**Economic Order Quantity (EOQ)
**

Economic Order Quantity is the level of inventory that minimizes the total inventory holding costs and ordering costs. It is one of the oldest classical production scheduling models. The framework used to determine this order quantity is also known as Wilson EOQ Model or Wilson Formula.

The model was developed by F. W. Harris in 1913, but R. H. Wilson, a consultant who applied it extensively, is given credit for his early in-depth analysis it.

Assume that the demand for a product is constant over the year and that each new order is delivered in full when the inventory reaches zero. There is a fixed cost charged for each order placed, regardless of the number of units ordered. There is also a holding or storage cost for each unit held in storage (sometimes expressed as a percentage of the purchase cost of the item).

We want to determine the optimal number of units of the product to order so that we minimize the total cost associated with the purchase, delivery and storage of the product.

The required parameters to the solution are the total demand for the year, the purchase cost for each item, the fixed cost to place the order and the storage cost for each item per year. Note that the number of times an order is placed will also affect the total cost, however, this number can be determined from the other parameters.

**Underlying assumptions**

The ordering cost is constant.

The rate of demand is constant

The lead time is fixed

The purchase price of the item is constant i.e no discount is available

The replenishment is made instantaneously, the whole batch is delivered at once.

EOQ is the quantity to order, so that ordering cost + carrying cost finds its minimum. (A common misunderstanding is that the formula tries to find when these are equal.)

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