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- W4312192688 abstract "We consider online hierarchical scheduling on m identical machines in shared manufacturing to minimize the total completion time. Each job has a unit-size processing time. The jobs arrive one by one and must be assigned to one of the m machines before the next job arrives. The jobs with a lower hierarchy can only be processed on the first k machines, 1≤k≤m−1, and the jobs with a higher hierarchy can be processed on any one of the m machines. We first show that the lower bound of the problem is at least 1+min{1m−k+1,max{2k⌈s⌉+3k+2m+4⌈s⌉,2k⌊s⌋+3k+2m+4⌊s⌋}}, where s=2m+4k. Proposing a greedy algorithm, we show that its tight competitive ratio is 1+2(m−k)km((4m−3k)k+k) by analyzing a set of instances that must contain a worst-case instance, which is different from the general method of calculating the competitive ratio. In addition, for the case where k = 1, we present an improved online algorithm with a tight competitive ratio of 1+max{2⌈2m+4⌉+2m+4⌈2m+4⌉+3,2⌊2m+4⌋+2m+4⌊2m+4⌋+3}, which is optimal for 2≤m≤5. Numerical experiments show that the greedy online algorithm has good performance, especially when k approaches 1 or m." @default.
- W4312192688 created "2023-01-04" @default.
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- W4312192688 date "2022-12-22" @default.
- W4312192688 modified "2023-09-26" @default.
- W4312192688 title "Online hierarchical parallel-machine scheduling in shared manufacturing to minimize the total completion time" @default.
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- W4312192688 doi "https://doi.org/10.1080/01605682.2022.2150576" @default.
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