Conservation of filtering in manufacturing systems

This paper addresses the issue of reliable satisfaction of customer demand by unreliable manufacturing systems. Using a simple Production-Storage-Customer model, we show that this can be accomplished by filtering out production randomness. The filtering of randomness is ensured by finished goods buffers (filtering in space) and shipping periods (filtering in time). The following question is considered: How are filtering in space and in time interrelated? As an answer, we show that there exists a conservation law: In lean manufacturing systems, the amount of filtering in space multiplied by the amount of filtering in time (both measured in appropriate dimensionless units) is practically constant. Along with insight into the behavior of manufacturing systems, this law offers practitioners a quantitative tool for managing lean finished goods buffers.