11. Expected demand during lead time = 300 units, standard deviation of demand d
ID: 383619 • Letter: 1
Question
11. Expected demand during lead time = 300 units, standard deviation of demand during
lead time = 30 units. Assuming that demand during lead time is normally distributed, determine
each of the following;
a) The ROP that will provide a risk of stockout of 1 percent during lead time. (369.9)
b) The safety stock needed to attain a 1 percent risk of stockout during lead time. (69.9)
c) Would a stockout risk of 2 percent require more or less safety stock than a 1 percent risk?
Explain and provide example step by step
Explanation / Answer
Risk of 1 percent stock out is equal to in-stock probability of 99 percent i.e. 0.99 probability
Corresponding Z value for instock probability of 0.99 = NORMSINV ( 0.99) = 2.326
Standard deviation of demand during lead time = 30 units
Therefore , safety stock needed to attain 1 percent risk of stockout during lead time
= Z value x Standard deviation of demand during lead time
= 2.326 x 30
= 69.78
Reorder point ( ROP ) that will provide a risk of stockout of 1 percent
= Expected demand during lead time + Safety stock
= 300 + 69.78
= 369.78
ROP THAT WILL PROVIVE A RISK OF STOCKOUT OF 1 PERCENT = 369.78
SAFETY STOCK NEEDED TO ATTAIN 1 PERCENT RISK OF STOCKOUT = 69.78
Stock out risk of 2 percent corresponds to instock probability of 98 % 9 0.98)
Corresponding Z value for probability 0.98 = NORMSINV ( 0.98) = 2.053
Standard deviation of demand during lead time = 30 units
Therefore , safety stock needed to attain 2 percent risk of stockout during lead time
= Z value x Standard( 69.78) deviation of demand during lead time
= 2.053 x 30
= 61.59
Thus safety stock needed ( 61.59 units) to attain 2 perent risk of stock out is less than safety stock needed ( 69.78) to attain 1 percent risk of stock out
STOCKOUT RISK OF 2 PERCENT WILL REQUIRE LESS SAFETY STOCK THAN 1 PERCENT RISK OF STOCK OUT
ROP THAT WILL PROVIVE A RISK OF STOCKOUT OF 1 PERCENT = 369.78
SAFETY STOCK NEEDED TO ATTAIN 1 PERCENT RISK OF STOCKOUT = 69.78
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