3. (12 points) Quick Print Inc. uses plain paper for copying needs. Weekly deman
ID: 339946 • Letter: 3
Question
3. (12 points) Quick Print Inc. uses plain paper for copying needs. Weekly demand for the plain paper is estimated to be normally distributed with mean 100 and standard deviation 75 (in boxes). The order is delivered in one week. 6 points) Quick Print re-orders when on-hand inventory is 123 boxes. What is the risk of stock-out before this order arrives? a. ( order interval of five weeks instead of ROP is used for reordering, i.e, reorder he order quantity given the on-hand inventory at the time of the order. Quick rvice level of 99.5%, what should be the order quantity if the on-hand inventory is five weeks (6 points) Assume that fixed every five weeks and adjust b. quantity given 123 boxes at the time of the order?Explanation / Answer
Answer to question a :
Reorder quantity as given = 123
Reorder point = Standard deviation of demand during lead time + Safety stock
Or, Reorder point = Mean demand during lead time + Z value x Standard deviation of demand during lead time
Or, 123 = 100 + 75Z
Or, 75.Z = 23
Or, Z = 23/75
Or, Z = 0.3066 ( 0.31rounded to 2 decimal places )
Corresponding probability for Z = 0.31 as derived from standard normal distribution table 0.6217
Therefore , in stock probability = 0.6217
Hence, probability of stock out = 1 – 0.6217 = 0.3783
Thus , risk of stock out = 0.3783 x 100 = 37.83 %
RISK OF STOCK OUT = 37.83 %
Answer to question b :
Required service level = 99.5%
Corresponding Z value = NORMSINV ( 0.995 ) = 2.5758
Order interval = T = 5 weeks
Lead time = L = 1 week
Therefore , Protection interval = P = T + L = 5 + 1 = 6 weeks
Therefore ,
Standard deviation of demand during protection interval of 6 weeks
= Standard deviation of weekly demand x Square root ( Protection interval )
= 75 x Square root ( 6 )
= 75 x 2.449
= 183.675
Therefore , safety stock
= Z value x Standard deviation of demand during protection interval
= 2.5758 x 183.675
= 473.11 ( 473 rounded to nearest whole number )
Theoretical Reorder point
= Average weekly demand x Protection interval ( weeks ) + safety stock
= 100 x 6 + 473
= 600 + 473
= 1073
On hand inventory at the time of order = 123
Therefore ,
Order quantity = Theoretical reorder point – quantity on hand = 1073 – 123 = 950
REQUIRED ORDER QUANTITY =950
RISK OF STOCK OUT = 37.83 %
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