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In this paper, we consider a deficient production system with permissible shortages. The production system consists of a unique machine that manufactures a number of products that a part of them are imperfect in form of rework or scrap. These defective products are identified 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 kinds of errors creating dissimilar breakdown severity and rework. Moreover, reworks have non-zero setup times that makes the problem closer to real-world instances where 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 classified into several categories based on their type of failure and rework rate. The aim of this study is to obtain optimum production time and shortage in each period that minimizes 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 proposed to assess efficiency and validation of proposed algorithm.

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