### Use the order-up-to model to control inventory

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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 S-220. You are about to place an order and note that your inventory levelis 100 and you have 85 desks on order. How many desk 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 to order. How many desk will you order?

c. What is the optimal order-up-to level if yo uwant to target a 98 percent in stock probability?

d. Suppose your order-up-to level is S=120. What is your expected on-hand inventory?

e. Suppose your order-up-to level is S=120. Yout internal cost of capital is 15 percent and each desk costs \$200. What is your total coat of capital for the year for inventory in the store?

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