00:00:07 Introduction and the importance of small numbers in supply chain performance.
00:01:00 How small numbers affect computing performance and cost.
00:03:33 The history and evolution of numerical precision in finance and supply chain systems.
00:06:00 The impact of data size on computational performance and bottlenecks.
00:07:44 Achieving significant computational speedup by reducing data size.
00:08:47 The importance of paying attention to technological stack and tools in supply chain optimization.
00:10:17 Balancing compute cost and more powerful mathematical models for better supply chain results.
00:12:50 Analyzing historical data and using predictive supply chain software for better decision-making.
00:15:04 Impact of data aggregation on perceived performance gain and granularity loss.
00:16:00 Challenges of consolidating supply chain decisions.
00:17:33 Revisiting core statistical assumptions and mechanical sympathy.
00:20:01 Importance of mechanical sympathy in supply chain management.
00:20:58 Moving from law of small numbers to big data perspective.
00:23:20 Conclusion: less data can be more in certain situations.


Joannes Vermorel, the founder of supply chain optimization software company Lokad, discusses the law of small numbers and its impact on supply chain performance with Kieran Chandler. Vermorel highlights the significance of small numbers in supply chain data and the importance of choosing the right numbers to optimize computing speed and performance. The discussion emphasizes the need for greater design sympathy in achieving performance gains, the trade-off between computational efficiency and examining all possible futures and decisions, and the challenge of using statistical models in complex retail environments. The interview stresses the importance of balancing computational resources and sophisticated modeling to optimize supply chain performance.

Extended Summary

In this interview, Kieran Chandler speaks with Joannes Vermorel, founder of Lokad, a software company specializing in supply chain optimization. They discuss the law of small numbers and its potential for improving supply chain performance, the significance of small numbers in supply chain data, and the impact of choosing the right numbers on computing speed and performance.

Vermorel explains that small numbers, specifically single-digit numbers, are ubiquitous in supply chains. While barcodes may have many digits, they serve as identifiers rather than quantities. Quantities in supply chains tend to involve very small numbers, which is surprising because most statistics are geared toward the laws of large numbers. This observation is important because it highlights the need for greater design sympathy in order to achieve performance gains, especially as the rate of improvement in processing power is slowing.

The interview then turns to the impact of small numbers on computing. Vermorel states that although computers can handle any number, they can perform calculations much faster if the right numbers are chosen. For example, computers can be 10 to 20 times faster at performing mundane operations with numbers if the correct numbers are selected. This can make a significant difference in the overall performance of a supply chain optimization system.

Kieran asks Vermorel to explain the difference in sending numbers between systems and the physical reality of computing hardware. Vermorel emphasizes that the cost of data processing and crunching is important for supply chain optimization. Computers have become cheaper in terms of raw processing power, which allows for more powerful algorithms to improve forecasting accuracy and supply chain performance. However, the balance between computing cost and supply chain performance is crucial.

Vermorel argues that if raw computing costs are significantly reduced, it doesn’t mean that computer costs will vanish. Instead, companies will leverage their newfound resources to develop more complex models, ultimately increasing computing costs. Therefore, attention must be paid to the impact of small numbers on computing costs in order to optimize supply chain performance.

The discussion was of the origins of arithmetic calculation needs in enterprise systems, which primarily came from the world of finance. The first enterprise systems were designed with financial calculations in mind, and this history has implications for how small numbers are used and understood in the context of supply chain optimization.

The law of small numbers has the potential to significantly improve supply chain performance if companies can successfully leverage the right numbers in their computing systems. By paying attention to the balance between computing costs and supply chain performance, companies can develop more complex models and achieve greater optimization results.

Vermorel explains how supply chain practices adopted from the finance and accounting industries in the 70s and 80s led to the use of high numerical precision in supply chain systems. The need for high precision in finance and accounting arose from a series of frauds in the early 80s, where rounding errors were exploited to siphon off millions of dollars.

However, the high precision used in finance is not always necessary in supply chain management. Vermorel observes that in 80% of store transactions, the quantity of a product being purchased is just one. This means that only two bits of precision are needed on average to represent quantities in a store. Kieran questions the significance of data size in the context of supply chain management, considering the affordability of storage devices with terabytes of capacity.

Vermorel clarifies that the performance of most calculations is driven by the size of the data, as the bottleneck lies in loading and unloading data rather than the processing capabilities of the CPU. He highlights that reducing data size can lead to significant and sometimes super-linear gains in computational speed. For example, when Lokad managed to shrink data by a factor of 10, they experienced a 50 times speed up in computation.

The challenge for supply chain management is to differentiate between data that requires high precision and data that can be represented with less precision. Vermorel suggests that a platform like Lokad can handle this task, emphasizing the importance of someone paying attention to the technological stack or the tools used by the IT department. Ignoring data optimization can result in systems with massive computing hardware but disappointing performance.

Vermorel also addresses the trade-off between computational efficiency and the goal of examining all possible futures and decisions in supply chain optimization. By making computations faster, it becomes possible to analyze more scenarios without significantly increasing compute costs.

They discusses supply chain optimization and the challenges of using statistical models. He emphasizes that using moving averages and other simple models is not sufficient for complex retail environments, such as hypermarkets, where there is a need for more sophisticated predictive tools to handle seasonality, trends, and other factors.

Vermorel also highlights the problem of the “law of small numbers,” which arises when dealing with a large number of products with few daily transactions. Traditional statistical approaches, relying on the law of large numbers, are often inadequate in these situations. To overcome this, many companies aggregate their data, such as consolidating sales by week or month. However, this approach sacrifices granularity and can lead to poor decision-making, since supply chain decisions are still made on a daily basis.

The conversation suggests that advanced supply chain software, like Lokad, can provide better guidance by analyzing historical data and considering product life cycles. It is crucial for such tools to be designed around the reality of small numbers, as they often need to be relevant for a significant portion of a product’s lifetime. Ultimately, the interview highlights the importance of balancing computational resources and sophisticated modeling to optimize supply chain performance.

The founder discusses the importance of questioning core assumptions and using appropriate statistical tools in supply chain optimization. He emphasizes that many current statistical methods are geared towards large numbers, which may not be suitable for smaller-scale supply chain decisions. Vermorel also suggests that practitioners should develop “mechanical sympathy” for their supply chain systems, like Formula One drivers do for their cars, to maximize performance. Despite the increase in data collection, Vermorel argues that relevant supply chain data often remain limited, which can be misleading when applying big data perspectives.

Full Transcript

Kieran Chandler: Today on Lokad TV, we’re going to be discussing the law of small numbers and how it can be exploited to improve supply chain performance. So Joannes, as a company that specializes in big data, it’s probably surprising we’re talking about small numbers today. What’s the idea behind this?

Joannes Vermorel: The idea is that small numbers, not large numbers, are ubiquitous in supply chain. When I say small numbers, I’m specifically referring to all the numerical choices and quantities that really matter. Yes, you can have a barcode with 13 or 14 digits, but that’s more of an identifier, not a quantity. So when you look at things that are like quantities, what is very surprising is that it’s always about very small numbers all the time. When I say very small numbers, I mean single digit small, like super small. It’s intriguing because most statistics are geared toward the laws of large numbers. In terms of computing, you would think it doesn’t matter, but it turns out it does, quite a lot.

Kieran Chandler: Can you explain a bit more about how it matters for computing?

Joannes Vermorel: For a computer, a number is a number, right? It doesn’t matter. However, it turns out that if you correctly choose your numbers, your computer can not only be fast at doing those additions or mundane operations with numbers, but it can be something like 10 to 20 times faster. So, it makes a big difference in the end. It’s not just a small difference.

Kieran Chandler: Okay, so for people who might not be aware of what happens when computers send information, what do you mean by sending a number? How can that be different between one system to another?

Joannes Vermorel: Here, we’re going into the details of the physical reality of the computing hardware that we have. It matters because, if you want to do supply chain optimization or quantitative supply chain optimization, you’re going to do a lot of data processing and crunching, which costs money. Even though computers have become vastly cheaper than they used to be, there’s always a balance between the computing cost and the supply chain performance that you can achieve. If your raw computing cost is lowered vastly, then you could say the computer costs are going to vanish. However, that’s not true because you’re going to leverage your newfound resources to have a more complex model, which, in turn, gives you the next stage of forecasting accuracy or performance in terms of supply chain optimization.

Kieran Chandler: That can do better and thus, you know, that will just increase in turn. Um, the computing cost, thus you need to pay a bit of attention to that. Now back to those numbers and lower small numbers in computers. Um, more especially enterprise systems. Most of the need towards your calculation, arithmetic calculation originated from, I would say, the world of finance. The first enterprise systems were all geared towards, you know, accounting, finance, supply chain. That’s what emerged in the ’70s. Supply chain came a bit later in the ’80s, and, um, a lot of the practices that were already established at the time, especially with regard to the high precision numbers, were imported into supply chain. So why do you need super high numerical precision for money?

Joannes Vermorel: Well, it turned out that, in the early ’80s, there were a lot of relatively spectacular frauds where people had just used the fact that, when you round the cents, you can actually create magic. You can actually steal money if you just round a few cents in every single transaction that your company is making. And it’s completely invisible for the system because it was rounded away, but actually, it was real money. And people, when you had like billions of transactions, some people were managing to literally extract millions of dollars out of the system by just taking only the fraction of a cent and redirecting them to their own accounts. So the world of finance and accounting upgraded to very high precision numbers where those problems don’t appear. The problem is that, I would say, you know, supply chain, too, but as a result, you have numbers that are like super, super high precision by default in pretty much all the systems. And you have to ask yourself, what is the usual quantity that is going to be bought by a client in a store? And our answer at Lokad because we observe the data is 80% of the transaction in the store is the quantity is just one for the product. So, literally, the question is, you have a number, how many bits of precision do you need? Well, the answer is you need something like two bits of precision on average to represent, you know, a number in a store, for example, for quantity being purchased.

Kieran Chandler: But why should we really care about how many bits are used to send data? Because, I mean, if we’re looking at the whole entire supply chain, I mean, does it really make that much difference?

Joannes Vermorel: So, grand scheme of things, you would think that nowadays, you can buy hard drives that are terabytes at literally your nearby supermarkets for just something like 200 or something. So, you would think it’s super cheap. Why do I even care about that? Well, it turned out that the performance of most calculations is literally driven by the size of the data. If the data is bigger, it’s going to be slower. Why? Because the bottom neck is not your CPU. It’s just loading and unloading the data. Yes, you can buy a hard drive that is one terabyte, but if you actually try to just fill this hard drive with data, it’s likely to take you one or even two days, just because the drive is slow. And so, just literally writing data on the disk or reading the disk entirely takes a very long time. So, it’s not again, if you can just minify the data, you can literally accelerate.

Kieran Chandler: So, Joannes, can you tell us more about how the size of the data affects the speed of calculations in supply chain optimization?

Joannes Vermorel: Significantly the computation and what I say significantly, usually you even have like super linear gains. So, if you divide the size of the dr by two, you don’t speed up the calculation by two, you speed up the calculation by more than two. We have seen that at Lokad, there are many situations where if we managed to shrink the data by a factor of 10, we were literally having like a 50 times speed up. And, again if we go back to our numbers, let’s go back, you know we had a double precision number so 64. By the way, what it’s called the bit in computer science is just a zero one. And, so if you have a number that is represented with 64 bits, compared to a number that is only represented with two bits, well you have literally 32 times more. You know it takes one number literally takes 32 times more space. So, if you can compact vastly those numbers and turn this big data into much smaller data, you can have competition that is much faster. And, that’s yeah, supply chains are still kind of dealing with all of that kind of big financial data as well in terms of some of the transactions they have to do.

Kieran Chandler: So, how are you kind of sorting between what needs to be kind of smaller data and what should be kind of the bigger data?

Joannes Vermorel: So, literally you want your supply chain specialist to pay attention to that. You really want to have a platform like Lokad, you know shameless plug, that does that for you. But, my message, you know, my broader message is that somebody has to pay attention. It can be your vendor if they are very careful with their technological stack. It can be your IT department if they are very careful in the tools that they choose. But, in the end somebody has to pay attention. If nobody pays attention, what you end up with is systems where you have like massive amounts of computing hardware and performance that is usually completely disappointing. Where it literally takes seconds to get a result, and even seemingly semi-trivial calculations takes quite a long time. The idea of having the supply chain of looking at all possible futures, probabilities, confront that with all possible decision or this idea just remains a distant dream just because the system is already so slow just to cope with one scenario. So, one possible future that the idea of having the system dealing with millions of possible futures is like a complete lunacy.

Kieran Chandler: But, if we’re looking at all possible futures, all possible decisions, surely that goes against the whole kind of goal which is to reduce compute cost. But if you’re looking at all possible futures, surely that’s going to multiply that compute cost by far more?

Joannes Vermorel: Yes, but that’s the trade-off that I was describing. If you make your computation much faster, you don’t want to just have like a super super cheap computer to run your entire supply chain. You know, if we were still using the techniques used in the 80s in terms of supply chain optimization, we could, on a smartphone, run a Walmart. We could literally run Walmart on a smartphone. Doesn’t make any sense to do so, but if you’re just up to the challenge of proving the point that how…

Kieran Chandler: So, Joannes, you were talking about how the idea is that when computation becomes cheaper, you adopt a mathematical or statistical model that is more powerful, right?

Joannes Vermorel: Yes, that’s right. When the computation becomes cheaper, you can adopt a more powerful model that delivers better supply chain results at the expense of consuming more computing resources. It’s a trade-off.

Kieran Chandler: And even if we say we look at all possible futures, the whole idea of laws of small numbers still applies, right?

Joannes Vermorel: That’s correct. Even if we look at all possible futures, we don’t need to look at the probability of selling one million bottles of anything in a single store in a single day because the probability is just zero. The reality is that even for a flagship product, it’s very rare that you’re going to sell more than 100 units any given day, and for the vast majority of products, you’re only looking at zero units that are going to be sold. That’s actually the majority of products. Like 80% of the products in the hypermarket are not even sold once every day, and for 95% of the products, the question will be only: do I sell this product like zero, one, two, or three units every given day? And the probability that you can even reach 10 units is already vanishingly small. So, it’s all about the laws of small numbers.

Kieran Chandler: Okay, so in that kind of hypermarket example, they’re dealing with thousands of transactions a day, and you’ve got massive stock holdings. How do you know where to draw the limits for each of the individual items?

Joannes Vermorel: That’s where you need proper tools that analyze historical data. You’re guided in your analysis because when you look at the recorded data, you know, but also a good supply chain software, especially predictive software like Lokad, there are things that you know upfront. You know you’re not discovering that in a hypermarket for the first time. And yes, you have many transactions and many products being sold, but when you look at every single product, you don’t have that many transactions. I mean, if you look at the fact that a product is going to have a life cycle on the market of maybe three years, then it will be replaced by another product. If you look at the fact that the product is not even sold every single day, it means that maybe to reach a point where you have 100 being sold in your entire set history for this product, which would be maybe the lowest level one that you need to consider, you have a large number. I mean, saying that 100 is a large number is quite a stretch, especially from a…

Kieran Chandler: So, from a statistical perspective, but you know that would be like a low bar for that. It might actually take more than a year. So, that means that if you have a statistical tooling that is designed around this idea that you will be able to leverage loads of large numbers, it will maybe take more than a year so that your tool even starts to become relevant. And remember we are talking about a product that is only going to have like a three years life cycle, so it means that for a third of its lifetime, you, the two many many statistical tools will not even be relevant.

Joannes Vermorel: Okay, a lot of companies kind of consolidate their sales by kind of week or month, and how well does that work if you’re kind of getting probably in a perceived kind of performance game. How much does that work compared to the trade-off of your losing a bit of granularity in your data? So, that’s very interesting because I said, you know you have those problems of the laws of small numbers are ubiquitous, and the problem is that all the tools, at least the classical tools, certainly not look at. But the classical tools certainly are geared toward the laws of large numbers. So, what do you do? Well, you aggregate stuff.

Kieran Chandler: And why do you aggregate not because it’s the right thing but just because it’s a way so that you can end up with not with results that are not completely dysfunctional, but you’re not doing that because it’s something smart and relevant for your supply chain. You’re just doing it because otherwise, your logic that is driven by averages would just fall apart because, again, implicitly what you try to leverage is the law of large numbers.

Joannes Vermorel: So indeed you consolidate, but the point is that when you, for example, consolidate decisions up to you know monthly aggregation so that you can have bigger numbers, the problem is that your supply chain decisions are still taken on a daily basis. So, yes, you have a better monthly analysis just because you’ve consolidated all the data, but you’re still taking decisions on a daily basis, and it turned out that your monthly analysis doesn’t tell you anything about what is happening within the month. So, yes, you know that over a month you have 100 units that are being consumed on average. Now today, should I push zero one or three units to the store? And similar decisions also exist when you aggregate not time-wise but category-wise.

Kieran Chandler: So, if you, for example, say okay, today in terms of sodas, I sold 500 units, yes, but it was spread over 100 product references, so it doesn’t really help because in the end, in supply chain, you’re not taking a decision at the category level like, for example, the fresh food segments. You don’t take a decision at the level of the fresh food segment of your hyper market. You take a decision on this specific product reference and what should happen with it. Okay, we start sort of wrapping things up then for somebody kind of watching this, and what should they be looking to exploit in order to introduce that design symphony and make the best use of the processing power that’s kind of at their fingertips?

Joannes Vermorel: They should really start looking, you know, revisit. First, I would say on the statistical side, I really suggest revisiting all the core assumptions. I mean, whenever people tell you, “Oh, we have safety stocks,” yes, it’s normal distributions. Again, is this you should really ask yourself.

Kieran Chandler: Am I looking at the problem with the statistical tools that are relevant for the laws of small numbers that I’m facing? And most of the 19th century statistics that people are using nowadays are clearly geared toward laws of large numbers. So, my suggestion is to be aware that the tools you are using are not designed for the kind of situation that you are facing. And again, we are going back to pseudoscience and fake rationalism. It’s not because you’re using a mathematical tool that it makes it rational. Maybe your statistical framework came with core assumptions that are just violated by your domain. So, I would say, revisit the basics, make sure that you’re not missing something big.

Joannes Vermorel: Yes, that’s right. And then, in terms of mechanical sympathy, my message is, it’s just like the great champions for Formula One. When you see interviews of the champions, they know a lot about their cars. They don’t know how to build a Formula One, but they know the mechanics. They have what it’s called the mechanical sympathy. They know a lot about how the car works so that they can really get the best out of the machine that they have. And they literally know a lot about combustion, about resonance, about the right temperature for the tires that you have, like maximal adherence to the ground. I mean, they know a lot about the technicalities and the physics of their engine. And that’s how they can become really great pilots. It’s not just being good at driving, it’s knowing the tool that you’re using. And I believe supply chain is a bit like that. You’re not driving a supply chain by sheer muscle. Nowadays, you have computers to support you. But if you really want to be very good, you don’t have to become an engineer that is capable of producing a Formula One. That’s not a pilot. A pilot is not the mechanical engineer that is able to design the next generation of the engine. But they know a lot to get the most out of it. So, my suggestion is to get enough mechanical sympathy about all those computer systems that support your supply chain so that you know intuitively what makes those things tick and how you can really max out the performance that you have.

Kieran Chandler: That’s a really good analogy. So, what we’re kind of seeing at the minute as well with the industry is…

Kieran Chandler: So, more data and people are collecting more data to make all their kind of decisions. Would you say that kind of perspective is really moving away from that kind of law of small numbers and people are more heading towards kind of a big data perspective?

Joannes Vermorel: Again, the problem with that is that the data that are the most important are always in small numbers. Yes, you can collect a massive amount of data on your website for the traffic, but if you look at the traffic for an obscure product, unfortunately, obscure products are like 80% of what companies are selling on average. You know, it’s obviously that detail, and then you will realize that you have only a handful of web visitors per day. So it’s not, yes, you might have millions of clicks, but when you scale it down to the time scale that matters, which is usually the day or within the day because your supply chain decisions are taken on a daily basis or even sub-daily basis. If you look at the granularity that matters, which is the product, the reference at the lowest level, so the exact size, the exact color shape, you know, the exact variant, not the generic product because in supply chain, you don’t decide to produce a generic t-shirt. You produce a t-shirt of this color, this size, this shape. So when you start to look at it at the lowest level, which is the one that matters, you go back to data that are limited. So yes, people are saying they are doing big data, but the reality is when you look supply chain through the eyes of what is relevant, it’s not that big actually. And the biggest, and I wish it was but because from a statistical perspective, it would be so much easier, you know, but this is not the case. So don’t be confused. I believe this big data gives people, you know, it’s super misleading because they can think, “Oh, that’s okay. I have millions of data points.” No, again, if you’re looking at a factory, even the factories that produce millions of units, the question is how many batches are you producing, and maybe in terms of batches, you have something like a single-digit number of batches. And you’ve only had the factory operating with this mode for the last two years. So we are talking of a few hundred batches, and this is it. This is not a big deal, even if you collect a large amount of the air.

Kieran Chandler: Okay, we’ll have to leave it out there with the bombshell that in terms of data, less is maybe more. So that’s everything for this week. Thanks very much for tuning in, and we’ll see you again in the next episode. Thanks for watching, you.