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This investigation considers the problem of nonpreemptively assigning a set of independent tasks to a system of identical processors to maximize the earliest processor finishing time. While this goal is a nonstandard scheduling criterion, it does have natural applications in certain maintenance scheduling and deterministic fleet sizing problems. The problem is NP-hard, justifying an analysis of heuristics such as the well-known LPT algorithm in an effort to guarantee near-optimal results. It is proved that the worst-case performance of the LPT algorithm has an asymptotically tight bound of 43 times the optimal.
Deuermeyer et al. (Tue,) studied this question.