If you are running a business that involves ordering and holding inventory, you may be wondering how to optimize your order size and minimize your total inventory cost. One of the factors that you need to consider is the interest cost, which is a nonlinear cost related to order size.

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**What is Interest Cost?**

Interest cost is the opportunity cost of investing your money in inventory rather than in other alternatives, such as a bank account, a bond, or a stock. Interest cost is also known as carrying cost or holding cost, and it includes other expenses such as insurance, taxes, storage, and obsolescence.

Interest cost is nonlinear because it depends on the amount of inventory you hold and the length of time you hold it. The more inventory you have and the longer you keep it, the higher your interest cost will be. Conversely, the less inventory you have and the shorter you keep it, the lower your interest cost will be.

**How to Calculate Interest Cost?**

To calculate interest cost, you need to know three things: the average inventory level, the annual interest rate, and the unit cost of each item.

The average inventory level is the average amount of inventory you have on hand during a certain period of time. You can estimate it by adding the beginning and ending inventory levels and dividing by two.

The annual interest rate is the percentage of interest you pay or earn on your money per year. You can use the market interest rate or your own opportunity cost of capital.

The unit cost of each item is the amount of money you spend to acquire one unit of inventory. It includes the purchase price and any other costs related to ordering, such as transportation, inspection, and handling.

The formula for interest cost is:

Interest cost = Average inventory level x Annual interest rate x Unit cost

For example, suppose you have an average inventory level of 100 units, an annual interest rate of 10%, and a unit cost of $50. Your interest cost would be:

Interest cost = 100 x 0.1 x 50 Interest cost = $500

**How to Optimize Order Size?**

To optimize your order size, you need to balance your interest cost with your ordering cost. Ordering cost is the fixed cost of placing an order, such as administrative, clerical, and communication expenses. Ordering cost is linear because it does not depend on the amount of inventory you order.

The optimal order size is the one that minimizes your total inventory cost, which is the sum of your interest cost and your ordering cost. To find it, you can use a formula called the economic order quantity (EOQ), which is:

EOQ = √(2 x Annual demand x Ordering cost) / (Annual interest rate x Unit cost)

For example, suppose you have an annual demand of 1,000 units, an ordering cost of $100 per order, an annual interest rate of 10%, and a unit cost of $50. Your EOQ would be:

EOQ = √(2 x 1,000 x 100) / (0.1 x 50) EOQ = √(200,000 / 5) EOQ = √(40,000) EOQ = 200 units

This means that you should order 200 units at a time to minimize your total inventory cost.

**Conclusion**

Interest cost is a nonlinear cost related to order size that represents the opportunity cost of investing your money in inventory rather than in other alternatives. To optimize your order size, you need to balance your interest cost with your ordering cost using the EOQ formula.

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