Too much efficiency leads to delays

As the world saw in the 2021 supply chain crisis, delays and bottlenecks in interdependent systems can pile up dramatically – leading to empty supermarket shelves (pictured), limited supplies of essential medicines and unexpected problems like a lack of carbon dioxide in soft drinks. One of the factors driving the crisis was the ubiquity of the just-in-time model, an approach that companies use to increase efficiency by receiving goods only when they are needed. Minimizing inventory reduces storage costs and potential waste, but means that if a supplier runs out of goods, the delay spreads throughout the supply chain. Registered mail Natural physicsJosé Moran and colleagues provide a theory of statistical mechanics to explain the risks. Their model shows that the supply chain can avoid system-wide delays if companies’ buffers against delays are large enough. However, at a critical value there is a transition to a state in which delays can accumulate without limit.

In this middle-field case, if the noise terms are exponentially distributed and the buffer is the same for each node, it is possible to solve the model precisely in the limit of infinite nodes to reveal a transition at a critical buffer value.