In mathematics, the law of large numbers is a fundamental principle of probability theory, which states that when a random experiment is repeated many times, the average of the results obtained converges toward the theoretical mean value (the mathematical expectation) of this experiment.
Let’s keep it simple. If you roll a die once, you’ll get 1, 2, 3, 4, 5, or 6. It’s all highly variable. If you roll the same die 100 times and average the values obtained, you’ll find about 3.5. Try it, you’ll see. Not convinced? Roll the die 10,000 times and see. You can also test with the random function in Excel, which takes less time.
In the supply chain, this law of large numbers is very important. It says that the more you aggregate a signal, the less variability, and therefore uncertainty, there will be. This plays a critical role in supply chain variability, allowing businesses to predict demand more accurately.
This has many advantages. For example, if you make a forecast at the family level, it will be more reliable than at the detailed level. Aggregating demand reduces errors, which improves supply chain forecasting. Let’s take an example: your forecast for total T-shirt sales in Europe for the month of June is much more reliable than your forecast for sales of your size S blue T-shirt in the Milan store next Wednesday.
If you can stock a semi-finished product that can be used to make multiple variants of finished products, you can more easily respond to random demand for multiple variants, with delayed product differentiation. The demand variability you face for central hub stock is lower than that of your secondary distribution centers and lower than that of your stores. By focusing on aggregate demand forecasting, you reduce variability.
If you keep products in a central hub, you can deploy them in stores only as late as possible, depending on actual consumption. This will make it easier to ensure that the right stock is available centrally to meet global demand. You can then define a simple, low-risk pull logic to deploy stock in the right store—or even on a click-and-collect basis.
Curiously, many software solutions work against this. Conventional DRP logic, for example, will encourage you to develop detailed forecast sets—by country, by store, by customer—and then feed this requirement back upstream through a logic similar to MRP requirement calculation. In other words, we forecast at the most detailed level—so we make the most erroneous forecast possible—and then we add all these errors upstream, crossing our fingers that they compensate for each other. This approach neglects the value of demand planning strategies focused on aggregate levels.
Machine learning enthusiasts are also pushing in this direction: the more detailed you are, the more you’ll be able to associate causal factors—local promotion, this weekend’s attendance, local weather, etc.—so the AI model can draw conclusions. This method, however, doesn’t account for the law of large numbers and demand variability reduction.
Forecasting for the Milan store to sell a specific size or color on a specific day doesn’t make sense. In reality, the Milan store may sell about 3 blue T-shirts in size S this quarter. Or 2. Or 1. Or zero. Or 6.
Worse still, solutions often call for stock to be deployed rapidly at the most detailed point, to be “as close to the customer as possible.” It’s a recipe for too much stock in the wrong place. Instead, inventory management optimization should follow the principles of the law of large numbers, centralizing stocks where demand is most predictable.
The law of large numbers is simple and common sense and should guide you in designing your supply chain and planning practices:
- If you can position decoupling points upstream, on components or semi-finished products, your response to random demand will be more agile and reliable than on finished products. This is the essence of supply chain variability management.
- Only deploy your stocks in your distribution network as late as possible, with short lead times and pull flows based on recent consumption. This ensures inventory management optimization.
- Focus your forecasts on aggregate levels and let the detailed level react to actual consumption. This approach will improve forecast accuracy in the supply chain. Make sure your local sales teams and demand planners don’t waste time forecasting unpredictable things.
By incorporating decoupling points, demand planning strategies, and focusing on aggregate demand forecasting, you can significantly enhance supply chain forecasting and performance.
