Economic production quantity models for an imperfect manufacturing system with strict inspection

Some sensitive industries with precise specifications in their manufacturing process, such as aircraft engine parts, impose 100% inspection processes in their inventory-manufacturing system. In some cases, a lot of small dimensions are measured and compared with strict acceptable tolerances during these inspection processes, causing manufacturing process times (machine time speed) to be less than inspection times. This study is relevant to manufacturing enterprises that implement comprehensive 100% inspection protocols within their production procedures, encompassing sectors such as pharmaceuticals, aerospace, electronics, medical devices, and textiles. In this paper, such a phenomenon is investigated, as an inventory system with a strict inspection model is deployed under three conditions: a) an inventory-manufacturing system with scrapped items without shortage, b) an inventory-manufacturing system with reworked items without shortage, and c) an inventory-manufacturing system with scrapped and reworkable items with backorder. The aim is to minimize total cost by considering strict inspection during production process. These proposed models are suitable for managing systems where quality control is a bottleneck due to its speed such as high-precision manufacturing systems. The optimal solutions for each model are obtained as a closed-form expression. In models 1 and 2, where the shortage is not allowed, the closed-form expression is focused on determining the economic production quantity. However, in model 3, there are two expressions of significance. First, it addresses the economic production quantity, like models 1 and 2. Additionally, it provides an optimal value for the shortage in each cycle, as it considers a scenario where shortages are permitted within the inventory-manufacturing system. This study has included a numerical example to illustrate the practical applicability of each model. Based on the optimal solutions obtained, it is evident that Model 3 stands out as the superior choice. This outcome aligns with expectations, as Model 3 encompasses and comprehensively addresses the scenarios presented in the two other models. Finally, a sensitivity analysis is performed to investigate the effects of key parameters on the optimal solutions of each model, and the results are summarized to present a comparison between them.