Skip to main content

Cutting Planes for Solving Logistic Flow Problems

  • Conference paper
  • First Online:
Computational Logistics (ICCL 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12433))

Included in the following conference series:

  • 2615 Accesses

Abstract

In logistic problems, an Integral Multi-Commodity Network Design Problem on a time-space network is often used to model the problem of routing transportation means and assigning freight units to those means. In Physical Internet and Synchromodal networks an interactive planning approach is preferable, meaning that calculation times of a single planning step should be short. In this paper we provide ways to reduce the size of the problem formulation based on cutting planes, that are effective in reducing the computation time for Integer Linear Programming problem-based solution methods.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Aardal, K., Weismantel, R., Wolsey, L.A.: Non-standard approaches to integer programming. Discrete Appl. Math. 123(1–3), 5–74 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Andersen, J., Crainic, T.G., Christiansen, M.: Service network design with asset management: Formulations and comparative analyses. Transp. Res. Part C: Emerg. Technol. 17(2), 197–207 (2009)

    Article  Google Scholar 

  3. Balakrishnan, A., Magnanti, T., Wong, R.: A dual-ascent procedure for large-scale uncapacitated network design. Oper. Res. 37(5), 716–740 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chouman, M., Crainic, T.: MIP-based Matheuristic for Service Network Design with Design-balanced Requirements. CIRRELT (2012)

    Google Scholar 

  5. Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., Schrijver, A.: Combinatorial Optimization. Wiley Interscience (1998)

    Google Scholar 

  6. Crainic, T.: Service network design in freight transportation. Eur. J. Oper. Res. 122(2), 272–288 (2000)

    Article  MATH  Google Scholar 

  7. Crainic, T., Frangioni, A., Gendron, B.: Bundle-based relaxation methods for multicommodity capacitated fixed charge network design. Discrete Appl. Math. 112(1), 73–99 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Crainic, T., Gendreau, M., Farvolden, J.: A simplex-based tabu search method for capacitated network design. Inf. J. Comput. 12(3), 223–236 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. De Juncker, M.A.M., Huizing, D., del Vecchyo, M.R.O., Phillipson, F., Sangers, A.: Framework of synchromodal transportation problems. ICCL 2017. LNCS, vol. 10572, pp. 383–403. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68496-3_26

    Chapter  Google Scholar 

  10. Ghamlouche, I., Crainic, T.G., Gendreau, M.: Path relinking, cycle-based neighbourhoods and capacitated multicommodity network design. Ann. Oper. Res. 131(1–4), 109–133 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Holmberg, K., Hellstrand, J.: Solving the uncapacitated network design problem by a lagrangean heuristic and branch-and-bound. Oper. Res. 46(2), 247–259 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  12. Holmberg, K., Yuan, D.: A lagrangian heuristic based branch-and-bound approach for the capacitated network design problem. Oper. Res. 48(3), 461–481 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  13. Huizing, D.: General methods for synchromodal planning of freight containers and transports. Master’s thesis, TU Delft (2017)

    Google Scholar 

  14. IBM: Cplex optimizer (2017). https://www.ibm.com/analytics/data-science/prescriptive-analytics/cplex-optimizer

  15. IBM: Zero-half cuts (2017). https://www.ibm.com/support/knowledgecenter/SSSA5P_12.5.0/ilog.odms.cplex.help/CPLEX/UsrMan/topics/discr_optim/mip/cuts/38_zerohalf.html

  16. Janic, M.: Modelling the full costs of an intermodal and road freight transport network. Transp. Res. Part D: Transp. Environ. 12(1), 33–44 (2007)

    Article  Google Scholar 

  17. Joborn, M., Crainic, T.G., Gendreau, M., Holmberg, K., Lundgren, J.T.: Economies of scale in empty freight car distribution in scheduled railways. Transp. Sci. 38(2), 121–134 (2004)

    Article  Google Scholar 

  18. Letchford, A.N., Lodi, A.: Strengthening Chvátal-Gomory cuts and Gomory fractional cuts. Oper. Res. Lett. 30(2), 74–82 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  19. Li, X., Wei, K., Aneja, Y., Tian, P.: Design-balanced capacitated multicommodity network design with heterogeneous assets. Omega 67, 145–159 (2017)

    Article  Google Scholar 

  20. Magnanti, T.L., Wong, R.T.: Network design and transportation planning: Models and algorithms. Transp. Sci. 18(1), 1–55 (1984)

    Article  Google Scholar 

  21. Magnanti, T.L., Mirchandani, P., Vachani, R.: Modeling and solving the two-facility capacitated network loading problem. Oper. Res. 43(1), 142–157 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  22. Marchand, H., Martin, A., Weismantel, R., Wolsey, L.: Cutting planes in integer and mixed integer programming. Discrete Appl. Math. 123(1–3), 397–446 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  23. Pedersen, M., Crainic, T., Madsen, O.: Models and tabu search metaheuristics for service network design with asset-balance requirements. Transp. Sci. 43(2), 158–177 (2009)

    Article  Google Scholar 

  24. Sharypova, K.: Optimization of Hinterland Intermodal Container Transportation. Ph.D. thesis, Eindhoven University of Technology (2014)

    Google Scholar 

  25. Vu, D.M., Crainic, T.G., Toulouse, M., Hewitt, M.: Service network design with resource constraints. Transp. Sci. 50(4), 1380–1393 (2014)

    Google Scholar 

Download references

Acknowledgement

This work has been carried out within the project ‘Complexity Methods for Predictive Synchromodality’ (Comet-PS), supported by NWO (the Netherlands Organisation for Scientific Research), TKI-Dinalog (Top Consortium Knowledge and Innovation) and the Early Research Program ‘Grip on Complexity’ of TNO (The Netherlands Organisation for Applied Scientific Research).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Frank Phillipson .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kalicharan, K., Phillipson, F., Sangers, A. (2020). Cutting Planes for Solving Logistic Flow Problems. In: Lalla-Ruiz, E., Mes, M., Voß, S. (eds) Computational Logistics. ICCL 2020. Lecture Notes in Computer Science(), vol 12433. Springer, Cham. https://doi.org/10.1007/978-3-030-59747-4_37

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-59747-4_37

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-59746-7

  • Online ISBN: 978-3-030-59747-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics