Assignment D: Stock and flow diagramming with System Dynamics (SD) Nikki Doorhof (5767792) Introduction The goal of system dynamics is to explain behaviour by providing a causal theory (Lane, 2008). This theory will then be used as the basis to change the system structure and the resulting behaviour and improve performance. System dynamics is created by Jay W. Forrester at MIT in the late 1950s. There are two main diagramming techniques that are used in system dynamics: causal loop diagrams (CLDs) and stock/flow diagrams (SFDs). In this paper I will provide a description and examples of the latter technique, based on the article of Lane (2008) about system dynamics. The procedure of developing a model with system dynamics starts with a problem. In most cases people have established a set of causal assumptions about the problem. They have already developed a mental model of the dynamic system (MMODS). The main purpose of diagrams is to develop a presentation of the mental model in order to communicate the underlying assumptions. This way they can be discussed and possibly changed in order to improve performance of the system. This communication can have two different forms. The diagram can be used to represent an existing model in order to explain its behaviour, which is called model exposition. In the other case, the diagram is used for model conceptualization. The diagram serves as a tool to understand the problem and its underlying assumptions and eventually develop a simulation model. Figure 1. Illustration of the bathtub analogy (Lane,2008) As described by Lane (2008) there are three types of variables and two types of causal links in system dynamics. The bathtub analogy can be used to explain the elements in a system dynamics model (see figure 1). The first variable type is the state variable, or stocks in the case of a stock/flow diagram. In the model (figure 2) represented by rectangles. The quantity of this variable can only be affected by the flow variable, valve or regulator symbol in the model. This variable represents the value that is added or subtracted from the state variable. In the example of the bathtub, the water flow adds value to the water volume. The third type is the ordinary variable (indicated in the model by a circle), which does not directly influence the state variables. The link between the stock and flow is called the conserved flow, in the model indicated by a double or thick arrow. The other causal link is the information link, which passes information back to the flow
variable about the level of the stock variable. Feedback about the water volume can influence the tap angle and thereby influences the water flow. An important part of the model is the polarity of the causal links: this link can be a positive effect (+ or s) or a negative effect (- or o). Figure 2. Stock/flow diagram of the bathtub analogy (Lane, 2008) Example Stock/flow diagramming can be used on a wide variation of topics. It is used in science but also in psychology and environmental sustainability, which I will discuss at the section Related literature. As an example I would like to use a SFD of the rabbit and lynx population (Bosque & Salvador, 2010), which is shown in figure 3. The lynx is the predator and the rabbit is the prey. This makes that the first underlying assumption is that the crowding of the rabbits influences the food supply of the lynx. As the number of rabbits decreases the food supply of the lynx also decreases. This relation is indicated by number 1 in the model. Further the model communicates that the rabbit population is depended on two conserved flows, the birth rate of rabbits (which increases the stock) and the death rate of rabbits (which decreases the stock). The birth rate is affected by the value of the rabbit population and also the rabbit birth fraction is taken into account. There are two explanations for the increase the death rate of rabbits: starvation and diseases. Both are caused by the growth of the rabbit population, which naturally increases the number of rabbits with diseases and lowers the food supply which leads to starvation. The population of the lynx is highly dependent on the population of the rabbit. The death rate of the lynx is motivated by the starvation of the lynx, caused by a declining food supply. Both the death rate of the lynx and the rabbit are naturally influenced by their life expectancy.
1 Figure 3. Stock/flow diagram of the rabbit and lynx population
PDD
Activity table Activity Sub-Activity Description Define the purpose of the model Define the model boundary Describe the behaviour Diagram basic mechanisms Create stock and flow diagram Define problem statement Gather relevant data Narrow down audience List necessary components Separate the initial components into two groups Specify which components are stock and which are flow Create historically observed mode Create hypothesized reference mode Decide on a dynamic hypothesis Create diagram illustrating the basic mechanisms Categorize variables Identify causal links Define the underlying problem of the SYSTEM that creates a need for additional knowledge and understanding of the system. The modeller must gather data relevant to the problem statement. The MODEL s structure and behaviour should be understandable for the audience. Create the INITIAL COMPONENTS LIST. Divide the INITIAL COMPONENTS LIST in two lists. One containing the ENDOGENOUS COMPONENTS and the other containing the EXOGENOUS COMPONENTS. Divide the ENDOGENOUS COMPONENTS into STOCKS and FLOWS. The models constructs such a REFERENCE MODE to check for the existence of some phenomenon or behaviour worth modelling. This sub-task results in a HISTORICALLY OBSERVED REFERENCE MODE. The models constructs such a REFERENCE MODE to check for the existence of some phenomenon or behaviour worth modelling. This sub-task results in a HYPOTHESIZED REFENCE MODE. It is used to draw out and test the consequences of the feedback loops and results in a DYNAMIC HYPOTHESIS. Creating a DIAGRAM OF BASIC MECHANISMS is used to better understand feedback loops of the system. The VARIABLES derived from the INTITIAL COMPONENT LIST should be categorized. There are three types of VARIABLES. The CAUSAL LINKS should be divided into two types.
Define polarity of causal links Draw model The polarity of a CAUSAL LINK defines if the link has a positive effect (+) or a negative effect (-). The modeller constructs the model which consists of the VARIABLES and the CAUSAL LINKS between them. Concept table Concept SYSTEM MODEL PURPOSE INITIAL COMPONENTS LIST ENDOGENOUS COMPONENT EXOGENOUS COMPONENT STOCK FLOW REFERENCE MODE HISTORICALLY OBSERVED REFERENCE MODE HYPOTHESIZED REFERENCE MODE DYNAMIC HYPOTHESIS DIAGRAM OF BASIC MECHANISMS Description A system of forces that have created a problem continue to sustain it. A definition of the underlying problem in a SYSTEM, the MODEL s primary audience and the gathered relevant data. All components the modeller sees as necessary for creating a MODEL of the SYSTEM. Dynamic variables involved in the feedback loops of the SYSTEM. Components whose values are not directly affected by the SYSTEM. These will usually be constants or time varying constants, and not stock or flows. A value that can be visualized and measured (e.g. population), or an abstract idea (e.g. reputation). Changed in STOCKS, defined as rates and measured in units of STOCK over time (e.g. birth rate). A plot of the behaviour of key variables (components of the INITIAL COMPONENTS LIST) of a system over time. The graph has time on the horizontal axis and units of the variables on the vertical axis. It roughly simulates the mental model of the SYSTEM. This type of REFERENCE MODE is used when there is historical data available. It is used to generate knowledge about possible causes or solutions to the SYSTEM s problem. When there is no historical data available, the modeller must create a hypothesized reference mode. It consists of a simplified curve, typically drawn by hand, capturing the key features of the behaviour pattern of the important system components. An explanation of the REFERENCE MODE behaviour and should be consistent with the MODEL PURPOSE. The basic mechanisms represent the smallest set of realistic cause-andeffect relations capable of generating the REFERENCE MODE, i.e. the feedback loops in the MODEL.
VARIABLE STATE VARIABLE FLOW VARIABLE ORDINARY VARIABLE CAUSAL LINK CONSERVED FLOW INFORMATION FLOW MODEL There are three types of variables. This type of VARIABLE is only changed by the accumulation into them, or draining out of them, of some quantity. This type of VARIABLE is the quantity of the accumulating or draining process that effects the STATE VARIABLES. This type of VARIABLE does not directly influence the STATE VARIABLES. There are two types of causal links between VARIABLES. The type of CAUSAL LINK between a FLOW VARIABLE and a STATE VARIABLE The type of CAUSAL LINK between ORDINARY VARIABLES and FLOW VARIABLES. The final stock and flow diagram. Related literature System Dynamics can be used for quantitative modelling as well as qualitative modelling (Wolstenholme, 1999). Quantitative modelling was originally used as a computer simulation method to represent the structure of a system. Later on it was used in a qualitative way as a thinking tool in problem solving, with the aim to provide insight into the issue rather than quantify it. Wolstenholme (1999) concludes his paper with the statement that qualitative and quantitative can be blended as they both have important contributions to management thinking. Coyle (2000) reviews the debate between quantitative and qualitative modelling. He discusses the problems of quantification. One problem is the relation of the model to the real problem, which is sometimes insufficient in quantitative models. In these cases qualitative modelling (for example causal-loop diagrams) can be more effective. But in paper by Richardson from 1976 (edited and published by John Sterman in 1986), the problems of these qualitative modelling technique are discussed. These problems arise from the fact that these models are simplified models and make no distinction between information links and conserved flows. The technique of stock/flow diagramming can be used in a wide range of topics. It is often used when creating models about environmental issues. I have selected a couple papers that serve as an example. System Dynamics modelling is used to forecast municipal solid waste generation in a fastgrowing urban region (Dyson & Change, 2005). They used a case study to research the impact and used a simulation tool, Stella, to generate multiple models. The modelling results are used to plan the capacity and locations of material recovery facilities needed to process the generated solid waste. System dynamics is also used to create a model to analyse a hospital waste management system in a developing country (Chaerul et al., 2008). This research also used a case study and the Stella software package, and came to the same conclusion that system of waste production should be adjusted. In some cases models are used to increase public understanding of an (environmental) issue. In a study by Stave (2001) the purpose of the model was to make people aware of the importance of water conservation management in Las Vegas. The developed model effectively showed this and contributed to the understanding of management decision making in this field. In
the paper about environmental sustainability in an agriculture (Saysel et al., 2002) a model is developed and extensively analysed, which has led to improvements in the agricultural policies. References Albin, S., Forrester, J. W., & Breierova, L. (2001). Building a System Dynamics Model: Part 1: Conceptualization. MIT. Bosque, M. D. & N. R. Salvador (2010) Rabbits and Lynx in Northern Canada. Retrieved from https://bosquesalvador.wikispaces.com/case+6+rabbits+and+lynx+sfd Chaerul, M., Tanaka, M., & Shekdar, A. V. (2008). A system dynamics approach for hospital waste management. Waste Management, 28(2), 442-449. Coyle, G. (2000). Qualitative and quantitative modelling in system dynamics: some research questions. System Dynamics Review, 16(3), 225. Dyson, B., & Chang, N. B. (2005). Forecasting municipal solid waste generation in a fast-growing urban region with system dynamics modeling.waste management, 25(7), 669-679. Kainz, D., & Ossimitz, G. (2002). Can students learn stock-flow-thinking? An empirical investigation. In Proceedings of the 20th international conference of the system dynamics society. Lane, D. C. (2000). Diagramming conventions in system dynamics. The Journal of the Operational Research Society, 51(2), 241-245. Lane, D. C. (2008). The emergence and use of diagramming in system dynamics: a critical account. Systems Research and Behavioral Science,25(1), 3-23. Richardson, G. P. (1986). Problems with causal loop diagrams. System dynamics review, 2(2), 158-170. Saysel, A. K., Barlas, Y., & Yenigün, O. (2002). Environmental sustainability in an agricultural development project: a system dynamics approach. Journal of Environmental Management, 64(3), 247-260. Stave, K. A. (2003). A system dynamics model to facilitate public understanding of water management options in Las Vegas, Nevada. Journal of Environmental Management, 67(4), 303-313. Wolstenholme, E. F. (1999). Qualitative vs quantitative modelling: the evolving balance. Journal of the Operational Research Society, 422-428.