Input control in a batch production system with lead times, due dates and random yields

The presence of random yields in many manufacturing processes can considerably complicate production planning and control. We investigate a batch production system with due dates, where the yield of each batch is random and the production lead time is longer than the time interval between starting consecutive batches. To satisfy an order with a given due date, several input batches could be initiated. But the realized yields of batches still in process are unknown when the next batch size needs to be determined. We formulate this general problem as a dynamic program with the objective of minimizing the total expected discounted costs. For a simple version of the model with linear cost parameters and one work-in-process batch, we show that the structure of the optimal input control policy is of a single critical level type for the work-in-process batch size. We prove that, for given outstanding demand, this critical level becomes larger as the number of input opportunities becomes smaller. Furthermore, if the discount factor equals to 1, this critical level is shown to be strictly greater than the outstanding demand. Production often starts earlier than necessary in order to utilize yield realizations of initial batches for judicious choice of later batches, and to achieve diversification over time.