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On the Weber facility location problem with limited distances and side constraints

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Abstract

The objective in the continuous facility location problem with limited distances is to minimize the sum of distance functions from the facility to the customers, but with a limit on each of the distances, after which the corresponding function becomes constant. The problem has applications in situations where the service provided by the facility is insensitive after a given threshold distance. In this paper, we propose a global optimization algorithm for the case in which there are in addition lower and upper bounds on the numbers of customers served.

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Authors and Affiliations

  1. Universidade Federal do Rio Grande do Norte, Campus Universitário s/n, Natal, RN, 59072-970, Brazil

    Isaac F. Fernandes & Daniel Aloise

  2. Universidade do Estado do Rio Grande do Norte, Rua Almino Afonso, 478 Centro, Mossoró, RN, 59610-210, Brazil

    Dario J. Aloise

  3. GERAD and HEC Montréal, 3000, Chemin de la Côte-Sainte-Catherine, Montréal, QC, H3T 2A7, Canada

    Pierre Hansen

  4. LIX, École Polytechnique, 91128, Palaiseau, France

    Leo Liberti

Authors
  1. Isaac F. Fernandes
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  2. Daniel Aloise
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  3. Dario J. Aloise
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  4. Pierre Hansen
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  5. Leo Liberti
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Corresponding author

Correspondence to Daniel Aloise.

Additional information

DA is partially supported by CNPq (Brazil) grant 305070/2011-8. DJA was partially supported by CNPq (Brazil) grant 483846/2009-0. LL and PH are grateful to Digiteo (contracts RMNCCO-2009-14D and ARM-2009-55D). LL is also grateful to the Microsoft-CNRS Chair on “Optimization and Sustainable Development” for financial support. PH is also partially supported by NSERC (Canada) grant 105574-07.

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Fernandes, I.F., Aloise, D., Aloise, D.J. et al. On the Weber facility location problem with limited distances and side constraints. Optim Lett 8, 407–424 (2014). https://doi.org/10.1007/s11590-012-0538-9

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  • DOI: https://doi.org/10.1007/s11590-012-0538-9

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