Abstract
Recently, Shabtay and Bensoussan (2012) developed an original exact pseudo-polynomial algorithm and an efficient \(\upvarepsilon \)-approximation algorithm (FPTAS) for maximizing the weighted number of just-in-time jobs in a two-machine flow shop problem. The complexity of the FPTAS is \(O\)((\(n^{4}/\upvarepsilon \))log(\(n\)/\(\upvarepsilon \))), where \(n\) is the number of jobs. In this note we suggest another pseudo-polynomial algorithm that can be converted to a new FPTAS which improves Shabtay–Bensoussan’s complexity result and runs in \(O(n^{3}/\upvarepsilon )\) time.
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Acknowledgments
The authors wish to thank Refael Hassin and the anonymous reviewer for helpful suggestions that improved the paper.
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Elalouf, A., Levner, E. & Tang, H. An improved FPTAS for maximizing the weighted number of just-in-time jobs in a two-machine flow shop problem. J Sched 16, 429–435 (2013). https://doi.org/10.1007/s10951-013-0320-6
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DOI: https://doi.org/10.1007/s10951-013-0320-6