Controlling adverse effect on work in process inventory while reducing machine setup time

Earlier research has found that the presence of setup time variance can cause an adverse effect on waiting time and inventory as one reduces setup time for a product on a single machine that processes a number of products in a cyclic production system [Sarkar, D., Zangwill, W.I., 1991. Variance effects in cyclic production systems. Management Science 37 (4) 444–453; Zangwill, W.I., 1987. From EOQ towards ZI. Management Science 33 (10) 1209–1223]. This finding validates what other researchers had believed from a rather anecdotal perspective: “variability reduction” is extremely important for improving overall effectiveness of a pull or JIT system [Schonberger, Richard J., 1982. Japanese Manufacturing Techniques: Nine Hidden Lessons in Simplicity. The Free Press, New York]. In this paper, we offer explicit mathematical equations that characterize the variance levels in order to offer exact conditions under which WIP improves or worsens when one reduces setup time.