Optimising the speed of screening in an EPQ model with speed-dependent defect detection rate

A manufacturing process with two stages of quality control is being considered. The screening during the initial production process is of high priority at the company since the proportion of defections at this stage is rather high, and the following production steps are expensive. Based on these facts, all the items are checked at both stages.
Due to the complexity of the product, the speed of the screening during initial production might be adjusted and the defect detection rate depends on the speed of the screening. Furthermore, devoting more time to the screening prolongs the leadtime and decreases the production rate. We also assume different processing and screening costs at both stages in addition to the setup and inventory costs. A mathematical model is proposed and analyzed to find the optimal production parameters jointly with the optimal speed of screening during production, i.e. the optimal capacities at the first stage of quality control.