A product with an annual demand of 1200 units has Co = $20.5 and Ch = $7. The de
ID: 365318 • 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 = ????
Explanation / Answer
Annual Demand (D)= 1,200 units
Order cost (S)= $ 20.5
Holding cost (H) = $7
Recommedned order quantity (Qopt) = sqrt (2*D*S / H) = sqrt(2*1200(20/7) = 83.83 units
Recommended order quantity = 83.83 units
2. Demand per day = 1200/365 = 3.29 units
When Lead time is variable:
Mean lead time = 28 days, SD of Lead time demand= 5 days
R = Lead time demand + Z * SD (lead time demand)
Z = 2.054 for 98% Service level
R = 28 + 2.054 *5 = 38.27
Re order point = 38.27 units
Safety stock = Z*SD(L) = 2.054*5 = 10.27 units
3. Reorder point = 34 units
34 = 28+ z*5
z= 1.2
Probability of stockout as per normal table for value 1.2 = 11.51%
P(Stockout/cycle) = 11.51%
Number of orders per year = 1,200/83.83 ~ 15
Number of orders with stockout = 15*11.51% = 2
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