In this paper, we investigate the effects of yield randomness for lot-sizing in a multi-stage production system. The practical importance of incorporating yield randomness into production models has been emphasized by many researchers. Yield randomness, especially in semiconductor manufacturing, poses a mojor challenge for production planning and control. The task becomes even more difficult if the demand for final product is uncertain. An attempt to meet the demand with a higher level of confidence forces one to release more input in the fabrication line. This leads to excessive work-in-process (WIP) inventories which cause jobs to spend unpredictably longer time waiting for the machines. The result is that it is more difficult to meet demand with exceptionally long cycle time and puts further pressure to increase the safety stocks. Due to this spiral effect, it is common to find that the capital tied in inventory is the msot significant factor undermining profitability. We propose a policy to determine the 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 rework.