Model explains spontaneous explosions of delays in supply chains

Ever Given blocking the Suez Canal. Contains modified Copernicus Sentinel data [
Ever Given blocking the Suez Canal. Contains modified Copernicus Sentinel data [2021], processed by Pierre Markuse
A group of scientists has developed a model that explains how schedule-based systems, such as supply chains and railways, can be prone to spontaneous explosions of large-scale delays. The researchers recommend system operators to prioritize resilience, alongside efficiency, for better long-term outcomes. The study had been published today in the scientific journal Nature Physics .

How can some local delays in railway systems cascade to a nationwide disruption? The question was answered in January 2021 by Mark Dekker, who was at the time a PhD candidate with Complex Systems scientist Deb Panja, a key author of the Nature Physics publication. Dekker and Panja developed a model that unearthed the cascading mechanism underlying the spreading of delays in Dutch railways. In that article, they also speculated that the same mechanism should also hold for supply chains. Soon after, in spring 2021 - as if to vindicate their speculation - the container ship Ever Given obstructed the Suez Canal for six days. The blockage of the popular trade route had an enormous cascading impact , tangible for a few months, according to the Danish shipping giant Maersk.

In the new study, Panja, his current PhD candidate Matthijs Romeijnders, and colleagues from other institutions, now show that there is a universal criticality mechanism underlying delay cascades in schedule-based systems.

A buffer can eventually absorb delays, but only up to that critical point



Deb Panja, key author

Tight schedules

The timeliness mechanism, as the researchers call it, has to do with the elements of any scheduled-based system being present at the right place at the right time. In such systems, the elements can be goods, services, or people. For example, in a production system, raw materials are needed for a component to be produced, which in turn is used to produce something else. If, for some reason, the delivery of the raw material is delayed, the scheduled component cannot be made on time, which in turn will lead to more delays downstream in the production process.

To maximize costand time-efficiencies, often reinforced by competitive pressures, system operators prioritise fitting their schemes into ever tighter schedules. In the extreme limit, there is simply no room for delays - in other words, there is no buffer.

Critical point

The new model reveals the existence of a critical point in schedule-based systems as the size of these buffers is reduced. More precisely, the authors show that above a critical (and nonzero) buffer size, delays can be arrested by buffers. In contrast, below that critical buffer size, delays accumulate throughout the entire system without bounds. "The buffer can eventually absorb the delay, but only up to that critical point", Panja summarises. Importantly, the researchers found that, while there are always delays in the system, the closer to the critical point a system operates, the higher the delay magnitudes become, and the longer they last: the authors call these ’delay avalanches’.

Operators should prioritize resilience alongside efficiency for better long-term outcomes



Deb Panja, key author

Real world cases

The researchers demonstrate the existence of the critical point with a stylised model. Such a model is a simplified representation of a system, highlighting the systems’ key elements and the relationships between them. To bridge the gap between the model and the real world, the researchers also looked at two real-world examples, demonstrating that they too exhibit the existence of a critical point.

Prioritising resilience

In their study, the researchers argue that that timeliness is a universally adopted quality standard in systems based on schedules, yet it is often underestimated. "It is human tendency to focus fully on saving time or money at the short term", Panja states. "Low buffer levels as a consequence of high efficiency results in tensions building up within the system, in turn enhancing the chance that every ripple can potentially create a large-scale disruption." They recommend system operators to also prioritize resilience alongside efficiency for better long-term outcomes, and in doing so, engage in system-thinking.

Complex systems are systems composed of many interconnected elements or actors. They exhibit properties and behaviors that cannot be understood by studying the individual elements in isolation. Complex systems science is an interdisciplinary field that studies these systems, drawing on concepts and methods from various disciplines, including mathematics, physics, and computer science. Researchers aim to identify patterns, principles, and mechanisms underlying the dynamics of complex systems, as well as to develop models, theories, and tools for predicting and controlling their behavior. Examples of complex systems include ecosystems, climate systems, financial markets, and the human brain.

At Utrecht researchers at the Centre for Complex Systems Studies (CCSS) approach societally relevant issues from the perspective of complex systems science.