### Abstract

In this paper we consider the problem of preventive maintenance of a failure prone system, for which a number of maintenance actions has to be executed on a regular basis. For each action i the frequency is prescribed. Between consecutive actions of type i there is an integer interspacing of T(i) time units. The set-up costs are activity dependent. The set-up structure is supposed to be tree-like and additive over the set-up nodes involved in the action or group of actions. Hence, for different activities with common setup nodes joint execution leads to set-up costs reduction. The question is how the actions should be arranged in time in order to exploit this set-up costs reduction effect maximally. It is shown that the time averaged set-up costs are minimal if a main peak clustering property is satisfied: all maintenance actions are combined at one moment in time. Intuitively, this property is appealing, but it asks for some interesting and non-trivial applications of number theory and inductive reasoning, to prove it.

Original language | English |
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Place of Publication | Eindhoven |

Publisher | TU Eindhoven, Research School for Operations Management and Logistics (BETA) |

Publication status | Published - 1999 |

### Publication series

Name | BETA Working Paper |
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Publisher | University of Eindhoven, BETA |

No. | WP-45 |

### Keywords

- IR-95679
- METIS-128069

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## Cite this

van Harten, A., van Dijkhuizen, G. C., & Mars, J. G. M. (1999).

*On a number theoretic property of optimal maintenance grouping*. (BETA Working Paper; No. WP-45). Eindhoven: TU Eindhoven, Research School for Operations Management and Logistics (BETA).