. A company has performed an inventory analysis and has found that on average it
ID: 2806102 • Letter: #
Question
. A company has performed an inventory analysis and has found that on average it holds 10 000 units of inventory, including safety stock of 2000 units. It has also calculated that total inventory costs (including variable carrying costs and fixed ordering costs) are 126 500 euros. Fixed cost per order is 450 euros and the company makes orders 20 times a year.
a) How many units of inventory does the company order in one shipment?
b) Prove that the company is not ordering an economic order quantity (EOQ) in one shipment by calculating the actual EOQ.
c) In addition, find how many orders the company should make if EOQ were used and what is the interval in days between the orders?
d) What would be the total inventory costs (including safety stock) if goods were ordered with EOQ?
Explanation / Answer
Part A)
Ordering quantity = Average Inventory x 2 – safety stock
= 10,000 x 2 – 2000
= 18,000
Part B)
Annual Demand = Ordering quantity x No. of orders + safety stock
= 18000x 20 +2000
= 362,000
Ordering cost per order (O) = $450
Holding cost per unit (H) = 126,500/10000
= $12.65
EOQ = (2 x A x O/H)^0.50
= (2 x 362,500 x 450 / 12.65)^0.50
= 5078 units
Part C)
No. of orders to make = Annual demand / EOQ
= 362,000 / 5078
= 71.29 orders
Interval between orders = operational Days in a years/ No. of orders
= 365 /71.29
= 5.12 days
Part D)
Total Inventory cost = EOQ/2 x H + No. of orders x O
= 5078/2 x 12.65 + 71.29 x 450
= 32118.35 + 32080.50
= $64,198.85
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