If one have a continuous review $($S$1,$S$)$ inventory system

with constant lead time

and Poisson demand with arrival rate $\backslash$lambda $.$

$1)$ Assume that a customer is lost if stock on hand is zero when the customer arrives at the inventory. Then, what is the maximum number of outstanding orders?

$2)$ Assume that a customer is backordered if stock on hand is zero when the customer arrives. Then, what is the maximum number of outstanding orders?

$3)$ Assume again that a customer is lost if stock on hand is zero when the customer arrives at the inventory. Given that Pi $=$ P$($IL $=$ i$)$ is known for all i$,$ what is the average number of lost customers per unit of time?