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In today’s digital age, industrial methods are shifting away from humans and toward machines. We choose automated systems for various jobs related to production systems, such as screening, manufacturing. A smart manufacturing system is one in which machines take the place of humans. Under the influence of inflation, this study proposes a smart production-inventory model with partial backlogging, and an imperfect manufacturing process where the deterioration rate is constant. Every production system, in reality, has a random defect rate. A screening procedure is required due to the manufacture of some defective items, which is carried out by machine, i.e., by an automated system. Carbon is released during the manufacturing process due to actions such as holding deterioration. As a result, carbon emissions are taken into account in the current study. The goal of this study is to reduce total inventory costs as much as possible. To demonstrate the proposed model’s practical application, many numerical examples and sensitivity assessments with graphs are provided.