Optimal control of work‐in‐process inventory of a two‐station production line

Most production lines keep a minimal level of inventory stock to save storage costs and buffer space. However, the random nature of processing, breakdown, and repair times can significantly affect the efficiency of a production line and force the stocking of work‐in‐process inventory. We are interested in the case when starvation and blockage are preferentially avoided. In this study, a mathematical model has been developed using asymptotic approximation and simulation that provides asymptotic results for the expected value and the variance of the stock level in a buffer as a function of time. In addition, the functional relationship between buffer capacity and the first stopping time caused by starvation or blockage has been determined.