A paint store in Rolla sells a specific paint. The monthly demand of this paint
ID: 370591 • Letter: A
Question
A paint store in Rolla sells a specific paint. The monthly demand of this paint follows a normal distribution with mean of 100 and variance of 144. The excess demand can be backordered. It takes the paint store one month to receive the order it placed to the manufacturer. The unit purchase price the paint store will pay is $16. The holding cost is estimated based on the annual rate of 8%. The fixed cost per ordering is $20. The store reviews it inventory continuously and will place order with size Q when the inventory level hits R. The owner of this paintstore decides to use a service level model to determine its inventory strategy. The target service level is that there is no stock-out in 90% of the cycles.
1) Find the resulting order size (Q) and reorder point (R).
2) If the owner of the store wants to satisfy 90% of the demand from the stock (achieve a 90% fill rate), what is reorder point R?
3) If the lead time is two months, what will be the Q and R if the store still hopes to achieve the target of service level that 90% of the cycles should not have any stock-outs?
Please show all work!
Explanation / Answer
The order size Q will be determined on basis of Economic Order Quantity ( EOQ ) model.
Accordingly,
EOQ = Square root ( 2 x Co x D/Ch)
D = Annual demand = 100/ month x 12 months = 1200
Co = $20
Ch = Annual unit holding cost = 8% of $16 = $1.28
Therefore,
EOQ = Square root ( 2 x 20 x 1200 /1.28)
= 193.649 ( 194 rounded to nearest whole number )
Corresponding Z value for service level of 90 %
= NORMSINV ( 0.90) = 1.281
Lead time for order placement = 1 month
Variance of demand during lead time = 144
Hence standard deviation of demand during lead time = Square root ( 144) = 12
Hence,
Safety stock = Z value x Standard deviation of demand during lead time
= 1.281 x 12
= 15.372
Thus reorder point
= Average monthly demand x Lead time ( months ) + Safety stock
= 100 x 1 + 15.372
= 115.372 ( 115 rounded to nearest whole number )
RESULTING ORDER SIZE = 194
REORDER POINT WITHOUT SAFETY STOCK = 100
REORDER POINT WITH 90% SERVICE LEVEL = 115
When Lead time = 2 months
Q remains unchanged at 194
Standard deviation of demand during lead time of 2 months
= Standard deviation of monthly demand x Square root ( Lead time in months)
= 12 x Square root ( 2 )
= 12 x 1.414
= 16.968
Z value for 90 % service level as calculated earlier = 1.281
Therefore safety stock = Z value x Standard deviation of demand during lead time
= 1.281 x 16.968
= 21.736
Reorder level
= Average monthly demand x Lead time ( months) + safety stock
= 100 x 2 + 21.736
= 221.736 ( 222 rounded to nearest whole number )
Q LEVEL = 194
REORDER LEVEL = 222
RESULTING ORDER SIZE = 194
REORDER POINT WITHOUT SAFETY STOCK = 100
REORDER POINT WITH 90% SERVICE LEVEL = 115
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