5. A producer operates on 8 units/day in the assembly line. The OM department as
ID: 342973 • Letter: 5
Question
5. A producer operates on 8 units/day in the assembly line. The OM department assumes that the process has a normal distribution and standard deviation of the line is 3 units/day. The ordering cost is $10 and holding cost/roll/year is $0.30. Lead time is 2 days. (Total work day/year is 250 days) (Show Your Work!)
a) What is the economic order quantity?
b) What is the safety stock level for 97% order-cycle service level?
c) What is the safety stock level for 99% order-cycle service level?
d) What is reorder point for 97% order-cycle service level?
e) Calculate reorder point for 99% order-cycle service level?
Explanation / Answer
Given are following data :
Annual demand = D = 8 units/ day x 250 days = 2000 units
Ordering cost = Co = $10
Annual unit holding cost = Ch = $0.30
= Square root ( 2 x Co x D / Ch)
= Square root ( 2 x 10 x 2000/0.30)
= 365.148 ( 365 rounded to nearest whole number )
ECONOMIC ORDER QUANTITY = 365 UNITS
= NORMSINV ( 0.97 )
= 1.880
Daily standard deviation = 3 units
Lead time = 2 days
Standard deviation of demand during lead time
= Daily standard deviation x Square root ( Lead time )
= 3 x Square root ( 2 )
= 3 x 1.414
= 4.242
Safety stock
= Z value x Standard deviation of demand during lead time
= 1.880 x 4.242
= 7.974 ( 8 rounded to nearest whole number )
SAFETY STOCK = 8 UNITS
= NORMSINV ( 0.99)
= 2.326
Daily standard deviation = 3 units
Lead time = 2 days
Standard deviation of demand during lead time
= Daily standard deviation x Square root ( Lead time )
= 3 x Square root ( 2 )
= 3 x 1.414
= 4.242
Safety stock
= Z value x Standard deviation of demand during lead time
= 2.326 X 4.242
= 9.866 ( 10 rounded to nearest whole number )
SAFETY STOCK = 10 UNITS
= Daily demand x Lead time ( days ) + Safety stock at 97% service level
= 8 x 2 + 8
= 16 + 8
= 24 units
REORDER POINT = 24 UNITS
= Daily demand x Lead Time( days) + safety stock at 99% service level
= 8 x 2 + 10
= 26 units
REORDER POINT = 26 UNITS
ECONOMIC ORDER QUANTITY = 365 UNITS
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