Fancy Paints is a small paint store that stocks 200 different SKUs (stock keepin
ID: 364367 • Letter: F
Question
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.
Explanation / Answer
Answer to question a :
Standard deviation of weekly demand = 10 items
Lead time = 4 weeks
Therefore ,
Standard deviation of demand during lead time
= Standard deviation of weekly demand x Square root (Lead time )
= 10 x Square root ( 4 )
= 20
Z value corresponding to instock probability of 95% 9 0.95 )
= NORMSINV ( 0.95 )
= 1.6448
Therefore,
Safety stock for each SKU
= Z value x Standard deviation of demand during lead time
= 1.6448 x 20
= 32.896 ( 33 rounded to nearest whole number )
Therefore , total number of safety stocks for 200 SKUs = 200 x 33 = 6600
TOTAL NUMBER OF SAFETY STOCK TO BE HELD = 6600
Answer to question b :
5 basic SKUs are stored in lieu of 200SKUs , i.e. 1 basic SKU in lieu of 200/ 5 = 40 SKUs
Standard deviation of weekly demand of 1 SKU = 10
Standard deviation of weekly demand of 40 SKUs = 10 x Square root ( 40)
Standard deviation of demand of 40 SKUs ( i.e. 1 Basic SKU) during lead time
= Standard deviation of weekly demand of 40 SKUs x Square root ( Lead time )
= 10 x Square root ( 40) x Square root ( 4 )
= 10 x 6.324 x 2
= 126.48
Z value for in stock probability of 95 % = 1.6448
Hence, safety stock requirement for 1 Basic SKU
= Z Value x Standard deviation of demand for 1 Basic SKU during Lead time
= 1.6448 x 126.48
= 208.03
Therefore , safety stock requirement for 5 basic SKUs
= 208.03 x 5
= 1040.15 ( 1040 by rounding to nearest whole number )
SAFETY STOCK REQUIREMENT = 1040
By consolidating multiple SKUs, the overall variability of such consolidate groups are reduced Since overall variability (i.e. standard deviation) of such group is less than sum of standard deviation of individual items, safety stock requirement of such consolidated groups also thus gets reduced. As a result, the overall safety stock requirement thus gets reduced from 6600 to 1040
TOTAL NUMBER OF SAFETY STOCK TO BE HELD = 6600
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