00:00:07 Safety stock and its drawbacks.
00:00:39 Definition and concept of safety stock.
00:02:05 Origins of the safety stock concept and why it remains popular.
00:04:10 Problems with safety stock: ignoring seasonality and unrealistic normal distribution assumptions.
00:07:15 Situations where safety stock doesn’t work and the need for alternative approaches.
00:09:06 How safety stocks underestimate risk and lead to overstocking.
00:12:00 The paradox of safety stocks and their inefficiency in addressing uncertainties.
00:13:20 Actionable decisions and control in supply chain management.
00:15:00 Alternative approaches between safety stocks and probabilistic methods.
00:16:00 Refining parametric models in supply chain.
00:18:54 The problem of wastage in safety stock and its consequences.
00:20:37 The role of forecasts and their impact on safety stock.
00:22:29 Addressing mistakes in supply chain management for improvements.
00:23:01 Key message: Don’t trust outdated mathematical models in supply chain.


In this interview, Kieran Chandler and Lokad founder Joannes Vermorel discuss safety stock’s drawbacks in supply chain management. Safety stock, the additional inventory to buffer demand variability, can be overly conservative, resulting in overstock and waste. Its popularity is due to its simplicity and historical improvement over manual calculations, but it fails to account for complex supply chain uncertainties. The model’s reliance on a normal distribution for demand and lead times is unrealistic, and it doesn’t adjust for large deviations or surprising events. Instead, Vermorel suggests a probabilistic approach for better optimization and inventory management, while addressing consequences of uncertainty and improving processes after forecasting.

Extended Summary

In this interview, host Kieran Chandler and Lokad founder Joannes Vermorel discuss the concept of safety stock and its shortcomings in supply chain management. Safety stock refers to the additional inventory purchased to protect against variability in demand and lead times. Despite its simplicity, this method is often too conservative, leading to overstock and wasted inventory. The interview explores the origins of safety stock, its limitations, and alternative approaches for supply chain professionals.

Safety stock emerged from the idea that, given a demand forecast, a company should hold more inventory than the forecasted amount to reduce the risk of stockouts. This additional inventory, or “safety stock,” serves as a buffer for potential fluctuations in demand. Over time, the industry has converged on a specific method for calculating safety stock: assuming that future demand and lead times are normally (Gaussian) distributed and applying this model to determine the necessary buffer.

According to Vermorel, the popularity of safety stock can be attributed to its reassuring name and the fact that, historically, it represented an improvement over manual calculations. Early computers in the 1960s and 1970s struggled with more complex calculations, so safety stock calculations provided a good enough solution at the time. However, many practitioners continued to rely on safety stock even as computational capabilities advanced, leading to its widespread use today.

The fundamental issue with safety stock is the assumption that all uncertainty can be reduced to a normal distribution for both demand and lead times. This assumption is particularly problematic for lead times. By relying on safety stock calculations, companies tend to create a constant fraction of their demand as a buffer, ignoring factors such as seasonality. While demand forecasts often account for seasonal fluctuations, the uncertainty in these forecasts is not similarly adjusted.

In summary, the concept of safety stock, while simple and seemingly reassuring, is flawed due to its reliance on normal distribution assumptions for demand and lead times. This approach often leads to overstocking and wasted inventory, as it fails to account for the complex nature of supply chain uncertainty. As the discussion progresses, the interview aims to explore alternative methods for supply chain optimization that move beyond the limitations of traditional safety stock calculations.

The conversation begins with an analysis of the classical safety stock model, which Vermorel argues is a poor approximation for managing supply chain uncertainties.

Vermorel explains that the safety stock model’s assumption of a normal distribution for both demand and lead times is unrealistic. For example, lead times might be consistently short, except in cases of supplier stockouts, which could lead to much longer lead times. This results in a distribution that is not bell-shaped, but rather a spike around the nominal time and a long tail for rare events.

The safety stock model also fails to account for large deviations or surprising events that can have a significant impact on supply chains. These events, like the avian flu affecting chicken sales, are not considered in the normal distribution model. In practice, these large deviations happen frequently enough to cause problems.

One might assume that an underestimation of risk would lead to more stockouts, but in practice, supply chain practitioners adapt and inflate their safety stocks to compensate for the underestimated risk. They do this by introducing inflation factors, either explicitly or by setting higher service level targets. This leads to overstocking, which is counterintuitive for a model designed to ensure safety.

The issue with this approach is that the inflated safety stock is applied uniformly across all products, resulting in overstocks and inefficiencies. This is compounded by practitioners who micromanage their forecasts but then inflate their safety stocks, essentially negating the precision of their calculations.

Vermorel suggests that a probabilistic approach is better suited for managing supply chain uncertainties. This approach acknowledges that safety stocks are both unsafe and ineffective. In reality, there are no separate piles of working stock and safety stock in warehouses; there is only one pile of stock. The question becomes whether this stock is suitable for serving clients.

In order to communicate this message to customers who are adamant about having a safety stock buffer, Vermorel emphasizes that safety stocks are unsafe and ineffective. Instead, a probabilistic approach that accurately models the uncertainties in the supply chain can lead to better optimization and inventory management.

Vermorel explains that safety stocks can distract businesses from focusing on the decisions they can make, such as purchase orders and manufacturing orders. He argues that probabilistic approaches are more suitable for supply chain management, as they allow for better control over decisions that directly impact supply chains.

However, Chandler points out that probabilistic approaches are complex, as they require different demand curves for each item in a catalog. He asks if there is an intermediate solution for supply chain executives that is less complex than the Lokad approach but more advanced than safety stock calculations. Vermorel admits that while there is a paradox in modern statistical analysis, it is possible to use more complex parametric models. However, these models quickly become challenging to work with and understand, often leading to opaque mathematical notation. As a result, Vermorel suggests that it may be simpler to use machine learning techniques that can fit any distribution, even though they lack explicit formulas.

The conversation then turns to the issue of wasted money due to safety stocks. Vermorel believes that the focus on safety stocks and demand forecasting is misguided, as it does not address other sources of uncertainty, such as lead times. He also notes that the idea of a perfect forecast is a delusion, as forecasts will always be imperfect. Instead, supply chain practitioners should focus on the consequences of uncertainty and work to improve their processes after forecasting.

In many situations, it is hard to significantly improve on a well-tuned moving average for demand forecasting. Vermorel explains that blaming forecasts for discrepancies is often futile, as the real problems often lie in the steps that follow. He encourages supply chain practitioners to focus on improving these areas, as they often represent low-hanging fruit for substantial gains.

Full Transcript

Kieran Chandler: Today on Lokad TV, we’re going to explain why this method doesn’t work and also discuss what the alternatives are that are open to supply chain professionals. So Joannes, before we get into the problems with safety stock, perhaps we should start by explaining a little bit more about it. How would you define safety stock?

Joannes Vermorel: Safety stock emerged from the idea that once you have a forecast, if you put an amount of stock that is equal to your forecast and if your forecast is balanced, then you have a 50% chance to be out of stock. That’s pretty much the definition of a balanced demand forecast. So, as a consequence, you need to have more in stock than what you forecast. This difference between what you forecast and what you actually need to reasonably cover future demand is this so-called safety stock. The general concept is to add some extra buffer on top of your average forecast.

However, safety stock nowadays has a much more narrow definition. The industry converged on one way of computing safety stock, which is basically to assume that future demand and future lead times are normally distributed. And by “normally”, I mean Gaussian. Then, this specific model is applied to compute how much you should put in this safety stock.

Kieran Chandler: When did these ideas come about and why is it something that the market is so hung up on?

Joannes Vermorel: I believe that safety stock is a good name. It sounds reassuring and we should never underestimate the power of a good brand. Safety stocks feel more safe. It seems like a good move to say, “We are playing it safe, we have those safety stocks.” If you have to choose between a safe method and an unsafe method, of course, you would choose the safe one.

So, I think having a catchy name was part of what made this very specific approach successful. Then again, for a long time, computers were exceedingly weak. We transitioned from computation done by hand, where a normal distribution was the best thing we could do, which was better than no numerical recipe at all. Then in the early computers era, in the late 60s and early 70s, it was good enough. I think many practitioners just fell asleep and the whole thing stayed there.

However, the key concept of having the idea of this extra buffer still makes sense nowadays. What doesn’t make sense is to say that all the uncertainty can be kind of collapsed to a normal distribution, both for demand and lead times. This is especially absurd as far as lead times are concerned.

Kieran Chandler: This idea of it being unsafe might sound a little bit extreme to some people. Why do we think it is a little bit unsafe? Where do these key difficulties with safety stock come from?

Joannes Vermorel: Safety stock, just to give you an idea of how it works, starts with your demand. What you end up with is to create a stock that is a certain fraction of the demand. So, if you’re forecasting 100, you might add 80 units, which is 80% of your original demand, and that’s your safety stock. That’s a direct consequence of choosing a specific service level with a normal distribution assumption on top of the demand.

The problem is that when you do this, you completely ignore seasonality. Your demand forecast is frequently seasonal, and that’s very expected. But the reality is that uncertainty is seasonal as well.

Kieran Chandler: You’re suggesting that the classic stock model entirely dismisses all patterns that impact uncertainty. You also mention that applying a normal distribution to the demand is quite a stretch. Can you elaborate more on that?

Joannes Vermorel: Of course. Applying a normal distribution, particularly to lead times, can be misleading. For instance, consider a supplier who generally delivers to you within two days. In Europe, it usually takes just one day to ship items, so your lead time is typically two days. However, if your supplier experiences a stock-out, the delay could be up to three months.

Kieran Chandler: So, it’s not a bell-shaped curve, is it?

Joannes Vermorel: Absolutely not. It’s a completely different pattern. We see a significant spike around your nominal lead time, followed by potential for extensive delays. This occurs if you face a specific event such as a supplier stock-out. So it’s a bad approximation to model this as a normal distribution - it’s like trying to fit a square into a circle.

Kieran Chandler: Does this imply that any small amount of variability or any unknowns disrupt the effectiveness of safety stock?

Joannes Vermorel: Indeed. Any element that could disrupt the status quo, that could trigger a situation where demand for a product can evaporate, makes the safety stock model inadequate. For instance, if you’re selling chicken, and an outbreak of avian flu is reported, people might stop eating chicken for six months. This is a significant deviation from the norm, and it’s not accounted for in a normal distribution.

Kieran Chandler: So, large deviations are common in real supply chains?

Joannes Vermorel: Surprisingly, yes. While not constantly occurring for all products, any large company will have at least a few big surprises each quarter. Safety stock models, however, suggest that such large deviations don’t exist. When you optimize your supply chain under this assumption, and then such deviations occur, it can be really costly.

Kieran Chandler: Given these bumps and surprises, would a probabilistic approach be better? What are the key benefits of this approach over safety stocks?

Joannes Vermorel: When you have a model that significantly underestimates your risk, it can lead to inadequate stock levels. In theory, safety stock should counter this by buffering against unexpected demand. However, in practice, supply chain practitioners adapt in a way that can exacerbate the problem. They use safety stock models that underestimate the risk, aiming for a high service level like 98%. But because the risk is underestimated, the actual service level is lower.

Kieran Chandler: In terms of tail events both in time and demand, you’re likely to get, let’s say, an 85 percent service level. This is very far from your 98 percent target for your service level. So what do you do?

Joannes Vermorel: You use the silver bullet which is an extra multiplicative parameter to your safety stock. You start with your model with normal distribution assumption, then because literally everyone who has been using safety stock realized that we have these problems, we need to inflate our safety stocks. Companies are going to introduce these inflation factors in two ways. Either you explicitly put a factor, or you say in the software that you want 98 percent service level, but you enter 99.9 because it’s the way to empirically obtain this 98 percent.

What is happening is that because your model underestimates your risk, you inflate your safety stocks quite uniformly. This creates a significant problem by generating substantial overstocks. The paradox is that you have a model that underestimates the risk so you inflate your safety stocks everywhere and in the end, you generate a lot of overstocks. It’s funny because you start with something that’s called safety stocks, but it’s inherently unsafe because of this very process.

Kieran Chandler: So what you’re saying is you’re always fine-tuning for a worst-case scenario. Everyone fine-tunes to that day when they really need the stock, and then if the stock or demand changes, they still have that added safety factor in place.

Joannes Vermorel: Yes, and you’re going to have this added safety stock everywhere. People are going to micromanage their forecasts, spend a lot of time tuning the forecast. They’ll compute everything down to the last gram to be super precise and then thanks to this safety stock, they round it all to the next metric ton just because they have this inflation factor that is applied uniformly across all products. I’m a bit stereotyping, but it’s a loose approximation of what is actually happening or what I’ve seen happen many times.

Kieran Chandler: So how do you deal with those customers that are adamant they need that extra safety value, that safety stock, that buffer? What’s the key message you need to translate to them?

Joannes Vermorel: The key message is first, safety stocks are unsafe and they are also ineffective. It’s a fiction. In your warehouse, you don’t have two kinds of stock; working stock that serves the demand and safety stocks that serve the uncertainty. You have only one pile of stock. The question is whether this amount of stock is suitable to serve your clients. You don’t actually have that much control on the level of stocks because you don’t have control of customer demand. What you do have control over are the purchase orders or the manufacturing orders that you pass.

The problem with safety stocks is that it distracts you away from the decisions that you can make that are in your hands and that have a real physical impact on your supply chains, such as those purchase orders or supply orders or manufacturing orders. The key message would be to focus on the decision that you’re making, not on the relatively arbitrary parameters of your ERP.

Kieran Chandler: The problem with a probabilistic approach is that it’s relatively complex. You’ve got a different demand curve for every single item in your catalog, whereas the nice thing about safety stock is it’s relatively simplistic. You’re just adding on a certain buffer for every item. Is there anything in between for supply chain executives that they can use? Something not quite as complex as Lokad’s probabilistic approach, but a little bit better and more advanced than a safety stock kind of approach?

Joannes Vermorel: I believe we are touching on a small paradox of modern statistical analysis. The safety stock is a parametric approach in statistics, where you have a model with parameters such as a mean and variance, and you use this model to tune the parameters. However, you can quickly realize that this parametric model is a complete misfit for the situation, like a square is a very bad approximation of a circle. You can try to add more complexity to the model, but very soon, it becomes cryptic and difficult to understand for supply chain practitioners.

You could go for more complex explicit models, but these become very hard in terms of mathematical notation. It’s actually simpler to use machine learning techniques, which are a bit more opaque but can fit any kind of distribution. The reality is that as you want to properly combine the uncertainty of lead times with demand, you cannot expect a simple, closed formula. It’s going to be complicated no matter what, but it’s also required to account for subtle interactions between lead times and demand.

Kieran Chandler: We’ve spoken a lot about the wastage in safety stock and that it’s wasted money. Why is it something that people haven’t tried to improve, and why hasn’t it been focused on?

Joannes Vermorel: I think it’s because safety stock is well-understood by many supply chain practitioners. They tend to underestimate that having a good understanding of future demand is only the start. Future demand is not the only source of uncertainty; future lead times are another source, and there are other problems as well. Practitioners can become distracted by the pure demand forecast, and there’s also this illusion that if they can fix the forecasting problem once and for all, all other problems will be solved.

Kieran Chandler: It seems like there’s a belief that having a perfect forecast eliminates all other problems. However, you’re suggesting that this is a delusion, and what we need to do is embrace the probabilistic approach, acknowledging that the forecast will always be imperfect. Can you expand on this?

Joannes Vermorel: Absolutely. The probabilistic approach is about giving up the dream of a perfect forecast. It is accepting that forecasts will always be imperfect and dealing with the consequences of this imperfection. For instance, one of the consequences is the need to start considering the impact of uncertainties, such as safety stocks, which are a very crude way of modeling the consequences of this uncertainty.

Kieran Chandler: So, are you suggesting that the forecast often gets blamed unnecessarily?

Joannes Vermorel: Yes, that’s exactly what I’m saying. With safety stocks, people tend to blame the forecast when in reality, the forecast was just as good as it could have been. It’s hard to do much better than a well-tuned moving average. Sure, you can improve it a bit by considering factors like seasonality, but even then, it’s hard to reduce the error by more than a third. So, blaming the forecast is moot. Very often, the real mistakes are made afterwards, and those are the areas where we can make significant improvements.

Kieran Chandler: As we wrap up, what’s the key message for supply chain executives? Should they start discarding their safety stock calculations and embrace the stock outs, or understand their forecasts better?

Joannes Vermorel: The key message is not to trust mathematical models that were primarily invented for manual computation. It’s not reasonable to run your supply chain based on a method that doesn’t require computers. Just as it wouldn’t make sense to keep a large number of backpacks just in case trucks stop working. The problem with safety stocks is that they persist due to good branding and what seems like an obscure technicality of supply chain optimization. I would suggest challenging your assumptions when dealing with numeric optimization of your supply chain. You don’t need to be a mathematician to do this. Just check whether these assumptions match the reality of your supply chain.

Kieran Chandler: I see, so, could we see a shift from referring to ‘safety stocks’ to ‘unsafety stocks’ in the future?

Joannes Vermorel: Who knows? That could very well be the case.

Kieran Chandler: Thank you, Joannes. That’s all for this week. Thanks to our listeners for tuning in, and we’ll see you next time. Goodbye for now.