Skip to main content
SpringerLink
Log in

Optimized load planning of trains in intermodal transportation

  • Regular Article
  • Published:
OR Spectrum Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

m :

Number of wagons

p :

Number of wagon types

c(j):

Type of wagon j

G :

Total weight limit of the train

n :

Number of load units

q :

Number of load unit types

\({\mathcal{N}_t}\) :

Set of load units belonging to type t

l i :

Length of load unit i

g i :

Weight of load unit i

d ij :

Transportation cost for load unit i to wagon j

\({\mathcal{K}_{\tau}}\) :

Set of physical configurations for wagons of type τ

\({\mathcal{B}_k}\) :

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

\({\mathcal{B}_k'}\) :

Set of weight distributions for configuration k (second IP)

\({\mathcal{S}_j}\) :

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

\({\kappa_{jk}^0}\) :

Initial configuration k of wagon j

α tbs :

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

γ bs :

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

λ tks :

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)

\({\beta^+_{ks},\beta^-_{ks}}\) :

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

\({\mathcal{S}'_j}\) :

Set of slots on wagon j (third IP)

γ τ :

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

d τ :

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

t τ :

Tare mass for wagons of type τ (third IP)

δ τs :

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

e τs :

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

a j , b j :

Bogie payloads for wagon j (third IP)

w 1, . . . , w 5 :

Weighting factors

References

  • Achterberg T (2007) Constraint integer programming. PhD thesis, Technische Universität Berlin

  • 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): 1–34

    Article  Google Scholar 

  • Bostel N, Dejax P (1998) Models and algorithms for the container allocation problem on trains in a rapid transshipment yard. Transp Sci 32(4): 370–379

    Article  Google Scholar 

  • Corry P, Kozan E (2006) An assignment model for dynamic load planning of intermodal trains. Comput Oper Res 33: 1–17

    Article  Google Scholar 

  • Corry P, Kozan E (2008) Optimised loading patterns for intermodal trains. OR Spectr 30(4): 721–750

    Article  Google Scholar 

  • Corvers K, Weißenburger R (2007) Transport- und Lademittel im Kombinierten Verkehr

  • Feo TA, Gonzáles-Velarde JL (1995) The intermodal trailer assignment problem. Transp Sci 29(4): 330–341

    Article  Google Scholar 

  • Ilog SA (2007) ILOG CPLEX 11.0 user’s manual

  • Kombiverkehr (2008) Frachtbehälter Einteilung nach Längenklassen UIC

  • Lougee-Heimer R (2003) The common optimization interface for operations research. IBM J Res Dev 47(1): 57–66

    Article  Google Scholar 

  • Powell WB, Carvalho TA (1998) Real-time optimization of containers and flatcars for intermodal operations. Transp Sci 32: 110–126

    Article  Google Scholar 

  • SBB and HUPAC (2006) Neue Beladeschema für Wechselbehälter- und Containerwagen

  • 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, Berlin

  • Stahlbock R, Voß S (2008) Operations research at container terminals: a literature update. OR Spectr 30(1): 1–52

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Technical University of Clausthal, 38678, Clausthal-Zellerfeld, Germany

    Florian Bruns & Sigrid Knust

Authors
  1. Florian Bruns
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sigrid Knust
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sigrid Knust.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bruns, F., Knust, S. Optimized load planning of trains in intermodal transportation. OR Spectrum 34, 511–533 (2012). https://doi.org/10.1007/s00291-010-0232-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00291-010-0232-1

Keywords

Search

Navigation