A model of an integrated supply chain with imperfect production, product deterioration, and quality inspection errors

An integrated production-distribution model is presented in this article to determine the optimal policy for deteriorating and defective items within a single-vendor, single-buyer system. Deterioration is a widely recognized inherent characteristic that is attributed to most objects. Furthermore, the feasibility of producing products without defects is quite impractical. Nevertheless, the imperfect quality issue, as demonstrated by damaged products, can be attributed to a poorly managed manufacturing and production process. Conducting inspection from the viewpoint of both the buyer and the vendor exposes both parties to the possibility of making errors. This study estimates the optimal number of shipments and production run time by incorporating buyer demand fulfilment, inspection, transportation-related carbon emissions, deterioration and defectiveness into a single model. The study mainly intends to minimize supply chain costs to maximize the potential profit. We also investigate a production model without screening to emphasize the significance of inspection. To enhance the illustrative power of the proposed methodology, numerical example and sensitivity analysis are carried out which further assess the validity of the proposed theory.