Nonlocal failures in complex supply networks by single link additions

How do local topological changes affect the global operation and stability of complex supply networks? Studying supply networks on various levels of abstraction, we demonstrate that and how adding new links may not only promote but also degrade stable operation of a network. Intriguingly, the resulting overloads may emerge remotely from where such a link is added, thus resulting in nonlocal failure. We link this counter-intuitive phenomenon to Braess' paradox originally discovered in traffic networks. We use elementary network topologies to explain its underlying mechanism for different types of supply networks and find that it generically occurs across these systems. As an important consequence, upgrading supply networks such as communication networks, biological supply networks or power grids requires particular care because even adding only single connections may destabilize normal network operation and induce disturbances remotely from the location of structural change and even global cascades of failures.Comment: 12 pages, 10 figure

Physics, Stability and Dynamics of Supply Networks

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the non-linear behaviour is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting new features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed "bull-whip effect" in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.Comment: For related work see http://www.helbing.or

Big data and humanitarian supply networks: Can Big Data give voice to the voiceless?

This is the author's accepted manuscript. The final published article is available from the link below. Copyright © 2013 IEEE.Billions of US dollars are spent each year in emergency aid to save lives and alleviate the suffering of those affected by disaster. This aid flows through a humanitarian system that consists of governments, different United Nations agencies, the Red Cross movement and myriad non-governmental organizations (NGOs). As scarcer resources, financial crisis and economic inter-dependencies continue to constrain humanitarian relief there is an increasing focus from donors and governments to assess the impact of humanitarian supply networks. Using commercial (`for-profit') supply networks as a benchmark; this paper exposes the counter-intuitive competition dynamic of humanitarian supply networks, which results in an open-loop system unable to calibrate supply with actual need and impact. In that light, the phenomenon of Big Data in the humanitarian field is discussed and an agenda for the `datafication' of the supply network set out as a means of closing the loop between supply, need and impact

Optimizing operations of large water supply networks: a case study

In this paper we propose a mathematical programming model for a large drinking water supply network and discuss some possible extensions. The proposed optimization model is of a real water distribution network, the largest water supply network in Flanders. The problem is nonlinear, nonconvex and involves some binary variables, making it belong to the class of NP-hard problems. We discuss a way to convexify the nonconvex term and show some results on two case instances of the actual network

Modeling Supply Networks and Business Cycles as Unstable Transport Phenomena

Physical concepts developed to describe instabilities in traffic flows can be generalized in a way that allows one to understand the well-known instability of supply chains (the so-called ``bullwhip effect''). That is, small variations in the consumption rate can cause large variations in the production rate of companies generating the requested product. Interestingly, the resulting oscillations have characteristic frequencies which are considerably lower than the variations in the consumption rate. This suggests that instabilities of supply chains may be the reason for the existence of business cycles. At the same time, we establish some link to queuing theory and between micro- and macroeconomics.Comment: For related work see http://www.helbing.or

Network-Induced Oscillatory Behavior in Material Flow Networks

Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of power grids remains to be explored. Based on a simple model of supply networks, we offer an interpretation of instabilities and oscillations observed in biological, ecological, economic, and engineering systems. We find that most supply networks display damped oscillations, even when their units - and linear chains of these units - behave in a non-oscillatory way. Moreover, networks of damped oscillators tend to produce growing oscillations. This surprising behavior offers, for example, a new interpretation of business cycles and of oscillating or pulsating processes. The network structure of material flows itself turns out to be a source of instability, and cyclical variations are an inherent feature of decentralized adjustments.Comment: For related work see http://www.helbing.or

Optimizing operations of large-scale water supply networks: a case study

In this paper we propose a mathematical programming model for a large drinking water supply network and discuss some possible extensions. The proposed optimization model is of a real water distribution network, the largest water supply network in Flanders. The problem is nonlinear, nonconvex and involves some binary variables, making it belong to the class of NP-hard problems. We discuss a way to convexify the nonconvex term and show some results on two case instances of the actual network