Skip to main content
Springer Nature Link
Log in

Approximation algorithms for the robust/soft-capacitated 2-level facility location problems

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

In this work, we consider the robust/soft-capacitated 2-level facility location problems. For the robust version, we propose a primal-dual based \((3+\epsilon )\)-approximation algorithm via construction of an adapted instance which explores some open facilities in the optimal solution. For the soft-capacitated version, we propose a \( (4+ 1/ (e-1) +\epsilon )\)-approximation algorithm via construction of the associated uncapacitated version whose connection cost is re-defined appropriately.

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
$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

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Arya, V., Garg, N., Khandekar, R., Meyerson, A., Munagala, K., Pandit, V.: Local search heuristics for \(k\)-median and facility location problems. In: Proceedings of STOC, pp. 21–29 (2001)

  2. Ageev, A.A., Ye, Y., Zhang, J.: Improved combinatorial approximation algorithms for the \(k\)-level facility location problem. SIAM J. Discrete Math. 18, 207–217 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bumb, A.F., Kern, W.A.: Simple dual ascent algorithm for the multilevel facility location problem. In: Proceedings of APPROX-RANDOM, pp. 55–62 (2001)

  4. Byrka, J., Rybicki, B.: Improved LP-rounding approximation algorithm for \(k\)-level uncapacitated facility location. In: Proceedings of ICALP, pp. 157–169 (2012)

  5. Charikar, M., Khuller, S., Mount, M., Narasimhan, G.: Algorithms for facility location problems with outliers. In: Proceedings of SODA, pp. 642–651 (2001)

  6. Chudak, F.A., Shmoys, D.B.: Improved approximation algorithms for the capacitated facility location problem. In: Proceedings of SODA, pp. 875–876 (1999)

  7. Gabor, A., van Ommeren, J.: A new approximation algorithm for the multilevel facility location problem. Discrete Appl. Math. 158, 453–460 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jain, K., Vazirani, V.V.: Approximation algorithms for metric facility location and \(k\)-median problems using the primal-dual schema and Lagrangian relaxation. J. ACM 48, 274–296 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Jain, K., Mahdian, M., Markakis, E., Saberi, A., Vazirani, V.V.: Approximation algorithms for facility location via dualfitting with factor-revealing LP. J. ACM 50, 795–824 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kaufman, L., Eede, M.V., Hansen, P.: A plant and warehouse location problem. Oper. Res. Q. 28, 547–557 (1977)

    Article  MATH  Google Scholar 

  11. Krishnaswamy, R., Sviridenko, M.: Inapproximability of the multi-level uncapacitated facility location problem. In: Proceedings of SODA, pp. 718–734 (2012)

  12. Li, G., Du, D., Xu, D., Yang, R.: A cost-sharing method for the multi-level economic lot-sizing game. Sci. China Inf. Sci. 57, 1–9 (2014)

    MathSciNet  Google Scholar 

  13. Mahdian, M., Ye, Y., Zhang, J.: A \(2\)-approximation algorithm for the soft-capacitated facility location problem. In: Proceedings of APPROX, pp. 129C140 (2003)

  14. Sviridenko, M.: A note on maximizing a submodular set function subject to a knapsack constraint. Oper. Res. Lett. 32, 41–43 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Tcha, D., Lee, B.: A branch-and-bound algorithm for the multi-level uncapacitated facility location problem. Eur. J. Oper. Res. 18, 35–43 (1984)

    Article  MATH  Google Scholar 

  16. Wu, C., Xu, D.: Improved approximation algorithms for the \(k\)-level facility location problem with soft capacities. Accepted by Acta Mathematicae Applicatae Sinica

  17. Wu, C., Du, D., Xu, D.: Primal-dual approximation algorithm for the two-level facility location problem via a dual quasi-greedy approach. Theor. Comput. Sci. 562, 213–226 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wu, C., Du, D., Xu, D.: An improved per-scenario bound for the two-stage stochastic facility location problem. Sci. China Math. 58, 213–220 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wang, F., Xu, D., Wu, C.: Combinatorial approximation algorithms for the robust facility location problem with penalties. J. Glob. Optim. 28, 1102–1114 (2016)

    MathSciNet  MATH  Google Scholar 

  20. Xu, D., Du, D.: The \(k\)-level facility location game. Oper. Res. Lett. 34, 421–426 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhang, J.: Approximating the two-level facility location problem via a quasi-greedy approach. Math. Program. 108, 159–176 (2006)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The research of the first author is supported by Natural Science Foundation of China (No. 11501412) and Tianjin 131 innovative talent training project. The second author’s research is supported by Natural Science Foundation of China (No. 11371001). The third author’s research is supported by Higher Educational Science and Technology Program of Shandong Province (No. J15LN23). The fourth author’s research is supported by Natural Science Foundation of China (No. 61672323).

Author information

Authors and Affiliations

  1. College of Science, Tianjin University of Technology, Tianjin, 300384, People’s Republic of China

    Chenchen Wu

  2. Department of Information and Operations Research, College of Applied Sciences, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Dachuan Xu

  3. School of Computer Science and Technology, Shandong Jianzhu University, Jinan, 250101, People’s Republic of China

    Dongmei Zhang

  4. School of Computer Science and Technology, Shandong University, Jinan, 250101, People’s Republic of China

    Peng Zhang

Authors
  1. Chenchen Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dachuan Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dongmei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dongmei Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, C., Xu, D., Zhang, D. et al. Approximation algorithms for the robust/soft-capacitated 2-level facility location problems. J Glob Optim 70, 207–222 (2018). https://doi.org/10.1007/s10898-017-0566-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-017-0566-1

Keywords