The Impact of Uncertainty on a Production Line

This paper presents a discrete time model of a multi-stage production system that faces two major types of uncertainties: the output rate at each production stage and the demand for the finished product. Our goal is to analyze the impact of these uncertainties on the production level and on the inventory level at each stage in order to provide insights for production planning, inventory control, quality improvement, and capacity planning. We propose a scheme in which a complex production rule is approximated by a linear production rule (that follows the “restoration” concept introduced by Denardo and Tang 1988). This linear production rule leads the system to steady state in which the means and the variances of the production and inventory levels can be expressed in closed form. These closed form expressions enable us to develop a simple approach for determining a “good” production rule and for analyzing the impact of increasing the yield rates and reducing the variance of the demand. The goodness of this approximation scheme is illustrated by an example.