In this paper, we have developed a model to determine the input quantity to be processed at each stage of a multi-stage production system in which the yield at each stage may be random and may need reworking at this stage. Yield randomness. especially in a semiconductor industry, is a most challenging problem for production control. The demand for flnal product is uncertain. We have extended the model proposed in Park and Kim[9] to consider a multiple number of reworkings which can be done at any stage prior to or tat the stage whose output in bad, depending on the level of the defect.