# Lead Time

## Dealing with the lead time demand

It’s monday morning and you have just placed an order of 300 boxes of your top selling product. Delivery is expected for tomorrow: today you are left with your current inventory to satisfy demand: no one can help you if demand is more than those 25 boxes you have available. Until tomorrow no new box will be added to your inventory. This period of time, in which you are left alone with your customers’ demand is the **lead time**.

Maybe you are relaxed: your demand forecasting tool gives 25 as the expected demand, why should you worry? I would not stay so calm if I were in your position…

Let me keep things simple enough: are you really sure that the demand will be exactly 25? Oh yes, your demand forecasting tool is the best available, so why shouldn’t you trust it? Well, of course you should trust your tool, as it was designed to extract all the available information just to assist you in rationally planning.

However, numbers should be read an interpreted. No software is magic and no tool will give you the possibility of knowing the future: you surely knew this, but sometimes you forgot…

Maybe that behind that 25 forecast, your demand forecasting tool estimates that it will be equally likely that demand today will be 24, 25, or 26. You see the point? If this will be the case (but things might get even worse for unpredictable reasons) you will have a 33% chance of an unsatisfied customer. Is this a risk you are ready to take? Unfortunately, if not, it is too late to remedy: you should have planned your order before!

Let me expand this case: maybe your forecast of 25 comes from the fact that you expect 23,24,25,26,27 as possible and equally likely demand: each one is expected in 20% cases (oh yes, I know: this is not the usual gaussian or normal distribution you find in textbooks: I could work out an example with gaussians, but your sales will **never** be gaussian, recall! As a minimum, they are integer and non negative, while gaussians may be fractional as well as negative).

Sorry, back to the example: the chances you will face a stockout is an estimated 40%. With the same 25 forecast! I expect one unsatisfied customer in 20% cases, 2 in another 20%. This makes an expected unsatisfied demand of 0.6: there will never be a 0.6 demand: this is to say that your risk of stockout is positive and you expect some customer to be affected by this.

If the predicted demand had been 0, 1, …, 25, …., 49, 50 equally likely (this means you are almost totally unsure, maybe this is a new product with no historical data to help your forecasting), than the chances of stockout will be pretty close to 50%. And the expected unsatisfied demand will be 19. Sure that it was a good idea to use a forecast as the true demand?

Who was responsible of this disaster? Easy question: variability!

You did not take into account the variability around your forecast and your risk of stockout and of dissatisfied customers is really very high! This means that you are at risk of losing a lot of money! I will give you some ideas on how to protect against uncertainty in another page.

But you can see, things are going bad. And it is only Monday!

### Planning In Advance

Maybe your lead time is longer. Say, 2 days. Maybe, with a predicted demand of 25 per day, you thaught you had chosen the best option by keeping an inventory of 50.

We have already seen this: variability is there to generate headaches both on Monday as well as on Tuesday. What can we expect in the 23,24,…,27 case? They call this elementary probability, but it might not be so trivial…

You might think that, given a cumulated demand in two days between 0 and 100 your stockout chances remain the same. Or, maybe, you think that having 50 in the inventory for two days is like having 25 per day, so the chances of stockout are almost 40%+40%, a pretty sure disaster! Lucky: this one is wrong! It is true that the chances of stockout remain 40%.

But how much stockout do you expect? It was 0.6 in one day, shall we expect 1.2 in two days? Lucky again, it is “just” 0.8. I am not going to show the calculus. But the rationale is that it is unlikely that you will have demand above the average both on Monday and also on Tuesday. So, the lesson is: **plan in advance** (see the reorder point discussion), don’t base your decision just on forecast but take variability into account. And when your lead time increases, do not exaggerate…