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, 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 where Proposing a greedy algorithm, we show that its tight competitive ratio is 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 which is optimal for Numerical experiments show that the greedy online algorithm has good performance, especially when k approaches 1 or m.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
