Wilson's formula: the magic formula for optimizing your inventory management?

By Jennifer Montérémal & Coralie Petit

Published: November 17, 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 rescue your logistics function!

But is this method adapted to your company's reality?

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 aim 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, and further developed by R.H. Wilson in 1934, Wilson's model is also known by 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 given period.

What's at stake?

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

And with good reason, the logistics manager must often 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 inventory holding rates,
reduce ordering costs,
and, ultimately, ensure better overall inventory management.

When to use Wilson's formula?

Is the Wilson formula a magic formula?

Yes and no, because its use is conditional on a certain stability in the criteria required for its calculation: product demand, purchase price, costs linked to the quantity of merchandise in stock, etc.., which is far from being a general rule in the tumultuous world of inventory management.

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

How do you calculate the economic order quantity?

Step 1: Determine the individual 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 product demand, 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 must include :

order placement costs, including accounting and administrative processes, invoice processing, etc,
transportation costs,
merchandise reception costs.

💡 There isn't really a formula for the cost of placing an order. As you can see, 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 inventory:

labor,
building rental,
warehouse upkeep and maintenance,
heating,
electricity,
insurance costs,
inventory discrepancies,
cash costs, etc.

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

Step 2: do the math

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

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

The result is Q, the famous economic order quantity.

Step 3: other calculations

Once you've calculated the economic quantity, you'll no doubt want to know the number of annual orders to be made (N). It's easy: just 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 applying Wilson's formula

Theory is all very well, but practice speaks louder. 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 an order is 40 euros.

The cost of carrying stock is 3 euros.

Here are the calculations to be performed:

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 be made.

👉 For frequency :

365 / 14 = 26,07

Finally, our batch of 365 pairs of ballerinas 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 1000 pairs of ballet flats 1 time than 1000 pairs of ballet flats 1 time.
If you order too much, you'll reduce your ordering costs... but your inventory carrying costs will increase.

The Wilson formula guarantees improved inventory management, with no overstocking or understocking. The result: savings for your company.

In addition, 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 disadvantages

If this method seems simple, it's because it's conditioned by a certain regularity in all the parameters to be considered for 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 reaches its limits for goods subject to strong seasonality.
The purchase price varies little or not at all. If you're 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 labor costs.

Finally, Wilson's method doesn't take into account :

increasingly volatile markets, which require safety stocks,
supplier uncertainties, even though risks in terms of supply lead times remain very real.

Wilson's formula isn't a magic formula that works every time. In fact, if your company doesn't meet the above-mentioned conditions of consistency, inventory management software will prove to be a much better ally.

However, the Wilson method is still a good tool, as it helps to guide the stock manager, revealing a course to follow. It's then up to you to take the necessary distance from the various data, to stay as close as possible to the reality of your business.