Lean buffering in serial production lines with non-exponential machines

In this paper, lean buffering (i.e., the smallest level of buffering necessary and sufficient to ensure the desired production rate of a manufacturing system) is analyzed for the case of serial lines with machines having Weibull, gamma, and log-normal distributions of up- and downtime. The results obtained show that: (1) the lean level of buffering is not very sensitive to the type of up- and downtime distributions and depends mainly on their coefficients of variation, CVup and CVdown; (2) the lean level of buffering is more sensitive to CVdown than to CVup but the difference in sensitivities is not too large (typically, within 20%). Based on these observations, an empirical law for calculating the lean level of buffering as a function of machine efficiency, line efficiency, the number of machines in the system, and CVup and CVdown is introduced. It leads to a reduction of lean buffering by a factor of up to 4, as compared with that calculated using the exponential assumption. It is conjectured that this empirical law holds for any unimodal distribution of up- and downtime, provided that CVup and CVdown are less than 1.