Off-line and on-line production control: A diffusion approximation

We employ a diffusion approximation to model a manufacturing system facing a stochastic production yield and stochastic customer demand. The objective of the 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 our comparative analysis of the two approaches, we characterize the probability distribution of inventories, assess the damage associated with the inability to adjust production and show when the gap between the two approaches can be insignificant.