Problem:

Suppose you are the manager of the office furniture department at Nebraska Furniture Mart. One of your products is a cherry study desk. The weekly demand for this desk can be represented by a normal distribution with mean 40 and standard deviation 20. Your review period is 1 week while the lead?time for replenishment is 2 weeks.

Required

Question a) Suppose your order up to level is 220. You are about to place an order and note that your inventory level is 100 and you have 85 desks on order. How many desks will you order?

Question b) Suppose your order up to level is 220. You are about to place an order and note that your inventory level is 160 and you have 65 desks on order. How many desks will you order?

Question c) What is the optimal order up to level if you want to target a 98% in stock probability?

Question d) What is the optimal order up to level if you want to target a 98% fill rate?

Question e) Suppose your order up to level is 120. What is your expected on hand inventory?

Question f) Suppose your order up to level is 120. What is the annual holding cost? (Assume 365 days per year and it costs Nebraska Furniture Mart $20/year to keep one desk in stock)

Question g) Suppose your order up to level is 200. What fraction of customer demand is met immediately from stock?

Question h) Suppose your order up to level is 200. What is the average amount of inventory on order?

Question i) Suppose you want to maintain 95% in?stock probability for the desk. What is the expected fill rate in this case?

Solve the given numerical problem and illustrate step by step calculation.