A product with an annual demand of 900 units has Co = $23 and Ch = $5. The deman
ID: 3270321 • Letter: A
Question
A product with an annual demand of 900 units has Co = $23 and Ch = $5. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with =26 and =6. a.What is the recommended order quantity? b. What are the recorder point and safety stock if the firm desires at most a 7% probability of stockout on any given order cycle? c. If a manager sets the reorder point at 31, what is the probability of a stockout on any given order cycle? d. How many times would you expect a stockout during the year if the reorder point were used?
Explanation / Answer
a)
Annual demand of the product = D = 900 units
Cost of ordering = Co = $23
Cost of holding = Ch = $5
Recommended order quantity
= ( 2 x Co X D /Ch )
= ( 2 x 23 x 900 /5)
=91
b)
Probability of stockout = 7%
Therefore, Service level = 100% - probability of stockout = 100% - 7% = 93%
Z value for service level of 93% = NORMSINV (0.93) in excel = 1.476
Safety stock = Zvalue x Standard deviation of demand during led time =1.476 x 6 = 8.856
( 9 when rounded to next higher integer)
Thus,
Reorder point = Lead time demand + Safety stock = 26+9=35
c)
At reorder point = 31:
Reorder point = Demand during lead time + Zvalue x Standard deviation of demand during lead time
Or, 31 = 26 + 6.Z
Or, Z = 5/6 = 0.8333
From Normal distribution table , corresponding probability = 0.7967
Therefore probability of stockout = 1 – 0.7967 = 0.2033
d)
Average number of orders in a year
= Annual demand / Optimum order quantity
= 900/91
Therefore expected number of stockouts
= Average number of stockouts x Probability of stockout
= 900/91 x 0.2033
= 2 ( rounded to nearest integer)
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