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The classical manufacturing systems assume that all of produced items are of perfect quality. They also do not consider the rework process in manufacturing operations. Moreover, most of the previous literature consider single stage production-inventory systems and do not consider multi stage options. However, in real world production-inventory systems, production of defective items is inevitable, and a fraction of the produced items may be defective. In addition, to avoid extra costs and consider environmental issues, organizations tend to reworking activities. We propose single and multi-stage production-inventory systems in manufacturing operations where the process is defective, rework is possible and a percent of items are scrapped. A main assumption, in the current paper, is that the defective rate is assumed to be uncertain parameter. The grey systems theory, as a mathematical tool to address the uncertain information in real-world situations, is utilized to model the random defective rate via a grey nonlinear programming problem. The proposed issues are investigated via numerical examples to assess the impact of grey parameters on optimal solutions.