On the tradeoff between optimal order-base-stock levels and demand lead-times

We investigate the tradeoff between finished-goods inventory and advance demand information for a model of a single-stage make-to-stock supplier who uses an order-base-stock replenishment policy to meet customer orders that arrive a fixed demand lead-time in advance of their due-dates. We show that if the replenishment orders arrive in the order that they are placed, then the tradeoff between the optimal order-base-stock level and the demand lead-time is "exhaustive", in the sense that the optimal order-base-stock level drops all the way to zero if the demand lead-time is sufficiently long. We then provide a sufficient condition under which this tradeoff is linear. We verify that this condition is satisfied for the case where the supply process is modeled as an M/M/1 queue. We also show that the tradeoff between the optimal order-base-stock level and the demand lead-time is linear for the case where the supply process is modeled as an M/D/1 queue. More specifically, for this case, we show that the optimal order-base-stock level decreases by one unit if the demand lead-time increases by an amount equal to the supplier's constant processing time. Finally, we show that the tradeoff between the optimal order-base-stock level and the demand lead-time is exhaustive but not linear in the case where the supply process is modeled as an M/D/[infinity] queue. We illustrate these results with a numerical example.