This paper derives the optimal replenishment policy for imperfect quality economic manufacturing quantity (EMQ) model with rework and backlogging. The classic EMQ model assumes that all items produced are of perfect quality. However, in real-life manufacturing settings, generation of imperfect quality items is almost inevitable. In this study, a random defective rate is assumed. All items produced are inspected and the defective items are classified as scrap and repairable. A rework process is involved in each production run when regular manufacturing process ends, and a rate of failure in repair is also assumed. Unit disposal cost and unit repairing and holding costs are included in our mathematical modelling and analysis. The renewal reward theorem is employed in this study to cope with the variable cycle length. The optimal replenishment policy in terms of lot-size and backlogging level that minimizes expected overall costs for the proposed imperfect quality EMQ model is derived. Special cases of the model are identified and discussed. Numerical example is provided to demonstrate its practical usage. today [2][3][4]. A noticeable amount of research has since been accomplished to enhance the classic EOQ model by addressing its unrealistic assumptions [5][6][7][8]. In manufacturing sector, for items that are produced in-house the economic manufacturing quantity (EMQ) model is often used to determine the optimal lot-size that minimizes total production-inventory costs. The classic EMQ model implicitly assumes that items produced are of perfect quality. However, in real-life situations, due to process deterioration or other factors, generation of defective items is inevitable. Therefore, a considerable amount of research has been carried out to enhance the classic EMQ model by addressing issues of imperfect quality items (see, for example, Rosenblatt and Lee [9], Lee and Rosenblatt [10], Schwaller [11], Zhang and Gerchak [12], and others [13][14][15][16][17][18][19]).The non-conforming items generally fall into two groups: the repairable and the scrap (the latter are discarded). The reworking of the repairable defective items can be initiated as soon as the regular production stops in the same production cycle. Certainly, by adopting rework there will be extra costs for repairing and holding that are proportional to number of items reworked; however, the overall production-inventory costs can be reduced once defective items are repaired. For instance, manufacturing processes in plastic goods in the plastic injection moulding process, the printed circuit board assembly (PCBA), in the PCBA manufacturing, and production process in other industries, such as chemicals, textiles, metal components, etc. sometimes employ rework as an acceptable process in terms of level of quality. Examples of articles that address the imperfect quality production system with rework are surveyed below. Liu and Yang [20] derived an average long-term profit function based on a simple control policy which allows the work centre to load one b...