The effect of foreknowledge of demand in case of a restricted capacity: The single-stage, single-product case

Foreknowledge of demand is useful in the control of a production-inventory system. Knowing the customer orders in advance makes it possible to anticipate properly. It is an important condition to produce and deliver the right quantity of the right product “just-in-time”. It reduces the need of safety stock and spare capacity. But the question of the effectiveness of foreknowledge is not an easy one. Having foreknowledge of the customer orders does not remove the demand uncertainty completely. The effect of foreknowledge has to be considered in a stochastic dynamic setting. The subject of this paper is the effect of foreknowledge in combination with a restricted production capacity. The lost-sales case is considered. The main result is that for high utilization rates and small forecast horizon, the inventory reduction due to foreknowledge is equal to (1-ρ).h, with h the forecast horizon