## Abstract

We consider a rather large class of p-facility location models including the p-median, p-center, and other related and more general models. For any such model of interest with p new facilities, let v(p) denote the minimal objective function value and let n be the number of demand points. Given 1 ≤ p < q ≤ n, we find easily computed positive constants k(p, q), where v(q)/v(p) ≤ k(p, q) ≤ 1. These resulting inequalities relating v(p) and v(q) are worst case, since they are attained as equalities for a class of "hub-and-spoke" trees. Our results also provide insight into some demand point aggregation problems, where a graph of the function v(q) can provide an upper bound on aggregation error.

Original language | English |
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Pages (from-to) | 139-143 |

Number of pages | 5 |

Journal | Networks |

Volume | 39 |

Issue number | 3 |

DOIs | |

State | Published - May 2002 |

## Keywords

- Aggregation
- Incremental analysis
- Location
- Worst case
- p-median