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.
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Acknowledgements
This work was supported by the French ANR project ROLSES (Robust and Optimal Locations for Sustainable Environment and Systems). The authors gratefully acknowledge the many helpful suggestions of the referees.
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Ciligot-Travain, M., Traoré, S. On a robustness property in single-facility location in continuous space. TOP 22, 321–330 (2014). https://doi.org/10.1007/s11750-012-0257-5
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DOI: https://doi.org/10.1007/s11750-012-0257-5