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A tight approximation algorithm for problem \(P2\rightarrow D|v=1,c=1|C_{\max }\)

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Abstract

This paper focuses on the scheduling problem on two parallel machines with delivery coordination. In particular, given a set of n jobs, we aim to find a schedule with a minimal makespan such that all jobs are first executed on two parallel machines then delivered at the destination with a transporter. This problem is known to be NP-hard Chang and Lee (Eur J Oper Res 158(2):470–487, 2004), cannot be solved with an approximation ratio strictly less than 3/2 unless P=NP. We close the gap by proposing a polynomial time algorithm whose approximation ratio is \(3/2+\varepsilon \) with \(\varepsilon >0\), improve the previous best ratio \(14/9 + \epsilon \).

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Acknowledgements

This research was partially supported by NSFC(11971091,11701062), Liaoning Natural Science Foundation(2019-MS-062).

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Correspondence to Xin Han.

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Wang, Y., Lan, Y., Chen, X. et al. A tight approximation algorithm for problem \(P2\rightarrow D|v=1,c=1|C_{\max }\). J Comb Optim 44, 2195–2206 (2022). https://doi.org/10.1007/s10878-020-00593-1

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