The effect of foreknowledge of demand in case of a restricted capacity: the single-stage, singleproduct case with lost sales

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