Optimal Batch Sizes for a Two-Stage Production System

A 2-stage production model is considered in which items are processed in batches at both stages. Items processed at Stage 1 are stored until needed at Stage 2 and new batches are processed at Stage 1 only when necessary to meet second stage demand. It is shown that in an optimal policy the batch size at the first stage must be an integer multiple of second stage batch size. This can be used in an analytical derivation of the optimum batch sizes.