## Abstract

We consider the a priori traveling repairman problem, which is a stochastic version of the classic traveling repairman problem. Given a metric (V,d) with a root r∈V, the traveling repairman problem (TRP) involves finding a tour originating from r that minimizes the sum of arrival-times at all vertices. In its a priori version, we are also given independent probabilities of each vertex being active. We want to find a master tour τ originating from r and visiting all vertices. The objective is to minimize the expected sum of arrival-times at all active vertices, when τ is shortcut over the inactive vertices. We obtain the first constant-factor approximation algorithm for a priori TRP under independent non-uniform probabilities. Our result provides a general reduction from non-uniform to uniform probabilities, and uses (in black-box manner) an existing approximation algorithm for a priori TRP under uniform probabilities.

Original language | English |
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Journal | Operations Research Letters |

Volume | 48 |

Issue number | 5 |

Pages (from-to) | 599-606 |

ISSN | 0167-6377 |

DOIs | |

Publication status | Published - Sep 2020 |

## Keywords

- A priori optimization
- Approximation algorithms
- Traveling repairman problem