Competitive analysis of online machine rental and online parallel machine scheduling problems with workload fence

Zheng, Feifeng; Chen, Yuhong; Liu, Ming; Xu, Yinfeng

doi:10.1007/s10878-022-00882-x

J Comb Optim

2022

DOI: 10.1007/s10878-022-00882-x

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Competitive analysis of online machine rental and online parallel machine scheduling problems with workload fence

Feifeng Zheng

Yuhong Chen²,

Ming Liu³

et al.

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Cited by 3 publications

References 34 publications

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Mathematical models and an effective exact algorithm for unrelated parallel machine scheduling with family setup times and machine cost

Li,

Xie,

Chen

et al. 2024

OR Spectrum

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Mathematical models and an effective exact algorithm for unrelated parallel machine scheduling with family setup times and machine cost

Li,

Xie,

Chen

et al. 2024

OR Spectrum

View full text Add to dashboard Cite

Semi-online scheduling on two uniform parallel machines with initial lookahead

Zheng,

Chen,

Liu

2024

RAIRO-Oper. Res.

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This work studies the problem of semi-online scheduling on two uniform parallel machines with speeds 1 and s≥2, respectively. We introduce a novel concept of initial lookahead in which any deterministic online algorithm has the full knowledge of the first k jobs at the beginning, while the remaining jobs are released one-by-one in the online over-list mode. The objective of the considered problem is to minimize the makespan. We focus on the case where the first k jobs are of a total processing time not less than (s+1)Δ where Δ is the largest job length, and it is assumed that s is an integer. We prove a lower bound of (s2+s+1)/(s2+s), and propose a deterministic online algorithm with competitive ratio of (s+1)2/(s2+s+1). The ratio is at most 9/7 and much less than that of 1.618 for the basic case without initial lookahead (Cho and Sahni [7]). Our results demonstrate that a finite ability of initial lookahead can greatly improve the competitiveness of online algorithms.

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Scheduling equal-length jobs with arbitrary sizes on uniform parallel batch machines

Xin

Khan

2023

Open Mathematics

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We consider the problem of scheduling jobs with equal lengths and arbitrary sizes on uniform parallel batch machines with different capacities. Each machine can only process the jobs whose sizes are not larger than its capacity. Several jobs can be processed as a batch simultaneously on a machine, as long as their total size does not exceed the machine’s capacity. The objective is to minimize makespan. Under a divisibility constraint, we obtain two efficient exact algorithms. For the general problem, we obtain an efficient 2-approximation algorithm. Previous work has shown that the problem cannot be approximated to within an approximation ratio better than 2, unless P = NP, even when all machines have identical speeds and capacities.

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Competitive analysis of online machine rental and online parallel machine scheduling problems with workload fence

Cited by 3 publications

References 34 publications

Mathematical models and an effective exact algorithm for unrelated parallel machine scheduling with family setup times and machine cost

Mathematical models and an effective exact algorithm for unrelated parallel machine scheduling with family setup times and machine cost

Semi-online scheduling on two uniform parallel machines with initial lookahead

Scheduling equal-length jobs with arbitrary sizes on uniform parallel batch machines

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