Year: 2024
Type: article
Abstract: In this paper, we study the problem of online scheduling on uniform machines, in which the jobs have arbitrary release times and the objective function is to minimize the maximum completion time. The speeds of the machines are 1 for the first $m-1$ machines, but the last one's is $s$ $(s>1)$. The performance of the LS (list scheduling) algorithm is analyzed. When the numbers of machines are $m=2$ and $m\ge~3$, it is presented that the competitive ratios of the LS algorithm are $\frac{3+\sqrt{5}}{2}$ and $4-\frac{4}{m+1}$, respectively. In general, a better algorithm called MLS (modified list scheduling) is also designed for the problem and it is shown that the competitive ratio of the MLS is no more than 3.8626.
Source: Scientia Sinica Mathematica
Authors: Cheng Xiayan, Zhao Congcong, Ma Lina, Li Rongheng
Language: English
Subfield: Industrial and Manufacturing Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4404732953