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On a robustness property in single-facility location in continuous space

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  • Marc Ciligot-Travain
  • Sado Traoré

Abstract

We consider a single-facility location problem in continuous space—here the problem of minimizing a sum or the maximum of the possibly weighted distances from a facility to a set of points of demand. The main result of this paper shows that every solution (optimal facility location) of this problem has an interesting robustness property. Any optimal facility location is the most robust in the following sense: given a suitable highest admissible cost, it allows the greatest perturbation of the locations of the demand without exceeding this highest admissible chosen cost. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Marc Ciligot-Travain & Sado Traoré, 2014. "On a robustness property in single-facility location in continuous space," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 321-330, April.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:1:p:321-330
    DOI: 10.1007/s11750-012-0257-5
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    References listed on IDEAS

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    1. Drezner, Zvi & Guyse, Jeffery, 1999. "Application of decision analysis techniques to the Weber facility location problem," European Journal of Operational Research, Elsevier, vol. 116(1), pages 69-79, July.
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    3. F. Plastria & E. Carrizosa, 2001. "Gauge Distances and Median Hyperplanes," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 173-182, July.
    4. Emilio Carrizosa & Stefan Nickel, 2003. "Robust facility location," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 331-349, November.
    5. Roy, Bernard, 2010. "Robustness in operational research and decision aiding: A multi-faceted issue," European Journal of Operational Research, Elsevier, vol. 200(3), pages 629-638, February.
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