Economic Order Quantity Equation: Example and How to Calculate



The Economic Order Quantity is used to minimize the ordering cost and total inventory costs. Organizations use this method to determine an order quantity to minimize ordering costs and inventory holding costs.

The EOQ determines the amount of units to be added to the inventory so that the inventory costs such as holding, shortage and order costs can be minimized. Usually companies use the EOQ on a regular basis as part of their inventory system. This way each time a fixed quantity is ordered when the inventory reaches the reorder point. This way the inventory is replenished with the right amount at the right amount, without any shortage to the inventory. This is most ideal for small businesses to determine the inventory to be kept, how much to order every time and the frequency of reordering in order to minimize the costs.


Definition
The Economic Order Quantity more commonly known as EOQ is used to determine the most favorable quantity to produce or purchase in order to minimize inventory holding costs and production/purchase costs.

Some Assumptions for EOQ
These assumptions are necessary in order for the Economic Order Quantity to work to its full potential.
·         The Ordering Cost needs to be constant
·         The annual demand rate should be known and spread throughout the 12 months evenly
·         Fixed Lead time
·         Constant Purchase Price, that means no discounts
·         The EOQ should be applied to one product
·         Restocking is done without delay and the order delivery is  of the complete batch

These assumptions are necessary for companies to keep in mind when applying the EOQ model so that the shortcomings of applying this model are highlighted.

Variables of the Equation
C= per unit cost
Q= order quantity
Q*= Economic Order Quantity
D= Annual Quantity Demanded
K= Fixed Per Order Cost
h= Annual per unit carrying cost

Example
Let’s look into an example to understand how the EOQ actually works.
·         Annual Quantity Requirement (D) = 10000 units
·         Per Order Cost (K)= $2
·         Per Unit Cost (c)= $8
·         Percentage of Carrying Cost= 0.02
·         Annual Per Unit carrying cost= $0.16


EOQ=   \sqrt{\frac{2D*K}{h}}   = \sqrt{\frac{2*10000*2}{8*0.02}}  = 500 units

Annual number of orders   = {\frac{10000}{500}} = 20
Total cost = c * D + K(D/EOQ) + h(EOQ/2)

Total cost = 8 * 10000 + 2(10000/500) = 0.16(500/2) = $80080

If the total cost is checked on the basis of another quantity than 500, then the cost would result as higher. Let us have a look at the cost of the quantity order is increased to 600 instead of 500.

Total cost = 8 * 10000 + 2(10000/600) + 0.16/2) = $80081
Likewise, if the order quantity is reduced from 500 to 300, then the total cost is as follows

Total cost= 8 * 10000 +2(10000/300) + 0.16(300/2) = $80091

With the help of this example we can see that EOQ is in the best interest of the business to be applied in order to minimize the costs.

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Objectives of economic order quantity model (EOQ Model)



The main objective economic order quantity model (EOQ Model) is to minimize inventory carrying cost while at the same time limiting the probability of stocking out of the inventory item. In recent years, retail stores have increasingly been using their computers to perform this reordering activity. Their cash registers are connected tot heir computers, and each sale automatically adjusts the store’s inventory record. When the inventory of an item hits the critical point, the computer tells management to reorder.

The objective of the economic order quantity (EOQ) model is to minimize the total costs associated with the ordering and carrying costs as the mount ordered gets larger, average inventory increases and so do carrying costs.

 Example

For example, if annual demand for an inventory item is 27,000 units, and a firm orders 500 each time, the firm will place 52 [27,000/500] orders per year. This order frequency gives the organizations an average inventory of 250 [ 500/ 2] units. If the order quantity is increased to 2,200 units, fewer orders (13) [27,000 / 2,000] will be placed. However, average inventory on hand will increased to 1,000 [2,000 / 2] units.

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