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 100 and standard deviation 65 (demands for the two colors are independent). The lead time from the assembly plant to the retail store is two weeks and you order inventory replenishments weekly. 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 97 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 two weeks. Furthermore, you still choose an order- up-to level for each top to generate a 97 percent in-stock probability.
b. What is the expected on-hand inventory of black tops?
c. 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?