A lumped parameter model for product flow times in manufacturing lines

Based upon basic drivers for the flow time, a lumped parameter model for a manufacturing line has been derived by using Kingman's approximation. The lumped parameter model for the flow time consists of a workstation and delay time. The workstation is characterized by the effective process time of the bottleneck workstation and the weighted sum of the coefficients of variation of all workstations. The delay time is determined by the sum of all effective process times of the nonbottleneck workstations. The advantage of the application of the lumped parameter model is that the variability of the total line is determined by a measurement at the operating point of the actual manufacturing line. This variability depends upon the operating point. Examples show that this dependency is not too strong for lines with a distinct bottleneck workstation in the actual line. From the derivation of the lumped parameter model it can be concluded that an improvement of the effective process time of the bottleneck workstation of the line results in an increase of the total variability of the line. This variability can be reduced by either reducing the variability of all workstations or the effective process times of the nonbottleneck workstations. Index Terms--Lumped parameter model, manufacturing systems, performance, variability.