## Spherical Location Problems with Restricted Regions and Polygonal Barriers

- This thesis investigates the constrained form of the spherical Minimax location problem and the spherical Weber location problem. Specifically, we consider the problem of locating a new facility on the surface of the unit sphere in the presence of convex spherical polygonal restricted regions and forbidden regions such that the maximum weighted distance from the new facility on the surface of the unit sphere to m existing facilities is minimized and the sum of the weighted distance from the new facility on the surface of the unit sphere to m existing facilities is minimized. It is assumed that a forbidden region is an area on the surface of the unit sphere where travel and facility location are not permitted and that distance is measured using the great circle arc distance. We represent a polynomial time algorithm for the spherical Minimax location problem for the special case where all the existing facilities are located on the surface of a hemisphere. Further, we have developed algorithms for spherical Weber location problem using barrier distance on a hemisphere as well as on the unit sphere.

Author: | Mangalika Jayasundara Dedigama Dewage |
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URN (permanent link): | urn:nbn:de:hbz:386-kluedo-18142 |

Advisor: | Horst W. Hamacher |

Document Type: | Doctoral Thesis |

Language of publication: | English |

Year of Completion: | 2005 |

Year of Publication: | 2005 |

Publishing Institute: | Technische Universität Kaiserslautern |

Granting Institute: | Technische Universität Kaiserslautern |

Acceptance Date of the Thesis: | 2005/02/01 |

Date of the Publication (Server): | 2005/02/14 |

Tag: | Arc distance; Barriers; Restricted Regions; Spherical Location Problem |

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 |