Online Scheduling on Two Uniform Unbounded Parallel-Batch Machines to Minimize Makespan

doi:10.1007/s40305-018-0192-8

Journal of the Operations Research Society of China ›› 2019, Vol. 7 ›› Issue (2): 303-319.doi: 10.1007/s40305-018-0192-8

所属专题： Scheduling

收稿日期:2017-07-06 修回日期:2017-09-13 出版日期:2019-06-30 发布日期:2019-06-30
通讯作者: Jin-Jiang Yuan, Li-Li Ren, Ji Tian, Ru-Yan Fu E-mail:yuanjj@zzu.edu.cn;lily_8461@126.com;jitian@cumt.edu.cn;furuyan@126.com

Online Scheduling on Two Uniform Unbounded Parallel-Batch Machines to Minimize Makespan

Jin-Jiang Yuan¹, Li-Li Ren¹, Ji Tian², Ru-Yan Fu²

1 School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China;
2 School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China

Received:2017-07-06 Revised:2017-09-13 Online:2019-06-30 Published:2019-06-30
Contact: Jin-Jiang Yuan, Li-Li Ren, Ji Tian, Ru-Yan Fu E-mail:yuanjj@zzu.edu.cn;lily_8461@126.com;jitian@cumt.edu.cn;furuyan@126.com
Supported by:
The first author was supported by the National Natural Science Foundation of China (No. 11671368) and Natural Science Foundation of Henan Province (No. 15IRTSTHN006). Tian was also supported by Natural Science Foundation of Jiangsu Province (No. BK20130169) and the National Natural Science Foundation of China (No. 61573362).

摘要/Abstract

Abstract: We study an online (over time) scheduling problem on two uniform unbounded parallel-batchmachines with processing speed 1 and v(0 < v ≤1),respectively, to minimize the makespan. We first show that no online algorithm can have a competitive ratio less than 1 + α_L, where α_L=(√5-1)/2 ≈ 0.618 if 0 < v 1/2, and α_L=α₂(v) is the positive root of α³+3α²+(3-1/v)α-1/v=0 if 1/2 < v 1. This lower bound is still valid when all jobs have the same processing times. Then, we provide an online algorithm with a competitive ratio at most min{(√5+1)/2, √2/v}. When the jobs have the same processing times, we present the best possible online algorithm with a competitive ratio 1 + α_L.

Key words: Online scheduling, Uniform parallel-batch machines, Makespan, Competitive ratio

中图分类号:

90B35
90C27

. [J]. Journal of the Operations Research Society of China, 2019, 7(2): 303-319.

Jin-Jiang Yuan, Li-Li Ren, Ji Tian, Ru-Yan Fu. Online Scheduling on Two Uniform Unbounded Parallel-Batch Machines to Minimize Makespan[J]. Journal of the Operations Research Society of China, 2019, 7(2): 303-319.

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Online Scheduling on Two Uniform Unbounded Parallel-Batch Machines to Minimize Makespan

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