### Abstract

We analyze the unit-demand Euclidean vehicle routeing problem, where n customers are modeled as independent, identically distributed uniform points and have unit demand. We show new lower bounds on the optimal cost for the metric vehicle routeing problem and analyze them in this setting. We prove that there exists a constant ĉ > 0 such that the iterated tour partitioning heuristic given by Haimovich and Rinnooy Kan (1985) is a (2 - ĉ)-approximation algorithm with probability arbitrarily close to 1 as the number of customers goes to ∞. It has been a longstanding open problem as to whether one can improve upon the factor of 2 given by Haimovich and Rinnooy Kan. We also generalize this, and previous results, to the multidepot case.

Original language | English (US) |
---|---|

Pages (from-to) | 259-278 |

Number of pages | 20 |

Journal | Journal of Applied Probability |

Volume | 44 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2007 |

### Keywords

- Heuristic
- Probabilistic analysis of algorithms
- Vehicle routeing problem

### ASJC Scopus subject areas

- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty

## Fingerprint Dive into the research topics of 'Probabilistic analysis of unit-demand vehicle routeing problems'. Together they form a unique fingerprint.

## Cite this

*Journal of Applied Probability*,

*44*(1), 259-278. https://doi.org/10.1239/jap/1175267177