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On the convergence of the Cooper’s algorithm

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Abstract

In this paper, we consider the Cooper’s alternate location and allocation algorithm for solving the constrained uncapacitated multi-source Weber problem. The convergence of the sequence generated by Cooper’s algorithm to a local optimal solution proved under mild assumption. Furthermore, an approach for finding the global optimal solution is proposed.

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References

  1. Brimberg, J., Hansen, P., Mladenovic, N., Taillard, E.D.: Improvements and comparison of heuristics for solving the uncapacitated multi-source Weber problem. Oper. Res. 48, 444–460 (2000)

    Article  Google Scholar 

  2. Cooper, L.: Heuristic methods for location-allocation problems. SIAM Rev. 6, 37–53 (1964)

    Article  MathSciNet  Google Scholar 

  3. Gamal, M.D.H., Salhi, S.: Constructive heuristics for the uncapacitated location-allocation problem. J. Oper. Res. Soc. 52, 821–829 (2001)

    Article  Google Scholar 

  4. Gamal, M.D.H., Salhi, S.: A cellular type heuristic for the multisource Weber problem. Comput. Oper. Res. 30, 1609–1624 (2003)

    Article  MathSciNet  Google Scholar 

  5. Hansen, P., Mladenovic, N., Taillard, E.: Heuristic solution of the multisource Weber problem as a p-median problem. Oper. Res. Lett. 22, 55–62 (1998)

    Article  MathSciNet  Google Scholar 

  6. Jiang, J.L., Yuan, X.M.: A heuristic algorithm for constrained multi-source Weber problem—the variational inequality approach. Eur. J. Oper. Res. 187, 357–370 (2008)

    Article  MathSciNet  Google Scholar 

  7. Levin, Y., Ben-Israel, A.: A heuristic method for large-scale multi-facility location problems. Comput. Oper. Res. 31, 257–272 (2004)

    Article  MathSciNet  Google Scholar 

  8. Luis, M., Said, S., Nagy, G.: A guided reactive GRASP for the capacitated multi-source Weber problem. Comput. Oper. Res. 38, 1014–1024 (2011)

    Article  MathSciNet  Google Scholar 

  9. Nobakhtian, S., Raeisi Dehkordi, A.: An algorithm for generalized constrained multi-source Weber problem with demand substations. 4OR-Q. J. Oper. Res. 16, 343–377 (2018)

    Article  MathSciNet  Google Scholar 

  10. Raeisi Dehkordi, A.: The optimal solution set of the multi-source Weber problem. Bull. Iran. Math. Soc. 45, 495–514 (2019)

    Article  MathSciNet  Google Scholar 

  11. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)

    Book  Google Scholar 

  12. Sherali, H.D., Nordai, F.L.: NP-hard, capacitated, balanced p-median problems on a chain graph with a continuum of link demands. Math. Oper. Res. 13, 32–49 (1998)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The author was partially supported by University of Isfahan and a Grant from Iran National Science Foundation (INSF) (No. 96012472).

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Correspondence to Ahmadreza Raeisi Dehkordi.

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Raeisi Dehkordi, A. On the convergence of the Cooper’s algorithm. Optim Lett 14, 2539–2547 (2020). https://doi.org/10.1007/s11590-020-01572-5

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