## Abstract

In this paper we consider the problem of no-wait cyclic scheduling of identical parts in an m-machine production line in which a robot is responsible for moving each part from a machine to another. The aim is to find the minimum cycle time for the so-called 2-cyclic schedules, in which exactly two parts enter and two parts leave the production line during each cycle. The earlier known polynomial-time algorithms for this problem are applicable only under the additional assumption that the robot travel times satisfy the triangle inequalities. We lift this assumption on robot travel times and present a polynomial-time algorithm with the same time complexity as in the metric case, O (m^{5} log m).

Original language | English |
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Pages (from-to) | 339-355 |

Number of pages | 17 |

Journal | Discrete Applied Mathematics |

Volume | 157 |

Issue number | 2 |

DOIs | |

State | Published - 28 Jan 2009 |

Externally published | Yes |

### Bibliographical note

Funding Information:The research of the second author was supported in part by the Ministry of Education and Science of Spain, grant SAB2005-0161.

### Funding

The research of the second author was supported in part by the Ministry of Education and Science of Spain, grant SAB2005-0161.

Funders | Funder number |
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Ministerio de Educación, Cultura y Deporte | SAB2005-0161 |

## Keywords

- Complexity
- Cyclic scheduling
- Euler formula
- No-wait condition
- Polynomial-time algorithms
- Robotic scheduling