### Abstract

Here, we revisit the bounded batch scheduling problem with nonidentical job sizes on single and parallel identical machines, with the objective of minimizing the makespan. For the single machine case, we present an algorithm which calls an online algorithm P (chosen arbitrarily) for the one-dimensional bin-packing problem as a sub-procedure, and prove that its worst-case ratio is the same as the absolute performance ratio of P. Hence, there exists an algorithm with worst-case ratio 17 10, which is better than any known upper bound on this problem. For the parallel machines case, we prove that there does not exist any polynomial-time algorithm with worst-case ratio smaller than 2 unless P=NP, even if all jobs have unit processing time. Then we present an algorithm with worst-case ratio arbitrarily close to 2.

Original language | English |
---|---|

Pages (from-to) | 351-358 |

Number of pages | 8 |

Journal | Naval Research Logistics |

Volume | 61 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- bin-packing
- online algorithm
- scheduling
- worst-case analysis

### ASJC Scopus subject areas

- Ocean Engineering
- Modelling and Simulation
- Management Science and Operations Research

### Cite this

*Naval Research Logistics*,

*61*(5), 351-358. https://doi.org/10.1002/nav.21587

**Improved bounds for batch scheduling with nonidentical job sizes.** / Dosa, Gyorgy; Tan, Zhiyi; Tuza, Zsolt; Yan, Yujie; Lányi, Cecília Sik.

Research output: Contribution to journal › Article

*Naval Research Logistics*, vol. 61, no. 5, pp. 351-358. https://doi.org/10.1002/nav.21587

}

TY - JOUR

T1 - Improved bounds for batch scheduling with nonidentical job sizes

AU - Dosa, Gyorgy

AU - Tan, Zhiyi

AU - Tuza, Zsolt

AU - Yan, Yujie

AU - Lányi, Cecília Sik

PY - 2014

Y1 - 2014

N2 - Here, we revisit the bounded batch scheduling problem with nonidentical job sizes on single and parallel identical machines, with the objective of minimizing the makespan. For the single machine case, we present an algorithm which calls an online algorithm P (chosen arbitrarily) for the one-dimensional bin-packing problem as a sub-procedure, and prove that its worst-case ratio is the same as the absolute performance ratio of P. Hence, there exists an algorithm with worst-case ratio 17 10, which is better than any known upper bound on this problem. For the parallel machines case, we prove that there does not exist any polynomial-time algorithm with worst-case ratio smaller than 2 unless P=NP, even if all jobs have unit processing time. Then we present an algorithm with worst-case ratio arbitrarily close to 2.

AB - Here, we revisit the bounded batch scheduling problem with nonidentical job sizes on single and parallel identical machines, with the objective of minimizing the makespan. For the single machine case, we present an algorithm which calls an online algorithm P (chosen arbitrarily) for the one-dimensional bin-packing problem as a sub-procedure, and prove that its worst-case ratio is the same as the absolute performance ratio of P. Hence, there exists an algorithm with worst-case ratio 17 10, which is better than any known upper bound on this problem. For the parallel machines case, we prove that there does not exist any polynomial-time algorithm with worst-case ratio smaller than 2 unless P=NP, even if all jobs have unit processing time. Then we present an algorithm with worst-case ratio arbitrarily close to 2.

KW - bin-packing

KW - online algorithm

KW - scheduling

KW - worst-case analysis

UR - http://www.scopus.com/inward/record.url?scp=84904459142&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904459142&partnerID=8YFLogxK

U2 - 10.1002/nav.21587

DO - 10.1002/nav.21587

M3 - Article

AN - SCOPUS:84904459142

VL - 61

SP - 351

EP - 358

JO - Naval Research Logistics Quarterly

JF - Naval Research Logistics Quarterly

SN - 0028-1441

IS - 5

ER -