Parallel-machine scheduling in shared manufacturing

<p style='text-indent:20px;'>We consider parallel-machine scheduling in the context of shared manufacturing where each job has a machine set to which it can be assigned for processing. Such a set is called the processing set. In the shared manufacturing setting, a job can be assigned not only to certain machines for processing, but can also be processed on the remaining machines at a certain cost. Compared with traditional scheduling with job rejection, the scheduling model under study embraces the notion of sustainable manufacturing. Showing that the problem is <i>NP</i>-hard, we develop a fully polynomial-time approximation scheme to solve the problem when the number of machines is fixed.</p>