Quantitative Principles for Supply Chain (Lecture 1.6 Summary)

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Meaningful supply chain optimization is mastering the optionality one encounters as a result of the variability inherent to the flow of goods, and this mastery is sympathetic to quantitative analysis. Supply chain problems are similarly quantitative but wicked and occasionally downright weird, running contrary to traditional analysis. Adopting quantitative principles at both the observation and optimization stage can help practitioners avoid many obscure but nonetheless predictable supply chain pitfalls.

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Observational Principles

Overarchingly, the types of decisions and constraints supply chain practitioners wrestle with are invariably quantitative - such as replenishment values, service level targets, MOQs, etc. However, supply chains themselves defy direct observation. One cannot take a snapshot of the entire supply chain the way one can a piece of machinery, despite both arguably being CapEx, both being composed of many observable physical subparts, and both (generally) resulting in a physical output.

Despite that limitation, supply chains are not hostile to quantitative analysis. To the contrary, a quantitative analysis of supply chain reveals several instructive though debatably counterintuitive observations.

Supply chain problems are not normal(ly distributed)

Perhaps despairingly, supply chain problems do not tend to follow normal distributions, resulting in a lot of the organizational difficulties one encounters when trying to optimize them. With a normal distribution, a large number of small, independent factors can influence a value in either of two directions (e.g., more or fewer, up or down). In other words, a normal distribution results from many small random changes that can increase or decrease a value1.

However, supply chain problems often arise from a small number of greater, systemic factors rather than a multitude of small, independent ones. These factors include:

  • Demand Variability: Demand for products is often highly variable and can be influenced by a wide range of factors like seasonal trends, economic conditions, and marketing campaigns. This variability can lead to issues like stockouts or overstocking.

  • Supplier Reliability: Supplier performance can significantly impact a supply chain, and variability in supplier reliability can lead to problems such as delayed deliveries and quality issues.

  • Logistical Disruptions: Issues like transportation delays, customs hold-ups, or natural disasters can cause significant disruptions in a supply chain.

The above issues are not trivial threats to supply chain continuity (and optimization). Rather, they are disproportionately large, wicked problems that can have dramatically outsized impacts.

Furthermore, supply chain problems often exhibit a certain level of skewness, meaning there are typically a few major issues that cause a large proportion of the problems, rather than a symmetrical distribution of problems around a predictable average. In many cases, these problems also exhibit a “long tail” - i.e., a large number of different issues each occurring infrequently.

The interdependencies and feedback loops inherent in supply chains (for example, how present stock levels influence future ordering decisions) also make the occurrence of problems depart from normality. Such non-linear, complex systems are more accurately described by other statistical models (detailed in the following section).

The inverse relationship between frequency and rank

A better quantitative model for scrutinizing supply chain problems (and values in general) is Zipf’s Law. Simply stated, there are two main elements to Zipf’s Law:

  1. A few values in a data set occur very frequently, while most occur rarely.

  2. A value’s frequency is inversely proportional to its rank.

Consider word frequency in a textbook. The most common word in any given book (if it is written in a language that uses a definite/indefinite case system) will likely be the. The second most frequent word may be of, and its frequency will be (approximately) half that of the. This trend will continue down the rankings2.

A relevant retail example is the common discovery that a small number of items in one’s catalog account for a large portion of one’s sales, while a long tail of other items sell infrequently. This pattern - a few “hits” and many “misses” - matches the Zipf distribution. This is a similar concept to the The Pareto Principle, which states that roughly 80% of effects come from 20% of causes. The asymmetry described here is, in fact, the driving principle behind inventory management systems like ABC and ABC-XYZ. However, there are some key differences between the Pareto and Zipf distribution that are worth unpacking.

  • Pareto Distribution: Imagine an online retail company with an extensive catalog. The supply chain division might discover that 80% of the company’s revenue is generated by only 20% of its offering, thus suggesting resources are better directed at maintaining stock levels of these popular items. Though this might be a useful general guide, it lacks the kind of resolution the division needs in order to properly analyze the sales data (beyond a simple matter of identifying which SKUs generated the most revenue).

  • Zipf Distribution: If the same supply chain division were to use a Zipf distribution, an interesting additional layer of granularity would be introduced to the analysis. By investigating all the sales and their frequencies, the team might discern patterns that a Pareto distribution misses. For example, they might discover that while electronics and home appliances are indeed the top performers, there are also other product categories, such as books or clothing, which collectively add a substantial amount to the total sales - while not significant margin contributors in isolation. A Zipf distribution would also reveal potential interesting relationships between the catalog that might be worth exploring, such as why the third most popular product contributes roughly a third the revenue of the most popular one, despite being interchangeable and receiving comparable levels of advertisement.

The tyranny of small numbers

A Zipfian distribution is perhaps most evident when it comes to quantifying explicit supply chain problems, particularly situations where an outsized negative impact is attributable to only a few causes.

Consider the negative impact of a B2B company losing their biggest supplier, particularly if that supplier contributes twice as much as the B2B’s second biggest supplier. Similarly, losing the two biggest clients would result in an extraordinary drop in revenue, given the third biggest client purchases approximately one third that of the biggest one.

Importantly, if supply chain problems were normally distributed, they would be more predictable and standard mitigation strategies would be sufficient. However, the fact that a few significant problems (as described here) can cause the majority of disruptions means that practitioners must focus their resources on identifying and mitigating these high-impact issues. This requires a more strategic, proactive, and holistic approach to supply chain management.

Optimization principles

Having circumnavigated the bias-ridden terrain of human observation, embarking on the supply chain optimization leg of the journey is equally prone to obstacles. Supply chain optimization initiatives are often bug-ridden, not just in terms of software (think ERPs) but also wetware (think inherited wisdom).

Software issues, such as Heisenbugs, are commonly resolved through iterative applications of the program. Wetware bugs, however, have the uncanny trait of being largely hard-coded, thus requiring additional deprogramming efforts.

Latent wisdom in aged supply chains

Supply chains that have endured for a few decades have accrued, at minimum, a baseline level of wisdom. It is, at face value, difficult to imagine encountering a company that has functioned for 20 or more years and has not at least accidentally stumbled across some useful strategies or rules of thumb. As such, any extant practices and operational norms embody a form of quasi-optimality, in that they may propel the company in the right direction (overall net profitability), but with significant imperfection3.

Much like a river carving its way through a mountain range, such wisdom tends to tether itself to a single driving force. The same way gravity pulls a river through sediment, aged supply chains are often dragged in pursuit of a sole KPI, such as increasing service level or reducing dead stock. While these might seem like sensible goals, they implicitly reduce supply chain to a discrete bundle of disconnected elements that can be tweaked in isolation.

This essentially results in a Boolean mentality where supply chain optimization is expressed in naively binary terms. Consider the following:

  • If service levels improve, the supply chain must have been improved. This, naturally, overlooks the fact that an increase in service level generally necessitates an overall increase in stock levels (assuming a non-quantitative supply chain optimization). Increasing stock levels, in turn, generally increases dead stock, resulting in reduced net profits.

  • If dead stock levels lower, the supply chain must have been improved. Similarly, this blinkered view of optimization ignores the impact that reducing inventory levels will likely have on service and customer satisfaction targets, thus negatively influencing purchases (and often customer loyalty).

Aged supply chains of this kind possess unidirectional quasi-optimality which, like a little knowledge, can be a terribly dangerous thing. That the supply chains default in the direction of quasi-success is what likely helps them endure and ossifies suboptimal practices.

Grand, unidirectional improvement in aged supply chains tends to be on a first-name basis with failure, not due to lack of sincere effort, but rather a lack of consideration for the vast, systemic, and interlocking complexity attendant in modern supply chains.

The fallacy of local optimization

Fundamental to optimizing a system as sprawling and interdependent as supply chain is the understanding that local optimization does not solve problems, it merely displaces them. As illustrated in the previous section, optimizing a local (here meaning “in isolation”) supply chain problem typically upsets equilibrium and produces an undesired side-effect somewhere else in the supply chain.

Much like installing a Solid State Drive (SSD) in a 30-year-old computer does not improve the system’s overall memory (or performance)4, optimizing a supply chain network (or supply chain system) is an end-to-end, system-wide process.

This concept is manifestly evident in the retail industry. In a retail network consisting of multiple stores, one’s intuition might be to optimize stock levels in each store (mayhap even manually). One might even preferentially allocate resources to the best-selling location in the network.

However, such an approach fails to consider the broader network of distribution centers serving these stores, as well as the downstream consequences of a policy that allocates stock without considering the impact on other stores. Choosing to narrowly focus on one store might enhance its performance but could be detrimental to the others.

It also misses the core concern of a retail stock allocation mission, namely the identification of where a given unit/SKU is most needed to optimize overall system performance.

Hence, optimizing retail stock allocation is a problem that only makes sense at the system level, underscoring the importance of a holistic, system-wide perspective5.

Redefining problems for superior outcomes

Classic education (and vendor pitches) present problems as most fittingly resolved through a superior solution. At first glance, this seems perfectly reasonable, given the shortest distance between two points is indeed a straight line. However, this pleasingly linear approach is prone to oversimplifying problems and, at base, assumes that one should be attempting to join these two points in the first place.

Given the various costs inflicted in trying to optimize a supply chain, this is not a trivial philosophical observation. In both theory and practice, a better understanding of one’s problems trumps (in the long term) a great solution to a poorly understood problem (in the short term).

A textbook example is the problem of demand forecasting. Supply chain vendors and academics alike might pitch an advanced time series forecasting tool as the ideal solution for quantifying demand (and thus setting inventory levels). On the surface, this seems intuitive: if a company cannot accurately predict demand, then better demand forecasting software is apt, and the two distant points are joined with a straight(ish) line6.

This is an overly linear mentality and quite possibly orthogonal to the supply chain problem of interest: the discovery of what is actually causing the demand forecasting difficulty. It is entirely conceivable that other underlying issues, such as logistical inefficiencies, unreliable suppliers, or flawed retail stock allocation policies, may be the forces of flux.

Redefining one’s problems, rather than racing to a supply chain red light, can properly orient supply chain optimizations and redirect bandwidth (and resources) from short-term quick-fixes.


  1. Height is a classic example of a normal (or Gaussian) distribution. This is because height is influenced by many independent genetic and environmental factors, creating a symmetrical bell curve around an average value. According to the Central Limit Theorem, the sum of many independent and identically distributed random variables tends to form a normal distribution. This results in most individuals clustering around the average height, with fewer individuals at the extremes (very short or very tall), resulting in a typical bell curve. ↩︎

  2. In contrast to the previous example of height (a phenomenon that is influenced by a multitude of independent genetic and epigenetic forces), a Zipf distribution applies to ranked data (like city populations or word frequencies), where rank and frequency are inversely proportional. As height is not a comparative or ranked measurement, it does not follow a Zipf distribution. For example, at a typical gathering the tallest person in a room is not twice the height of the second tallest person, nor an order of magnitude taller than the 10th. ↩︎

  3. Contrary to appearance, quantitative supply chain theory neither discredits nor discounts the value of human wisdom. In fact, such a philosophy is entirely agnostic to the possibility of an individual visionary who could, like Warren Buffett, predict consumer demand with preternatural accuracy. Even if such edge cases were commonplace, it would not vitiate the overriding criticisms of such an approach: namely, gut-instinct does not scale, nor does it - in all likelihood - represent the greatest application of the mind behind the gut. Given these limitations, and the fact that such people are the supply chain equivalent of promethium, this is a purely academic matter when discussing the optimization of large-scale, geographically distributed supply chain networks. ↩︎

  4. A 30-year-old computer almost certainly has hardware and an operating system incompatible with modern SSDs. Even if it somehow accepts the SSD, the outdated CPU, RAM, and bus speeds would severely limit performance improvements. Also, the OS might not support SSD features like TRIM, causing decreased SSD lifespan. Software and hardware incompatibilities could cause further issues, such as malfunction, data corruption, or complete non-functionality. In sum, do not try this at home. ↩︎

  5. It is essential to note that this principle applies not just in a strictly geographical sense, but logically within and throughout the supply chain itself. A good example here is the lifecycle of electronics. Devices - such as smartphones - tend to exist at various intervals along a four-stage cycle: introduction, growth, maturity and decline. Trying to optimize a single stage in isolation would be to the detriment of the overall product’s lifecycle, such as trying to optimize the maturity phase (wherein sales of the device stabilize) without considering the downstream effects on the decline phase (wherein any inventory missteps earlier in the lifecycle will be most acutely felt). ↩︎

  6. This concept is demonstrated, quite literally, in the lecture using the example of route optimization. Granted, in context Vermorel uses route optimization as an example of patterns in supply chain, however it just as easily functions as a metaphor for redefining problems. In short, route optimization is not limited to a single route, but rather a system-wide understanding of each route and why the routes are difficult to optimize. For example, why do some delivery hot spots shift throughout the year? Why is there seasonality to peak traffic hours in Paris? By asking better questions one can pinpoint the true problems of interest before attempting to address them. ↩︎