The economic order quantity seeks to find the order amount that minimizes the total cost of the company's inventory
One of the tools used to determine the optimal order amount for an inventory item is the Economic Order Quantity (CEP) model. It takes into account the different financial and operating costs and determines the order amount that minimizes the inventory costs of the company.
The economic order quantity model is based on three fundamental assumptions, the first is that the company knows what is the annual use of the items that are in inventory, second that the frequency with which the company uses the inventory does not it varies over time and finally that orders that are placed to replace inventory stocks are received at the exact moment that inventories are depleted.
Basic costs
Among the costs that must be taken into account for the implementation of this model are:
- Order costs: These include the fixed office costs to place and receive an order, that is, the cost of preparing a purchase order, processing and verification against delivery. These are expressed in terms of expenses or costs per order. Inventory maintenance costs: These are the unit variable costs of keeping an item in inventory for a specified period. Among the most common are storage costs, insurance costs, spoilage and obsolescence costs, and opportunity cost. These are expressed in terms of costs per unit per period. Total costs: It is determined by the sum of the order and the inventory maintenance costs. Your goal is to determine the order amount that will minimize them.
CEP. This model can be used to control the items in stock in the company's inventories.
Calculation and application methods
The economic order quantity can be calculated by two main methods, one of the graphic type and the other of the mathematical type, below are its fundamentals.
Graphical method
The economic order quantity can be found graphically by plotting order amounts on the x-axis and costs on the y-axis.
Thus the following aspects are appreciated:
- The Order Cost function varies inversely with the order amount, this is explained by the fact that as the annual utilization is fixed, if larger quantities are ordered, there are fewer orders and consequently fewer costs are incurred. Inventory holding costs are directly related to order amounts. The Total Cost function is shaped like a "U", which means that there is a minimum function value. The Total Cost line represents the sum of the costs of order and inventory holding costs for each order amount. The total cost function is very low slope, indicating that the total cost is relatively indifferent to small deviations that deviate from the CEP.
Mathematical method
As previously expressed, the economic order quantity is one that minimizes the total cost function, mathematically this total minimum cost is presented when the order cost and the maintenance cost are equal. The formula to calculate the CEP is:
Where:
R = Number of units required per period.
S = Order cost.
C = Inventory maintenance cost per period unit.
The economic order amount helps financial management by its nature against the decisions made by the financial manager.
With the following example you can see the bases of its implementation.
| Order quantity | Order number | Cost per order | Annual order cost | Average inventory | Inventory maintenance cost per unit per year | Annual maintenance cost | Total cost |
| (units) | (2. 3) | (1) ÷ 2 | (5) * (6) | (4) + (7) | |||
| (one) | (two) | (3) | (4) | (5) | (6) | (7) | (8) |
| 1600 | one | $ 50 | $ 50 | 800 | $ 1 | $ 800 | $ 850 |
| 800 | two | $ 50 | $ 100 | 400 | $ 1 | $ 400 | $ 500 |
| 400 | 4 | $ 50 | $ 200 | 200 | $ 1 | $ 200 | $ 400 |
| 200 | 8 | $ 50 | $ 400 | 100 | $ 1 | $ 100 | $ 500 |
| 100 | 16 | $ 50 | $ 800 | fifty | $ 1 | $ 50 | $ 850 |
Applying the formula of the economic order quantity, we have:
CEP = 400 Units
As shown in the table, the minimum total cost is presented in an order for a quantity of 400 units, consequently this is the economic order quantity.
Defects of the CEP model
The economic order quantity model has certain defects that are directly attributable to the assumptions on which it is based, among the most notable are:
- The assumption of a constant rate of utilization and instant stock renewal is rather dubious. Most companies maintain buffer stocks as a safeguard against unexpected increases in demand or slow deliveries. It is very difficult to know in advance the annual demand for items.
Although these structural defects are present, the model provides a better basis for the decision maker within the company. Although normally the financial manager is not directly related to the use of this methodology, he must know its foundations and use, since it must be presented in the information regarding financial costs.
In the following series of videos, Professor Ignacio Mira Solves, from the Miguel Hernández University of Elche, explains the model of the economic order quantity, starting with the basic model and going through the gradual variations and discounts. An excellent complement to understand and apply this model. (4 videos - 1 hour and 57 minutes)
