System Dynamics
Modeling with
STELLA software
Learning objective

After this class the students should be
able to:






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Understand basic concepts of system
dynamics,
Stock Variable;
Flow Variable;
Information Flow;
Material Flow; and
Time Delay;
Understand how these basics elements interact
with policies and decisions to determine the
behavior of dynamic systems.
Time Management

The expected time to deliver this module is 50
minutes. 20 minutes are reserved for team
practices and exercises and 30 minutes for
lecture.
System Dynamics

Methodology to study systems behavior

It is used to show how the interaction between structures of the
systems and their policies determine the system behavior

Approach developed to study system behaviors taking into
account complex structures of feedbacks and time delays
Warm-up

Each team is invited to describe through any kind of
diagram the process to fill a cup of water.

Imagine this as an exercise of operation management

(5 minutes)
Feedback Loop

Feedback refers to the situation of X affecting Y and Y in
turn affecting X perhaps through a chain of causes and
effects.
Y
X
Z
Time Delay
\It’s the time between the action and the result
(consequence) of this action.
Time Delay
X
Y
Causal Diagram
Desired
Water
Level
Faucet
Position
Perceived
Gap
Water
Flow
Current
Water
Level
Population Dynamic
+
Births
+
+
Population
-
feedbacks and time delays
Deaths
Basic Elements

This methodology use five basics elements:

Stock Variable;

Flow Variable;

Information Flow;

Material Flow; and

Time Delay
Object Oriented Language
Material Flow
Activity
Stock
Information Flow
Converter
A Model
Control
Material Flaw
to Stock
Control
Material Flaw
from Stock
Stock
Send
information
from the Stock
Add New
information
Exploring a simple example



To explore modeling with STELLA, we will
develop interactively with you, a basic
model of the dynamics of a fish
population.
Assume you are the owner of a pond that
is stocked with 200 fish that all reproduce
at a fixed rate of 5% per year.
For simplicity, assume also that none of
the fish die. How many fish will you own
after 20 years?
Stock - Fish Inventory

We begin with the first tool, a stock
(rectangle). In our example model, the
stock will represent the number of fish in
our pond.
Figure 1
Click here
to open the
stella
software
This stock is known as a reservoir. In our
model, this stock represents the number of
fish we have in this time are in our the
pond
What control the number of fish

As we assumed that the fish in our pond
never die, we have one control variable:
REPRODUCTION.
200 Fishes
Figure 2
We use the flow tool (the right-pointing arrow,
second from the left) to represent the control
variable, so named because it controls the states
(variables).
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Converter

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Next we need to know how the fish in our
population reproduce, that is, how to
accurately estimate the number of new
fish per annum. Remember? We assumed
our fish population reproduce at 5% per
year.
This can be represented as a transforming
variable. A transforming variable is
expressed as a converter, the circle that
is second from the right in the STELLA
toolbox.
Connector

At the right of the STELLA, toolbox is the connector
(information arrow). We use the connector to pass
on information about the REPRODUCTION RATE to
REPRODUCTION and another to pass on information
from FISH population to REPRODUCTION.
Figure 3
Our first model

Once you draw the information arrow from the
transforming variable REPRODUCTION RATE to the
control and from the stock FISH to the control,
open the control (REPRODUCTION) and converter
(REPRODUCTION RATE) and type respectively
5/100 and the equation: REPRODUCTION RATE*
FISH
5/100
200
REPRODUCTION RATE*FISH
Figure 4
Run the model

We get Figure 5. We see a graph of exponential
growth of the fish population in your pond.
Figure 5
What-if?
From now on, the professor can practice “what-if” with the
teams
For example:

What would happen if we decided to extract fish at a
constant rate of 3% per year, and the reproduction rate
varied with the fish population as it is seen in figure 6?

Figure 6
New model
Results
Figure 7
Reference


The Fifth Discipline. Peter Senge,
Currency Doubleday, 1994, Chapter 5.
Modeling Dynamic Economic System.
Ruth, M. & Hannon, B. Springer, 1997,
Chapter 1