A dynamic programming approach for batch sizing in a multi-stage production process with random yields

This paper proposes a dynamic programming approach to modeling and determining batch sizes in a single period, multi‐stage production process with random yields for each stage. To improve the computational performance of the proposed approach, a statistical bound is developed. A key decision incorporated into the model is whether to continue onto the next stage of processing or to scrap the entire current batch of product. This decision is based on the expected total profit from the remaining items for processing following the removal of all defectives. The decisions involving the locations of test stations after stages are also incorporated into the modeling approach.