Using information about machine failures to control flowlines

We study the problem of using information about the type of machine failures to control production. When each station in a two stage flowline has a single machine, the processing time distributions are Erlang, and the time to fail as well as the time to repair a machine are exponentially distributed; we show that the optimal policy for controlling the flowline is completely specified by selecting a produce up to level called threshold level corresponding to each type of machine failure. These threshold levels are shown to be ordered as per the rate at which the failed downstream station can be repaired. These results are partially extended to the case when there are multiple machines at the two stations of the flowline. We then summarize numerical results that illustrate when it is worth while to use information about failures in controlling inputs to the flowline.