How System Dynamics modelling works

System Dynamics (SD) modelling is a computer-based simulation modelling application developed in the 1960s by Prof Jay Forrester that has been used to model a wide range of social and organisational systems.

The fundamental idea of SD is that flows and accumulations are fundamental to understanding the dynamics of all systems. Examples of flows and accumulations are the way that motorcars flow along road systems and accumulate at traffic lights and in parking stations, the way material flows into a factory and accumulates at various points where it is processed to become the finished goods or the way that students flow into a university program and accumulate in various subjects before they graduate.

The software uses a very simple but powerful iconography to model this particular phenomenon. It’s called a stock-flow diagram and comprises inflows, outflows and accumulations. Some people refer to this as “bath tub” dynamics with the inflows being the tap, the accumulation being the bath and the outflow being the plughole.


A common application of this particular stock-flow is a staffing model.


The inflow is Hires, the outflow is Fires and Accumulation is the number of Staff in the organisation.

By plugging in numbers for each of these elements in the stock-flow diagram, we can understand the staffing dynamics.


In this case, Hires a running above Fires so the total number of staff is increasing. The model can also capture the random resignations of staff, recruitment drives and all of the normal dynamics of staffing in an organisation.

Another application of the stock-flow diagram is work coming into an organisation:


Here the structure and dynamics are identical to the staffing model. In this case, the number of cases coming in is greater than the number of cases going out, so the backlog increases.


The great strength of this modelling  technology is that it allows managers to capture these two separate dynamics in one model where the rate at which cases go out of the organisation is directly related to the number of staff.


An interesting demonstration of the power of this software is to try to imagine what the relationship between staff and the backlog will be given the dynamics that have been presented in this example.

It’s actually quite a complex mathematical problem, one that most people are unable to solve in their heads. Yet the software deals with it very easily.

sand bWhat has happened here is that the backlog rises steeply for a short period of time, but the increasing staff numbers very quickly bring it back to zero. It is now obvious  that the organisation is overstaffed.

The model can be expanded to capture increasingly complex dynamic Interactions such as ensuring that the organisation does not become overstaffed.


In this iteration of the model, the Hires are now related to the level of the Backlog. When the backlog reaches zero hires only replace fires.


Once the backlog has disappeared, staffing levels out at 14.

The final oration of the model includes a final quality audit that has a 20% failure rate. This 20% is sent back into the backlog for revisions.


Because the organisation hires staff to deal with the level of the backlog, this increase in workload results in an extra staff member being hired. This extra staff member ensures that the backlog stays at zero.


The strength of this modelling is that it allows managers to test  the impact of organisational decision-making.  In this case, the organisation has decided that it will maintain its backlog at 10 and staff the organisation to achieve this.

However, it is extremely simple to change that assumption allow the backlog to rise to 20 then examine the staffing implications. It is also possible to examine the impact of improving the revision rate by getting  it below the 20% it is currently running at.

Each time these assumptions are changed, the software completes around 1000 calculations. Without simulation, these calculations are extremely complex and time-consuming. Even using Excel spreadsheets, it is not possible to capture the feedback loops between staffing levels and levels of the backlog.

The great strength of using simulation software is that managers can test organisational assumptions much the way engineers test aircraft in a wind tunnel.  It is never possible to test a range of assumptions in real life as the time periods required to get results are prohibitively long and the consequences of bad decisions disastrous. Yet simulation software allows assumptions, some of which may be purely speculative but potentially useful, to be tested in a matter of seconds.

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