1. Timbuk2 Inc. manufactures over 100,000 different versions of a messenger bag (illustrated on the right). 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 two weeks. Demand is approximately normally distributed with a mean of 2,300 units per week and a standard deviation of 1,300. 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%?

2. Timbuk2 Inc. manufactures over 100,000 different versions of a messenger bag (illustrated on the right). 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 2,500 units per week and a standard deviation of 1,200. 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 99.5%?