Algorithm for Single Allocation Problem on Hub-and-Spoke Networks in 2-Dimensional Plane

  • Ryuta Ando
  • Tomomi Matsui
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

Abstract

This paper deals with a single allocation problem in hub-and-spoke networks. We handle the case that all the nodes are embedded in a 2-dimensional plane and a transportation cost (per unit flow) is proportional to Euclidean distance. We propose a randomized (1 + 2/π)-approximation algorithm based on a linear relaxation problem and a dependent rounding procedure.

Keywords

Transportation Cost Mixed Integer Programming Transportation Problem Discrete Apply Mathematic Total Transportation Cost 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adams, W.P., Sherali, H.D.: A tight linearization and an algorithm for zero-one quadratic programming problems. Management Science 32, 1274–1290 (1986)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bertsimas, D., Teo, C., Vohra, R.: On dependent randomized rounding algorithms. Operations Research Letters 24, 105–114 (1999)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Bryan, D.L., O’Kelly, M.E.: Hub-and-spoke networks in air transportation: an analytical review. Journal of Regional Science 39, 275–295 (1999)CrossRefGoogle Scholar
  4. 4.
    Burkard, R.E., Klinz, B., Rudolf, R.: Perspectives of Monge properties in optimization. Discrete Applied Mathematics 70, 95–161 (1996)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Campbell, J.F.: Integer programming formulations of discrete hub location problems. European Journal of Operational Research 72, 387–405 (1994)CrossRefMATHGoogle Scholar
  6. 6.
    Chekuri, C., Khanna, S., Naor, J., Zosin, L.: A linear programming formulation and approximation algorithms for the metric labeling problem. SIAM Journal on Discrete Mathematics 18, 608–625 (2005)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Ge, D., Ye, Y., Zhang, J.: The Fixed-Hub Single Allocation Problem: A Geometric Rounding Approach (October 2007) (manuscript)Google Scholar
  8. 8.
    Hamacher, H.W., Labbé, M., Nickel, S., Sonneborn, T.: Adapting polyhedral properties from facility to hub location problems. Discrete Applied Mathematics 145, 104–116 (2004)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Iwasa, M., Saito, H., Matsui, T.: Approximation Algorithms for the Single Allocation Problem in Hub-and-Spoke Networks and Related Metric Labeling Problems. Discrete Applied Mathematics 157, 2078–2088 (2009)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Labbé, M., Yaman, H.: Projecting the flow variables for hub location problems. Networks 44, 84–93 (2004)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Labbé, M., Yaman, H., Gourdin, E.: A branch and cut algorithm for hub location problems with single assignment. Mathematical Programming 102, 371–405 (2005)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    O’Kelly, M.E.: A quadratic integer program for the location of interacting hub facilities. European Journal of Operational Research 32, 393–404 (1987)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Saito, H., Fujie, T., Matsui, T., Matuura, S.: The Quadratic semi-assignment polytope. Discrete Optimization 6, 37–50 (2009)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Saito, H., Matuura, S., Matsui, T.: A linear relaxation for hub network design problems. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E85-A, 1000–1005 (2002)Google Scholar
  15. 15.
    Sohn, J., Park, S.: A linear program for the two-hub location problem. European Journal of Operational Research 100, 617–622 (1997)CrossRefMATHGoogle Scholar
  16. 16.
    Sohn, J., Park, S.: The single allocation problem in the interacting three-hub network. Networks 35, 17–25 (2000)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ryuta Ando
    • 1
  • Tomomi Matsui
    • 1
  1. 1.Department of Information and System Engineering, Faculty of Science and EngineeringChuo UniversityTokyoJapan

Personalised recommendations