## Abstract

We revisit the classic problem of preemptive scheduling on m uniformly related machines. In this problem, jobs can be arbitrarily split into parts, under the constraint that every job is processed completely, and that the parts of a job are not assigned to run in parallel on different machines. We study a new objective which is motivated by fairness, where the goal is to minimize the sum of the two maximal job completion times. We design a polynomial time algorithm for computing an optimal solution. The algorithm can act on any set of machine speeds and any set of input jobs. The algorithm has several cases, many of which are very different from algorithms for makespan minimization (algorithms that minimize the maximum completion time of any job), and from algorithms that minimize the total completion time of all jobs.

Original language | English |
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Pages (from-to) | 115-127 |

Number of pages | 13 |

Journal | Journal of Scheduling |

Volume | 20 |

Issue number | 2 |

DOIs | |

State | Published - 1 Apr 2017 |

### Bibliographical note

Publisher Copyright:© 2016, Springer Science+Business Media New York.

## Keywords

- Makespan completion times
- Preemptive scheduling
- Uniformly related machines

## ASJC Scopus subject areas

- Software
- Engineering (all)
- Management Science and Operations Research
- Artificial Intelligence