Initiation of an inventory control system when the demand starts at a given time

This paper considers a single-echelon, continuous review, inventory system with a warehouse facing compound Poisson customer demand. The replenishment lead-time is constant. Demand that cannot be met directly is backordered. There are standard linear holding and backorder costs but no set-up or ordering cost. It is assumed that the demand process starts at a certain given time. Consequently, before the demand starts, the lead-time demand is lower than in steady state. This affects the optimal ordering policy. We derive the optimal ordering policy under these assumptions.