Abstract
In this paper, we investigate a single machine scheduling problem of minimizing the sum of job flow times subject to scheduled maintenance. We first provide an NP-completeness proof for the problem. This proof is much shorter than the one given in Adiri et al. [1]. The shortest processing time (SPT) sequence is then shown to have a worst case error bound of 2/7. Furthermore, an example is provided to show that the bound is tight. This example also serves as a counter-example to the 1/4 error bound provided in Adiri et al. [1].
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Garey MR, Tarjan RE, Wilfong GT: One-processor scheduling with symmetric earliness and tardiness penalties. Math. Oper. Res.13, 330–348 (1988)
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Lee, CY., Liman, S.D. Single machine flow-time scheduling with scheduled maintenance. Acta Informatica 29, 375–382 (1992). https://doi.org/10.1007/BF01178778
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DOI: https://doi.org/10.1007/BF01178778