OR Spectrum

, Volume 34, Issue 3, pp 511–533 | Cite as

Optimized load planning of trains in intermodal transportation

  • Florian Bruns
  • Sigrid KnustEmail author
Regular Article


In this paper the problem of load planning for trains in intermodal container terminals is studied. The objective is to assign load units to wagons of a train such that the utilization of the train is maximized, and setup and transportation costs in the terminal are minimized. Contrary to previous approaches additionally weight restrictions for the wagons are integrated into our model. We present three different integer linear programming formulations and test them on some real-world instances. It is shown that even non-commercial MIP-solvers can solve our models to optimality in reasonable time.


Load planning Intermodal transportation Integer linear programming 

List of symbols


Number of wagons


Number of wagon types


Type of wagon j


Total weight limit of the train


Number of load units


Number of load unit types


Set of load units belonging to type t


Length of load unit i


Weight of load unit i


Transportation cost for load unit i to wagon j


Set of physical configurations for wagons of type τ


Set of type-weight lines for configuration k (first IP)


Set of weight distributions for configuration k (second IP)


Set of slots on wagon j (first and second IP)


Initial configuration k of wagon j


Feasible load unit length type t for slot s in type-weight line b (first IP)


Maximum payload for slot s in type-weight line or weight distribution b (first and second IP)


Feasible load unit fixation-type t for slot s in configuration k (second and third IP)

\({u^+_{i}, u^-_{i}}\)

overhangs of load unit i (second and third IP)


Feasible overhangs for slot s in configuration k (second and third IP)


Set of slots on wagon j (third IP)


Maximum bogie payloads for wagons of type τ (third IP)


Distance in between the bogie attachments for wagons of type τ (third IP)


Tare mass for wagons of type τ (third IP)


Maximum slot payload for wagons of type τ (third IP)


Lever for slot s for wagons of type τ (third IP)

aj, bj

Bogie payloads for wagon j (third IP)

w1, . . . , w5

Weighting factors


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  1. Achterberg T (2007) Constraint integer programming. PhD thesis, Technische Universität BerlinGoogle Scholar
  2. Bontekoning YM, Macharis C, Trip JJ (2004) Is a new applied transportation research field emerging? A review of intermodal rail-truck freight transport literature. Transp Res A Policy Pract 38(1): 1–34CrossRefGoogle Scholar
  3. Bostel N, Dejax P (1998) Models and algorithms for the container allocation problem on trains in a rapid transshipment yard. Transp Sci 32(4): 370–379CrossRefGoogle Scholar
  4. Corry P, Kozan E (2006) An assignment model for dynamic load planning of intermodal trains. Comput Oper Res 33: 1–17CrossRefGoogle Scholar
  5. Corry P, Kozan E (2008) Optimised loading patterns for intermodal trains. OR Spectr 30(4): 721–750CrossRefGoogle Scholar
  6. Corvers K, Weißenburger R (2007) Transport- und Lademittel im Kombinierten VerkehrGoogle Scholar
  7. Feo TA, Gonzáles-Velarde JL (1995) The intermodal trailer assignment problem. Transp Sci 29(4): 330–341CrossRefGoogle Scholar
  8. Ilog SA (2007) ILOG CPLEX 11.0 user’s manualGoogle Scholar
  9. Kombiverkehr (2008) Frachtbehälter Einteilung nach Längenklassen UICGoogle Scholar
  10. Lougee-Heimer R (2003) The common optimization interface for operations research. IBM J Res Dev 47(1): 57–66CrossRefGoogle Scholar
  11. Powell WB, Carvalho TA (1998) Real-time optimization of containers and flatcars for intermodal operations. Transp Sci 32: 110–126CrossRefGoogle Scholar
  12. SBB and HUPAC (2006) Neue Beladeschema für Wechselbehälter- und ContainerwagenGoogle Scholar
  13. Souffriau W, Vansteenwegen P, Vanden Berghe G, Van Oudheusden D (2009) Variable neighbourhood descent for planning crane operations in a train terminal. Lecture notes in economics and mathematical systems, vol 624. Springer, BerlinGoogle Scholar
  14. Stahlbock R, Voß S (2008) Operations research at container terminals: a literature update. OR Spectr 30(1): 1–52CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Institute of MathematicsTechnical University of ClausthalClausthal-ZellerfeldGermany

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