Managing Uncertainty in a Serial Production Line

This paper studies a serial production line that is uncertain. We introduce a linear model of the uncertainty that can exist in the demand for the product and in each stage's processing time, yield, rework probability, and reliability. We construct a linear discrete-time rule for controlling production, and we show that repeated application of this rule leads the system to steady-state conditions, which include closed-form formulas for the mean and variance of each buffer's stock and the mean and variance of the workload in each stage. We optimize these operating characteristics by a convex nonlinear program. For the case of identical stages with no scrap, we show that this optimal solution tends to place larger buffer stocks toward the end of the line. We adapt these discrete-time results to the short-period surrogate of the analogous continuous-time control problem.