per diem rental rates,” Management Sci., vol. 18, no. 10, pp. B-567–B-574, 1972.CrossRefGoogle Scholar
  2. 2.
    C. Barnhart, H. Jin, and P.H. Vance, “Railroad blocking: A network design application,” Oper. Res., vol. 48, no. 4, pp. 603–614, 2000.CrossRefGoogle Scholar
  3. 3.
    N.J. Bojović, “Application of optimization techniques to the railroad empty car distribution process: A survey,” Yugoslav J. Oper. Res., vol. 10, no. 1, pp. 63–74, 2000.zbMATHGoogle Scholar
  4. 4.
    A. Charnes and M.H. Miller, “A model for the optimal programming of railway freight train movements,” Management Sci., vol. 3, pp. 74–92, 1956.MathSciNetCrossRefGoogle Scholar
  5. 5.
    E. Dahlhaus, P. Horak, M. Miller, and J.F. Ryan, “The train marshalling problem,” Discrete Appl. Math., vol. 103, nos. 1–3, pp. 41–54, 2000.MathSciNetCrossRefGoogle Scholar
  6. 6.
    M.R. Garey and D.S. Johnson, “Computers and intractability—a guide to the theory of NP-completeness,” W.H. Freeman and Company: San Francisco, 1979.zbMATHGoogle Scholar
  7. 7.
    J. Håstad, “Some optimal inapproximability results,” in Proceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing, 1997. ACM Press: El Paso, Texas, pp. 1–10.Google Scholar
  8. 8.
    K. Holmberg, M. Joborn, and J.T. Lundgren, “Computational experiments with an empty freight car distribution model,” in Computers in Railways V, J. Allan, C.A. Brebbia, R.J. Hill, G. Sciutto, and S. Sone (Ed.), Computational Mechanics Publications: Southampton, UK, 1996, pp. 511–520.Google Scholar
  9. 9.
    K. Holmberg, M. Joborn, and J.T. Lundgren, “Improved empty freight car distribution,” Transportation Sci., vol. 32, no. 2, pp. 163–173, 1998.CrossRefGoogle Scholar
  10. 10.
    E.L. Lawler, Combinatorial Optimization: Networks and Matroids, Dower: Mineola, New York, 2001, Unabrigded reprint of the 1976 edition.Google Scholar
  11. 11.
    M.E. Lübbecke and U.T. Zimmermann, “Engine routing and scheduling at industrial in-plant railroads,” Transportation Sci., vol. 37, no. 2, pp. 183–197, 2003.CrossRefGoogle Scholar
  12. 12.
    H.N. Newton, C. Barnhart, and P.H. Vance, “Constructing railroad blocking plans to minimize handling costs,” Transportation Sci., vol. 32, no. 4, pp. 330–345, 1998.CrossRefGoogle Scholar
  13. 13.
    Y.-S. Shan, “A dynamic multicommodity network flow model for real time optimal rail freight car management,” PhD Thesis, Princeton Unviersity, Princeton, NJ, 1985.Google Scholar
  14. 14.
    H.D. Sherali and A.B. Suharko, “A tactical decision support system for empty railcar management,” Transportation Sci., vol. 32, no. 4, pp. 306–329, 1998.CrossRefGoogle Scholar
  15. 15.
    T. Winter and U.T. Zimmermann, “Real-time dispatch of trams in storage yards,” Ann. Oper. Res., vol. 96, pp. 287–315, 2000.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany
  2. 2.Institute of Mathematical OptimizationBraunschweig University of TechnologyBraunschweigGermany

Personalised recommendations