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## Weber s Problem with attraction and repulsion under Polyhedral Gauges

- Given a finite set of points in the plane and a forbidden region R, we want to find a point X not an element of int(R), such that the weighted sum to all given points is minimized. This location problem is a variant of the well-known Weber Problem, where we measure the distance by polyhedral gauges and allow each of the weights to be positive or negative. The unit ball of a polyhedral gauge may be any convex polyhedron containing the origin. This large class of distance functions allows very general (practical) settings - such as asymmetry - to be modeled. Each given point is allowed to have its own gauge and the forbidden region R enables us to include negative information in the model. Additionally the use of negative and positive weights allows to include the level of attraction or dislikeness of a new facility. Polynomial algorithms and structural properties for this global optimization problem (d.c. objective function and a non-convex feasible set) based on combinatorial and geometrical methods are presented.

Author: | Stefan Nickel, Eva Maria Dudenhöffer |
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URN (permanent link): | urn:nbn:de:hbz:386-kluedo-4893 |

Serie (Series number): | Report in Wirtschaftsmathematik (WIMA Report) (5) |

Document Type: | Preprint |

Language of publication: | English |

Year of Completion: | 1999 |

Year of Publication: | 1999 |

Publishing Institute: | Technische Universität Kaiserslautern |

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

Tag: | Location Theory; discretization; geometrical algorithms; global optimization |

Faculties / Organisational entities: | Fachbereich Mathematik |

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

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