List scheduling for jobs with arbitrary release times and similar lengths
Journal of Scheduling
Approximation schemes for constrained scheduling problems
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Semi on-line algorithms for the partition problem
Operations Research Letters
Ordinal algorithms for parallel machine scheduling
Operations Research Letters
Semi-online scheduling with decreasing job sizes
Operations Research Letters
Semi-on-line problems on two identical machines with combined partial information
Operations Research Letters
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In this paper we consider three semi-online scheduling problems for jobs with release times on m identical parallel machines. The worst case performance ratios of the LS algorithm are analyzed. The objective function is to minimize the maximum completion time of all machines, i.e. the makespan. If the job list has a non-decreasing release times, then $2-\frac{1}{m}$ is the tight bound of the worst case performance ratio of the LS algorithm. If the job list has non-increasing processing times, we show that $2-\frac{1}{2m}$ is an upper bound of the worst case performance ratio of the LS algorithm. Furthermore if the job list has non-decreasing release times and the job list has non-increasing processing times we prove that the LS algorithm has worst case performance ratio not greater than $\frac{3}{2} -\frac{1}{2m}$.