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In this paper, we consider the problem of scheduling jobs with release dates and rejection on a bounded single parallel batching machine.Our objective is to minimize the sum of total completion time of the accepted jobs and the total penalty of the rejected jobs.We need to determine how to choose jobs for processing, divide these jobs into batches, and sequence these batches so that the objective function is minimized.We give a simplified enumeration approximation scheme for this problem by applying combinatorial optimization techniques with delicate analysis.