Abstract
In this note, we investigate the time complexity of non-preemptive shop scheduling problems with two jobs. First we study mixed shop scheduling where one job has a fixed order of operations and the operations of the other job may be executed in arbitrary order. This problem is shown to be binary NP-complete with respect to all traditional optimality criteria even if distinct operations of the same job require different machines. Moreover, we devise a pseudo-polynomial time algorithm which solves the problem with respect to all non-decreasing objective functions. Finally, when the job with fixed order of operations may visit a machine more than once, the problem becomes unary NP-complete.
Then we discuss shop scheduling with two jobs having chain-like routings. It is shown that the problem is unary NP-complete with respect to all traditional optimality criteria even if one of the jobs has fixed order of operations and the jobs cannot visit a machine twice.
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Received July 28, 2001; revised May 15, 2002 Published online: July 26, 2002
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Kis, T. On the Complexity of Non-preemptive Shop Scheduling with Two Jobs. Computing 69, 37–49 (2002). https://doi.org/10.1007/s00607-002-1455-z
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DOI: https://doi.org/10.1007/s00607-002-1455-z