### Abstract

This paper examines the openshop problem with machine dependent processing times. Two objectives are considered; minimizing the maximal completion (makespan), and minimizing the mean flow time. For this problem with the makespan criteria and the number of jobs greater or equal to the number of machines we present an O(mn) optimal algorithm and prove that the same problem with the number of jobs less than the number of machines but greater or equal three is NP-hard. We also present an O(n) optimal algorithm for this problem with mean flow time criteria but two machines only, and for a special case with m machines describe an optimal O(mn) algorithm. The three machine openshop problem with machine dependent processing times and mean flow time criteria remains open.

Original language | English (US) |
---|---|

Pages (from-to) | 197-205 |

Number of pages | 9 |

Journal | Discrete Applied Mathematics |

Volume | 39 |

Issue number | 3 |

DOIs | |

State | Published - Nov 11 1992 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**Openshop scheduling with machine dependent processing times.** / Dror, Moshe.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 39, no. 3, pp. 197-205. https://doi.org/10.1016/0166-218X(92)90176-B

}

TY - JOUR

T1 - Openshop scheduling with machine dependent processing times

AU - Dror, Moshe

PY - 1992/11/11

Y1 - 1992/11/11

N2 - This paper examines the openshop problem with machine dependent processing times. Two objectives are considered; minimizing the maximal completion (makespan), and minimizing the mean flow time. For this problem with the makespan criteria and the number of jobs greater or equal to the number of machines we present an O(mn) optimal algorithm and prove that the same problem with the number of jobs less than the number of machines but greater or equal three is NP-hard. We also present an O(n) optimal algorithm for this problem with mean flow time criteria but two machines only, and for a special case with m machines describe an optimal O(mn) algorithm. The three machine openshop problem with machine dependent processing times and mean flow time criteria remains open.

AB - This paper examines the openshop problem with machine dependent processing times. Two objectives are considered; minimizing the maximal completion (makespan), and minimizing the mean flow time. For this problem with the makespan criteria and the number of jobs greater or equal to the number of machines we present an O(mn) optimal algorithm and prove that the same problem with the number of jobs less than the number of machines but greater or equal three is NP-hard. We also present an O(n) optimal algorithm for this problem with mean flow time criteria but two machines only, and for a special case with m machines describe an optimal O(mn) algorithm. The three machine openshop problem with machine dependent processing times and mean flow time criteria remains open.

UR - http://www.scopus.com/inward/record.url?scp=38249008024&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249008024&partnerID=8YFLogxK

U2 - 10.1016/0166-218X(92)90176-B

DO - 10.1016/0166-218X(92)90176-B

M3 - Article

AN - SCOPUS:38249008024

VL - 39

SP - 197

EP - 205

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 3

ER -