Fancy Paints is a small paint store that stocks 200 different SKUs (stock keeping units = different colors). For each of these SKUs, the average weekly demand is normally distributed with mean 50 items and standard deviation 10 items. Inventory for each SKU is maintained with an s,Q policy, aiming for an in- stock-probability of 95% each. Delivery lead time is 4 weeks.
a) What is the total number of safety stock that has to be held in order to reach the desired service level?
b) Now suppose Fancy Paints purchases a color-mixing machine. This machine is expensive but instead of stocking 200 different SKU colors, it allows Fancy Paints to only stock 5 basic SKUs and to obtain all the other colors by mixing. If the desired in-stock-probability remains unchanged for each of the 5 colors, how much safety stock will be required? Compare the results to a) and explain the difference.