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pp 1–13 | Cite as

Inverse and reverse balanced facility location problems with variable edge lengths on trees

  • Shahede Omidi
  • Jafar FathaliEmail author
  • Morteza Nazari
Theoretical Article
  • 5 Downloads

Abstract

This paper deals with the inverse and reverse balanced facility location problems with considering the variable edge lengths. The aim of the inverse problem is modifying the length of edges with minimum cost, such that the difference between the maximum and minimum weights of clients, allocated to the given facilities is minimized. On the other hand, the reverse case of the balanced facility location problem considers the modifying the lengths of edges with a given budget constraint, such that the difference between the maximum and minimum weights of vertices, allocated to the given facilities is reduced as much as possible. Two algorithms with time complexity O(nlogn) are presented for the inverse and reverse balanced 2-facility location problems.

Keywords

Facility location Inverse Reverse Balanced allocation Equality measure Variable edge length 

Mathematics Subject Classification

90B90 90B06 

Notes

References

  1. 1.
    Alizadeh, B., Afrashteh, E., Baroughi, F.: Combinatorial algorithms for some variants of inverse obnoxious median location problem on tree networks. J. Optim. Theory Appl. 178, 914–934 (2018)CrossRefGoogle Scholar
  2. 2.
    Alizadeh, B., Burkard, R.E., Pferschy, U.: Inverse 1-center location problems with edge length augmentation on trees. Computing 86, 331–343 (2009)CrossRefGoogle Scholar
  3. 3.
    Alizadeh, B., Burkard, R.E.: Combinatorial algorithms for inverse absolute and vertex 1-center location problems on trees. Networks 58, 190–200 (2011)CrossRefGoogle Scholar
  4. 4.
    Alizadeh, B., Etemad, R.: Optimal algorithms for inverse vertex obnoxious center location problems on graphs. Theor. Comput. Sci. 707, 36–45 (2018)CrossRefGoogle Scholar
  5. 5.
    Barbati, M., Piccolo, C.: Equality measures properties for location problems. Optim. Lett. 10, 903–920 (2015)CrossRefGoogle Scholar
  6. 6.
    Berman, O., Drezner, Z., Tamir, A., Wesolowsky, G.O.: Optimal location with equitable loads. Ann. Oper. Res. 167, 307–325 (2009)CrossRefGoogle Scholar
  7. 7.
    Berman, O., Ingco, D.I., Odoni, A.: Improving the location of minisum facilities through network modification. Ann. Oper. Res. 40, 1–16 (1992)CrossRefGoogle Scholar
  8. 8.
    Berman, O., Ingco, D.I., Odoni, A.: Improving the location of minimax facilities through network modification. Networks 24, 31–41 (1994)CrossRefGoogle Scholar
  9. 9.
    Baroughi-Bonab, F., Burkard, R.E., Gassner, E.: Inverse p-median problems with variable edge lengths. Math. Methods Oper. Res. 73, 263–280 (2011)CrossRefGoogle Scholar
  10. 10.
    Burkard, R.E., Gassner, E., Hatzl, J.: A linear time algorithm for the reverse 1-median problem on a cycle. Networks 48, 16–23 (2006)CrossRefGoogle Scholar
  11. 11.
    Burkard, R.E., Gassner, E., Hatzl, J.: Reverse 2-median problem on trees. Discrete Appl. Math. 156, 1963–1976 (2008)CrossRefGoogle Scholar
  12. 12.
    Burkard, R.E., Pleschiutschnig, C., Zhang, J.Z.: Inverse median problems. Discrete Optim. 1, 23–39 (2004)CrossRefGoogle Scholar
  13. 13.
    Burkard, R.E., Pleschiutschnig, C., Zhang, J.Z.: The inverse 1-median problem on a cycle. Discrete Optim. 5, 242–253 (2007)CrossRefGoogle Scholar
  14. 14.
    Cai, M.C., Yang, X.G., Zhang, J.: The complexity analysis of the inverse center location problem. J. Glob. Optim. 15, 213–218 (1999)CrossRefGoogle Scholar
  15. 15.
    Eiselt, H.A., Laporte, G.: Objectives in location problems. In: Drezner, Z. (ed.) Facility Location: A Survey of Applications and Methods, pp. 151–180. Springer, Berlin (1995)CrossRefGoogle Scholar
  16. 16.
    Fathali, J., Zaferanieh, M.: The balanced 2-median and 2-maxian problems on a tree (2018). arXiv:1803.10332 [math.OC]
  17. 17.
    Galavii, M.: The inverse 1-median problem on a tree and on a path. Electron. Notes Discrete Math. 36, 1241–1248 (2010)CrossRefGoogle Scholar
  18. 18.
    Gavalec, M., Hudec, O.: Balanced location on a graph. Optimization 35, 367–372 (1995)CrossRefGoogle Scholar
  19. 19.
    Guan, X.C., Zhang, B.W.: Inverse 1-median problem on trees under weighted Hamming distance. J. Glob. Optim. 54, 75–82 (2012)CrossRefGoogle Scholar
  20. 20.
    Landete, M., Marin, A.: Looking for edge-equitable spanning trees. Comput. Oper. Res. 41, 44–52 (2014)CrossRefGoogle Scholar
  21. 21.
    Lejeune, M.A., Prasad, S.Y.: Effectiveness-equity models for facility location problems on tree networks. Networks 62, 243–254 (2013)CrossRefGoogle Scholar
  22. 22.
    Marin, A.: The discrete facility location problem with balanced allocation of customers. Eur. J. Oper. Res. 210, 27–38 (2011)CrossRefGoogle Scholar
  23. 23.
    Marsh, M.T., Schilling, D.A.: Equity measurement in facility location analysis: a review and framework. Eur. J. Oper. Res. 74, 1–17 (1994)CrossRefGoogle Scholar
  24. 24.
    Nazari, M., Fathali, J.: Reverse backup 2-median problem with variable coordinate of vertices. J. Oper. Res. Appl. 15, 63–88 (2018)Google Scholar
  25. 25.
    Nazari, M., Fathali, J., Nazari, M., Varedi-Koulaei, S.M.: Inverse of backup 2-median problems with variable edge lengths and vertex weight on trees and variable coordinates on the plane. Prod. Oper. Manag. 9, 115–137 (2018)Google Scholar
  26. 26.
    Nguyen, K.T.: Reverse 1-center problem on weighted trees. Optimization 65, 253–264 (2016)CrossRefGoogle Scholar
  27. 27.
    Nguyen, K.T.: Inverse 1-median problem on block graphs with variable vertex weights. J. Optim. Theory Appl. 168, 944–957 (2016)CrossRefGoogle Scholar
  28. 28.
    Nguyen, K.T., Sepasian, A.R.: The inverse 1-center problem on trees with variable edge lengths under Chebyshev norm and Hamming distance. J. Comb. Optim. 32, 872–884 (2016)CrossRefGoogle Scholar
  29. 29.
    Sepasian, A.R., Rahbarnia, F.: An O(nlogn) algorithm for the inverse 1-median problem on trees with variable vertex weights and edge reductions. Optimization 64, 595–602 (2015)Google Scholar
  30. 30.
    Zhang, J., Liu, Z., Ma, Z.: Some reverse location problems. Eur. J. Oper. Res. 124, 77–88 (2000)CrossRefGoogle Scholar

Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  1. 1.Faculty of Mathematical SciencesShahrood University of TechnologyShahroodIran

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