An imperfect multi-item single-machine production system with shortage, rework, and scrap considering inspection, dissimilar deciency levels, and non-zero setup times

In this paper, we consider a decient production system with permissible shortages. The production system consists in a unique machine that manufactures a number of products with a part being imperfect in the form of rework or scrap. These defective products are identied by 100% inspection during production; then, they are whether reworked or disposed of after normal production process. Like real-world production systems, there are diverse types of errors creating dissimilar breakdown severity and rework. Moreover, rework has non-zero setup time, which makes the problem closer to real-world instances, and the machines require some preparations before starting a new production cycle. Thus, we introduce an Economic Production Quantity (EPQ) problem for an imperfect manufacturing system with non-zero setup times for rework items. The rework items are classied into several categories based on their types of failure and rework rates. The aim of this study is to obtain optimum production time and shortage in each period minimizing total inventory system costs. Convexity of the objective function and exact solution procedure for the current nonlinear optimization problem are also proposed. Finally, a numerical example is presented to assess eciency and validity of the proposed algorithm.