Computational Optimization and Applications

, Volume 53, Issue 1, pp 131–153 | Cite as

An intermodal multicommodity routing problem with scheduled services



We study a multicommodity routing problem faced by an intermodal service operator that uses ground and maritime transportation. Given a planning horizon, a set of commodities to be picked up at their release times and to be delivered not later than their duedates, the problem is to decide on routes for these commodities using trucks and scheduled and capacitated maritime services at minimum cost of transportation and stocking at the seaports. Two mixed integer programming formulations and valid inequalities are proposed for this problem. The results of a computational study to evaluate the strength of the linear programming relaxations and the solution times are reported.


Intermodal routing Multicommodity flows Scheduled services Valid inequalities 


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  1. 1.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Prentice Hall, New York (1993) MATHGoogle Scholar
  2. 2.
    Barnhart, C., Ratliff, H.D.: Modeling intermodal routing. J. Bus. Logist. 14, 205–223 (1993) Google Scholar
  3. 3.
    Barnhart, C., Hane, C.A., Vance, P.H.: Using branch-and-price-and-cut to solve origin-destination integer multicommodity flow problems. Oper. Res. 48, 318–326 (2000) CrossRefGoogle Scholar
  4. 4.
    Bektas, T., Crainic, T.G.: A brief overview of intermodal transportation. Technical Report, CIRRELT-2007-03, Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (2007) Google Scholar
  5. 5.
    Boardman, B.S., Malstrom, E.M., Butler, D.P., Cole, M.H.: Computer assisted routing of intermodal shipments. Comput. Ind. Eng. 33, 311–314 (1997) CrossRefGoogle Scholar
  6. 6.
    Bontekoning, Y.M., Macharis, C., Trip, J.J.: Is a new applied transportation research field emerging?—A review of intermodal rail-truck freight transport literature. Transp. Res. A 38, 1–34 (2004) CrossRefGoogle Scholar
  7. 7.
    Bookbinder, J.H., Fox, N.S.: Intermodal routing of Canada-Mexico shipments under NAFTA. Transp. Res. E 34, 289–303 (1998) CrossRefGoogle Scholar
  8. 8.
    Boussedjra, M., Bloch, C., El Moudni, A.: An exact method to find the intermodal shortest path. In: Proceedings of the IEEE International Conference on Networking, Sensing & Control, pp. 1075–1080 (2004) CrossRefGoogle Scholar
  9. 9.
    Chang, T.S.: Best routes selection in international intermodal networks. Comput. Oper. Res. 35, 2877–2891 (2008) MATHCrossRefGoogle Scholar
  10. 10.
    Christiansen, M., Fagerholt, K., Nygreen, B., Ronen, D.: Maritime transportation. In: Barnhart, C., Laporte, G. (eds.) Handbook in OR & MS, vol. 14, pp. 189–284. Elsevier, Amsterdam (2007) Google Scholar
  11. 11.
    Crainic, T.G., Kim, K.H.: Intermodal transportation. In: Barnhart, C., Laporte, G. (eds.) Handbook in OR & MS, vol. 14, pp. 467–537. Elsevier, Amsterdam (2007) Google Scholar
  12. 12.
    Garey, M.R., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-Completeness. Freeman, New York (1979) MATHGoogle Scholar
  13. 13.
    Grasman, S.E.: Dynamic approach to strategic and operational multimodal routing decisions. Int. J. Logist. Syst. Manag. 2, 96–106 (2006) CrossRefGoogle Scholar
  14. 14.
    Kim, H.J., Chang, Y.T., Lee, P.T.T., Shin, S.H., Kim, M.J.: Optimizing the transportation of intermodal container cargoes in Korea. Marit. Policy Manag. 35, 103–122 (2008) CrossRefGoogle Scholar
  15. 15.
    Macharis, B., Bontekoning, Y.M.: Opportunities for OR in intermodal freight transportation research: a review. Eur. J. Oper. Res. 153, 400–416 (2004) MATHCrossRefGoogle Scholar
  16. 16.
    Min, H.: International intermodal choices via change-constrained goal programming. Transp. Res. A 25, 351–362 (1991) CrossRefGoogle Scholar
  17. 17.
    Moccia, L., Cordeau, J.F., Laporte, G., Ropke, S., Valentini, M.P.: Modeling and solving a multimodal routing problem with timetables and time windows. Networks (to appear) Google Scholar
  18. 18.
    Pedersen, M.B.: Optimization models and solution methods for intermodal transportation. PhD Thesis, Technical University of Denmark, Centre for Traffic and Transport (2005) Google Scholar
  19. 19.
    Slack, B.: Intermodal Transportation. In: Brewer, A.M., Button, K.J., Hensher, D.A. (eds.) Handbook of Logistics and Supply-Chain Management, pp. 141–154. Pergamon, Elmsford (2001) Google Scholar
  20. 20.
    Song, H., Chen, G.: Minimum cost delivery problem in intermodal transportation networks. In: Proceedings of the 2007 IEEE IEEM, pp. 1502–1506 (2007) Google Scholar
  21. 21.
    Wolsey, L.A.: Integer Programming. Wiley, New York (1998) MATHGoogle Scholar
  22. 22.
    Ziliaskopoulos, A., Wardell, W.: An intermodal optimum path algorithm for multimodal networks with dynamic arc travel times and switching delays. Eur. J. Oper. Res. 125, 486–502 (2000) MathSciNetMATHCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Industrial EngineeringBilkent UniversityAnkaraTurkey

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