Central University uses $123,000 of a particular toner cartridge for laser printers in the student computer labs each year. The purchasing director of the university estimates the ordering cost at $45 and thinks that the university can hold this type of inventory at an annual storage cost of 22% of the purchase price. How many months' supply should the purchasing director order at one time to minimize the total annual cost of purchasing and carrying?

Question

Business

Nikolai Blackburn

7 September, 11:30

Central University uses $123,000 of a particular toner cartridge for laser printers in the student computer labs each year. The purchasing director of the university estimates the ordering cost at $45 and thinks that the university can hold this type of inventory at an annual storage cost of 22% of the purchase price. How many months' supply should the purchasing director order at one time to minimize the total annual cost of purchasing and carrying?

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Chauncey · Answer 1

We have to calculate the Economic Order Quantity (EOQ). In this case, the "units" are dollars, and the "price" of each is 1.

One month's usage is 123000/12 = $10,250.

EOQ = 7094.

Month's usage = 7094/10250 = 0.69

Data

Demand rate, D 123000

Setup cost, S 45

Holding cost, H 22.00%

Unit Price, P 1

Results

Optimal Order Quantity, Q * 7093.530984

Maximum Inventory 7093.530984

Average Inventory 3546.765492

Number of Setups 17.3397424

Holding cost $780.29

Setup cost $780.29

Unit costs $123,000.00