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Dynamic Modeling
From SystemsWiki
Models are the things we build to help us better understand situations. When dealing with concepts of reality we have as the only alternative those abstractions we develop as models, or in situations where it is simply to costly to build the real thing, we build models to help us understand. In short models are simplifications, or abstractions, of reality intended to promote understanding. Whether the models we create are good models or poor models depends on the extent to which they aid us in developing the understanding we seek. As to whether a model is correct or incorrect is probably something which will only become evident in time.
The difficulty, or I should say limiting characteristic, of most of the models we build is that they are static in nature. That is, they are models that represent a snapshot of something at a particular point in time. Yet, reality is not static. Reality is constantly changing through our interactions with it, and the interactions between all of its parts, reality is dynamic in its nature. The question arises as to how we can believe that it is possible to build static models of dynamic reality and expect them to aid our understanding to anything more than a very limited extent.
The answer to this question is provided by something call Dynamic Modeling, or as it was probably better known in a prior incarnation, Simulation. Reality operates "in" time, real time. Dynamic Modeling operates "on" time, serving to compress it in such a way that it provides us with a view of the evolution of our constructions through time.
[edit] Savings Account
As an example, consider the interpretation we have of a bank savings account. We know that if we put money in our savings account the bank will periodically pay us interest on the money in the account. This may be represented by the following very simple model in Fig. 1.
This diagram, a very simplistic model, says if I give money to the bank then the bank will give interest to me. Pretty simple, yes? Yet what does this model tell us about how things change over time? Not much.
Now consider the diagram in Fig. 2.
This is what is typically referred to as a Causal Loop Diagram. The intent is to add a bit more information than is found in Fig. 1. If you're not familiar with these diagrams don't let it get to you. They're not as difficult to read as you might think. For addition information on reading these diagrams please refer to the Causal Loop Diagram page.
What the diagram indicates is simply influences between various parts of the system, with indicators as to the nature of the influence being either adds to (+) or subtracts from (-). Fig. 2 has only adds to relations.
Fig. 2 reads as follows: money and interest both serve to increase the principal. Principal acting in conjunction with interest rate adds to interest. This interest then feeds into principal serving to increase it even further. The (R1) loop in the center indicates that this is a Reinforcing Loop in that it feeds upon itself.
Fig. 2 gives some additional information beyond what was provided in Fig. 1. Additional information in terms of how the parts of the system influence each other, yet Fig. 2 still gives us little information about how the system operates "in" time. Fig. 2 is a qualitative view of how a Savings Account operates.
To obtain a quantitative view of what's happening with the Savings Account we really need a different kind of diagram called a Stock & Flow Diagram that can actually be simulated. Fig. 3 is Fig. 2 represented as a Stock & Flow diagram.
There are several aspects of this diagram which are completely hidden in the diagram of Fig. 1.
- principal is something which accumulates, which is why it is represented as represented as a rectangle and referred to as a Stock.
- interest is something which flows into the Stock principal and is referred to as a Flow. The cloud at the left end of the Flow simply indicates we're not concerned where the interest actually comes from in the context of this model.
- deposit another Flow which represents money deposited into the account.
- The connectors between principal and interest, interest rate and interest, money and principal are referred to as Links and only convey information. The Link from money to principal is a bit different as it represents the initial deposit into the Savings Account. If we wanted to take into account regular deposits into the account we would use another Flow to do that.
Suppose we consider the following scenario. If I put $100 in the bank and the bank pays an interest of 1% quarterly, how much money will I have in 8 years? Yes, there is a mathematical formula by which you can calculate this though in most dynamic systems the formulas are of such complexity as to become completely unmanageable.
Fig. 4 is the result of associating, or embedding, equations into the model and running it with quarterly calculations. As a result, the model indicates you would have $137.71 at the end of the 8th year.
Now suppose the bank was paying 1.5% interest as opposed to 1%. How would this change the result? This is presented in Figure 5, which compares the result with Figure 4. This would result in $188.45 at the end of 8 years.
Now suppose I also put another $10 in the account every quarter.
Figure 5 indicates that simply adding $10 a quarter to the account will produce $572.32 at the end of 8 years. A substantial increase, when compared with the result of Fir. 4 and Fig. 5, for a small ongoing addition to the principal.
In each of these examples the static model of the system has not changed, yet the dynamic result is markedly different in each of the examples cited.
Now let's consider an example which isn't quite as simplistic as the Interest and Principal one.
[edit] Consulting Company
Consider a rather high profile consulting company with 120 employees. Of these 120 employees 60 are professionals and 60 are rookies in training to be professionals. The company bills their clients at a rate of $15k per month for professionals and $5k per month for rookies. Also, it takes 6 months to train a rookie to be a professional. Currently the company wants to remain at 120 employees, and since there are 10 professionals that quit each month, the company hires a new rookie for each professional that quits. Figure 6 is a systems thinking diagram of this description.
The overall result of this system is that it is in a steady state as depicted in Fig. 8. The 120 employees of this company will generate $1.2 million a month in revenue, if they're all on billing, which I understand is a somewhat far fetched assumption.
Now, what happens if the Pro Quits rate jumps from 10 to 12 per month beginning in the 4th month? I don't think you're going to find a straight forward mathematical formula which will provide an indication of the implications of this change in the system operation. Plugging this change into the model in Fig. 7 and running the simulation produces the following operational changes in the system.
What Fig. 9 portrays is that in month 4 pro quits jumps from 10 to 12. This one time change sets off a 6 month transition in the system where the number of pros declines from 60 to 48 and the number of Rookies increases from 60 to 72. While this transition is in progress revenue drops accordingly from $1.2 M per month to $1.08 M/month.
This example should provide a foundation for the value of Dynamic Modeling in terms of providing a way of seeing the time compression of reality.
[edit] References
- MapSys used for Causal Loop Diagrams, Stock & Flow Diagrams and Simulations
- Modeling: Where's the Best Place to Start?
- Formulating Questions
- Simulation is not the Answer
- Simulate a Model
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