## Robust facility location

- Let A be a nonempty finite subset of R^2 representing the geographical coordinates of a set of demand points (towns, ...), to be served by a facility, whose location within a given region S is sought. Assuming that the unit cost for a in A if the facility is located at x in S is proportional to dist(x,a) - the distance from x to a - and that demand of point a is given by w_a, minimizing the total trnsportation cost TC(w,x) amounts to solving the Weber problem. In practice, it may be the case, however, that the demand vector w is not known, and only an estimator {hat w} can be provided. Moreover the errors in sich estimation process may be non-negligible. We propose a new model for this situation: select a threshold valus B 0 representing the highest admissible transportation cost. Define the robustness p of a location x as the minimum increase in demand needed to become inadmissible, i.e. p(x) = min{||w^*-{hat w}|| : TC(w^*,x) B, w^* = 0} and solve then the optimization problem max_{x in S} p(x) to get the most robust location.

Author: | Stefan Nickel, Emilio Carrizosa |
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URN (permanent link): | urn:nbn:de:hbz:386-kluedo-4787 |

Serie (Series number): | Report in Wirtschaftsmathematik (WIMA Report) (35) |

Document Type: | Preprint |

Language of publication: | English |

Year of Completion: | 1998 |

Year of Publication: | 1998 |

Publishing Institute: | Technische Universität Kaiserslautern |

Date of the Publication (Server): | 2000/04/03 |

Faculties / Organisational entities: | Fachbereich Mathematik |

DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |

Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |