A product with an annual demand of 800 units has C_0 = $24.50 and C_h = $9. The
ID: 3232781 • Letter: A
Question
A product with an annual demand of 800 units has C_0 = $24.50 and C_h = $9. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with mu = 26 and sigma = 6. a. What is the recommended order quantity? Round your answer to the nearest whole number. b. What are the reorder point and safety stock if the firm desires at most a 5% probability of stock-out on any given order cycle? If required, round your answers to the nearest whole number. Record point = Safety stock = c. If a manager sets the reorder point at 32, 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? Round your answer to the nearest whole number. Number of Orders =Explanation / Answer
CVP = Cost Volume Profit
Profit = Expense - Income
where Expenses includes over head costs and other costs
Safety Margin = Expected Sales – Break Even Point Sales
Safety Margin % = (Expected Sales – Break Even Point Sales) / Expected Sales
A.
Values given in the question:
D = Demand = 800 units per annum
Cost o = $24.50
Cost h = $9.00
Average = mean = Miu = 26
Sigma = SD = Standard Deviation = 6
ReOrder Point (ROP) = Recommended order quantity = Economic Order Quantity (EOQ) = Z * SD + Miu
Z Value 0.5 from the students table.
EOQ = 0.5 * 6 + 26 = 3 + 26 = 29
EOQ = 29
Hence Q* = Recommended order quantity = 29
B)
Reorder point (looks like a typo in the question as Record point) =
The maximum out of stock condition can be less than or equal to 9%
Likely stock out can occur at:
annual demand 800
SD = 6
Hence Highest demand = 800+6 = 806, lowest demand = 800-6 = 794 (grossly approximated)
Reorder Qty = 29
Number of reorders required = (806/29 + 794/29 ) / 2
= ( 27.79 + 27.40 ) / 2 = 27.6
Hence Reorder Point = 27 or rounded to 28
Reorder point (looks like a typo in the question as Record point) =
The maximum out of stock condition can be less than or equal to 9%
SS = Safety stock = Maximum demand per day * highest lead time to replenish stock after reorder ) – ( Average daily demand or the mean * average lead time )
Daily demand = Annual demand / number of days per year = 800 / 365 = 2.2
Let the highest lead time be 26 days and average be 6 days
SS = 2.2 * 26 – (2.2 * 6) = 57.2 – 13.2 = 44
hence maintain a safety stock of 44 units at all times to avoid stock out or out of stock embarassement.
C)
old reorder point = 27 to 29; old probability of stock out = 7%
new reorder point = 32 new probability of stock out = 9% (as illustrated in the calculation below)
Rise in reorder point = 32– 27 = 5
Hence rise in lead time = 26 + 4 = 30 days (worst case), = 10 days average case
SS = 2.2 * 30 – (2.2 * 10) = 66 – 22 = 44 units => 9%
P(Stockout/cycle) = 9%
( = probability of stock out occurring )
D) How many times would you expect a stock-out during the year if this reorder point were used? Round your answer to the nearest whole number.
Number of Orders = 32
Number of expected stock outs at the rate of 9% = 365*9/100 = 3285/100
=32.85 =~ 33
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