In the first article of this series we described how logistic chains work. We also talked about the ”just-in-time” model, and we discussed the phenomenon that small delays can have cascading effects when we schedule the whole process in an optimal way. The main idea is that the system can't absord such small delays. In the second article, we went one step further and dived in the mathematics.We discussed how we can use mathematics, and more specifically networks, to study logistics chains. In our research, we found that you can compute how large the buffers should be to make sure that you can meet the demand but also keep the whole system safe from cascading small delays.
The global perspective
There are empirical indications that this cascading effect plays a role not only in train route movements in various countries (the examples mentioned before) but also in international aviation and shipping. The after-effects of the blocking of the Suez Canal by a container ship at the end of March 2021 were estimated at the time to last for many months, which port congestion data that summer appeared to confirm. These are examples that apparently innocuous events, or events that appear to have a very local character, lead to large cascades of delays in transportation of people or of goods. If a particularly crucial component of a production chain, such as a computer chip for instance, is delayed in supply, an entire industry of heavy machinery production (such as cars) which use that computer chip for operation and control, can grind to a halt.
If such an industry is important for a national economy this effect of delay cascading through production networks, can even be a cause of excess variation in countries’ GDPs. The widely known macro-economic ”excess volatility puzzle” could therefore well find its origin here. The reason to do this research, from the point of view of economics, is thus clear. Supply chains are increasingly global; with consumer goods being manufactured in very many steps out of many subcomponents, spreading manufacture out over many continents. The associated cost-effectiveness and consequent benefit for consumers, of lower prices for goods, has a price in the vulnerability to disruption. Having a late delivery of an airfryer or garden gnome might be considered no more than an inconvenience, but delays in the manufacture of an ambulance or an air-defence system can cost lives, and delays in supplies of fossil fuels can still negatively affect the economy of a whole country, despite the growth of renewable energy generation.
Combining forces and investing in quality
The seeds for starting this research project were sown in 2021 when Dr. Debrabata Panja and his student Mark Dekker worked on train operations data provided by the Dutch national railway operator NS. After that Dr. Panja (Utrecht) and Dr. Bouchaud (Paris) commenced generalising the delay propagation highlighted in these data to more general (but also somewhat more abstract) socio-technical systems, making the link to dynamical graph theory using mathematical approaches which are also quite well known in statistical physics. Together with five more researchers from various countries, including myself, and having expertise in a range of disciplines, both analytical results for regular graphs and simulations for somewhat more general types of graphs were carried out. Evidently, in real-world processes the delays do not develop at discrete time steps. Real firms are not located on a regular lattice nor are their buffers all the same. Further research into more realistic network configurations is therefore still necessary and the combination of this with stock management is ongoing.
There is a broader view of this type of interdisciplinary research, where in this case physicists, economists, and mathematicians try to tackle problems which are at the same time fundamental, as well as having a clear application to a real-world problem. Personally, one of my research goals, together with other researchers from a range of disciplines in the exact and social sciences, is to understand the complex social mechanisms behind inequality, segregation and polarisation, in which different types of networks than supply chains play a role. Such research is necessary to design serious, effective, ways to tackle the societal problem that substantial numbers of households continue to experience poor health as well as poor education opportunities and also a poor economic outlook. Along the way, some rather fundamental questions about phase transitions in heterogeneous mixtures and in finite populations are to be tackled too.
The growth of interest in such interdisciplinary research should not be interpreted, as it appears in the media here and there, that the classical exact disciplines of mathematics, physics or chemistry are somehow ‘finished’. Rather, we are seeing the benefits of the deliberate and substantial efforts over the past decades by universities, by institutes of advanced study and by institutes of interdisciplinary studies or institutes for complex systems research, to create an environment where researchers from within disciplines learn from each other and together form a new generation of scientists that take up these new challenges. Interdisciplinary research does not replace the other disciplines but instead it becomes a new branch in its own right. It depends in part on one’s views on the merits of giving prizes for scientific research at all, whether then perhaps a new prize should be created alongside the older ones for the ‘classical’ disciplines to avoid controversies over where particular research ’belongs’.
Such emergence of new scientific endeavour does not happen easily or quickly, and it does not easily fit within the most common existing funding mechanisms for the support of the sciences and of universities. Very often researchers can only remain in research careers by producing very many papers to supply ‘proof of productivity’ in time for their next application for yet another temporary contract. Interdisciplinary research is ‘slow science’ because it takes time for researchers with distinct backgrounds to understand each others’ vocabulary and paradigms. This is true at an individual level for researchers, but also the academic system as a whole needs time to adapt.
For the individual this is time not spent writing another paper, and so engaging in such interdisciplinary research is a luxury only few scientists have. It is paradoxical that, over the past half-century or so, funding of universities (in the Netherlands but also in other countries) has increasingly become grant-dependent, and hence short-term focussed, rather than being funded directly as structural investment by government. This change was implemented by governments with a variety of political flavours over those past decades, sometimes justified as being an answer to a call for more valorisation or profit-generating research. A grant-based system does immediately provide a wide array of handy metrics for output, making demonstrating an increase in such metrics an easy target to pursue. However, the actual goal - of promoting science benefiting society (also for, but not restricted to monetary gains) and creating scientists motivated to pursue such research - is more likely to have been hindered by an over-reliance on a grants-based funding system rather than that it helped, and there is some supporting evidence for that view.
There are therefore arguments in favour of patience rather than immediate gratification, when designing a better way to fund all academic effort (the exact sciences and the social sciences and the humanities and the arts and interdisciplinary). Radical net reductions of funding do not exemplify the required patience for achieving foundational change or breakthroughs. Clearly public funds are not inexhaustible and there are many and varied demands for public spending. What is most popular is not always most necessary and vice versa. With lower funding, over the longer term those societal innovations that for instance can reduce inequities, or improve a country’s earning power, become slower to arrive or are stopped. Even in the short term the effects are felt: those households which already have sufficient assets to access the best (most appropriate) education for their younger members will continue to do so, as opposed to precisely those households which might benefit the most from education. Reducing funding of any form of further education, including academic institutions, is thus likely to be most harmful to precisely those subgroups in society that any government tends to claim to support the most.
Think of a local car dealer selling cars in your region. To make sure new cars are delivered on time a whole mechanism involving various people, factories, and transport companies, must operate in coordination. This is a highly complex process where mathematics plays an important role.
We can use mathematics and more specifically networks to study logistics chains. In the first article we described how logistic chains work. In this second part, we go one step further and dive in the mathematics.
In this article, dear reader, I am going to show you in which way the development of your opinion during the last political issue, the spread of a virus among your acquaintances during the current pandemic, and the alignment of some particles lying inside the device from which you are reading this article are extremely comparable phenomena.
It is safe to say that traveling impacts the peak performance of teams and athletes in general - studies have been done across all kinds of sports that confirm this intuitive idea. Thus, to avoid unfair- and unhappiness, an organizer should aim to minimize the effect of travel time disparities.
The Premier League of Darts is an annual competition where the best darts players of the world compete over several months for the title, and the prize of £275.000. However… the schedule chosen by the PDC is unbalanced: some matches between pairs of specific players will occur relatively often, while others will occur very rarely.
