Showing posts with label complex. Show all posts
Showing posts with label complex. Show all posts

Wednesday, 20 March 2013

System dynamics

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Dynamic stock and flow diagram of model New product adoption (model from article by John Sterman 2001)
System dynamics is an approach to understanding the behaviour of complex systems over time. It deals with internal feedback loops and time delays that affect the behaviour of the entire system.[1] What makes using system dynamics different from other approaches to studying complex systems is the use of feedback loops and stocks and flows. These elements help describe how even seemingly simple systems display baffling nonlinearity.

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[edit] Overview

System Dynamics (SD) is a methodology and mathematical modeling technique for framing, understanding, and discussing complex issues and problems. Originally developed in the 1950s to help corporate managers improve their understanding of industrial processes, system dynamics is currently being used throughout the public and private sector for policy analysis and design.[2]
Convenient GUI 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 (mutual causation) 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 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 for understanding the dynamic behavior of complex systems. The basis of the method is the recognition that the structure of any system — the 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. It is also claimed that because there are often properties-of-the-whole which cannot be found among the properties-of-the-elements, in some cases the behavior of the whole cannot be explained in terms of the behavior of the parts.

[edit] History

System dynamics was created during the mid-1950s[3] 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 (GE) 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 (or calculations) 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 beginning of the field of system dynamics.[2]
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 (Simulation of Industrial Management Problems with Lots of Equations) in the spring of 1958. In 1959, Phyllis Fox and Alexander Pugh wrote the first version of DYNAMO (DYNAmic MOdels), 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.[2]
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 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.[2]
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 (its sources of renewable and nonrenewable resources and its sinks for the disposal of pollutants) 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.[2]

[edit] Topics in systems dynamics

The 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.

[edit] Causal loop diagrams

In the System Dynamics methodology, a problem or a system (e.g., ecosystem, political system or mechanical system) is first represented as a causal loop diagram.[4] 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 (see figure below), 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.[5]
The causal loop diagram of the new product introduction may look as follows:
Causal loop diagram of New product adoption model
There are two feedback loops in this diagram. The positive reinforcement (labeled R) 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 (or "balancing" and hence labeled B). Clearly growth can not 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 would expect growing sales in the initial years, and then declining sales in the later years.
Causal loop diagram of New product adoption model with nodes values after calculus
In this dynamic causal loop diagram :
  • step1 : (+) green arrows show that Adoption rate is function of Potential Adopters and Adopters
  • step2 : (-) red arrow shows that Potential adopters decreases by Adoption rate
  • step3 : (+) blue arrow shows that Adopters increases by Adoption rate

[edit] 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.
A flow is the rate of accumulation of the stock
In our 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.
Stock and flow diagram of New product adoption model

[edit] 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.[6]
  • Simulate the model and analyse results.
In this example, the equations that change the two stocks via the flow are:
 \ \mbox{Potential adopters} = \int_{0} ^{t} \mbox{-New adopters }\,dt  \ \mbox{Adopters} = \int_{0} ^{t} \mbox{New adopters }\,dt 

[edit] 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 :
1) \ \mbox{Probability that contact has not yet adopted}=\mbox{Potential adopters} / (\mbox{Potential adopters } + \mbox{ Adopters}) 2) \ \mbox{Imitators}=q \cdot \mbox{Adopters} \cdot \mbox{Probability that contact has not yet adopted}3) \ \mbox{Innovators}=p \cdot \mbox{Potential adopters} 4) \ \mbox{New adopters}=\mbox{Innovators}+\mbox{Imitators} 4.1) \ \mbox{Potential adopters}\ -= \mbox{New adopters }\ 4.2) \ \mbox{Adopters}\ += \mbox{New adopters }\ 
\ p=0.03 \ q=0.4 

[edit] Dynamic simulation results

The dynamic simulation results show that the behaviour of the system would be to have growth in adopters that follows a classical s-curve shape.
The increase in adopters is very slow initially, then exponential growth for a period, followed ultimately by saturation.
Dynamic stock and flow diagram of New product adoption model
Stocks and flows values for years = 0 to 15

[edit] Equations in continuous time

To get intermediate values and better accuracy, the model can run in continuous time : we multiply the number of units of time and we proportionally divide values that change stock levels. In this example we multiply the 15 years by 4 to obtain 60 trimesters, and we divide the value of the flow by 4.
Dividing the value is the simplest with the Euler method, but other methods could be imployed instad, such as Runge–Kutta methods.
List of the equations in continuous time for trimesters = 1 to 60 :
  • They are the same equations as in the section Equation in discrete time above, except equations 4.1 and 4.2 replaced by following :
10) \ \mbox{Valve New adopters}\ = \mbox{New adopters} \cdot TimeStep 10.1) \ \mbox{Potential adopters}\ -= \mbox{Valve New adopters} 10.2) \ \mbox{Adopters}\ += \mbox{Valve New adopters } 
 \ TimeStep = 1/4 
  • In the below stock and flow diagram, the intermediate flow 'Valve New adopters' calculates the equation :
 \ \mbox{Valve New adopters}\ = \mbox{New adopters } \cdot TimeStep 
Dynamic stock and flow diagram of New product adoption model in continuous time

[edit] Application

System dynamics has found application in a wide range of areas, for example population, ecological and economic systems, which usually interact strongly with each other.
System dynamics have various "back of the envelope" management applications. They are a potent tool to:
  • Teach system thinking reflexes to persons being coached
  • Analyze and compare assumptions and mental models about the way things work
  • Gain qualitative insight into the workings of a system or the consequences of a decision
  • Recognize archetypes of dysfunctional systems in everyday practice
Computer software is used to simulate a system dynamics model of the situation being studied. Running "what if" simulations to test certain policies on such a model can greatly aid in understanding how the system changes over time. System dynamics is very similar to systems thinking and constructs the same causal loop diagrams of systems with feedback. However, system dynamics typically goes further and utilises simulation to study the behaviour of systems and the impact of alternative policies.[7]
System dynamics has been used to investigate resource dependencies, and resulting problems, in product development.[8][9]

[edit] Example

Causal loop diagram of a model examining the growth or decline of a life insurance company.[10]
The figure above is a causal loop diagram of a system dynamics model created to examine forces that may be responsible for the growth or decline of life insurance companies in the United Kingdom. A number of this figure's features are worth mentioning. The first is that the model's negative feedback loops are identified by "C's," which stand for "Counteracting" loops. The second is that double slashes are used to indicate places where there is a significant delay between causes (i.e., variables at the tails of arrows) and effects (i.e., variables at the heads of arrows). This is a common causal loop diagramming convention in system dynamics. Third, is that thicker lines are used to identify the feedback loops and links that author wishes the audience to focus on. This is also a common system dynamics diagramming convention. Last, it is clear that a decision maker would find it impossible to think through the dynamic behavior inherent in the model, from inspection of the figure alone.[10]

[edit] Example of piston motion

  • 1.Objective : study of a crank-connecting rod system.
We want to model a crank-connecting rod system through a system dynamic model. Two different full descriptions of the physical system with related systems of equations can be found hereafter (English) and hereafter (French) : they give the same results. In this example, the crank, with variable radius and angular frequency, will drive a piston with a variable connecting rod length.
  • 2.System dynamic modeling : the system is now modelled, according to a stock and flow system dynamic logic.
Below figure shows stock and flow diagram :
Stock and flow diagram for crank-connecting rod system dynamic
  • 3.Simulation : the behavior of the crank-connecting rod dynamic system can then be simulated.
Next figure is a 3D simulation, created using the Procedural animation technic. Variables of the model animate all parts of this animation : crank, radius, angular frequency, rod length, piston position.
3D Procedural animation of the crank-connecting rod system modeled in 2

[edit] See also

[edit] References

  1. ^ MIT System Dynamics in Education Project (SDEP)
  2. ^ a b c d e Michael J. Radzicki and Robert A. Taylor (2008). "Origin of System Dynamics: Jay W. Forrester and the History of System Dynamics". In: U.S. Department of Energy's Introduction to System Dynamics. Retrieved 23 Oktober 2008.
  3. ^ Forrester, Jay (1971). Counterintuitive behavior of social systems. Technology Review 73(3): 52–68
  4. ^ Sterman, John D. (2000). Business Dynamics: Systems Thinking and Modeling for a Complex World. New York: McGraw
  5. ^ Meadows, Donella. (2008). Thinking in Systems: A Primer. Earthscan
  6. ^ Sterman, John D. (2001). "System dynamics modeling: Tools for learning in a complex world". California management review 43 (4): 8–25.
  7. ^ System Dynamics Society
  8. ^ Repenning, Nelson P. (2001). "Understanding fire fighting in new product development". The Journal of Product Innovation Management 18 (5): 285–300. doi:10.1016/S0737-6782(01)00099-6.
  9. ^ Nelson P. Repenning (1999). Resource dependence in product development improvement efforts, Massachusetts Institute of Technology Sloan School of Management Department of Operations Management/System Dynamics Group, dec 1999.
  10. ^ a b Michael J. Radzicki and Robert A. Taylor (2008). "Feedback". In: U.S. Department of Energy's Introduction to System Dynamics. Retrieved 23 October 2008.

[edit] Further reading

[edit] External links

Systems Science

Systems, and System Science can have relevance to Economics. RS
 
 
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Impression of systems thinking about society[1]
Systems science is an interdisciplinary field that studies the nature of complex systems in nature, society, and science itself. It aims to develop interdisciplinary foundations that are applicable in a variety of areas, such as engineering, biology, medicine, and social sciences.
Systems science covers formal sciences such as complex systems, cybernetics, dynamical systems theory, and systems theory, and applications in the field of the natural and social sciences and engineering, such as control theory, operations research, social systems theory, systems biology, systems dynamics, systems ecology, systems engineering and systems psychology.

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[edit] Theories

Since the emergence of the General Systems Research in the 1950s systems thinking and systems science have developed into many theoretical frameworks.
Systems notes of Henk Bikker, TU Delft, 1991
Systems analysis
Systems analysis is the branch of systems science that analyzes systems and the interactions within those systems, often prior to their automation as computer models. This field is closely related to operations research.
Systems design
In computing, systems design is the process or art of defining the hardware and software architecture, components, modules, interfaces, and data for a computer system to satisfy specified requirements. One could see it as the application of systems theory to computing. Some overlap with the discipline of systems analysis appears inevitable.
System dynamics
System dynamics is an approach to understanding the behaviour of complex systems over time. It deals with internal feedback loops and time delays that affect the behaviour of the entire system.[2] What makes using system dynamics different from other approaches to studying complex systems is the use of feedback loops and stocks and flows. These elements help describe how even seemingly simple systems display baffling nonlinearity.
Systems engineering
Systems engineering (SE) is an interdisciplinary field of engineering, that focuses on the development and organization of complex artificial systems. Systems engineering has emerged into all kinds of sciences, and universities nowadays offer all kinds of specialized academic programs.[3]
Systems Methodologies
There are several types of Systems Methodologies, that is, disciplines for analysis of systems. For example:
  • Soft Systems Methodology (SSM) : in the field of organizational studies is an approach to organisational process modelling, and it can be used both for general problem solving and in the management of change. It was developed in England by academics at the University of Lancaster Systems Department through a ten-year Action Research programme.
  • System Development Methodology (SDM) in the field of IT development is a general term applied to a variety of structured, organized processes for developing information technology and embedded software systems.
  • Viable systems approach (vSa) is a methodology useful for the understanding and governance of complex phenomena; it has been successfully proposed in the field of management, decision making, marketing and service.
Systems theories
Systems theory is an interdisciplinary field that studies complex systems in nature, society, and science. More specifically, it is a conceptual framework by which one can analyze and/or describe any group of objects that work in concert to produce some result.
Systems science
Systems sciences are scientific disciplines partly based on systems thinking such as chaos theory, complex systems, control theory, cybernetics, sociotechnical systems theory, systems biology, systems ecology, systems psychology and the already mentioned systems dynamics, systems engineering, and systems theory.

[edit] Fields

Systems sciences cover formal sciences like dynamical systems theory and applications in the natural and social sciences and engineering, such as social systems theory and systems dynamics.

[edit] Systems scientists

General systems scientists can be divided into different generations. The founders of the systems movement like Ludwig von Bertalanffy, Kenneth Boulding, Ralph Gerard, James Grier Miller, George J. Klir,and Anatol Rapoport were all born between 1900 and 1920. They all came from different natural and social science disciplines and joined forces in the 1950s to established the general systems theory paradigm. Along with the organization of their efforts a first generation of systems scientists rose.
Among them were other scientists like Ackoff, Ashby and Churchman, who popularized the systems concept in the 1950s and 1960s. These scientists inspired and educated a second generation with more notable scientist like Ervin Laszlo (1932) and Fritjof Capra (1939), who wrote about systems theory in the 1970s and 1980s. Others got acquainted and started studying these works in the 1980s and started writing about it since the 1990s. Debora Hammond can be seen as a typical representative of these third generation of general systems scientists.

[edit] Organizations

The International Society for the Systems Sciences (ISSS) is an organisation for interdisciplinary collaboration and synthesis of systems sciences. The ISSS is unique among systems-oriented institutions in terms of the breadth of its scope, bringing together scholars and practitioners from academic, business, government, and non-profit organizations. Based on fifty years of tremendous interdisciplinary research from the scientific study of complex systems to interactive approaches in management and community development. This society was initially conceived in 1954 at the Stanford Center for Advanced Study in the Behavioral Sciences by Ludwig von Bertalanffy, Kenneth Boulding, Ralph Gerard, and Anatol Rapoport.
In the field of systems science the International Federation for Systems Research (IFSR) is an international federation for global and local societies in the field of systems science. This federation is a non-profit, scientific and educational agency founded in 1981, and constituted of some thirty member organizations from various countries. The overall purpose of this Federation is to advance cybernetic and systems research and systems applications and to serve the international systems community.
The best known research institute in the field is the Santa Fe Institute (SFI) located in Santa Fe, New Mexico, United States, dedicated to the study of complex systems. This institute was founded in 1984 by George Cowan, David Pines, Stirling Colgate, Murray Gell-Mann, Nick Metropolis, Herb Anderson, Peter A. Carruthers, and Richard Slansky. All but Pines and Gell-Mann were scientists with Los Alamos National Laboratory. SFI's original mission was to disseminate the notion of a separate interdisciplinary research area, complexity theory referred to at SFI as complexity science.
In India, the Indian Institute of Technology, Jodhpur has set up a Center of Excellence in Systems Science, offering a research as well as an academic platform for students at undergraduate, post graduate and doctoral levels.

[edit] See also

[edit] References

  1. ^ Illustration is made by Marcel Douwe Dekker (2007) based on an own standard and Pierre Malotaux (1985), "Constructieleer van de mensenlijke samenwerking", in BB5 Collegedictaat TU Delft, pp. 120-147.
  2. ^ MIT System Dynamics in Education Project (SDEP)
  3. ^ See for further details: List of systems engineering at universities

[edit] Further reading

  • B. A. Bayraktar, Education in Systems Science, 1979, 369 pp.
  • Kenneth D. Bailey, "Fifty Years of Systems Science:Further Reflections", Systems Research and Behavioral Science, 22, 2005, pp. 355–361. doi:10.1002/sres.711
  • Robert L. Flood, Ewart R Carson, Dealing with Complexity: An Introduction to the Theory and Application of Systems Science, 1988.
  • George J. Klir, Facets of Systems Science, Plenum Press, 1991.
  • Ervin László, Systems Science and World Order: Selected Studies, 1983.
  • Anatol Rapoport (ed.), General Systems: Yearbook of the Society for the Advancement of General Systems Theory, Society for General Systems Research, Vol 1., 1956.
  • Rugai, Nick, Computational Epistemology: From Reality to Wisdom, Second Edition, Book, 2013, Lulu Press, ISBN 978-1-300-47723-5
  • Li D. Xu, "The contributions of Systems Science to Information Systems Research", Systems Research and Behavioral Science, 17, 2000, pp. 105–116.
  • Graeme Donald Snooks, "A general theory of complex living systems: Exploring the demand side of dynamics", Complexity, vol. 13, no. 6, July/August 2008.
  • John N. Warfield, "A proposal for Systems Science", Systems Research and Behavioral Science, 20, 2003, pp. 507–520. doi:10.1002/sres.528

[edit] External links