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We consider bounded parallel-batch scheduling with proportional-linear deteriorating jobs and the objective to minimize the total completion time. We give some properties of optimal schedules for the problem and present for it a dynamic programming algorithm running in O(b 2 m 2 2 m) time, where b is the size of a batch and m is the number of distinct deterioration rates.

In this paper, we consider the scheduling with step-deteriorating jobs. The objective is to minimize the makespan. We first propose a property of any optimal schedule after analyzing the NP-hardness for the parallel-machine scheduling with a common deteriorating date, and then present a fully polynomial time approximation scheme for the case where the number of machines m is a constant and jobs have anti-agreeable parameters. Furthermore, we show that the single-machine scheduling is NP-hard in the strong sense if jobs have distinct release dates and distinct deteriorating dates.

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