Economic order quantity formula

General
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economic order quantity formula

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Economic Order Quantity Formula

Answer: The Economic Order Quantity (EOQ) formula is a fundamental principle in inventory management that helps businesses determine the optimal order quantity to minimize the total costs associated with ordering and holding inventory. This formula is crucial for efficient inventory control and cost management.

The EOQ formula is given by:

EOQ = \sqrt{\frac{2DS}{H}}

where:

  • ( D ) is the annual demand for the product (units per year).
  • ( S ) is the ordering cost per order (fixed cost per order).
  • ( H ) is the holding cost per unit per year (carrying cost).

Detailed Explanation:

  1. Annual Demand (D):

    • This represents the total number of units required over a year. It is a key input as it determines how much inventory needs to be ordered to meet customer demand.

  2. Ordering Cost (S):

    • This is the cost incurred every time an order is placed, regardless of the order size. It includes costs such as shipping, handling, and order processing. It is a fixed cost per order.

  3. Holding Cost (H):

    • This is the cost to hold one unit of inventory for a year. It includes storage costs, insurance, and opportunity costs of capital tied up in inventory. It is a variable cost per unit per year.

Derivation of EOQ:

The EOQ formula is derived from the total cost function, which is the sum of the ordering cost and the holding cost. The goal is to minimize the total cost.

  • Total Ordering Cost (TOC):

    TOC = \frac{D}{Q} \times S

    where ( Q ) is the order quantity.

  • Total Holding Cost (THC):

    THC = \frac{Q}{2} \times H

  • Total Cost (TC):

    TC = TOC + THC = \frac{D}{Q} \times S + \frac{Q}{2} \times H

To find the EOQ, we take the derivative of the total cost function with respect to ( Q ) and set it to zero to find the minimum point.

\frac{d(TC)}{dQ} = -\frac{DS}{Q^2} + \frac{H}{2} = 0

Solving for ( Q ):

\frac{H}{2} = \frac{DS}{Q^2}
Q^2 = \frac{2DS}{H}
Q = \sqrt{\frac{2DS}{H}}

Thus, the EOQ formula is derived.

Practical Application:

Using the EOQ model, businesses can determine the optimal order quantity that minimizes their total inventory costs. For example, if a company has an annual demand (( D )) of 10,000 units, an ordering cost (( S )) of $50 per order, and a holding cost (( H )) of $2 per unit per year, the EOQ can be calculated as follows:

EOQ = \sqrt{\frac{2 \times 10000 \times 50}{2}} = \sqrt{500000} = 707 \text{ units}

Therefore, the company should order 707 units each time to minimize the total inventory costs.

Conclusion:

The Economic Order Quantity formula is a vital tool for inventory management, helping businesses to balance ordering and holding costs effectively. By applying this formula, companies can achieve cost savings and improve their overall inventory efficiency.