Wilson's formula: the magic formula for optimising your stock management?

By Jennifer Montérémal & Coralie Petit

Published: 17 November 2024

When you're in charge of a warehouse, knowing exactly how much to buy of a given product can quickly become a real headache. In other words, how do you avoid overstocking or understocking, both of which are costly for the company?

Fortunately, Wilson's formula is there to come to the rescue of your logistics function!

But is this method adapted to the reality of your business?

To find out, read this article to find out when to use it and how to apply it, with concrete examples of calculations.

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What exactly is the Wilson formula?

Definition of the Wilson formula

The Wilson formula is a mathematical formula whose objective is to determine the optimum quantity of products per order (or economic batch), and by extension the frequency of orders.

Created by the American engineer Ford Whitman Harris in 1913, then developed by R.H. Wilson in 1934, we also find the Wilson model under the following names:

EOP, or Economic Order Quantity,
Economic Order Quantity,
Economic Lot Formula.

What is Wilson's formula?

More concretely, the formula is as follows.

To better understand each component :

Q is the optimum order quantity,
D is the annual demand for the raw material ordered,
K is the cost associated with each order placed,
G is the cost of storing a unit of product in the warehouse over a specific period.

What is at stake?

The ultimate aim of the Wilson method is to optimise the company's supply costs.

And with good reason, the logistics manager often has to play a balancing act, in order to achieve the right balance in terms of the quantity of product to order (raw materials, goods for direct sale, etc.) so as to :

reduce costs and stock holding rates,
reduce ordering costs,
and ultimately ensure better overall inventory management.

When should the Wilson formula be used?

So the Wilson formula is a magic formula?

Yes and no, because its use depends on a certain stability in the criteria used to calculate it: product demand, purchase price, costs linked to the quantity of goods in stock, etc.., which is far from being a general rule in the tumultuous world of stock management.

To make sense of this, let's look at the calculation method itself.

How do you calculate the economic order quantity?

Step 1: Determine the various components

To proceed with the calculation, start by gathering the following components.

💡 Good to know: some components are evaluated over a fixed period. This is generally 12 months.

Product demand, or D

To determine the demand for the product, anticipate how many units you intend to sell, or use for your production, over the chosen period.

Order cost, or OC

How do you calculate the order cost?

It should include :

the costs of placing the order, including those relating to accounting and administrative processes, invoice processing, etc,
transport costs
the costs of receiving the goods.

💡 There isn't really a formula for the cost of placing an order. As you will have realised, it all depends on the specifics of each company.

However, some experts recommend defining the number of working hours allocated to each operation, then converting them into money by multiplying by an hourly rate.

Example:

Storage cost, or SC

The unit cost of storage is calculated over a given period.

It involves taking into account a large number of parameters, in order to evaluate the costs incurred by the company due to the presence of stocks:

labour
building rental
warehouse upkeep and maintenance,
heating
electricity
insurance costs,
inventory differences,
cash flow costs, etc.

☝️ There's no magic formula for storage costs either. It depends on too many parameters specific to each organisation.

Step 2: Make the calculations

It's time to get out your calculator (or a sheet of paper and a pencil if you're a maths whizz!) to apply the formula!

💡 As a reminder, the formula is as follows: Q=√((2D×CC)/CS)

The result is Q, the famous economic quantity of the order.

Stage 3: the other calculations you need to know

Once you've calculated the economic quantity, you'll no doubt want to know the number of annual orders to be placed (N). It's very easy to do: all you have to do is divide :

D (the demand for the product),
by Q (the economic quantity of the order).

What about order frequency?

Simply divide the number of days in the year (approximately 365) by the number of annual orders to be placed.

Example of the application of Wilson's formula

Theory is all very well, but practice is much more telling. Let's take an example to illustrate the application of Wilson's model.

Online shoe retailer Au Beau Soulier plans to sell 5,000 units of its signature pair of black ballerinas in size 38.

The cost of placing the order is €40.

The cost of holding stock is 3 euros.

Here are the calculations to be made:

2 X 5000 X 40 = 400,000
400,000 / 3 = 133,333.33, rounded to 133,333
√133 333 = 365.14, rounded to 365

The economic order quantity is therefore 365 units.

👉 For the number of annual orders :

5000 / 365 = 13,69

Rounded up, we get 14 annual orders to complete.

👉 For frequency :

365 / 14 = 26,07

Finally, our batch of 365 pairs of ballet flats will have to be ordered every 26 days over the course of the year.

Advantages and disadvantages of Wilson's method

The advantages?

As we've seen, choosing the right number of products to order is no easy task:

If you order too few, you increase the frequency and therefore the cost of your orders. To put it simply, it's always cheaper to order 1 pair of ballerinas 1000 times than 1 pair of ballerinas 1000 times.
If you order too much, you'll reduce the cost of ordering... but you'll also increase the cost of stockholding.

The Wilson formula guarantees improved stock management, with no overstocking or understocking. And that means savings for your business.

What's more, the method helps avoid stock-outs: you know exactly how many products you need to buy and how often.

Finally, one of the undeniable advantages of the Wilson formula is the simplicity with which it can be set up - a simplicity which, paradoxically, is also its main limitation.

... and the drawbacks

If this method seems simple, it's because it is conditioned by a certain regularity in all the parameters to be considered in its calculation.

In other words, its effectiveness depends on a number of conditions being met:

Demand for the product (frequency and quantity) is stable throughout the year. As a result, Wilson's formula quickly presents limits for goods subject to strong seasonality.
The purchase price varies little or not at all. If you are in a market where prices fluctuate, which is often the case for raw materials, Wilson won't be much help.
Storage costs remain stable. But unforeseen events often occur, such as labour costs.

Finally, Wilson's method does not take into account :

Increasingly volatile markets, which means that safety stocks need to be built in,
supplier uncertainties, even though the risks in terms of supply lead times remain very real.

So Wilson's formula is not a magic formula every time. What's more, if your company does not meet the conditions for consistency mentioned above, inventory management software will prove to be a much better ally.

However, the Wilson method is still a good tool, because it can guide the stock manager and show him or her the direction to follow. It is then up to you to take the necessary distance from the various data, to remain as close as possible to the reality of your business.