Modeling Defaults of Companies in Multi-Stage SC Networks

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Agent-based supply chain models are build using small entities (agents), which might represent a single company.
Each of the agents has its own goals and rules of operation programmed into a computer. The interaction between several agents of this kind leads to a more realistic and complex behavior of the system.

There are several different schools for the quantitative analysis of supply chain risks. Simulation is one of them and agent-based models show several distinct advantages: They are both easier to understand and allow for a more complex system behavior, than other quantitative methods.

After this introduction I would like to have a look at a current agent-based supply chain model, which analyzes the effect of bankruptcies on supply chains. The full paper can be downloaded here.


The authors focus on a comprehensive view on the supply chain: several stages (horizontally and vertically) are modeled. Figure 1 shows an exemplary supply chain.

The structure of the supply chain network.
Figure 1: Exemplary Supply Chain Structure (Mizgier et al. 2012)

Each circle represents one node or agent, the connections are drawn as lines.
The model features five additional characteristics worth mentioning:

  1. Price dispersion (prices can vary between companies)
  2. Evolution of supply chain topology (links between companies can be changed, by the agents themselves)
  3. Network reconfiguration (the reconfiguration is based on the price)
  4. Production dynamics (output is determined by the invested working capital)
  5. Dynamics of costs of production (random changes to the environment every five periods, lead to changes in the cost function of the companies)

Last but not least, companies may go bankrupt if they are not able to perform their short therm debts. There are no loans.


First, the network performs as expected. During the first period turbulences can be observed. Figure 2 shows the utilization of working capital during the simulation (1 equals 100%).

Performance of the network
Figure 2: Capacity Utilization (Mizgier et al. 2012)

After 200 iterations a typical start scenario might look like figure 3.

State of the network after the test period
Figure 3: Network Structure after Initialization Period (Mizgier et al. 2012)

Starting from this state the

The firms with the best profit/cost ratio are growing and adding new suppliers, whereas the working capital of the firms whose sales price is higher than the mean price of the given stage is slowly decaying and results in the defaults of firms.

A stable state might look like figure 4.

State of the network after reaching the stable configuration.
Figure 3: Network Structure after Stabilization (Mizgier et al. 2012)

The authors deduce three implications from those results:

  • The first implication is that during the process of assessment of the company’s risk exposure, managers should keep their focus on the global structure of the supply chain network instead of being restricted to the own portfolio of suppliers and customers.
  • Secondly, as a result of the dynamics of the topology of the supply chain network, strong competition in prices and fast changing technology, even the most reliable firms should be monitored and constantly re-evaluated in terms of their production capacity and risks associated with their structure of connections.
  • Third and most important, managers should find ways to cut costs and reinvest the free cash flows in new technology of production, which will allow further cost reductions and the development of new innovative and cheaper products.


Being stuck in the supply chain can lead to negative consequences, when ripple effects cause multiple suppliers and customers to default. Furthermore, these supply chain partners might also not be the most efficient ones, and these prices affect each participating company.
All in all, a great paper, but I would have liked to read more about the authors’ efforts to validate and verify the model’s integrity.


Mizgier, K., Wagner, S., & Holyst, J. (2012). Modeling defaults of companies in multi-stage supply chain networks International Journal of Production Economics, 135 (1), 14-23 DOI: 10.1016/j.ijpe.2010.09.022

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