Problem
Willy Wonka is a candy wholesaler. He purchases cases of chocolate from a distributor at $100 each and pays a fixed $2,048 shipping and handling charge per order. The total lead time from the distributor is 2 weeks. Assume an annual rate of 15% for inventory carrying charges and 50 weeks per year. Weekly demand is normally distributed with a mean of 3,000 cases and a standard deviation of 141 cases. Assume full backorders.
i. What is the optimal order quantity?
ii. Suppose that Wonka wants to provide a 86% service level (regardless of what is optimal). What reorder point should he use to provide such service level?