Abstract
We consider a generalized version of the classical parallel machine scheduling problem, in which the m machines are available at time a j⩾0, j=1,2,…,m . The objective function is to maximize the minimum machine completion time. Using the conventional weighting function technique, previously, a lower bound of 5 8 has been shown for the worst-case performance ratio of the famous Longest Processing Timing (LPT) approximation. In this paper, we develop a new method, called matching, and show that the worst-case performance ratio of LPT is exactly (2 m−1)/(3 m−2). We also give an instance to indicate the tightness of this ratio.
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