Parallel-batch scheduling with deterioration and rejection on a single machine

The single machine parallel-batch scheduling with deteriorating jobs and rejection is considered in this paper. A job is either rejected, in which a rejection penalty should be paid, or accepted and processed on the machine. Each job's processing time is an increasing linear function of its starting time. The machine can process any number of jobs simultaneously as a batch. The processing time of a batch is equal to the largest processing time of the jobs in the batch. The objectives are to minimize the makespan and the total weighted completion time, respectively, under the condition that the total rejection penalty cannot exceed a given upper boundQ. We show that both problems areNP-complete and present dynamic programming algorithms and fully polynomial time approximation schemes (FPTASs) for the considered problems.