### Abstract

We consider the following natural scheduling problem: Given a sequence of jobs with weights and processing times, one needs to assign each job to one of m identical machines in order to minimize the sum of weighted completion times. The twist is that for machine the jobs assigned to it must obey the order of the input sequence, as is the case in multi-server queuing systems. We establish a constant factor approximation algorithm for this (strongly NP-hard) problem. Our approach is necessarily very different from what has been used for similar scheduling problems without the fixed-order assumption. We also give a QPTAS for the special case of unit processing times.

Original language | English |
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Title of host publication | Integer Programming and Combinatorial Optimization - 20th International Conference, IPCO 2019, Proceedings |

Editors | Andrea Lodi, Viswanath Nagarajan |

Publisher | Springer Verlag |

Pages | 88-100 |

Number of pages | 13 |

ISBN (Print) | 9783030179526 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

Event | 20th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2019 - Ann Arbor, United States Duration: 22 May 2019 → 24 May 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11480 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 20th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2019 |
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Country | United States |

City | Ann Arbor |

Period | 22/05/19 → 24/05/19 |

### Fingerprint

### Cite this

*Integer Programming and Combinatorial Optimization - 20th International Conference, IPCO 2019, Proceedings*(pp. 88-100). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11480 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-17953-3_7

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*Integer Programming and Combinatorial Optimization - 20th International Conference, IPCO 2019, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11480 LNCS, Springer Verlag, pp. 88-100, 20th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2019, Ann Arbor, United States, 22/05/19. https://doi.org/10.1007/978-3-030-17953-3_7

**Fixed-Order Scheduling on Parallel Machines.** / Bosman, Thomas; Frascaria, Dario; Olver, Neil; Sitters, René Stougie, Leen.

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Fixed-Order Scheduling on Parallel Machines

AU - Bosman, Thomas

AU - Frascaria, Dario

AU - Olver, Neil

AU - Sitters, René

AU - Stougie, Leen

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We consider the following natural scheduling problem: Given a sequence of jobs with weights and processing times, one needs to assign each job to one of m identical machines in order to minimize the sum of weighted completion times. The twist is that for machine the jobs assigned to it must obey the order of the input sequence, as is the case in multi-server queuing systems. We establish a constant factor approximation algorithm for this (strongly NP-hard) problem. Our approach is necessarily very different from what has been used for similar scheduling problems without the fixed-order assumption. We also give a QPTAS for the special case of unit processing times.

AB - We consider the following natural scheduling problem: Given a sequence of jobs with weights and processing times, one needs to assign each job to one of m identical machines in order to minimize the sum of weighted completion times. The twist is that for machine the jobs assigned to it must obey the order of the input sequence, as is the case in multi-server queuing systems. We establish a constant factor approximation algorithm for this (strongly NP-hard) problem. Our approach is necessarily very different from what has been used for similar scheduling problems without the fixed-order assumption. We also give a QPTAS for the special case of unit processing times.

UR - http://www.scopus.com/inward/record.url?scp=85065867793&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065867793&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-17953-3_7

DO - 10.1007/978-3-030-17953-3_7

M3 - Conference contribution

SN - 9783030179526

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 88

EP - 100

BT - Integer Programming and Combinatorial Optimization - 20th International Conference, IPCO 2019, Proceedings

A2 - Lodi, Andrea

A2 - Nagarajan, Viswanath

PB - Springer Verlag

ER -