Thomas Kratzer is the purchasing manager for the headquarters of a large insuran
ID: 2722013 • Letter: T
Question
Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas's fastest-moving inventory item has a demand of 6,050 units per year. The cost of each unit is $101, and the inventory carrying cost is $9 per unit per year. The average ordering cost is $29 per order. It takes about 5 days for an order to arrive, and the demand for 1 week is 121 units. (This is a corporate operation, and the are 250 working days per year.) A) What is the EOQ? B) What is the average inventory if the EOQ is used? C) What is the optimal number of orders per year? D) What is the optimal number of days in between any two orders? E) What is the annual cost of ordering and holding inventory? F) What is the total annual inventory cost, including cost of the 6,050 units?
Explanation / Answer
A) What is the EOQ?
EOQ = Underroot of ((2*Annual usage in units* order cost ) / Annual carrying cost per unit)
= Underroot of (( 2*6050 units *$29) / $9
= Underroot of (38,989)
= 197.46 units
B) What is the average inventory if the EOQ is used?
Average inventory = EOQ/2 = 197.46 units/ 2 = 98.73 units
C) What is the optimal number of orders per year?
= Annual Demand / EOQ
= 6050 unit / 197.46 units
= 30.64 optimal order per year
D) What is the optimal number of days in between any two orders?
= Number of working days per year / optimal order per year
= 250 days / 30.64 optimal order per year
= 8.16 days
E) What is the annual cost of ordering and holding inventory?
Annual cost of ordering =6050 unit / 197.46 units * $29 per order
= 30.64 optimal order per year *$29 per order
= $888.56
Annual cost of holding = 197.46 units /2 * $9 per unit per year = $888.56
Total annual cost of ordering and holding inventory = $888.56+$888.56 = $1,777.12
F) What is the total annual inventory cost, including cost of the 6,050 units?
Total Inventory cost = Total purchase cost + Annual cost of holding +Annual cost of ordering
= (6050 units * $101) + $888.56 +$888.56
= $611,050+ $888.56 +$888.56
= $612,827.12
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