Determining the optimal lot size for the finite production model with an imperfect rework process of defective items

This paper examines the finite production model with an imperfect reworking of the defective items and shortage not permitted. One unrealistic assumption of the classic finite production model is that it assumes manufacturing process will always function perfectly. However, in most real-life production settings, due to different factors, the production of defective items is inevitable. In this paper, we assume that the defective rate is a random variable and all of the defective items are reworked when the regular production process ends. The rework process itself is assumed to be imperfect, a portion of defective items fail the reworking and become scrap items and are discarded. Disposal cost per scrap item and repairing and holding cost for each reworked item are included in the cost analysis. The renewal reward theorem is involved in the proposed mathematical modeling to cope with the variable cycle length. An optimal lot size that minimizes the expected overall costs is derived for the finite production model with an imperfect rework process. An example is provided to demonstrate its practical usage.