Mathematical Programming

, Volume 102, Issue 2, pp 371–405 | Cite as

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

  • Martine Labbé
  • Hande Yaman
  • Eric Gourdin


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.


Hub location Polyhedral analysis Branch and cut 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aardal, K., Pochet, Y., Wolsey, L.A.: Capacitated Facility Location: Valid Inequalities and Facets. Math. Oper. Res. 20, 562–582 (1995)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Aardal, K.: Capacitated Facility Location: Separation Algorithms and Computational Experience. Math. Program. 81, 149–175 (1998)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Andrews, M., Zhang, L.: Approximation Algorithms for Access Network Design. Algorithmica 34, 197–215 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    Avella, P., Sassano, A.: On the p-Median Polytope. Math. Program. 89, 395–411 (2001)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Balas, E.: Facets of the Knapsack Polytope. Math. Program. 8, 146–164 (1975)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Beasley, J.E.: OR-Library: distributing test problems by electronic mail. J. Oper. Res. Soc. 41, 1069–1072 (1990)Google Scholar
  7. 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. 373–407Google Scholar
  8. 8.
    Dantzig, G.B.: On the Significance of Solving Linear Programming Problems with Some Integer Variables. The Rand Corporation, document, 1958, p. 1486Google Scholar
  9. 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, 1992Google Scholar
  10. 10.
    Ernst, A.T., Krishnamoorthy, M.: Solution Algorithms for the Capacitated Single Allocation Hub Location Problem. Ann. Oper. Res. 86, 141–159 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 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. 275–305Google Scholar
  12. 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. 144–191Google Scholar
  13. 13.
    Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Springer-Verlag, Berlin, 1988Google Scholar
  14. 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)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Hammer, P.L., Johnson, E.L., Peled, U.N.: Facets of Regular 0-1 Polytopes. Math. Program. 8, 179–206 (1975)zbMATHMathSciNetGoogle Scholar
  16. 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)CrossRefzbMATHGoogle Scholar
  17. 17.
    Leung, J.M.Y., Magnanti, T.L.: Valid Inequalities and Facets of the Capacitated Plant Location Problem. Math. Program. 44, 271–291 (1989)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations, Wiley, New York, 1990Google Scholar
  19. 19.
    Padberg, M.W.: On the Facial Structure of Set Packing Polyhedra. Math. Program. 5, 199–215 (1973)zbMATHMathSciNetGoogle Scholar
  20. 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)CrossRefzbMATHGoogle Scholar
  21. 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. 256–269Google Scholar
  22. 22.
    Wolsey, L.: Faces for a Linear Inequality in 0-1 Variables. Math. Program. 8, 165–178 (1975)zbMATHMathSciNetGoogle Scholar
  23. 23.
    Yaman, H.: Concentrator Location in Telecommunication Networks, Ph.D. Thesis, Université Libre de Bruxelles, 2002. Available at
  24. 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, 2001Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Université Libre de Bruxelles, Service d’OptimisationBruxellesBelgium
  2. 2.Department of Industrial EngineeringBilkent UniversityBilkentTurkey
  3. 3.France Telecom R&D, DAC/OATIssy-les-Moulineaux Cedex 9France

Personalised recommendations