Solving Large Scale Uncapacitated Facility Location Problems

  • Francisco Barahona
  • Fabián A. Chudak
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 42)


We investigate the solution of instances of the uncapacitated facility location problem with at most 3000 potential facility locations and similar number of customers. We use heuristics that produce a feasible integer solution and a lower bound on the optimum. In particular, we present a new heuristic whose gap from optimality was generally below 1%. The heuristic combines the volume algorithm and a recent approximation algorithm based on randomized rounding. Our computational experiments show that our heuristic compares favorably against DUALOC.


Volume algorithm randomized rounding facility location. 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S. Ahn, C. Cooper, G. Cornuéjols, and A.M. Frieze. Probabilistic analysis of a relaxation for the k-median problem. Mathematics of Operations Research, 13: 1–31, 1988.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    M.L. Balinski. Integer programming• methods, uses, computation. Management Science, 12 (3): 253–313, 1965.zbMATHGoogle Scholar
  3. [3]
    F. Barahona and R. Anbil. The volume algorithm: producing primal solutions with the subgradient method. Technical report, IBM Watson Research Center, 1998.Google Scholar
  4. [4]
    F.A. Chudak. Improved approximation algorithms for the uncapacitated facility location problem. PhD thesis, Cornell University, 1998.Google Scholar
  5. [5]
    F.A. Chudak. Improved approximation algorithms for uncapacitated facility location. In Proceedings of the 6th IPCO Conference, pages 180–194, 1998.Google Scholar
  6. [6]
    F.A. Chudak and D.B. Shmoys. Improved approximation algorithms for the uncapacitated facility location problem. In preparation, 1999.Google Scholar
  7. [7]
    G. Cornuéjols, G.L. Nemhauser, and L.A. Wolsey. The uncapacitated facility location problem. In P. Mirchandani and R. Francis, editors, Discrete Location Theory, pages 119–171. John Wiley and Sons, Inc., New York, 1990.Google Scholar
  8. [8]
    D. Erlenkotter. A dual-based procedure for uncapacitated facility location. Operations Research, 26: 992–1009, 1978.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    D. Erlenkotter, 1991. Program DUALOC — Version II. Distributed on request.Google Scholar
  10. [10]
    S. Guha and S. Khuller. Greedy strikes back: improved facility location algorithms. In Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 649–657, 1998.Google Scholar
  11. [11]
    M. Held, P. Wolfe, and H.P. Crowder. Validation of subgradient optimization. Mathematical Programming, 49: 62–88, 1991.MathSciNetGoogle Scholar
  12. [12]
    C. Lemaréchal. Nondifferential optimization. In G.L. Nemhauser, A.H.G Rinnoy Kan, and M.J. Todd, editors, Optimization, Handbooks in Operations Research, pages 529–572. North Holland, 1989.Google Scholar
  13. [13]
    P. Mirchandani and R. Francis, eds. Discrete Location Theory. John Wiley and Sons, Inc., New York, 1990.zbMATHGoogle Scholar
  14. [14]
    D.B. Shmoys, É. Tardos, and K. Aardal. Approximation algorithms for facility location problems. In Proceedings of the 29th ACM Symposium on Theory of Computing, pages 265–274, 1997.Google Scholar
  15. [15]
    M.I. Sviridenko, July, 1998. Personal communication.Google Scholar
  16. [16]
    P. Wolfe. A method of conjugate subgradients for minimizing nondifferentiable functions. Mathematical Programming Study, 3: 145–173, 1975.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Francisco Barahona
    • 1
  • Fabián A. Chudak
    • 1
  1. 1.IBM T.J. Watson Research CenterYorktown HeightsUSA

Personalised recommendations