Timbuk2 Inc. manufactures over 100,000 different versions of messenger bags. Suppose Timbuk2 implements an order-up-to model to manage its inventory of a particular plastic buckle. The lead time to receive these buckles is three weeks. Demand is approximately normally distributed with a mean of 2300 units per week and a standard deviation of 1300. Each week’s demand is independent of the demand in the other weeks.
What is the order-up-to level that achieves a target in-stock probability of 99.6%? Round to the nearest integer.