The System Dynamics Modeling Methodology

An Overview

Advances in computer technology have given rise to a new generation of simulation modeling methods. For the first time, engineers can operate virtual machines and strategists can command virtual battlefields. Of greater importance, however, these new simulation technologies apply equally well to management decision-making. State-of-the-art software applications now allow decision-makers to “flight-test” virtual management systems and to quantify the cost and performance tradeoffs of alternative “what-if?” options. Sophisticated simulations of complex management systems promise to revolutionize the way we make decisions. Models will save time, save money, reduce risk and improve performance.

At the forefront of the new simulation technologies, system dynamics extends modeling methods traditionally associated with engineering design and “virtual” battlefield simulation into the arena of management decision-making. Three characteristics distinguish system dynamics from traditional management support tools:

its foundation rests in engineering science, not statistics; it relies on data to support, not control model development; and it presents a dynamic, not static, environment for decision analysis.

Engineering Foundation. System dynamics is rooted in the engineering traditions of control theory and feedback analysis. The engineering approach to model-building emphasizes system structure rather than collection of data. While many traditional modeling techniques apply statistical tools to data sets and infer causal relationships between correlated variables, system dynamics develops explicit descriptions of causal relationships within a formal feedback structure. With this model structure in place, model-builders can then draw upon a wide range of data to calibrate parameter values. The resulting model, verifiable by both common sense and formal mathematics, represents an operational statement about how the world works; the model serves as a simulation testbed for tracing the logical consequences of alternative “what-if?” assumptions, program designs and strategy options.

Data Support. System dynamics models draw upon a much broader set of data than do traditional statistical models yet require far less data for quantifying model parameters. System dynamics models often include parameters that are critical to understanding system behavior but have not been measured through the collection of “hard” data. Because system dynamics methods base model design on system structure, both anecdotal evidence and logical inferences can provide credible values for important “soft” variables. Further, automated routines can quickly identify those model parameters that have the greatest impact on system behavior. With a “short list” of critical data points, analysts can focus limited resources on gathering and verifying only essential data, and not waste resources in the collection of unnecessary data.

Dynamic Environment. In contrast to traditional modeling techniques, system dynamics models capture the highly complex, non-linear feedback relationships that exist in the real world and incorporate the variable time delays that separate actions from events. System dynamics models also include the variables that affect specific management actions. The models recreate dynamic behavior, rather than solving for a steady-state solution. By mimicking system behavior under a wide range of alternative scenarios, system dynamics models allow managers to test alternative assumptions, decisions and policies within a simulated program environment. This dynamic analytical environment provides a method to anticipate and plan for likely future events.

A fuller understanding of the power of system dynamics models in analyzing and controlling system behavior can be found in an explanation of the mechanics of the modeling technology. Model validity depends upon both a clear specification of system structure and an analysis of system behavior. The following material describes both structural and behavioral issues in model-building.

The Mechanics of System Dynamics Modeling

System dynamics models capture the key structural relationships that define a management system. The resulting simulation mirrors reality because the underlying model structure:

Incorporates feedback Distinguishes between correlation and causality; and Captures nonlinear relationships.

Feedback. System dynamics models explicitly incorporate the feedback relationships that define complex systems. Understanding feedback is critical for understanding and controlling system behavior. Management systems like production, acquisition, logistics and technology development consist of complex, non-linear feedback interrelationships. Many variables, linked in complicated webs of interrelationships, affect each other in often surprising ways. We are sometimes surprised by dynamic behavior because, without the aid of computer models, we cannot anticipate how the myriad feedback linkages reinforce or offset each other over time. Most feedback systems are too complex to yield to mental analysis. Yet understanding these feedback mechanisms is essential for effective management of any complex system.

Within any management program, many feedback links connect decision-making with technology, costs, performance and risk. As an example of this feedback structure, Figure 1 diagrams the key relationships within a weapons production program. One would be hard put, even with the aid of the figure, to quantify how a design change that increases the amount of Work To Do (1) will impact Labor Costs (7) and the Work Schedule (10). Decisions concerning design alternatives involve difficult tradeoffs among cost, schedule and performance, tradeoffs that demand considerable management experience and judgment skills.

Figure 1: A Web of Feedback Relationships Controls the Dynamic Behavior of Complex Development Programs

In many programs, the real risk of production management lies in unwittingly creating a decision environment in which none of the tradeoffs appear acceptable. Actions aimed at solving immediate problems can lead to unintended consequences that create new problems while, at the same time, seeming to limit management's options. Costs and performance projections can begin to spiral out of control while the schedule inevitably lengthens. By offering a control structure to test the consequences of alternative “what-if?” assumptions and scenarios, system dynamics simulation models can help managers to avoid ineffective actions, reduce program risk and develop an affordable strategy to meet program requirements.

One of the reasons it is so difficult to foresee the full impact of alternative choices is that, although all of the feedback loops in Figure 1 all affect system behavior, some loops act much faster than others, and some are more powerful than others. Although each loop can affect the system over time, different loops may provide maximum leverage at different points in the production cycle.

A powerful loop with short delays, for example, forces change very quickly. Identification of such loops is critical for controlling system behavior. Weak loops with long delays, on the other hand, offer little leverage, and seldom respond in the short-term to even heroic management efforts. System dynamics models allow decision-makers to differentiate between weak and strong feedback relationships and identify the critical leverage points within a complex system.

By itself, the model structure in Figure 1 is too aggregated to address complex management issues that arise in such complex production processes as shipbuilding, aircraft production or space vehicle development. However, the modular flexibility of system dynamics allows model-builders to create a single structural module, test it for parameter accuracy and behavioral realism, and replicate it. The model structure in Figure 1 can be replicated dozens or hundreds of times to depict each component or subsystem in a complex design. Further, each of the submodels is interrelated -- as in the real world, the rate of work progress on any one element can be dynamically linked to the rate of progress on related elements. An extremely sophisticated model, then, may be easily developed by aggregating a large number of simpler modules. The result is a complex, but realistic model that remains easy to understand.

Correlation and Causality.In addition to feedback, the second characteristic of a structural approach to modeling is causality. In contrast to traditional modeling techniques, system dynamics models explicitly define cause-and-effect relationships. Statistical regression models, for example, only establish correlations -- causality must be inferred. Although critical to effective decision-making, understanding the difference between correlation and causality is not always intuitively easy. Regression studies show, for example, a positive correlation between the weight of a ship and its cost -- as weight increases, so does cost. Causality, however, is implicit; by itself, the regression model does not prove that reducing weight will reduce cost anymore than reducing cost will reduce weight.

Erroneous causal inferences based on correlations commonly occur. For example, in the 1970s, regression models used by the Department of Housing and Urban Development (HUD) correlated urban blight with an inadequacy of affordable housing. Policy makers concluded that the provision of better housing would eliminate blight. Decades later, after spending hundreds of millions of dollars on the construction of low-income housing, urban blight remains. If history is a guide, the correlation between housing and blight is not an indicator of a direct causal relationship. Other causal relationships, not recoverable from the data, must be at work.

System dynamics models explicitly incorporate causality, including feedback and delays, to build a system structure in which assumed causal relationships can be directly tested. Such causal models help to identify effective management options and avoid costly mistakes.

Nonlinear Relationships. The third important structural element is nonlinear relationships, critical to realistic simulations and projections. A non-linear relationship exists when the rate of change of one variable speeds up or slows down relative to a constant rate of change of another, related variable. For example, most managers would agree that production work done under schedule pressure is less likely to be as accurate as work done without schedule pressure. In a realistic model of a weapons production program, an increase in schedule pressure will lower design quality. Figure 2 provides a graph of the nonlinear relationship between schedule pressure and work quality. The heavy line shows that small amounts of schedule pressure have little effect on work quality, but increasing pressures can cause work errors to accumulate, rapidly driving down the quality of the on-going work and increasing the need for costly rework.

Figure 2: Non-Linear Lookup Tables Define Relationships Between Dependent System Elements

Often, just the process of establishing a shape for the nonlinear relationship can offer insight into the system, and help to focus discussion around specific model parameters. In Figure 2, “A” defines a relationship in which increasing schedule pressure has a significant effect on work quality, while “B” defines a relationship in which work quality is much less sensitive to schedule pressure. The model user can specify the shape of this function to reflect their own experience with a particular production process. Model users may even “agree to disagree”, and test the impact of both functions on system behavior. If the model exhibits markedly different behavior in the two cases, management knows the importance of resolving the disagreement; if the differences in model results are negligible, managers can direct resources to more important matters.

System dynamics models often draw upon a wide range of data sources to quantify causal relationships. The methodology is sufficiently flexible to incorporate "soft" variables such as the non-linear relationship assumed in Figure 2. Many static modeling methods omit soft variables because they are difficult to quantify using traditional methods. Because omitting such soft variables is tantamount to assuming the relationship is unimportant to system behavior, system dynamics models include every relationship believed to be critical to behavior, even if the model-builder must rely upon anecdotal data to quantify the variables. The engineering traditions behind the system dynamics methodology have proven that a realistic representation of system structure is far more important than hard data in creating models that accurately mimic the complex behaviors and decision processes that characterize the real world.

Dynamic Behavior. Once the system structure is specified and suitable parameter values chosen, the model is ready for simulation. Simulation takes the model from its initial conditions through a transit behavior to reach a dynamic equilibrium. A model's initial conditions normally define the historical or current conditions of the system. As the model steps through each day, week or month of a simulation run, the conditions evolve as each variable traces a unique path over time.

After a sufficient time, all of the model variables eventually reach an unchanging state. System dynamics models are deterministic. They will tend toward equilibrium. In the real world, however, we do not expect the system to actually reach equilibrium. Too many random disturbances will prevent that. By studying the differences between alternative equilibrium states (and by analyzing the path by which those states are reached), decision-makers can discover which policies and actions push the system toward the most desirable states.

Figure 3: Simulation Traces Dynamic Behavior as an Industrial Production Model Matches Shipments to Changes in Orders

Figure 3 provides a graph of the behavior of a simple economic system. For the purposes of analysis, the model has to be initialized in equilibrium. For the first ten weeks of the simulation, orders exactly match shipments. In week 10, however, a large step decrease in the order rate occurs followed in week 60 by a subsequent step increase in the order rate. The model responds to these unexpected changes in orders by first shedding production capacity and decreasing shipments and then by adding new capacity to meet the increased demand.

Shipments lag orders because the system cannot adjust instantly to changes in demand. At first, while shipments remain above orders, backlog drops. Later, as shipments rise slowly to catch up to increased demand, backlog inflates with unfilled orders. Eventually the system heads back toward equilibrium, with orders and shipments again balanced.

The ability to simulate realistic behavior in response to any "what-if?" scenario gives system dynamics models their power to help analyze policy options. In the example in Figure 3, no company may ever have actually experienced a 25% drop in orders followed a year later by a jump back to its original order rate. Yet the model can trace a realistic response -- shipments and backlog both exhibit reasonable behavior. If more rapid industrial expansion is desired, for example, then managers may change assumptions regarding production lag times or capacity expansion times to test the impact of alternative policy options on system behavior by changing assumptions regarding production lag times or capacity. Such tests help managers discover which actions are most likely to affect system behavior and which actions have little or no impact.

Benefits of System Dynamics

System dynamics models are powerful tools to help understand and leverage the feedback interrelationships of complex management systems. The models offer an operational methodology to support decision-making. Managers can use the models to test "what-if?" scenarios and explore what might have happened - or what could happen - under a variety of different past and future assumptions and across alternative decision choices.

From among many alternative simulation outcomes, it is then possible to choose those strategies that meet the established program objectives at the lowest cost. Models help to quantify cost and performance tradeoffs so that subsequent decision-making is based on more complete and accurate information. Models also help management explore the reasons why long-term costs rise or fall in response to alternative assumptions and policies.

Further, all system dynamics models utilize the same graphic language and hierarchical organization, creating a universal, highly intelligible language for exploring system behavior. Simple diagrams, and their underlying mathematical expressions, greatly facilitate communication. This common language removes many of the ambiguities that plague conventional decision analysis techniques and overcomes the “black box” phenomenon of traditional econometric models.

System dynamics can fundamentally improve the effectiveness of management decision-making and integrate all elements of management processes. What were once believed to be isolated management problems suddenly become interrelated pieces of a much larger puzzle. While system dynamics models will never substitute for practical management experience, models help to capture and structure that experience, and extend decision support throughout an organization.