### Abstract

Original language | English |
---|---|

Journal | Discrete Applied Mathematics |

Volume | 157 |

Issue number | 5 |

Pages (from-to) | 901-912 |

ISSN | 0166-218X |

DOIs | |

Publication status | Published - 2009 |

### Keywords

- facility location
- circular facility

### Cite this

*Discrete Applied Mathematics*,

*157*(5), 901-912. https://doi.org/10.1016/j.dam.2008.03.017

}

*Discrete Applied Mathematics*, vol. 157, no. 5, pp. 901-912. https://doi.org/10.1016/j.dam.2008.03.017

**Locating a minisum circle in the plane.** / Brimberg, Jack; Juel, Henrik; Schöbel, Anita.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Locating a minisum circle in the plane

AU - Brimberg, Jack

AU - Juel, Henrik

AU - Schöbel, Anita

PY - 2009

Y1 - 2009

N2 - We consider the problem of locating a circle with respect to existing facilities in the plane such that the sum of weighted distances between the circle and the facilities is minimized, i.e., we approximate a set of given points by a circle regarding the sum of weighted distances. If the radius of the circle is a variable we show that there always exists an optimal circle passing through two of the existing facilities. For the case of a fixed radius we provide characterizations of optimal circles in special cases. Solution procedures are suggested.

AB - We consider the problem of locating a circle with respect to existing facilities in the plane such that the sum of weighted distances between the circle and the facilities is minimized, i.e., we approximate a set of given points by a circle regarding the sum of weighted distances. If the radius of the circle is a variable we show that there always exists an optimal circle passing through two of the existing facilities. For the case of a fixed radius we provide characterizations of optimal circles in special cases. Solution procedures are suggested.

KW - facility location

KW - circular facility

U2 - 10.1016/j.dam.2008.03.017

DO - 10.1016/j.dam.2008.03.017

M3 - Journal article

VL - 157

SP - 901

EP - 912

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 5

ER -