A green inventory model with imperfect items considering inspection process and quality improvement under different shortages scenarios

Incorporation of environmental and quality considerations has made production and inventory models shift away from classical models to multi-facet models; however, proposing solutions to improve these considerations has been attended scarcely. Losing a specific number of items due to imperfect production is irrevocable. Inspection operations can detect the imperfect items to avoid reaching the items to the customer; however, inspectors are not faultless and they may detect the quality of some items with errors. To address this issue, quality improvement technologies that monitor the production progress to detect imperfection at the moment can be a favorable approach. On the other hand, carbon dioxide is emitted due to the operations related to production systems, and it is crucial to find means to mitigate emissions because of the sustainability responsibility of firms and governmental regulations in carbon capture. The main novelty of this study is determining how shortages can affect a sustainable inventory system of imperfect quality items considering both quality improvement and inspection process simultaneously. In fact, this study takes another step in this line of research and considers economic, environmental, and quality considerations of an inventory system simultaneously because of few discussions in this line of thought. Shortages are considered allowable and the model is solved under different shortage scenarios. Optimality conditions are developed as a solution procedure and the models are validated using numerical experiments. The results indicate that the scenarios with full backordering and lost sales lead to higher profit than the scenarios without shortages or with partial backordering.