(2014) Akkermans – Supply Chain Dynamics
chapter 2 – Introducing the language of
system dynamics
Chapter 2 Models of man: Introducing the language of System Dynamics
§2.1 Stocks & Flows Modeling and Dynamics
Stocks represent accumulations over time (represented by rectangles), while flows (represented by
double arrows) are the rates of change. Understanding the dynamics between stocks and flows is
crucial for system analysis and decision-making processes.
Besides stocks and flows, in a model you can also make use of extra variables to denote a piece of
information that is used to drive one of the other flows, we call this an auxiliary. Can take the form
of a function or a graphical function.
Operations management example: we see inventory as stocks, and production rates as flows.
As soon as there are more than two stocks in a model, it becomes problematic to "solve" the model.
Because of this limitation of calculus, we use simulations. In simulations we do not solve models, but
we calculate step by step in time what the various values are.
§2.2 Positive feedback
Example of a positive feedback loop: money in a bank account. The more money you have, the more
interest you receive, the more money you get, and the more interest you receive in the next period.
The rate of inflow into the stock is defined as some percentage of the stock. The rate of growth in
the bank example goes up every period, which is called exponential growth.
§2.3 Negative feedback
Negative feedback loops are goal-setting. Meaning that a certain value is moving towards a certain
goal (can be explicit or implicit), and correcting its behaviour when it deviates from this goal. The
value of the goal is usually zero. This phenomenon is called exponential decay. Example of decay in
bookvalue (implicit goal) -->
Negative feedback loops can also have an explicit goal. Example: The colder it gets in the room, the
hotter the heating becomes. The more tired I am, the greater the urge to slow down.
§2.4 Material Delays
Delays exist because everything takes time, both in the material world and in our heads. We
distinguish between two types of delays: material delays and information delays. All delays are a
special form of negative feedback and some form of exponential decay. When there is only one
independent stock involved, we call this a 1st order material delay. With two independent stocks a
2nd order dalay, etc.
Graph of a first order delay:
Graph of a third order delay:
chapter 2 – Introducing the language of
system dynamics
Chapter 2 Models of man: Introducing the language of System Dynamics
§2.1 Stocks & Flows Modeling and Dynamics
Stocks represent accumulations over time (represented by rectangles), while flows (represented by
double arrows) are the rates of change. Understanding the dynamics between stocks and flows is
crucial for system analysis and decision-making processes.
Besides stocks and flows, in a model you can also make use of extra variables to denote a piece of
information that is used to drive one of the other flows, we call this an auxiliary. Can take the form
of a function or a graphical function.
Operations management example: we see inventory as stocks, and production rates as flows.
As soon as there are more than two stocks in a model, it becomes problematic to "solve" the model.
Because of this limitation of calculus, we use simulations. In simulations we do not solve models, but
we calculate step by step in time what the various values are.
§2.2 Positive feedback
Example of a positive feedback loop: money in a bank account. The more money you have, the more
interest you receive, the more money you get, and the more interest you receive in the next period.
The rate of inflow into the stock is defined as some percentage of the stock. The rate of growth in
the bank example goes up every period, which is called exponential growth.
§2.3 Negative feedback
Negative feedback loops are goal-setting. Meaning that a certain value is moving towards a certain
goal (can be explicit or implicit), and correcting its behaviour when it deviates from this goal. The
value of the goal is usually zero. This phenomenon is called exponential decay. Example of decay in
bookvalue (implicit goal) -->
Negative feedback loops can also have an explicit goal. Example: The colder it gets in the room, the
hotter the heating becomes. The more tired I am, the greater the urge to slow down.
§2.4 Material Delays
Delays exist because everything takes time, both in the material world and in our heads. We
distinguish between two types of delays: material delays and information delays. All delays are a
special form of negative feedback and some form of exponential decay. When there is only one
independent stock involved, we call this a 1st order material delay. With two independent stocks a
2nd order dalay, etc.
Graph of a first order delay:
Graph of a third order delay:
