The purchasing manager for Alpa Enterprises requested the following data from th
ID: 367736 • Letter: T
Question
The purchasing manager for Alpa Enterprises requested the following data from the accounting department: Annual demand = 15,500, cost of placing an order= £180; Annualinventoryholdingcosts=20 percent; Unit cost- £75+last digit of your student number d for dentaldng Please calculate the following: The total annual inventory costs. Assume Alpha's demand for an item during the lead time is normally distributed with a mean of 5,000 and a standard deviation of 50. What reorder point should be used in order to average no more than one stock out every 20 re-order cycles? If safety stock is 70, how often will a stock out occur duringa re-order cycle?Explanation / Answer
1.
Unit cost = 75 + 5 (assumed as last digit of the student number)
Unit cost = 80
EOQ = (2*Annual demand*ordering cost/holding cost)^.5
EOQ = (2*15500*180/(.2*80))^.5
EOQ = 590.55 units or 591 units
Annual inventory cost = (EOQ/2)*holding cost per unit per year
Annual inventory cost = (591/2)*(20%*80) = $4728
2.
Service level = 19/20 = 95%
Z at 95% = 1.65
Reorder point = demand* lead time + Z*S.D.*(Lead Time)^.5
Reorder point = 5000*1 + 1.65*50*1
Reorder point = 5082.5 or 5083 units
If safety stock = 70
Then,
70 = Z*SD*1
Z = 70/50 = 1.4
Service level (at Z = 1.4) = .9192 or 91.92%
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