Chapter 9. Bulls Eye Diagrams

The structure of system dynamics models may be explained with stock and flow diagrams, equilibrium diagrams and causal loop diagrams. The best way to describe a model is with a combination of all of these diagrams coupled with time graphs of the simulation results.

There is one remaining diagram that can prove useful in describing computer models. It's called a bull's eye diagram because it's shaped like the bull's eye in the game of darts. Endogenous variables are placed in the center of the bull's eye; exogenous variables are placed in the outer ring. Excluded variables are placed outside the outer ring. These diagrams are a concise way to portray the system boundary of the model. They are particularly useful for describing a model that has grown too complex to be easily displayed with flow diagrams.

Examples

Let's begin with the sales force model used to study the s-shaped growth in the number of people selling widgets. The causal loop diagram is shown in Figure 9.1. It reveals that the exit rate, widget price, fraction to sales and average salary are exogenous variables. All the remaining variables appear in feedback loops, so they are endogenous.

Figure 9.1. Causal loop diagram of the sales model.

A bull's eye diagram of the sales model is shown in Figure 9.2. The seven endogenous variables are placed anywhere within the inner circle. The three exogenous variables are located anywhere in the outer ring. A few excluded variables are listed outside the outer circle. The diagram is used to emphasize that the model does not deal with widget quality, delivery delays or the color of the widgets. We also ignore the price of competing products and the price of used widgets. At this point, you are probably thinking that we could list hundreds of other variables that are excluded from the model. How many variables should be placed in the diagram? The custom is to list a few variables that might have been included because they are closely related to the model purpose. These might be candidates for inclusion in a future version of the model. Your purpose is to convey a sense for the boundary you have chosen for the model.

Figure 9.2. Bull's eye diagram of the sales model.