Lot sizing in case of defective items with investments to increase the speed of quality control

In many cases the quality of each item in a lot is checked. Speeding up the quality checking process increases the responsiveness of the system and saves cost. The percentage of defective items is a random variable and two models are proposed. In one of the models the system remains always at the same state, while in the other one after each order cycle, the state of the system may change, thus the percentage of defective items may be different in consecutive periods. In both cases the speed of the quality checking is a variable, and procedures are provided to find the optimal lot sizes and screening speed for general and specific investment cost functions. The characteristics of the two model settings will largely be different when the percentage of defective items is high. Among the important managerial insights gained is that a high unit backlogging cost, especially spurs the system to invest more intensively into improving the quality checking process.