Control of a Stochastic Production System with Estimated Parameters

For an uncertain production system, the rule that controls the flow of material relies on parameters, such as the yield rates and the demand rate. These parameters are estimates, and they are usually inaccurate. In this paper, we analyze a type of "pull" rule called a proportional restoration rule. We show that these rules are stable; they do not lead to erratic behavior even when the estimation error is significant. We also show that these rules localize the effect of mis-estimates; e.g., underestimating the demand rate lowers the level of finished goods inventory, but has scant effect within the line. We show that these rules exhibit other desirable attributes---that they are efficient, that they are easy to interpret, and that they recover from disruptions quickly.