**
**Graphical
Solution

If we minimize the sum of the ordering
and carrying costs, we are also minimizing the total costs. To help visualize this we can graph the ordering cost and the
holding cost as shown in the chart above.

This chart shows
costs on the vertical axis or Y axis and the order quantity on the horizontal or X axis. The straight line which commences
at the origin is the carrying cost curve, the total cost of carrying units of inventory. As expected, as we order more on
the X axis, the carrying cost line increases in a proportionate manner. The downward sloping curve which commences high on
the Y axis and decreases as it approaches the X axis and moves to the right is the ordering cost curve. This curve represents
the total ordering cost depending on the size of the order quantity. Obviously the ordering cost will decrease as the order
quantity is increased thereby causing there to be fewer orders which need to be made in any particular period of time.

The point at which these two curves intersect is the same point which is the minimum of the curve which represents the total
cost for the inventory system. Thus the sum of the carrying cost curve and the ordering cost curve is represented by the total
cost curve and the minimum point of the total cost curve corresponds to the same point where the carrying cost curve and the
ordering cost curve intersect.

How to Calculate

*Basic EOQ:*

The objective is to determine the quantity
to order which minimizes the total annual inventory management cost.

Thus: Minimize! Total cost per period = inventory
holding costs per period + order costs per period

where Order Cost = The Number of Orders Placed
in the period x Order Costs

and Carrying Cost = Average Inventory Level
x the Carrying Costs of 1 unit of Stock for one period

with:

·
Q = order quantity

·
A = demand per time period (e.g. Annual Demand)

·
S = Carrying / Holding Cost of 1 unit of Stock for one period

·
P = Order Cost

and the derivation set to zero we get the following
formula:

So we can see
that the two cost elements at the economic order quantity are equal, one to the other; (compare with the graphical solution!)

If
we now isolate the Q, we get the following Basic EOQ-Formula:

EOQ = Square root of 2AxP over S

*Production EOQ:*

Instead of instantaneous replenishment, we
include the finite Production Rate R which leads to the following formula: (You can see, that production rate must be greater
than demand rate, in order to fulfill the demand!)

EOQ = sqrt ( 2 * A * P / (S*(1-A/R))

#### *Backlogging EOQ:*

By including the Backlogging Cost B, which
is the cost of backlogging one unit per period, we get the following formula:

EOQ = sqrt (2 * A * P * (S+B) / S * B)

# Economic Order Quantity

Economic Order Quantity (EOQ), is an
inventory model that attempts to minimize total inventory cost by answering the following two questions.