### Abstract

Given are m identical machines, each of which performs the same N operations Oi, 1 ≤ i ≤ N, cyclically and indefinitely, i.e. a production run on a machine looksO1, O2,…,ON, O1, O2,…,ON, O1…. There are nim to to perform operation Oi. The tools are transported between the machines by means of an infinitely fast transport device.
Given a particular transport policy we prove the existence of stationary cyclic behaviour, determine the corresponding cycle time, and investigate the long run behaviour of the system starting from a given initial state.

Original language | Undefined |
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Pages (from-to) | 187-200 |

Number of pages | 14 |

Journal | European journal of operational research |

Volume | 104 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1998 |

### Keywords

- Production
- Eigenvalue problem
- Knapsack function
- METIS-140558
- Cycle time
- Minimax-algebra
- IR-73917

## Cite this

Nawijn, W. M. (1998). A cyclic production problem: an application of max-algebra.

*European journal of operational research*,*104*(1), 187-200. https://doi.org/10.1016/S0377-2217(96)00336-0