## Planar Location Problems with Line Barriers

- The Weber Problem for a given finite set of existing facilities {cal E}x = {Ex_1,Ex_2, ... ,Ex_M} subset R^2 with positive weights w_m (m = 1, ... ,M) is to find a new fcility X* such that sum_{m=1}^{M} w_{m}d(X,Ex_m) is minimized for some distance function d. A variation of this problem is obtained of the existing facilities are situated on two sides of a linear barrier. Such barriers like rivers, highways, borders or mountain ranges are frequently encountered in practice. Structural results as well as algorithms for this non-convex optimization problem depending on the distance function and on the number and location of passages through the barrier are presented. A reduction to convex optimization problems is used to derive efficient algorithms.

Author: | Kathrin Klamroth |
---|---|

URN (permanent link): | urn:nbn:de:hbz:386-kluedo-4549 |

Serie (Series number): | Report in Wirtschaftsmathematik (WIMA Report) (13) |

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 |

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 |