Your new company has decided to use a periodic review system. You have learned t
ID: 422625 • Letter: Y
Question
Your new company has decided to use a periodic review system. You have learned that average weekly demand is 48 units per week with a standard deviation of 8 units. You believe that your cycle-service level should be 94 percent. Lead time is two weeks. Initially, you believe that you should do a review every Friday. Determine the required safety stock and the target inventory level.
How would this procedure change if the cycle-service level needed to be 98 percent?
What is the impact of changing the review period from every Friday to every other Friday, assuming that the cycle-service level is 94 percent?
Explanation / Answer
Z value for cycle service level of 94 percent = NORMSINV ( 0.94 ) = 1.5547
Protection period = Review period ( weeks ) + Lead time ( weeks )
= 1 week ( i.e. review every Friday) + 2 weeks
= 3 weeks
Standard deviation of weekly demand = 8 units
Therefore , standard deviation of demand during protection period
= Standard deviation of weekly demand x Square root ( Protection period )
= 8 x square root ( 3 )
= 8 x 1.732
= 13.856
Safety stock required
= z value x standard deviation of demand during protection period
= 1.5547 x 13.856
= 21.541 ( 22 rounded to next higher whole number )
Target inventory level
= Average weekly demand x Protection period ( weeks ) + Safety stock
= 48 x 3 + 22
= 144 + 22
= 166
REQUIRED SAFETY STOCK = 22 UNITS
TARGET INVENTORY LEVEL = 166 UNITS
Z value of cycle service level of 98 percent = NORMSINV ( 0.98 ) = 2.0537
Safety stock now required
= Z value x Standard deviation of demand during protection period ( as calculated earlier )
= 2.0537 x 13.856
= 28.456 ( 29 rounded to next higher whole number )
Therefore increase in safety stock = Increase in inventory level = 29 – 22 = 7
PROCEDURE WILL CHANGE RESULTING IN INCREASE IN SAFETY STOCK BY 7 UNITS
When review period changes to every other Friday , it means review period = 2 weeks
Revised, protection period
= Review period + Lead time
= 2 weeks + 2 weeks
= 4 weeks
Standard deviation of weekly demand = 8 units
Standard deviation of demand during protection period
= Standard deviation of weekly demand x Square root ( protection period )
= 8 x square root ( 4 )
= 8 x 2
= 16 units
Z value for 94% service level = 1.5547
Therefore ,
Safety stock
=Z value x Standard deviation of demand during protection period
= 1.5547 x 16
= 24.875 ( 25 rounded to next higher whole number )
Required inventory level
= average weekly demand x Protection period ( weeks ) + safety stock
= 48 x 4 + 25
= 192 + 25
= 217
REVISED SAFETY STOCK = 25 UNITS
REVISED INVENTORY LEVEL = 217 UNITS
REQUIRED SAFETY STOCK = 22 UNITS
TARGET INVENTORY LEVEL = 166 UNITS
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