Abstract
In this paper, we consider the two-machine flow shop scheduling with an operator non-availability period in the first stage to minimize makespan, where the operator non-availability period is an open time interval in which a job can neither start nor complete. We first prove that the problem is NP-hard, even if the length of the operator non-availability period is no more than the processing time of any job on the first machine. Then we show that Johnson’s rule is a 2-approximation algorithm and the bound is tight. Moreover, a better tight 3/2-approximation algorithm is provided.
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Acknowledgements
This research was supported by the National Natural Science Foundation of China under Grant Nos. (11871213 and 71431004).
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Li, D., Lu, X. Two-machine flow shop scheduling with an operator non-availability period to minimize makespan. J Comb Optim 39, 1060–1078 (2020). https://doi.org/10.1007/s10878-020-00548-6
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DOI: https://doi.org/10.1007/s10878-020-00548-6