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## Mathematical Programming Formulations of the Planar Facility Location Problem

The facility location problem is the task of optimally placing a

given number of facilities in a certain subset of the plane. In

this thesis, we present various mathematical programming

formulations of the planar facility location problem, where

potential facility locations are not specified. We first consider

mixed-integer programming formulations of the planar facility

locations problems with squared Euclidean and rectangular distance

metrics to solve this problem to provable optimality. We also

investigate a heuristic approach to solving the problem by extending

the $K$-means clustering algorithm and formulating the facility

location problem as a variant of a semidefinite programming problem,

leading to a relaxation algorithm. We present computational results

for the mixed-integer formulations, as well as compare the objective

values resulting from the relaxation algorithm and the modified

$K$-means heuristic. In addition, we briefly discuss some of the

practical issues related to the facility location model under the

continuous customer distribution.

Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OWTU.10012/3283 |

Date | January 2007 |

Creators | Zvereva, Margarita |

Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |

Language | English |

Detected Language | English |

Type | Thesis or Dissertation |

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