Economical order size ( Wilson's formula, EOQ model ) - a model that determines the optimal volume of the ordered goods, which minimizes the total variable costs associated with ordering and storing stocks.
Key Assumptions
- Demand for the product is known.
- The time for the implementation of the order (delivery) is known and constant.
- Receipt of goods occurs instantly.
- The model does not include wholesale discounts.
- Deficit is not allowed.
Variables
- Q * - optimal order size
- C - costs of placing an order
- R - annual (annual) demand for a product
- P - unit purchase costs
- F is the ratio of the costs of storage stock; the proportion of the cost of buying a product that is used as storage cost (usually 10-15%, although under certain circumstances it can be set at a level from 0 to 1)
- H - storage costs per unit of product per year (H = PF)
Formula
The figure shows the relationship between the cost curves of placing an order, stock holding, the curve of total costs and the optimal order size.
The optimal order size formula for a single product can be represented as the minimum point of the following cost function:
Total costs = purchase costs + order placement costs + storage costs,
which corresponds to:
Differentiating both sides of the equation and equating the expression to zero, we obtain:
As a result, we get:
Decide on Q:
The sign (*) indicates the optimal order size.
Extensions
Some extensions can be applied to the optimal batch size model to allow for the costs of order backlogs and multi-inventory stocks. It should be noted that Wilson's formula was originally developed for large industrial enterprises. And this means that it cannot be used for its intended purpose in modern trading companies. Trying to use this formula should be on the most significant in turnover and stable products. Weighted goods are group A ( ABC analysis ), stable goods are group X ( XYZ analysis ).
See also
- Inventory Management
- ABC analysis
- XYZ analysis