## Abstract

We consider N unreliable machines that are maintained by M repairmen. The time until failure of machine i, and its repair by repairman j, are exponentially distributed random variable with parameters λ_{i} and μ_{j}respectively. All failure times and repair times are independent. Machine i earns c_{i}per unit time, while it is working. We wish to maximize the expected total discounted reward. It is shown that when the following conditions are satisfied -c_{1}≥ • • • ≥ c_{N} and c_{1}/λ_{1}≥ • • • > c_{N}/λ_{N}the policy that assigns the fastest repairman to the machine with the lowest index is optimal. Moreover, it is shown that when the second condition is replaced by λ < • • - < λ_{N}then this policy maximizes, stochastically, the number of the most reliable machines at every time t.

Original language | English |
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Pages (from-to) | 633-645 |

Number of pages | 13 |

Journal | Probability in the Engineering and Informational Sciences |

Volume | 9 |

Issue number | 4 |

DOIs | |

State | Published - Oct 1995 |

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Management Science and Operations Research
- Industrial and Manufacturing Engineering