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Exact algorithms for handling outliers in center location problems on networks using k-max functions

Author

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  • Schnepper, Teresa
  • Klamroth, Kathrin
  • Stiglmayr, Michael
  • Puerto, Justo

Abstract

In this paper, the identification and exclusion of very distant facilities in center location problems is modeled by k-max functions: One or several new facilities are to be located such that not the largest, but the kth largest weighted distance to the customers is minimized, with k ≥ 1. It is shown that k-max location problems on networks can be solved efficiently by enumerating candidate solutions from a finite dominating set (FDS) that is independent from the particular value of k. As a consequence, k-max locations can be found for all reasonable values of k at little extra cost as compared to a single solver call, for one fixed value of k. The location of several new facilities is naturally more complex. An FDS based recursive algorithm is developed for this case that allows the exact solution of medium size instances.

Suggested Citation

  • Schnepper, Teresa & Klamroth, Kathrin & Stiglmayr, Michael & Puerto, Justo, 2019. "Exact algorithms for handling outliers in center location problems on networks using k-max functions," European Journal of Operational Research, Elsevier, vol. 273(2), pages 441-451.
    • Handle: RePEc:eee:ejores:v:273:y:2019:i:2:p:441-451
    DOI: 10.1016/j.ejor.2018.08.030
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    References listed on IDEAS

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