System dynamics


System dynamics is an approach to understanding the nonlinear behaviour of complex systems over time using stocks, flows, internal feedback loops, table functions and time delays.

Overview

System dynamics is a mathematical modeling technique to frame, understand, and discuss complex systems. Originally developed in the 1950s to help corporate managers improve their understanding of industrial processes, SD is being used in the 2000s throughout the public and private sector for policy analysis and design.
Convenient graphical user interface system dynamics software developed into user friendly versions by the 1990s and have been applied to diverse systems. SD models solve the problem of simultaneity by updating all variables in small time increments with positive and negative feedbacks and time delays structuring the interactions and control. The best known SD model is probably the 1972 The Limits to Growth. This model forecast that exponential growth of population and capital, with finite resource sources and sinks and perception delays, would lead to economic collapse during the 21st century under a wide variety of growth scenarios.
System dynamics is an aspect of systems theory as a method to understand the dynamic behavior of complex systems. It is a property of complex systems that the structure of any system, with many circular, interlocking, sometimes time-delayed relationships among its components, is often just as important in determining its behavior as the individual components themselves. Examples are chaos theory and social dynamics. There are often emergent properties and behaviour of the system which are not properties and behaviour of the individual parts.

History

System dynamics was created during the mid-1950s by Professor Jay Forrester of the Massachusetts Institute of Technology. In 1956, Forrester accepted a professorship in the newly formed MIT Sloan School of Management. His initial goal was to determine how his background in science and engineering could be brought to bear, in some useful way, on the core issues that determine the success or failure of corporations. Forrester's insights into the common foundations that underlie engineering, which led to the creation of system dynamics, were triggered, to a large degree, by his involvement with managers at General Electric during the mid-1950s. At that time, the managers at GE were perplexed because employment at their appliance plants in Kentucky exhibited a significant three-year cycle. The business cycle was judged to be an insufficient explanation for the employment instability. From hand simulations of the stock-flow-feedback structure of the GE plants, which included the existing corporate decision-making structure for hiring and layoffs, Forrester was able to show how the instability in GE employment was due to the internal structure of the firm and not to an external force such as the business cycle. These hand simulations were the start of the field of system dynamics.
During the late 1950s and early 1960s, Forrester and a team of graduate students moved the emerging field of system dynamics from the hand-simulation stage to the formal computer modeling stage. Richard Bennett created the first system dynamics computer modeling language called SIMPLE in the spring of 1958. In 1959, Phyllis Fox and Alexander Pugh wrote the first version of
DYNAMO, an improved version of SIMPLE, and the system dynamics language became the industry standard for over thirty years. Forrester published the first, and still classic, book in the field titled Industrial Dynamics in 1961.
From the late 1950s to the late 1960s, system dynamics was applied almost exclusively to corporate/managerial problems. In 1968, however, an unexpected occurrence caused the field to broaden beyond corporate modeling. John F. Collins, the former mayor of Boston, was appointed a visiting professor of Urban Affairs at MIT. The result of the Collins-Forrester collaboration was a book titled Urban Dynamics. The Urban Dynamics model presented in the book was the first major non-corporate application of system dynamics. In 1967, Richard M. Goodwin published the first edition of his paper "A Growth Cycle", which was the first attempt to apply the principles of system dynamics to economics. He devoted most of his life teaching what he called "Economic Dynamics", which could be considered a precursor of modern Non-equilibrium economics.
The second major noncorporate application of system dynamics came shortly after the first. In 1970, Jay Forrester was invited by the Club of Rome to a meeting in Bern, Switzerland. The Club of Rome is an organization devoted to solving what its members describe as the "predicament of mankind"—that is, the global crisis that may appear sometime in the future, due to the demands being placed on the Earth's carrying capacity by the world's exponentially growing population. At the Bern meeting, Forrester was asked if system dynamics could be used to address the predicament of mankind. His answer, of course, was that it could. On the plane back from the Bern meeting, Forrester created the first draft of a system dynamics model of the world's socioeconomic system. He called this model WORLD1. Upon his return to the United States, Forrester refined WORLD1 in preparation for a visit to MIT by members of the Club of Rome. Forrester called the refined version of the model WORLD2. Forrester published WORLD2 in a book titled World Dynamics.

Topics in systems dynamics

The primary elements of system dynamics diagrams are feedback, accumulation of flows into stocks and time delays.
As an illustration of the use of system dynamics, imagine an organisation that plans to introduce an innovative new durable consumer product. The organisation needs to understand the possible market dynamics in order to design marketing and production plans.

Causal loop diagrams

In the system dynamics methodology, a problem or a system may be represented as a causal loop diagram. A causal loop diagram is a simple map of a system with all its constituent components and their interactions. By capturing interactions and consequently the feedback loops, a causal loop diagram reveals the structure of a system. By understanding the structure of a system, it becomes possible to ascertain a system's behavior over a certain time period.
The causal loop diagram of the new product introduction may look as follows:
Image:Adoption CLD.svg|centre|Causal loop diagram of New product adoption model|frame
There are two feedback loops in this diagram. The positive reinforcement loop on the right indicates that the more people have already adopted the new product, the stronger the word-of-mouth impact. There will be more references to the product, more demonstrations, and more reviews. This positive feedback should generate sales that continue to grow.
The second feedback loop on the left is negative reinforcement. Clearly, growth cannot continue forever, because as more and more people adopt, there remain fewer and fewer potential adopters.
Both feedback loops act simultaneously, but at different times they may have different strengths. Thus one might expect growing sales in the initial years, and then declining sales in the later years. However, in general a causal loop diagram does not specify the structure of a system sufficiently to permit determination of its behavior from the visual representation alone.

Stock and flow diagrams

Causal loop diagrams aid in visualizing a system's structure and behavior, and analyzing the system qualitatively. To perform a more detailed quantitative analysis, a causal loop diagram is transformed to a stock and flow diagram. A stock and flow model helps in studying and analyzing the system in a quantitative way; such models are usually built and simulated using computer software.
A stock is the term for any entity that accumulates or depletes over time. A flow is the rate of change in a stock.
Image:Simple stock and flow diagram.gif|centre|frame|A flow is the rate of accumulation of the stock
In this example, there are two stocks: Potential adopters and Adopters. There is one flow: New adopters. For every new adopter, the stock of potential adopters declines by one, and the stock of adopters increases by one.
Image:Adoption SFD.png|centre|Stock and flow diagram of New product adoption model|frame

Equations

The real power of system dynamics is utilised through simulation. Although it is possible to perform the modeling in a spreadsheet, there are a variety of software packages that have been optimised for this.
The steps involved in a simulation are:
  • Define the problem boundary.
  • Identify the most important stocks and flows that change these stock levels.
  • Identify sources of information that impact the flows.
  • Identify the main feedback loops.
  • Draw a causal loop diagram that links the stocks, flows and sources of information.
  • Write the equations that determine the flows.
  • Estimate the parameters and initial conditions. These can be estimated using statistical methods, expert opinion, market research data or other relevant sources of information.
  • Simulate the model and analyse results.
In this example, the equations that change the two stocks via the flow are:

Equations in discrete time

List of all the equations in discrete time, in their order of execution in each year, for years 1 to 15 :

Dynamic simulation results

The dynamic simulation results show that the behaviour of the system would be to have growth in adopters that follows a classic s-curve shape.

The increase in adopters is very slow initially, then exponential growth for a period, followed ultimately by saturation.
Image:Adoption SFD ANI.gif|centre|Dynamic stock and flow diagram of New product adoption model|frame
Image:SFDD VAL.gif|centre|Stocks and flows values for years = 0 to 15|frame