5.1. An Overview of the Modelling Process
In system dynamics, five steps of modelling can be identified as shown in Figure 5.1. Usually there is lots of to-and-fro between the steps as understanding of the situation improves by sketching diagrams, quantifying concepts, writing friendly algebra, and making simulations. Step 1 is problem articulation. It is the most important step of all because it shapes the entire study. Here the modeller or modelling team identify the issue of concern, the time frame, the level of analysis (business unit, firm, industry, etc.), the boundary of the study and the likely scope of factors involved. Step 2 is a dynamic hypothesis, a preliminary sketch by the modeller of the main interactions and feedback loops that could explain observed or anticipated performance. Step 3 is formulation, the transformation of a dynamic hypothesis into a reasonably detailed diagram of feedback processes and corresponding algebraic equations. Step 4 is testing. The model is simulated to see whether or not its behaviour over time is plausible and consistent with available evidence from the real world. Step 4 fixes errors and begins to build confidence in the model's integrity. Step 5 is policy formulation and evaluation. By now there is confidence that the model's structure is sound and that it is capable of reproducing the dynamic symptoms of the original problem. Hence, attention shifts to policy changes intended to improve performance and to alleviate the perceived problem. The new policies are then simulated to see how well they work.
Figure 5.1. Modelling is an iterative learning process
Source: Sterman, J. D. Business Dynamics: Systems Thinking and Modeling for a Complex World, © 2000, Irwin McGraw-Hill, Boston, MA. Reproduced with permission of the McGraw-Hill Companies.
Notice these steps are shown as a cycle and not as a linear sequence. The web-like symbol in the middle of the diagram and the circle of arrows around the edge mean that iteration is a natural and important part of the process. For example, it is common for modellers to revise the problem and model boundary as they develop a dynamic hypothesis and causal loops. Thus, step 2 influences step 1. Similarly, formulation and testing can reveal the need for new equations or new structure, because initial simulations contradict common sense (as in the 60-month run of the drug model in Chapter 3) or else reveal that the original dynamic hypothesis is incapable of generating observed or expected behaviour over time. So steps 3 and 4 can influence steps 1 and 2 or each other.
5.1.1. Dynamic Hypothesis and Fundamental Modes of Dynamic Behaviour
From a modeller's perspective, a dynamic hypothesis is a particularly important step of 'complexity reduction' - making sense of a messy situation in the real world. A feedback systems thinker has in mind a number of structure-behaviour pairs that give valuable clues or patterns to look for when explaining puzzling dynamics. Figure 5.2 shows six fundamental modes of dynamic behaviour and the feedback structures that generate them.
The trajectories in the top half of the diagram arise from simple feedback processes. On the left is pure exponential growth caused by a single reinforcing feedback loop in isolation. In the centre is pure goal-seeking behaviour caused by a balancing loop. On the right is s-shaped growth that occurs when exponential growth hits a limit. In this case, a reinforcing loop dominates behaviour to begin with, and then later (due to changing conditions) a balancing loop becomes more and more influential.
Figure 5.2. Dynamic hypothesis and fundamental modes of dynamic behavior
Source: Sterman, J.D., Business Dynamics: Systems Thinking and Modeling for a Complex World, © 2000, Irwin McGraw-Hill, Boston, MA. Reproduced with permission of the McGraw-Hill Companies.
The trajectories in the bottom half of the diagram arise from more complex feedback processes. On the left is classic oscillatory, goal-seeking behaviour with repeated overshoot and undershoot of a target, caused by a balancing loop with a time delay. In the centre is growth with overshoot, a pattern of behaviour where growth from a reinforcing loop hits a limit that is not immediately recognised. This lagged limiting effect is represented as a balancing loop with delay. On the right is overshoot and collapse, which is a variation on growth with overshoot, but here the limit itself is a floating goal that adds an extra reinforcing loop. This set of six structure–behaviour pairs is not exhaustive, but illustrates the principle that any pattern of behaviour over time can be reduced to the interaction of balancing and reinforcing loops.
Some of the most intriguing and complex dynamics arise in situations where multiple feedback loops interact and each loop contains time delays and non-linearities. We meet two such models later in the book, the market growth model in Chapter 7 and the oil producers' model in Chapter 8. Even quite simple linear models with two or three interacting loops and time delays, however, can prove to be very interesting as we will see in the factory model in this chapter. The main point for now is to realise that all such models take shape in a structured yet creative process of discovering feedback processes in everyday affairs.
5.1.2. Team Model Building
Often models are built by teams that include a facilitator, an expert modeller and policy makers/managers (Vennix, 1996). In such team model building, there are three distinct phases of work that cut across the five steps described above and show when and where team members should be most involved. Phase 1 is all about identifying the problem situation and mapping the relevant feedback structure. Normally the facilitator works with policy makers to capture their understanding of the situation and to reframe it dynamically. Phase 1 begins with problem articulation and ends with a stock and flow diagram. The first modelling challenge is to express the problem situation in terms of performance through time. The top of Figure 5.3 shows three examples. The time chart on the left is a sketch of volatile dynamics in a supply chain, where variations in factory production (the solid line) far exceed changes in retail demand (the dotted line). Why does the factory overreact in this way? The contrasting shape of the trajectories for production and demand is a good way to frame the factory's problem dynamically. The time chart in the centre shows drug-related crime as discussed in Chapters 2 and 3. The dynamic problem lies in the growth of crime (the solid line), which far outstrips tolerable crime (the dotted line). Finally, the time chart on the right shows trajectories for factory capacity in new product adoption. The strategic problem, expressed dynamically, is to retire old capacity (the dotted line) while growing new capacity (the solid line). The success of product adoption depends in part on how well the balance of old and new capacity is managed. A model examining this issue in the retail industry is presented in Chapter 10.
Figure 5.3. Team model building – phase 1
A pattern of performance over time is a clue in the search for feedback structure. It is important to realise that feedback loops and asset stocks do not just conveniently present themselves to modellers. There is a highly creative task to discover, among the views and information provided by the team, enduring feedback structure that is capable of generating the dynamics of interest. A dynamic hypothesis is a good starting point. Often a hypothesis is nothing more than a hunch that the structure of interest resembles a particular combination of feedback loops, such as a balancing loop with delay or a reinforcing loop linked to a balancing loop. The hunch can be refined in different ways to arrive at a refined causal loop diagram and ultimately a stock and flow diagram.
The rest of Figure 5.3 shows three alternative paths the modeller can take in going from performance over time to a stock and flow diagram. The appropriate path depends on the situation at hand and also on personal modelling style. One approach, shown on the left, is to sketch a causal loop diagram and then overlay the extra operating detail required for a full stock and flow diagram. This is the approach taken with the drug-related crime model in Chapter 3. However, in practice feedback loops may not be evident at first glance. Instead it is often helpful to create a sector map showing the main parts of the enterprise to be modelled and then to probe their interaction more deeply. This approach is shown on the right of Figure 5.3. It involves mapping the operating policies and stock accumulations in each sector in an effort to discover feedback loops, all the time bearing in mind the dynamic hypothesis. The resulting policy map is then converted into a detailed stock and flow diagram. Yet another approach is to draw the main asset stock accumulations, and then map the network of connections between them. This direct approach is shown in the centre of Figure 5.3.
Phase 1 defines the problem as well as the broad scope and architecture of the model and can be carried out quite quickly. It is not unusual for a team of 5–10 people to contribute. One or two days of work can yield maps of sufficient quality and content to guide algebraic modelling in phase 2. Active participation by policy makers and managers in phase 1 also enhances buy-in to the project and reduces the likelihood that the client will mistrust the model and treat it as a suspicious black box. For these reasons, it is entirely appropriate to involve senior managers and other experienced people in phase 1. Typically, they adopt a broad strategic view of the organisation consistent with the perspective of a feedback systems thinker (even if they themselves have never seen a causal loop before). Moreover, they usually enjoy the mapping process and the resulting overview of their organisation in causal loops or sector maps.
Phase 2 is algebraic modelling and simulation, as shown in Figure 5.4. The stock and flow diagram from phase 1 is converted into friendly algebra and a variety of diagnostic simulations are conducted. This work is demanding and time consuming and is carried out by a dedicated modelling team, usually a subset of the project team, perhaps three or more people, including the facilitator, the expert modeller and at least one person who knows the organisation very well. It can take weeks or even months to create a robust and well-calibrated simulator. There are equations to be written, parameters to be obtained and graphical functions to be sketched. When the formulations are finished simulations can begin, but it is very rare indeed for a model to run plausibly first time. It is best to be highly sceptical of initial runs and treat them as diagnostic simulations that may reveal inadvertent modelling errors. Frequently equation formulations do not work as intended and cause totally implausible behaviour over time, such as price that climbs sky-high or market share that falls below zero. Fixing equations to remove such anomalies of behaviour gradually builds confidence that the model is ready to use with the project team for what-ifs and scenarios. Incidentally, when anomalies cannot be fixed they often reveal a flaw in the way people have been thinking about the dynamics of strategy.
Figure 5.4. Team model building – phases 2 and 3
The model is showing counterintuitive behaviour from which people can learn something new.
Phase 3 is the transfer of insight organisation-wide. The model is transformed into a specially packaged simulator called a 'learning laboratory' or 'microworld', easy enough for anyone in the organisation to operate. It can be used in workshops to communicate the insights from a modelling project to hundreds or even thousands of people in an organisation. The shower simulator in Chapter 4 and the fisheries gaming simulator in Chapter 1 are small-scale examples of such technology, and there are other examples later in the book.