Production lot sizing with the reworking of imperfect quality items produced

This paper studies the effect of imperfect quality items on the finite production model. When production stops, defective items are assumed to be reworked at a constant rate. The percentage of imperfect quality items is considered to be a random variable with a known probability density function. The demand for the initial perfect items and the perfect items being reworked is continuous during the cycle. The optimal operating policy that minimizes the total inventory cost per unit time for the finite production model under the effect of imperfect quality is derived where shortages are allowed and backordered.