This paper investigates a production lot sizing problem where defective items produced during a production run can be reworked after inspections conducted during and at the end of production. The rework process is considered to produce a fixed proportion of scrapped items. Shortages are allowed and completely backordered. In process industries such as semiconductor manufacturing, understanding of the influence of rework on inventory is needed for effective and controlled planning The aim of this study is to determine the optimal production quantity and maximum shortage level to maximize the expected total profit per unit of time. A mathematical model is presented along with a proof of the concavity of the expected total profit function. A numerical example is presented to illustrate the effectiveness of the proposed model, as well as a sensitivity analysis of optimal solutions with respect to major parameters.