Production control under uncertainty: closed-loop versus open-loop approach

A basic production system facing two types of uncertainty (shocks), multiplicative and additive, is considered. The former is due to a stochastic yield; the other to a stochastic demand. The objective of the production system is to choose a production rate (control) that minimizes expected inventory and production costs. Stochastic production control is typically considered the prerogative of closed-loop or on-line approaches. However, in certain manufacturing systems, information about inventory levels may at best be imprecise. Moreover, the production rate cannot be instantaneously adjusted in response to inventory updates. This warrants the exploration of an open-loop or off-line control methodology. In the comparative analysis of the two approaches presented in this paper, the probability distribution of inventories is characterized, the damage associated with the inability to adjust production is assessed, and the conditions at when the gap between the two approaches are insignificant are highlighted.