1.0  ORIENTATION

System Dynamics  is a method for analyzing system problems.  It is based on a straightforward "stocks and flows" structure, designed for modeling systems with numerous variables, and with lagged feedbacks between variables.  Many managerial systems and most social systems have such feedbacks.  In their transient states, such systems are virtually impossible to solve mathematically, so they are usually simulated.  System dynamics simulates such systems on microcomputers, using inexpensive software that now includes graphic output, model documentation, and report generation.  This guide provides an introduction to systems, and modeling them using system dynamics.

System dynamics is useful in policy analysis. The following highly simplified planning problem for the U. S. Navy represents a typical policy problem:

"Three percent real budget growth is anticipated over the next ten years, and acquisitions must be traded off against ownership costs (manning, maintenance, and operations) in each year's planned budget.  Increasing acquisition of ships and aircraft means that ownership funds must be reduced, leading to readiness decay.  Increasing ownership funding, on the other hand, means less acquisitions and reduced future force levels, yet the enhanced readiness may compensate for the smaller forces.  How should the acquisition/ownership tradeoffs be appraised, and how should budgets be adjusted when an unexpected cut in a budget occurs?"

1.1  Introduction

Most realistic problems involve systems and the way they change.  We will discuss using the method of system dynamics for thinking about, understanding, and modeling processes so that problems can be explored and decisions made.

A changing system has two descriptive qualities.  The first concerns the materials flowing through the system.  The second is the configuration (or "structure") that contains and controls the flow of materials. Miser and Quade (1985) open their text on
"Systems Analysis" with an appropriate definition:

"Many of society's problems emerge from processes associated with structures that combine people and the natural environment with various artifacts of man and his technology; these structures can be thought of as systems."

 The manufacture of automobiles has material components such as raw materials and a production labor force, contained in a structure that includes factories, distribution systems, managerial controls, financial policies, and so forth.  The complex process of manufacturing cars occurs within a system that includes production, distribution, and marketing sectors.
A bathtub filling up with water is a more simple process.  Its only material flow is water.  The bath water flows within a structure composed of pipes and the bathtub itself.  The pipes and tub, with the water, make up the system.  If a human controls the water flow, then the human is part of the system.

Processes are modeled by defining the structure and its control variables and then letting the material flows occur.  This requires defining certain components of the system structure, the rules that cause the components to control the material flows, and the status of the material flows at the start time ("time zero"), and then calculating the values of the system variables as time passes.
"Materials" should be interpreted in the broad sense as anything that can be accumulated.  Automobiles and water are materials, but, in systems theory, so are humans.  More abstractly, a human quality, such as "worker productivity" can be material, for it accumulates as work accomplished.  Other human constructs, such as acceleration (which accumulates as velocity), price change (which accumulates as price level), and attitude change (which might accumulate as a community's political position) can all be considered "materials" flowing through a structure, even though some of the materials seem abstract.

System Dynamics is the study of processes through the use of systems and how they can be modeled, explored, and explained.  System modeling can be an elusive skill, and a discussion of modeling seems appropriate.

A model is the representation of a real process.  Models allow studying the process in a laboratory setting -- our lab will be a micro-computer and its predecessor, paper and pencil.  We want to be able to build models on a computer screen, or on a desk pad.

It is very different to build a model, than it is to use a model that has been built.  By modeling, we will mean model building.
To "model" something requires being able to structure one's thinking about the system being studied.  It means defining a model that works almost like the real system.  That is, when materials flow within the modeled system, the various flows and accumulations should provide insight into the real process under study.

Modeling requires both original thinking and practice.  It requires developing structure from non-structure, sometimes from chaos.  Transforming chaos into structure is aided if one understands systems, and how they control the materials flowing within them.

System dynamics provides definitions, bookkeeping tools, and communication methods for system modeling.  It is not so much a "technique", as it is a set of analytic tools for the modeler to use in structuring a problem.

1.2  Structure

 It is not always clear how to begin to model a system.  "Structure" provides the framework for beginning.  Seeing a house being constructed, the foundation poured and walls framed with 2x4 boards, provides a sense of how a house is structured.  Without ever seeing the building process, one might not know where to begin.

System dynamics provides a structure for modeling systems.  Let us begin to develop that structure by first considering a sample problem, and how it may be viewed.

The reader is asked to consider how one might model the process of a proprietor pricing tire gauges, one of the products sold in his hardware store.  How would you proceed?  What are the variables of this problem, and how they are related.  Feel free to scribble a few notes on the space that follows.

 One might try to apply microeconomic's supply and demand curves to determine equilibrium price.  It does not help in the proprietor's case.  Supply and demand theory is a "model" in the sense that it predicts where equilibrium price will be in steady state, that is, when the system of buying and selling tire gauges has stabilized.  The theory requires knowing supply and demand curves.

But these curves, along with the equilibrium condition that "supply equals demand", are the results of many proprietors' actions on pricing, not the causes for this proprietor to change prices.  We should use causes, not results, to predict actions.  Telling the proprietor to equate supply and demand to establish the price level would be like telling a golfer to hit the ball straight and far to establish a good swing.

What really happens in the hardware store is that the proprietor regularly checks inventory and compares it to a desired inventory level. The desired level probably depends on recent sales, a good indicator of future sales to be filled from the inventory.  The  magnitude of the difference between actual inventory and desired inventory causes the proprietor to change prices.  Price changes feedback to effect sales, which in turn affect both inventory and desired inventory to change again.  The variables are interrelated.  This dynamic, feedback problem is complex, yet we shall soon be able to model it quite easily.

The logic represents a causal modeling approach to the proprietor's problem.  It defines the underlying relationships producing actions and their impacts.  Still, building a model of the process requires a structure, that is a set of equations that allow simulating the inventory and pricing dynamics.  System Dynamics provides that structure based on the concept of stocks and flows.

Stocks are accumulations of flows -- an inventory is a stock accumulating the ordered goods flowing into the inventory, less those flowing out as sales.  Price is another stock, and changes to price are flows -- they are the rates of change of price, and are added up, or accumulated, to provide the current price.  The stocks of inventories and prices, their associated flows, and how they effect each other, would allow us to "model" the proprietor's pricing problem.  We will develop stock/flow models of this type as we proceed.

1.3  General Observations on Systems

Systems surround us.  Crime in the streets, the national deficit, a runner's physiology, the clock's pendulum, a lake filling  with water. All are systems.

The most interesting systems are those in a state of change -- in a "transient" state.  Systems that have stabilized are less interesting -- analytically at least.   Once they have reached a steady state, systems do not require further analysis or even observation, for they will not change.

 Some systems can be merely observed, while others need to be controlled.  Early man, and settlers in new lands, if surrounded by abundance, lived in environmental systems that did not need to be controlled.  Control becomes more important as an environment becomes crowded, and its resources scarce.  The early settlers in Florida hardly needed to worry about the water supply for irrigation.  Today, controlling Florida's water supply is a major policy issue.

As policy makers need better ways of observing and controlling systems, the need for system modeling to test policies becomes more important.

The ability to model systems not yet studied becomes a valuable skill as the world becomes complex and new problems arise.  The management scientist will need to incorporate, more and more, the simulation of complex systems in their transient states.

1.4  On Models and Modeling

It is typically easier to use something than to design or build it.  Many individuals can drive a car.  Few could design one, especially if it had not been done before.  The same is true of analytic models -- it is easier to apply one already designed to analyze a system, than to design and build one from scratch for a system not yet analyzed.

 Modeling requires the ability to think and to structure, abilities that are not easily acquired.  Modeling is an art, and while not everyone can be a successful artist, there are certain concepts of art that can be learned. Conceptualization, layout, color coordination, perspective, and the use of light and shadows, for example, can be studied by the prospective artist.  Different mediums can be learned.  The works of successful painters can be seen and evaluated, and selected objects and scenes can be drawn for practice.  Such knowledge helps one become an artist.

So it is with systems modeling.  System components and structure, system states and boundaries, and the use of variables and parameters can be studied.  Models previously developed can be studied, and simple systems can be modeled for practice.  Available software can be learned.

The art of modeling will be facilitated if the principles of systems are understood.  Fortunately, the fundamentals of systems are limited.  They include system components (levels, rates, and information "auxiliaries"), system states (initial, transient, and "steady state"), and system definition (the functional forms of equations defining the system).  They also include concepts such as accumulations, rates of change, delays, and feedbacks.  The remaining chapters deal with these concepts.

1.5  On Understanding and Control

Control requires understanding, and understanding is aided by the ability to quantitatively model a system.  The computer and modern software have made it possible to model and study systems, and therefore to begin to understand and control them.
 Controlling means more than being able to implement changes. In most managerial settings, control also requires observing, understanding, and communicating the need for, and effects of, policy changes, as policy makers must be convinced that change is needed before it will be authorized.

 System dynamics is not mathematically complex, and is  understandable to most audiences.  Mathematics is, after all, only one language to describe phenomena.  The computer, with the aid of modern simulation software and methods, provides another language.  Its graphical outputs are easily absorbed by managers and policy makers.

Deemphasizing mathematical exposition does not mean sacrificing systems that can be studied and controlled.  Quite the opposite.  Far more complex, dynamic, ill-behaved systems can be modeled using simulation, than can be analytically treated.   The systems that can be analyzed and controlled mathematically tend to be well defined, precise physical systems controlled by physical laws.  Orbitting satellites and swinging pendulums are such systems.  Most human problems are neither well defined nor well behaved, and are affected by human interactions and inconsistencies.  They therefore defy mathematical analysis.  They can only be understood and possibly controlled through more comprehensive, or perhaps more flexible approaches.  Simulation becomes approriate for such problems.

 1.6  On Solutions and Exploration

A final orientation issue involves the difference between solving and exploring.  Analytic (that is, mathematical) solutions to systems usually require satisfying an objective while controlling the system variables.  This typically means having an objective maximized or minimized while keeping the system within allowed boundaries.  Or, for a system in steady state, an analytic solution means solving a set of equations simultaneously.

Exploring, on the other hand, means asking "what-ifs", by changing the model values and then simulating the system again to see the impact of the changes.  There may be an objective, but while it can seldom be optimized, it can usually be explored.  "Exploring" allows seeing how the objectives change when the control variables are altered.  But while most problems can be explored, a disadvantage of simulation is that the problems cannot generally be "solved.

Further, only a limited set of explorations can be performed -- even with modern computers, there are still limits to the number of variables and time periods that can be investigated.  If 10 variables each have 10 possible values in each of 10 time periods, there will be more possible combinations to explore than there are atoms in the earth.  Fortunately, most of the combinations will not be feasible, and a logical direction of exploration will usually be apparent in the search, but seldom will the optimal path over the time horizon of interest be found.

In brief, while mathematical approaches allow finding optimal solutions, system simulations only find a solution better than the existing one -- but not always the best solution.  On the other hand simulation allows studying a very large number of realistic systems, most of which cannot be solved analytically, at least not in thier transient states.  Simulating a process -- such as a social or economic system -- from its present state through a logical sequence of follow on states resulting from a selected policy, allows seeing the results of that policy throughtout the time spectrum of interest.  That may determine whether a new policy should be effected or not.  Some of our legislative policies might benefit if analyzed that way.
 

(c) Rolf Clark