Matching Supply with Demand: An Introduction to Operations Management 2nd Edition by Cachon Terwiesch

Exercise 1

(Furniture Store) You are the store manager at a large furniture store. One of your products is a study desk. Weekly demand for the desk is normally distributed with mean 40 and standard deviation 20. The lead time from the assembly plant to your store is two weeks and you order inventory replenishments weekly. You use the order-up-to model to control inventory.
a. Suppose your order-up-to level is S = 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?
b. Suppose your order-up-to level is S = 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?
c. What is the optimal order-up-to level if you want to target a 98 percent in-stock probability?
d. What is the optimal order-up-to level if you want to target a 98 percent fill rate?
e. Suppose your order-up-to level is S = 120. What is your expected on-hand inventory?
f. Suppose your order-up-to level is S = 200. What is your fill rate?
g. Suppose you now decide to maintain a 95 percent in-stock probability for the desk. What is the expected fill rate in this case?
h. Suppose your order-up-to level is S = 120. Your internal cost of capital is 15 percent and each desk costs $200. What is your total cost of capital for the year for inventory in the store?