Asymptotic variance rate of the output in production lines with finite buffers

Abstract

Production systems that can be modeled as discrete time Markov chains are considered. A state-space-based method is developed to determine the variance of the number of parts produced per unit time in the long run. This quantity is also referred to as the asymptotic variance rate. The block tridiagonal structure of the probability matrix of a general two-station production line with a finite buffer is exploited and a recursive method based on matrix geometric solution is used to determine the asymptotic variance rate of the output. This new method is computationally very efficient and yields a thousand-fold improvement in the number of operations over the existing methods. Numerical experiments that examine the effects of system parameters on the variability of the performance of a production line are presented. The computational efficiency of the method is also investigated. Application of this method to longer lines is discussed and exact results for a three-station production line with finite interstation buffers are presented. A thorough review of the pertinent literature is also given.