A product with an annual demand of 1200 units has Co = $20.5 and Ch = $7. The de
ID: 3362851 • Letter: A
Question
A product with an annual demand of 1200 units has Co = $20.5 and Ch = $7. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with µ = 28 and = 5.
What is the recommended order quantity?
If required, round your answer to two decimal places.Q* ?????
2. What are the reorder point and safety stock if the firm desires at most a 2% probability of stock-out on any given order cycle? If required, round your answers to the nearest whole number. Record point = ????? Safety stock = ?????
3. If a manager sets the reorder point at 34, what is the probability of a stock-out on any given order cycle? If required, round your answer to four decimal places. P(Stockout/cycle) = ?????
How many times would you expect a stock-out during the year if this reorder point were used?
Number of Orders = ????
Last time i asked this i was given incorrect answers....
Explanation / Answer
Annual demand of the product = D = 1200 units
Cost of ordering = Co = $20.50
Cost of holding = Ch = $7
Answer to question a:
Recommended order quantity
= Square root ( 2 x Co X D /Ch )
= Square root ( 2 x 20.50 x 1200 / 7)
= Square root ( 7028.57)
= 83.836=84
RECOMMENDED ORDER QUANTITY = 84
Answer to question #b:
Probability of stockout = 2%
Therefore, Service level = 100% - probability of stockout = 100% - 2% = 98%
Z value for service level of 98% = NORMSINV (0.98) in excel = 2.053
Safety stock = Zvalue x Standard deviation of demand during led time = 2.053 x 5 = 10.268
( 11 when rounded to next higher integer)
Thus,
Reorder point = Lead time demand + Safety stock = 20.5 + 11 = 30.76=31
SAFETY STOCK = 11
REORDER POINT = 31
Answer to question #c:
At reorder point = 34
Reorder point = Demand during lead time + Zvalue x Standard deviation of demand during lead time
Or, 34 = 20.5 + 5*Z
Or, Z = 13.5/5 = 2.7
From Normal distribution table , corresponding probability = 0.9965
Therefore probability of stockout = 1 – 0.9965 = 0.00347
PROBABILITY OF STOCKOUT = 0.00347
Average number of orders in a year
= Annual demand / Optimum order quantity
= 1200/70
Therefore expected number of stockouts
= Average number of stockouts x Probability of stockout
= 1200/83 x 0.003467
= 0.05 ( 0 rounded to nearest integer)
WE WOULD EXPECT STOCKOUT OF 3 TIMES IN A YEAR
NUMBER OF ORDERS = 0
RECOMMENDED ORDER QUANTITY = 84
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