OR Spectrum

, Volume 38, Issue 1, pp 207–233 | Cite as

The basic train makeup problem in shunting yards

  • Nils BoysenEmail author
  • Simon Emde
  • Malte Fliedner
Regular Article


In shunting yards, railcars of incoming trains are uncoupled and reassembled to outbound trains. This time-critical process that employs a complex system of switches, hump hills, and classification tracks requires plenty interdependent decision problems to be solved. An elementary decision task among these is the train makeup problem, which assigns railcars of inbound freight trains to outbound trains, such that the priority values of the selected cuts of railcars are maximized and given train capacities are observed. This assignment decision is further complicated by the fact that railcars cannot facultatively be selected, but the buildup sequences of incoming trains need to be considered. This work introduces and discusses the basic train makeup problem, analyses its complexity status and develops suited exact and heuristic solution procedures that are tested in a comprehensive computational study.


Railway optimization Shunting yard Railcar classification  Train makeup 


  1. Ballis A, Golias J (2002) Comparative evaluation of existing and innovative rail-road freight transport terminals. Transp Res Part A Policy Pract 36:593–611CrossRefGoogle Scholar
  2. Bektas T, Crainic TG, Morency V (2009) Improving the performance of rail yards through dynamic reassignments of empty cars. Transp Res Part C 17C:259–273CrossRefGoogle Scholar
  3. Bontekoning Y, Priemus H (2004) Breakthrough innovations in intermodal freight transport. Transp Plan Technol 27:335–345CrossRefGoogle Scholar
  4. Boysen N, Fliedner M, Jaehn F, Pesch E (2012) Shunting yard operations: theoretical aspects and applications. Eur J Oper Res 220:1–14CrossRefGoogle Scholar
  5. Boysen N, Fliedner M, Jaehn F, Pesch E (2013) A survey on container processing in railway yards. Transp Sci 47:312–329CrossRefGoogle Scholar
  6. Daganzo CF, Dowling RG, Hall RW (1983) Railroad classification yard throughput: the case of multistage triangular sorting. Transp Res Part A 17A:95–106CrossRefGoogle Scholar
  7. Dahlhaus E, Horak P, Miller M, Ryan JF (2000) The train marshalling problem. Discrete Appl Math 103:41–54CrossRefGoogle Scholar
  8. Di Stefano G, Koci ML (2004) A graph theoretical approach to the shunting problem. Electron Notes Theor Comput Sci 92:16–33CrossRefGoogle Scholar
  9. European Commission (2001) White paper, European transport policy for 2010: time to decide. COM 370Google Scholar
  10. Freville A (2004) The multidimensional 0–1 knapsack problem: an overview. Eur J Oper Res 155:1–21CrossRefGoogle Scholar
  11. Gatto M, Maue J, Mihalák M, Widmayer P (2009) Shunting for dummies: an introductory algorithmic survey. In: Ahuja R, Möhring R, Zaroliagis C (eds) Robust and online large-scale optimization, lecture notes in computer science, vol 5868. Springer, Berlin, pp 310–337CrossRefGoogle Scholar
  12. Goldberg A, Tarjan R (1988) A new approach to the maximum flow problem. J ACM 35:921–940CrossRefGoogle Scholar
  13. Hansmann RS, Zimmermann UT (2008) Optimal sorting of rolling stock at hump yards. In: Krebs H-J, Jäger W (eds) Mathematics—key technology for the future. Springer, Berlin Heidelberg, pp 189–203Google Scholar
  14. He S, Song R, Chaudhry SS (2000) Fuzzy dispatching model and genetic algorithms for railyards operations. Eur J Oper Res 124:307–331CrossRefGoogle Scholar
  15. He S, Song R, Chaudhry SS (2003) An integrated dispatching model for rail yards operations. Comput Oper Res 30:939–966CrossRefGoogle Scholar
  16. Jacob R, Marton P, Maue J, Nunkesser M (2011) Multistage methods for freight train classification. Networks 57:87–105CrossRefGoogle Scholar
  17. Kraft ER (2000) A hump sequence algorithm for real time management of train connection reliability. J Transp Res Forum 39:95–115Google Scholar
  18. Kroon LG, Lentink RM, Schrijver A (2008) Shunting of passenger train units: an integrated approach. Transp Sci 42:436–449CrossRefGoogle Scholar
  19. Li H, Song R, Jin M, He S (2014) Optimization of railcar connection plan in a classification yard. In: Transportation research board 93rd annual meeting, No. 14-3091Google Scholar
  20. Lowerre B (1976) The Harpy speech recognition system. PhD thesis, Carnegie Mellon UniversityGoogle Scholar
  21. Lübbecke ME, Zimmermann UT (2005) Shunting minimal rail car allocation. Comput Optim Appl 31:295–308CrossRefGoogle Scholar
  22. Menakerman N, Rom R (2001) Bin packing with item fragmentation. In: Dehne F, Sack J-R, Tamassia R (eds) Algorithms and data structures. Springer, Berlin, pp 313–324Google Scholar
  23. Petersen ER (1977) Railyard modeling: part I. Transp Sci 11:37–49CrossRefGoogle Scholar
  24. Puchinger J, Raidl GR, Pferschy U (2010) The multidimensional knapsack problem: structure and algorithms. INFORMS J Comput 22:250–265CrossRefGoogle Scholar
  25. RPM (2014) Railroad performance measures. March 2014
  26. Shachnai H, Tamir T, Yehezkely O (2006) Approximation schemes for packing with item fragmentation. In: Erlebach T, Persinao G (eds) Approximation and online algorithms. Springer, Berlin Heidelberg, pp 334–347Google Scholar
  27. Shachnai H, Tamir T, Yehezkely O (2008) Approximation schemes for packing with item fragmentation. Theory Comput Syst 43:81–98CrossRefGoogle Scholar
  28. Shachnai H, Yehezkely O (2007) Fast asymptotic FPTAS for packing fragmentable items with costs. In: Csuhaj-Varjú E, Ésik Z (eds) Fundamentals of computation theory. Springer, Berlin, pp 482–493Google Scholar
  29. Tsamboulas D, Vrenken H, Lekka AM (2007) Assessment of a transport policy potential for intermodal mode shift on a European scale. Transp Res Part A Policy Pract 41:715–733CrossRefGoogle Scholar
  30. US DOT (1998) Transportation equity act for the 21st century, moving Americans into the 21st century. Department of TransportationGoogle Scholar
  31. Verband der Automobilindustrie e.V. (VDA) (2006) Jahresbericht 2006, Frankfurt am Main 2006 (in German) Google Scholar
  32. Weingartner HM, Ness DN (1967) Methods for the solution of the multidimensional 0/1 knapsack problem. Oper Res 15:83–103CrossRefGoogle Scholar
  33. Yagar S, Saccomanno FF, Shi Q (1983) An efficient sequencing model for humping in a rail yard. Transp Res Part A Gen 17:251–262CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Friedrich-Schiller-Universität Jena, Lehrstuhl für Operations ManagementJenaGermany
  2. 2.Universität Hamburg, Lehrstuhl für Operations ManagementHamburgGermany

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