A product with an annual demand of 1000 units has C0 = $25.50 and Cc = $8. The d
ID: 368263 • Letter: A
Question
A product with an annual demand of 1000 units has C0 = $25.50 and Cc = $8. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with = 25 and = 5. a. What is the recommended order quantity? b. What are the reorder point and safety stock if the firm desires at most a 2% probability of stock-out on any given cycle? c. If the manager sets the reorder point at 30, what is the probability of a stock-out on any given cycle? How many times would you expect a stock-out during the year if this reorder point were used?
Explanation / Answer
Answer to question a :
Recommended order quantity will be decided on basis of Economic Order Quantity ( EOQ )
EOQ will be determined as per following :
EOQ = Square root ( 2 x Co x D/ Cc)
Where,
Co = Ordering cost = $25.50
D = Annual demand = 1000 units
Cc = Annual unit inventory carrying cost = $8
Therefore ,
EOQ = Square root ( 2 x 25.50 x 1000/8)
= 79.84 ( 80 rounded to nearest whole number )
RECOMMENDED ORDER QUANTITY = 80
Answer to question b :
Probability of stock out = 2%
Therefore , cycle service level = 100 – probability of stock out = 98 % ( 0.98)
Z value corresponding tp probability 0.98 = NORMSINV( 0.98) = 2.053
Hence,
Required safety stock
= Z value x Standard deviation of demand during lead time
= 2.053 x 5
= 10.265
Reorder point
= Lead time demand + safety stock
= 25 + 10.265
= 35.265
SAFETY STOCK = 10.265
REORDER POINT = 35.265
Answer to question c :
Given,
Reorder point = 30
Since,
Reorder point = Demand during lead time + safety stock = Demand during lead time + Zvalue x Standard deviation of demand during lead time
Therefore,
30 = 25 + 5.Z
Or, Z = 1
Corresponding probability value for Z = 1 will be 0.84134
PROBABILITY OF STOCKOUT ON ANY GIVEN CYCLE = 0.84134
Number of orders in a year = Annual demand / EOQ = 1000/ 80 = 12.5
Thus,
Expected number of stockouts in a year
= Number of orders in a year x Probability of stockout in any given cycle
= 12.5 x 0.84134
=10.51
PROBABILITY OF STOCKOUT IN ANY GIVEN CYCLE = 0.84134
EXPECTED NUMBER OF STOCKOUTS IN A YEAR = 10.51
RECOMMENDED ORDER QUANTITY = 80
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