The fill rate (the proportion of demand that is satisfied from stock)
is a viable alternative in inventory models to the hard-to-quantify pe
nalty cost. However, a number of difficulties have impeded its impleme
ntation, among them that the existing cycle-based approximate solution
s do not reflect the possibility of multiple outstanding orders and th
at the optimal policy cannot be found directly, but must be iterativel
y calculated. We show that for a large family of leadtime demand distr
ibutions, the optimal policy depends on only two parameters: the fill
rate and the economic order quantity (EOQ) scaled by the standard devi
ation of demand over the constant leadtime. If we then assume that the
leadtime demand is normally distributed, we can use the asymptotic re
sults as the EOQ goes to zero and to positive infinity to fit atheoret
ic curves for the order quantity Q and the reorder point R. These fitt
ed curves yield a good (Q, R) policy without iteration. We also find t
hat, among the set of simple heuristics, the limit form as EOQ goes to
positive infinity provides a better alternative to simply setting Q e
qual to the EOQ.