The impact of inspection delay on process and inspection lot sizing

Models in which process quality and lot sizing interact have recently been developed. Lot sizes should be reduced to compensate for poor quality if no effective inspection is possible. This note introduces an inspection delay time, measured in units produced after an inspection is made until results are known. If the inspection delay is negligible, then the problem reduces essentially to two separate lot sizing problems: the classical EOQ lot sizing problem and an inspection lot sizing problem. If the delay is great, then only one inspection should be made and the lot size is as given by Porteus, and Rosenblatt and Lee. This note seeks the optimal production and inspection lot sizes for the full spectrum of inspection delays. The impact of the results is illustrated numerically. The value of automated defect control (with 100% inspection and immediate production stoppage upon detection of a defect) is discussed.