Stock Ordering Maths

OK, that’s a bit of a lie - it’s not really “simple” but it isn’t that “hard”. Leave your fear of stats at the door and step in - maths lurks here!

How do most business owners order stock?

Well, honestly, they probably just eyeball it. A lot of business owners have been “in the game” so long they can probably just guess at how much to buy.

I ran a company that supplied restaurants and hotels for a good while and can tell you that precisely 0% of our customers were doing anything other than calling us from inside their walk-in cold room with a list scratched on the back of a chopping board directly from memory.

One Step Up

Beyond just eyeballing, I’d guess the next most common method would be basing ordering off averages. Averages are a relatively simple metric - well understood by most and on the surface, a good indicator of what to order for the forthcoming weeks and months. Let’s take an example:

Acme Widgets have sold 10 widgets per week for the last 3 months and now needs to order stock for the next 3 months. Simple right? Start by working out the average monthly sales, which is just 10 x 4 = 40, then multiply that by the 3 months to get an order of 120 units.

The Hidden Problem with Averages

Let’s take a different example but with a common theme: a monthly average of 40.

This time though, instead of a constant 10 sales per week, the pattern looks like this:

• Week 1: 10

• Week 2: 29

• Week 3: 1

• Week 4: 5

• Week 5: 14

• Week 6: 12

• Week 7: 3

• Week 8: 6

• Week 9: 7

• Week 10: 11

• Week 11: 2

• Week 12: 20

That’s radically different right? Sales are not constant at all, they are pretty much all over the place. Honestly, though, this is probably a much more realistic scenario for most businesses.

Statisticians refer to this as variance - how much the individual numbers that go into an average vary around that average. You might remember studying standard deviation at school and variance is exactly what standard deviation quantifies. The higher the variance/standard deviation - the more “all over the place” the numbers that make up the average. The lower the variance/standard deviation - the more tightly packed together they are.

But what does this mean for stock ordering though? In the end we might still be tempted to add all those numbers up (120) and divide by the number of weeks (12) to get a weekly and monthly average (10, and 40 respectively) - which leaves us right back at square one.

Every Week Is Christmas

Look back at the numbers. What was the highest weekly number of sales? 29, right? So if we want to be sure we won’t run out of stock, we could assume we’ll sell 29 units each week for 3 months. That would mean an order of 348.

Compare that number to the 120 we decided we need to order earlier, based on the average. Ordering 348 gives would give us the advantage that we are MUCH less likely to run out of stock, but it comes with some BIG disadvantages from a business perspective - a big capital outlay, a risk of having a lot of stock lying around for a long time, and in the case of products with a shelf-life, the risk of expiry and having to throw some stock away.

So clearly, assuming every week is Christmas isn’t the best tactic. Is there a better one?

Every Week Is Not Christmas

Let’s summarise where we are.

We understand that ordering according to just the average is a poor strategy that doesn’t account for variance. We’ve also seen that ordering to the “best sales scenario” is also a poor tactic which could leave us hugely overstocked and potentially out of pocket.

What we want is to be “reasonably sure” we won’t run out of stock. In order to achieve that we’ll need to order more than the average, but less than the best case case scenario.

Luckily we don’t have to pick a number out of thin air. There’s a mathematical middle ground that can really help us and it’s based on a concept called confidence intervals - it lets us specify some threshold, like 99% or 95%, of “confidence” that we’ll be able to cover sales. It’s just a statistical measurement based on existing data, so it’s no guarantee - but it’s much better than an average.

Going back to the above numbers and running the calculations: for a 95% confidence interval, the “upper boundary” is approximately 14 and the lower boundary is approximately 6. This should be interpreted as “we are 95% confident that sales per week, during the period we are buying for, and based on past data, will be between 6 and 14.

That’s pretty cool right? 95% is plenty of confidence.

Scientists tends to use this statistical threshold when looking for “statistical significance” in experiments, so it’s certainly good enough for stock ordering!

So if we can be 95% confident that sales won’t exceed 14 per week, we can multiply that up by the 12 weeks to get an order of 168. Let’s now compare the different ordering strategies we’ve looked at:

• Basic average: 120

• Every week is Christmas: 348

• 95% confidence interval, upper bound: 168

Using the 95% CI technique, we’d be ordering “a bit more” than what the average tells us to, but in exchange we are getting MUCH more certainty we’ll be able to cover sales.

In Practice

Obviously you’re not going to be calculating confidence intervals on the back of an envelope. You could use a spreadsheet or perhaps a small script your developer could make for you. If you use Pakk, our integrated demand planner is based on this fundamental technique (see the detailed explanation of how the calculations work).