A business that orders or produces stock for sale has to tread a fine line between holding too much inventory with its associated storage and insurance costs, or running out of stock and disappointing its customers. The objective of inventory management is to minimize total inventory costs and provide answers to the questions, "How much should we produce?" and "When do we need it?" The classic method for calculating this is the economic production quantity, or EPQ, model.

## Calculate EPQ

Write down the following costs for your business:

Annual demand for your product (D): e.g., 10,000 Setup cost of each production run (s): e.g., $100 Daily demand rate for the product (d); total annual demand divided by the number of days when production takes place: e.g., 10,000 / 167 or ~60 Daily production rate on actual production days (p): e.g., 80 Holding cost per unit of production per year (h): e.g., $0.50

The formula for EPQ or Q is Sqrt (2Ds/[h(1-d/p)]). In other words, calculate the EPQ by multiplying twice the annual demand by the setup cost per unit; dividing the product by the holding cost per unit multiplied by the inverse of daily demand divided by daily production; and taking the square root of the result.

Multiply D by s by 2 -- in this example, 10,000 * 100 * 2, which equals 2,000,000.

Calculate 1 minus d divided by p, or 1 - 60 / 80, which equals 1 - 0.75 or 0.25.

Multiply h by the previous answer. For example, 0.50 * 0.25 equals 0.125.

Divide the first answer by the last. In this example 2,000,000 / 0.125 equals 16,000,000.

Calculate the square root of the previous answer. The square root of 16,000,000 is 4,000 and this is the economic production quantity.

## Calculate Inventory Value

Write down the production cost per unit for your business (P) -- for example, $5.

Calculate total setup costs for the year. Setup costs are equal to (D / Q) * s, or (10000 / 4000) * 100, which equals $250.

Calculate total holding costs, which are equal to the average inventory multiplied by the holding cost per unit. The formula is Q / 2 * (1-d/p) * h. For example 4000 / 2 * (1 - 60 / 80) * 0.50, or 2000 * 0.25 * 0.50 equals $250.

Calculate the total production cost, which is D multiplied by P, or 10,000 * $5, which equals $50,000.

Total all costs to arrive at a total inventory cost of $50,000 plus $250 plus $250, or $50,500.

#### Tips

Note that each production cycle will last for 4000 / 80 (Q/p) or 50 days.

The EPQ model assumes that you are making a single product with a constant demand rate and fixed setup and holding costs.

#### References

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