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 5,800 units per year. The cost of each unit is $103, and the inventory carrying cost is $9 per unit year. The average ordering cost is $31 per order. It takes about 5 days for an order to arrive, and the demand for 1 week is 116 units. (This is a corporate operation, and there are 250 working days per year).

A)What is the EOQ?   Units (round your response to two decimal places)

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 5,800 units?

Answer 1

A)

EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year) = sqrt((2*5800*31)/9) = 199.888858 = 199.89 (Rounded to 2 decimal places)

B) Average inventory if the EOQ is used = 199.888858/2 = 99.944429 = 99.94 (Rounded to 2 decimal places)

C) Optimal number of orders = Annual demand/EOQ = 5800/199.888858 = 29.01612455 = 29.02 (Rounded to 2 decimal places)

D)

optimal number of days in between any two orders = Number of working days in an year/Optimal number of orders = 250/29.01612455 = 8.615899052 = 8.62
(Rounded to 2 decimal places)

E)

annual cost of ordering and holding inventory = Optimal number of orders*ordering cost + Average inventory*holding cost per unit per year
=29.01612455*31+99.944429*9 = 1798.999722 = 1799 (Rounded to 2 decimal places)

F)

total annual inventory cost, including cost of the 5,800 units = 1798.999722+5800*103 =599198.9997 = 599198 (Rounded to 2 decimal places)