The variance paradox and its implications for Japanese production theory

In a recent Interfaces article, Zangwill [1992] presented a mathematical model of a production system and used it to show that reducing mean setup times can increase the overall work-in-process inventory in the model. He claims that such counter-intuitive observations "expose a flaw in the current theory" and that a new and improved production theory is needed to resolve the observed paradox. Many researchers from academia and from industry responded, protesting the validity of Zangwill's assertions. We show that the paradox Zangwill observed can occur even when the production system is operated using a policy chosen from the optimal class of policies, where optimal is taken to mean minimizing the expected total work in the system. In Zangwill's example, the mean setup time is reduced without any change in the setup time variance, which is unrealistic, and no well-managed production system will ever operate in this manner. Thus, while some parts of his article might be defensible, others clearly are not.