Skip to main content
Springer Nature Link
Log in

A branch and cut algorithm for hub location problems with single assignment

  • Published:
Mathematical Programming Submit manuscript

Abstract.

The hub location problem with single assignment is the problem of locating hubs and assigning the terminal nodes to hubs in order to minimize the cost of hub installation and the cost of routing the traffic in the network. There may also be capacity restrictions on the amount of traffic that can transit by hubs. The aim of this paper is to investigate polyhedral properties of these problems and to develop a branch and cut algorithm based on these results.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
€32.70 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (France)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aardal, K., Pochet, Y., Wolsey, L.A.: Capacitated Facility Location: Valid Inequalities and Facets. Math. Oper. Res. 20, 562–582 (1995)

    MathSciNet  MATH  Google Scholar 

  2. Aardal, K.: Capacitated Facility Location: Separation Algorithms and Computational Experience. Math. Program. 81, 149–175 (1998)

    Article  MathSciNet  Google Scholar 

  3. Andrews, M., Zhang, L.: Approximation Algorithms for Access Network Design. Algorithmica 34, 197–215 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Avella, P., Sassano, A.: On the p-Median Polytope. Math. Program. 89, 395–411 (2001)

    MathSciNet  MATH  Google Scholar 

  5. Balas, E.: Facets of the Knapsack Polytope. Math. Program. 8, 146–164 (1975)

    MATH  MathSciNet  Google Scholar 

  6. Beasley, J.E.: OR-Library: distributing test problems by electronic mail. J. Oper. Res. Soc. 41, 1069–1072 (1990)

    Google Scholar 

  7. Campbell, J.F., Ernst, A.T., Krishnamoorthy, M.: Hub Location Problems. In: Facility Location: Applications and Theory, Z. Drezner, H.W. Hamacher (eds.), Springer, 2002, pp. 373–407

  8. Dantzig, G.B.: On the Significance of Solving Linear Programming Problems with Some Integer Variables. The Rand Corporation, document, 1958, p. 1486

  9. Deng, Q., Simchi-Levi, D.: Valid Inequalities, Facets and Computational Results for the Capacitated Concentrator Location Problem. Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027-6699, 1992

  10. Ernst, A.T., Krishnamoorthy, M.: Solution Algorithms for the Capacitated Single Allocation Hub Location Problem. Ann. Oper. Res. 86, 141–159 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. Gourdin, E., Labbé, M., Yaman, H.: Telecommunication and Location. In: Facility Location: Applications and Theory, Z. Drezner, H.W. Hamacher (eds.), Springer, 2003, pp. 275–305

  12. Goemans, M.X., Williamson, D.P.: The primal-dual method for approximation algorithms and its application to network design problems. In: Approximation Algorithms for NP-Hard Problems, D.S. Hochbaum (ed.), PWS Publishing Company, 1997, pp. 144–191

  13. Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Springer-Verlag, Berlin, 1988

  14. Gu, Z., Nemhauser, G.L., Savelsbergh, M.W.P.: Cover Inequalities for 0-1 Linear Programs: Computation. INFORMS J. Comput. 10, 427–437 (1998)

    Article  MathSciNet  Google Scholar 

  15. Hammer, P.L., Johnson, E.L., Peled, U.N.: Facets of Regular 0-1 Polytopes. Math. Program. 8, 179–206 (1975)

    MATH  MathSciNet  Google Scholar 

  16. Jünger, M., Thienel, S.: The ABACUS system for branch-and-cut-and-price algorithms in integer programming and combinatorial optimization. Softw. Pract. Experience 30, 1325–1352 (2000)

    Article  MATH  Google Scholar 

  17. Leung, J.M.Y., Magnanti, T.L.: Valid Inequalities and Facets of the Capacitated Plant Location Problem. Math. Program. 44, 271–291 (1989)

    MathSciNet  MATH  Google Scholar 

  18. Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations, Wiley, New York, 1990

  19. Padberg, M.W.: On the Facial Structure of Set Packing Polyhedra. Math. Program. 5, 199–215 (1973)

    MATH  MathSciNet  Google Scholar 

  20. Skorin-Kapov, D., Skorin-Kapov, J., O’Kelly, M.: Tight linear programming relaxations of uncapacitated p-hub median problem. Eur. J. Oper. Res. 94, 582–593 (1996)

    Article  MATH  Google Scholar 

  21. Swamy, C., Kumar, A.: Primal-dual Algorithms for Connected Facility Location Problems. In: Approximation algorithms for combinatorial optimization, K. Jansen, S. Leonardi, V. Vazirani (eds.), 5th international workshop, APPROX 2002, Proceedings. Lect. Notes Comput. Sci. 2462, Springer, Berlin, 2002 pp. 256–269

  22. Wolsey, L.: Faces for a Linear Inequality in 0-1 Variables. Math. Program. 8, 165–178 (1975)

    MATH  MathSciNet  Google Scholar 

  23. Yaman, H.: Concentrator Location in Telecommunication Networks, Ph.D. Thesis, Université Libre de Bruxelles, 2002. Available at http://smg.ulb.ac.be/

  24. Yuan, D.: An Annotated Bibliography in Communication Network Design and Routing. In: Optimization Models and Methods for Communication Network Design and Routing. Ph.D. Thesis, Department of Mathematics, Linköping University, Sweden, 2001

Download references

Author information

Authors and Affiliations

  1. Université Libre de Bruxelles, Service d’Optimisation, Boulevard du Triomphe CP 210/01, 1050, Bruxelles, Belgium

    Martine Labbé

  2. Department of Industrial Engineering, Bilkent University, Bilkent, 06800, Ankara, Turkey

    Hande Yaman

  3. France Telecom R&D, DAC/OAT, 38-40, rue du General Leclerc, Issy-les-Moulineaux Cedex 9, 92794, France

    Eric Gourdin

Authors
  1. Martine Labbé
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hande Yaman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eric Gourdin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hande Yaman.

Additional information

Acknowledgement The research of the first author was partially supported by the Banque Nationale de Belgique. The research of the second author was supported by France Telecom R&D under contract no. 99 1B 774. Their support is gratefully acknowledged.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Labbé, M., Yaman, H. & Gourdin, E. A branch and cut algorithm for hub location problems with single assignment. Math. Program. 102, 371–405 (2005). https://doi.org/10.1007/s10107-004-0531-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10107-004-0531-x

Keywords

Search

Navigation