Double A stocks decorative coffee mugs that have been a big hit with the patrons
ID: 3311360 • Letter: D
Question
Double A stocks decorative coffee mugs that have been a big hit with the patrons. Each mug costs $3.00 and sells for $8.00. The cost of placing an order is $50.00, and once an order is placed, the mugs arrive in two weeks. During the two-week period, demand is normally distributed with a mean of 50 mugs and a standard deviation of 10 mugs. The cost of holding a mug in inventory is $.15/dollar value per year. If an item is out of stock, they will place the item on backorder and estimate that the cost of lost goodwill is $.20. Find the optimal ordering policy for Double A.
Explanation / Answer
The demand for two week period = 50 mugs
Annual demand D = 50*26 = 1300 Units (There 52 weeks in an year,the given value for 2 week)
The cost of Order Co = $50
The Cost holding Ch = $15
The Economic Order Qunatity = Squareroot (2*D*Co/Ch) = Squareroot (2*1300*50/15) = Square root (8666.66)=93.09 units
Number of orders in an year = 1300/93.09 = 13.96 = 14 orders
It is given that once an order is place the mug will arrive in two weeks, means you have to place an order when you have a stock of only for 2 weeks.
The stock required for weeks =(1300/52)*2 =50 (In this problem, it is directly given)
It's called SAFETY STOCK
The 90% service level = Safety stock +Z*Standard Deviation (The value of Z under standard Normal distribution with probability =0.9 (90%) is 1.645)
So, The 90% service level = 50+1.645*10 = 66.45,
In order to maintain 90 % service level, the firm must place an order when the stock reaches 66.45 =67 units
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