Question 1 (15 marks). 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 60 and standard deviation 25. The lead time from the assembly plant to your store

is four weeks and you order inventory replenishments weekly. You use order-up-to

model to control inventory.

a. Suppose your order-up-to level is 180 units. You are about to place an order and

note that your inventory level is 90 and you have 55 desks on order. How many

desks will you order?

b. Suppose your order-up-to level is 180 units. You are about to place an order and

note that your inventory level is 120 and you have 65 desks on order. How many

desks will you order?

c. Suppose your order-up-to level is 360 units, what is the in-stock probability?

d. What is the optimal order-up-to level if you want to target a 94 percent in-stock

probability?

Question 2 (15 marks). You are in charge of designing a supply chain for furniture

distribution. One of your products is a study desk. This desk comes in two colors: black

and cherry. Weekly demand for each desk type is normal with mean 120 and standard

deviation 75 (demands for the two colors are independent). The lead time from the

assembly plant to the retail store is three weeks and you order inventory replenishments

biweekly. There is no finished goods inventory at the plant (desks are assembled to

order for delivery to the store).

a. What is the expected on-hand inventory of desks at the store (black and cherry

together) if you maintain a 96 percent in-stock probability for each desk color?

You notice that only the top part of the desk is black or cherry; the remainder (base) is

made of the standard gray metal. Hence, you suggest that the store stock black and

cherry tops separately from gray bases and assemble them when demand occurs. The

replenishment lead time for components is still three weeks. Furthermore, you still

choose an order-up-to level for each top to generate a 96 percent in-stock probability.

b. How much less inventory of gray bases do you have on average at the store with

the new in-store assembly scheme relative to the original system in which desks are

delivered fully assembled? (Hint: Remember that each assembled desk requires one

top and one base.)