Nature of a Computer Simulation Model
MARVIN KORNBLUH and DENNIS LITTLE*
Introduction The last two decades have seen the emergence of what has come to be known as the “systems approach”. The systems approach is a methodology which attempts to be rational and objective-much like the scientific method-in approaching complex problems. This approach, at first successful in military, industrial and managerial contexts, has now become firmly embedded in practically every other discipline which tries to describe or predict observable phenomena. An important step in the systems approach is the development of models. Models are attempts to imitate systems. They try to capture the major components and interactions of a system. By referring to models one can obtain valuable insights into the behavior of a system. The development of models is a sophisticated combination of art and science. The purpose of this chapter is to provide a general background about systems and models. The paper begins with an explanation of the term system and how it is similar to the word organization. This is followed by a brief explanation of the purpose of the systems approach. This approach is then probed further through a discussion of system levels and some key system concepts. The discussion on systems is concluded with a listing of the steps involved in applying the approach. The paper continues with a discussion of the meaning of the term model. Then various types of models are delineated with special reference to the mathematical model. This leads to an exploration of a special class of mathematical models, namely simulation models. The role of the computer in the implementation of a simulation model is defined. The paper reviews the pluses and minuses of simulation models. Specifically, the purposes and uses of such models are spelled out along with their limitations and misuses. The question of how to validate simulation models is also addressed. The chapter then delves briefly and generally into the technique of model-building. Three major phases of simulation modeling are delineated: the conceptual phase, the implementation phase and the analysis of results phase. The major tasks within each of these phases are identified. The chapter concludes with an overview of three common policy oriented simulation models-econometric models, input-output models and system dynamics models. A brief reference is also made to an emerging policy oriented simulation model entitled probabilistic system dynamics. *The authors are members of the Futures Research Group of the Congressional Research Service in the Library of Congress. This article is a part of a report they prepared for the Subcommittee on Fisheries and Wildlife Conservation and the Environment of the Committee on Merchant Marine and Fisheries, U.S. House of Representatives. The report is entitled “Computer Simulation Methods to Aid National Growth Policy” (Serial No. 94-B). 0 American
The Systems Approach THE NOTION
OF A SYSTEM
To understand the system approach, we must first understand the word system. The notion of system has been assigned a variety of meanings. One common definition is: A system means a grouping of automobile is a system of components
parts that operate that work together
together for a common to provide transportation
purpose. [ 11,
An example of a very complex system is our economy. Its parts work together to produce, distribute and consume goods and services. In its broadest and most general sense, “systems” refers to a way of thinking. It concentrates on the analysis and design of the whole, as distinct from analysis and design of the parts. It implies that the whole is more than merely a sum of its parts, and that the parts acquire certain characteristics due to their existence in the whole. It tries to understand how system components interact with one another, what relationships are desirable and how they might be attained: [System’s] meaning is similar to the meaning of the word organization. Organization means the definable relation of parts to each other and to the whole. . Thus a living organism can be called a system because its structure and functions stand in specific relation to one another. If these relations are altered, either the organism ceases to exist or its function is impaired . . . sand heaps and mobs are not systems because arbitrarily selected parts of each can be removed without significantly changing the character of what is left . PURPOSE
OF THE SYSTEMS
The systems approach strives to be logical, consistent, objective and quantitative in analyzing systems and solving problems. It recognizes the need to make compromises and tradeoffs among the system factors. It facilitates the selection of the best approach from many alternatives. Through the process of model-building and simulation it makes possible the prediction of future system performance. A traditional method of studying systems was piecemeal and analytical. A system was divided into discrete and unique pieces and then each piece was examined in isolation from the others. Design of improved systems and policies for systems was frequently inadequate because it failed to consider objectives for the total system and the interrelationships of the parts and their effects. LEVELS
It should be clear that systems vary widely in scope and complexity and that all systems can be regarded as subsystems of larger systems. Some illustrations of systems in order of increasing scope and complexity are  : (1) A single machine viewed as a group of interrelated parts and performing one or more functions. (2) A group of machines working together to produce an end product. (3) All machines in a total assembly process. (4) The work of a group of assemblers acting together to produce an end product. (5) A collection of persons, processes and goals in an organizational setting, such as a company or a government agency-the management system. (6) A collection of all the information flows-formal or informal, manual or automated--the management information system.
The larger systems are a part but are not all of the subsystem’s total environment. Every system is part of a larger environment. The environment of a system contains conditions, forces and components which are defined as not formally part of the system being studied but nevertheless influence that system and, in turn, is influenced by it. Constituents are a good example of an environmental component of the Congressional system. While systems and their environments are concrete objective entities, they have to be studied subjectively. Different researchers on systems will likely have different interests, purposes and framevf references. Therefore, they will probably conceptualize the same system differently. f
Every part or component of a system has many properties called system attributes. Only those attributes that significantly affect system performance-called relevant attributes-are normally incorporated into a system study. For example, one major component of the Congressional system are Members of Congress. Some attributes of Members are party affiliation, committee affiliations, number of terms served, state affiliation and others. Another important concept in the systems approach is that of system state. The state of a system refers to the value or the nature of system attributes at a particular moment in time. In some cases the state may vary with time; in other cases the state may not vary. For instance, members rarely change party affiliation but committee affiliations and number of terms served do change. A description of the state of a system at any given instant is called a state description. Most commonly, states of a system are studied for a chronological succession of instances (which may be days, weeks or years) throughout some desired time interval. This leads to the construction of a state history. A state history consists of a succession of state descriptions and usually includes descriptions of only those aspects of a system which are most relevant to the purposes of the researcher studying the system. In addition, state histories often include descriptions of only a few of the instances contained in the interval spanned by the state history. These concepts of state description and state history are very important and will form the basis for the definition of simulation later in this chapter. A system is said to be stable when its (measured) performance varies within an acceptable range despite changes to its components and associated attributes. A system may also display erratic or unsatisfactory behavior. This occurs when its performance falls outside the range of acceptance-intermittantly or continuously. The system is then said to be unstable. This instability may be anticipated and corrected by feedback. Feedback is a process which consists of three major steps: (1) System outputs (the end results of system activities) are continuously monitored and recorded in some manner. (2) Comparisons are made between actual results and desired results of system activities. (3) When the differences between the actual and desired results are unacceptable adjustments to the system are usually made-as promptly as possible. These adjustments may take the form of changes to the input (the stimuli which signal system activity) or be
to the control elements of the system governing system behavior).
(the rules, policies,
Feedback may occur on two levels: (1) through automatic adjustments to a system; and (2) through feedback of data to a human monitor who interprets these data and makes the necessary adjustments. When the feedback provides information for and causes changes in the direction of system stability we call this negative feedback. Negative feedback helps a system adapt to unexpected and undesirable changes in system components, their attributes, and their relationships. However, there is another type of system feedback called positive feedback. This type of feedback tends to be [email protected]
because it tends to contribute to greater system instability. This distinction between positive and negative feedback might be clarified further by the following illustration of Professor Forrester, Sloan School of Management, Massachusetts Institute of Technology  . A feedback system controls action based on the result from previous action. The heating system of a house is controlled by a thermostat which responds to the heat previously produced by the furnace. Because the heat already produced by the system controls the forthcoming generation of heat, the heating system represents a negative feedback system that seeks that goal of proper temperature. A watch and its owner form a negative feedback system when the watch is compared with the correct bacteria which time as a goal and is adjusted to eliminate errors . . . Bacteria multiply to producemore increase the rate at which new bacteria are generated. In this positive feedback system the generation rate of new bacteria depends on the bacteria accumulated for past growth of bacteria.
Thus, negative feedback corrects to a balance accelerates prior movement toward the extremes. APPLICATION
or desired norm; positive feedback
OF THE SYSTEM APPROACH
Of all the proponents more lucid descriptions the method .
of the system approach, C. West Churchman has given one of the of it. He delineates five fundamental characteristics in applying
(1) Objectives of the total system.-These are. the goals toward which the system tends. Churchman makes a point of stating that the real objectives may not always be the same as the stated objectives. Only if the system will knowingly sacrifice other objectives to attain the stated objectives can the latter be. considered real objectives. He also observes that unless these objectives are quantified in some manner it will not be possible to measure the performance of the system. For example, an objective for a large socio-economic system like the U.S. economy might be to attain balanced growth in terms of equitable distribution of goods and services among urban and rural areas. Also, according to Churchman, it would be necessary to establish explicit measures of performance which would reveal whether the distribution was indeed equitable. (2) 7Yhesystems environment. -Two features characterize the system’s environment: a) it includes activities and conditions that lie outside the system’s control. Thus, the environment is considered to be fixed or given when incorporated into a systems study; b) it includes everything that can nfluence system performance. Therefore, the system is forced to interact with its environment to some degree. For instance, some aspects of the environment of the U.S. economy might be the constraints on capital investment, the supply of natural and human resources at large, and budgetary limits set by Congress. Further, when Congress sets explicit limitations on the spending of an executive agency, these limitations are environmental constraints for that system. (3) 7’he resources of the system.-These are all the means available to the system so it can function and attain its objectives. Unlike the environment, the system can change the
amount and mix of resources to its own advantage. The resources of our economy might be detailed in terms of available numbers and skills, mix of people, technological capabilities, political pressure groups, available dollars, and so on. (4) The components of the system.-These relate to the jobs or activities the system must perform to realize its objectives. Churchman concentrates on system function rather than on structure. As the performance of a critical activity improves so should the of our economy might relate to the performance of the total system. Components activities of its major sections like production, financial, household, labor and government. (5) 77re management of the system.-System management calls for planning the system and controlling the system. System planning involves the detailed aspects of the previous four steps. Control calls for making sure that the plans are being executed properly, and if not, why not. Control may also require changing of original plans. Further, without adequate feedback, systems management is likely to be inadequate. Management of the U.S. economy, if such were contemplated, would entail understanding of the forces that shape it, preparing and acting upon plans and policies that deal with growth and other problems (such as the proper level of government, use of federal land, transportation and housing needs, and so forth). Controls might be based on new and existing social and economic indicators and reveal the type of feedback actually occurring (negative or positive). In the “systems” method, phenomena and objects are classified by their functional characteristics (what they do) rather than their structural content (what they are). The approach also assumes that we can identify and understand all the significant cause and effect relationships within a system. This requirement can be a limitation to successful application of the method. SUMMARY
A system means a grouping of parts that operate together for a common purpose. It is similar in meaning to the word organization. The systems approach strives to be logical, consistent, objective and quantitative in analyzing systems. The approach is in contrast to traditional and piece-meal approaches to studying systems which analyzed system components in isolation from each other. Systems vary in scope and complexity and all systems can be regarded as subsystems of larger systems. Systems contain components which, in turn, possess attributes. The value or the nature of the system attributes at any particular moment in time constitutes a system state. A description of the system state at any given instant of time is a state description. A succession of state descriptions comprise a state history. A system is said to be stable if its performance varies within an acceptable range. Feedback is a process which can assist a system in maintaining stability. When applying the systems approach, emphasis is placed on five aspects, namely: (1) the objectives of the total system; (2) the system’s environment; (3) the resources of the system; (4) the components of the system; (5) the management of the system. The approach requires that all significant cause and effect relationships within the subject system be identified and understood. Concept of a Simulation Model One important tool of the systems analyst is model-building. Model-building is one way to understand complex relationships within a system. A model is an abstraction of
reality and can be conceptually regarded as a substitute for the real system. It is used to capture the functional essence, but not necessarily the detail of a system. Thus, instead of investigating and experimenting with the real system, we can interrogate the modelusually with less risk, less time and less money. A model permits experimentation among alternative policy strategies and can test the consequences of assigning different values to the variables involved. To the extent that a particular model is an appropriate representation of the system, it can be a valuable aid to policy analysis and policymaking. MEANING
OF A MODEL
In the relevant literature there are several distinctive Some of these definitions are:
of the term model.
A model is anything that illuminates and clarifies the interrelations of component parts, of action and reaction, and of cause and effect . Models are intellectual tools. . . . In the broadest sense, a model must be able to help us distinguish what is possible from what is impossible, and from the realm of the possible to distinguish the better from the worse. In other words a model should be used for defining our options [ 7 ] The model is a vehicle for arriving at a well-structured view of reality. A model may be a substitute representation of reality . . . [a] model may be some sort of idealization . Models are analogies. Scientific or engineering models are representations, or likenesses, of certain aspects of complex events, structures, or systems, made by using symbols or objects which in some way resemble the thing being modeled . We define a model as the body of information about a system gathered for the purpose of studying the system [lo].
These definitions have some similarities and also reveal some differences. The important thing to note is the implication from the meanings that an individual is probably using models whenever he tries to think systematically about some phenomena. Forrester expresses this idea very well [ 111. Our mental processes use concepts which we manipulate into new arrangements. These concepts are not, in fact, the real system that they represent. The mental concepts are abstractions based on our experience. This experience has been filtered and modified by our individual perception and organization processes to produce our mental models that represent the world around us.
Mental models are formed through our experience, knowledge and intuition. Because of this, they help us interpret and survive in the world around us. However, they may be inadequate for studying complex systems. To quote Forrester again [ 121 . The mind is excellent at manipulating models that associate words and ideas. But the unaided human mind, when confronted with modern social and technological systems, is not adequate for constructing and interpreting dynamic models that represent changes through time in complex systems. . . Our mental models are ill-defined. . , assumptions are not clearly identified in the mental model. . . The mental model is not easy to communicate to others. TYPES OF MODELS
Most policies are probably formulated by the interpretation and application of mental models-whatever their limitations. Mental modeling is a natural capability and it can be powerfully adopted to meet changing circumstances, by skilled practitioners. However, there are other types of models that can also make contributions to the study of complex systems and the formulation of policy stemming from such analysis. These can be conveniently grouped as shown in Fig. 1.
THE NATURE OF A COMPUTER SIMULATION MODEL
Fig. 1. Types of models. Physical models are constructed from concrete, tangible materials. An iconic physical model retains some of the physical characteristics of the system it represents but does not necessarily behave like it. A floor layout’and a three-dimensional mock-up of an atomic power plant are examples. An analog physical model, on the other hand, tries to act like the real system even though it may not look like it. An aircraft wind tunnel is an example of this type of model. Physical models are usually relatively easy to explain and relatively uncomplicated to work with. However, they suffer from an inability to represent information-flow processes. They also tend to be inflexible, in the sense that they are likely to be used only to study a particular, relatively uncomplicated system. Symbolic models tend to be less susceptible to the deficiencies inherent in mental and physical models. These kinds of models use symbols to designate the components of a model and the relationships among these components. Verbal symbolic models tend to be written narratives or oral expressions relating to a system. They explicitly reflect the implicit ideas of a mental model. Examples are plentiful and include abstracts, extracts, digests, news reports, speeches, stories, scripts and scenarios. Verbal models are probably the primary means of influencing an individual’s mental model and thus are important to the policymaking process.
MATHEMATICALMODELS Mathematical symbolic models use mathematical representation to describe a system. Three characteristics of mathematics make the use of these models attractive: (1) They are very precise in that little ambiguity is present in the meanings of mathematical symbols. (2) They are concise in that they require relatively few symbols to express relatively complex ideas and behavior. (3) They are usually easier to manipulate than words once the mathematical procedures are understood. Mathematical models have had limited applicability because mathematical symbology and rules of manipulation are not familiar to most policymakers. Thus, communication between the model-builders and the model-user may not be as simple and direct as verbal communication. In order to understand and utilize mathematical models, it is necessary to be aware of a few of their essential features. Mathematical models are constructed by formulating equations which describe system components and system states. Equations, in turn, are composed of variables, constants and parameters. Variables assume different values while the model is run or calculated. Constants, on the other hand, always have fixed values.
Parameters are variables experimentation. If the ment it is known as an variable it is known as an
and DENNIS LITTLE
that are arbitrarily assigned fixed values for the purpose of value of a variable is determined by conditions in the environ“exogenous variable”. If the system determines the value of a “endogenous variable”.
SIMULATION MODELS A special class of mathematical models is referred to as simulation models. The term simulation refers to the process by which a model is constructed. A simulation consists of the construction of a state (system) history-previously defined as a succession of state (system) descriptions. A simulation often (but not always) employs mathematical symbols to represent the interactions of system components at different points in time. Thus, simulation models are dynamic models. They involve changes in the state of the system through time. A simulation model expresses the dynamic relationships among the variables, constants and parameters. If changes in their values tend to produce proportionate changes in the values of the model outputs, the model is said to be linear. If disproportionate changes occur in the model outputs the model is considered to be nonlinear. For example, assume a variable called “productivity per man hour” was doubled during a simulation. If total productivity-the final output-also doubled, then the model tends to be linear with respect to that variable. If the final output was greater or less than double, the model tends to be non-linear with respect to that variable. Some simulation models may also be deterministic models. In deterministic models it is assumed that the exact values of all variables can be computed and the values of all parameters are known. If exact values for the model cannot be computed and are not known, then a probabilistic or stochastic model may be in order. In a probabilistic model, at least some variables or parameters have an unpredictable randomness and must be represented as statistical variables. This calls for the use of probability distributions for model inputs and model interactions and a random number generator or table to supply the needed values. In stochastic models, different results follow from the use of different sets of random numbers if no change is made to the models. Repeated running of a stochastic model produces a distribution of outputs. This is the so-called “Monte-Carlo” procedure. Another important characteristic of a simulation model is the level to which it aggregates the real system. The model can be a “micro” level model and deal with small units (variables) of the system or it can be a “macro” level model and group the small units into fairly large units. Roger Sisson discussed this ideas as follows [ 131 : For example, let us consider models intended to assist in making decisions about welfare allocations. The most detailed model would represent every individual who could come into the welfare process. . . The most aggregate model would represent the entire body of welfare recipients in the nation as a single entity; perhaps by one variable such as their income level (as is done in some econometric models). In between is a range of model structures which are more aggregate than the individual level but less than single representation. A model may be disaggregate in terms of age groupings, socioeconomic characteristics, geographic areas, and other factors. The more aggregation that is performed the fewer the variables and relationships the model will have. On the other hand, aggregate models stand a greater chance of being unrealistic for they deal with artificial groupings and not with actual representations of a system. There is a range of operational methods for implementing a simulation model. Three basic types, in order of decreasing abstraction can be distinguished [ 141 :
OF A COMPUTER
which use the large manipulative and (1) “Computer” or “machine simulation,” tabulational capabilities of modern computing machines to (a) “solve” closed, continuous mathematical models or (b) approximate open, discontinuous mathematical models; which merge gaming with computer simulations into one (2) “Gaming simulations,” vehicle. These simulations use players of roles and computer operations on models, or sets of linked models to “simulate” reality; and (3) “Games,” which attempt to simulate situations of conflict or of interdependence between actors frequently by condensing the roles, experience, and psychology of a large number of players into a few archetypal roles or player-positions, and by applying “rules” which simulate the restrictions of “real” life. All games, whether they are simple manual ones or heavily computerized, are played according to some specified criteria. One authority listed these criteria as follows [ 151 : 1. Rules of play to govern the “moves” and interactions between players and other variables of the game. 2. Objectives or goals; players may work cooperatively toward a joint goal or competitively towards goals which cannot be shared. (A single game may incorporate both modes, as in Monopoly when players decide to “gang-up” on the “apartment house owner.“) 3. A method of translating the moves of the players into indicators which measure the degree of attainment of goals. This device may be a game board, mathematical model, or another group of participants charged with responsibility of judging the effect of the players’ moves. 4. A display system to illustrate the progress of the game. 5. A set of exogenous variables to introduce “outside events into the play.”
The two most widely used forms of gaming are military games and business management games. Military gaming is essentially a learning device for military leaders which enables them to test the effects of alternative strategies under simulated war conditions. Business games are an education tool aimed at exposing managers to management-type decisions.
THE ROLE OF COMPUTERS
Digital electronic computers have evolved to the point where their influence on society is called a revolution. They rapidly process masses of data and calculate answers to complex mathematical problems. Further, because they are logic machines and general symbol manipulators they are said to expand the mind of man. A human problem solver using a computer need think through his problem only once, provided he articulates his thoughts in a language computers can translate into instructions. He can then use this computer program again and again to rethink and experiment with his problem, but with different data and under different circumstances. These capabilities of the computer have important implications for simulation models. Games in which live subjects interact with a computer which contains a simulation model have already been reviewed. When the entire experiment is conducted by a computer as it executes its program of instructions, it is known as all-computer simulation or just computer simulation. In computer simulation, the computer program represents the system. The experimenter runs this program by supplying values to the variables and parameters in the equations and by specifying the experimental controls. The experimenter can always rerun his experiment by modifying the controls, by assigning different values to the variables and parameters or by changing both the controls and values. The practical power of all-computer simulation arises then from two sources  :
(1) The ability tions. (2) The ability experimental run.
to replicate experiments to combine
rapidly under the same and different
into a single
A programming language is a language used by programmers to write instructions which the computer can understand. Many programming languages have been developed to simplify the programming of simulation models. Some of these languages are “general purpose” while others are “special purpose”. General purpose languages are geared to general mathematical or common business tasks. For example “FORTRAN” (Formula Translator) is a programming language aimed at the scientist and engineer who works with numerical problems. Another language is “COBOL” (Common Business Oriented Language) which is focused on the record-keeping, sorting, and report preparation tasks in business. Still another language entitled PL/l has been developed to solve both scientific and commercial problems. Special purpose simulation languages have also been developed. These languages are generally thought of as easier to learn and apply and provide considerable flexibility for making changes to the structure of the model (its variables, parameters and their relationships). However, special purpose simulation languages also tend to increase the running time of the model on the computer, thereby increasing costs. In addition, they are limited to the specific use of developing and implementing simulations.
AND USES OF SIMULATION
A simulation model is a particular type of model. Like most other models, it imitates and represents a system. It differs from other types of models in that it actually tries to imitate the behavior of a system, step-by-step over time. Thus, model builders say that a simulation is run or executed rather than solved. This reasoning, however, is not absolute. A simulation may use solution techniques to supply values for certain variables. For example, equations in an econometric model are solved (updated) periodically as the simulation proceeds through time. Further, since a simulation model is run many times, it normally yields a range of outputs. These must be analyzed and interpreted. These interpretations are, in effect, solutions. It is possible for different interpretations to be obtained from the same outputs of a simulation model simply because human judgment is required. In principle, everything that can be accomplished by simulation can also be accomplished by experimenting directly on the system of concern. However, it may be impossible or impractical to experiment with the system itself. As one authority put it  : Even when analysts have the confidence and ability to arrive at a theoretical prediction of the behavior of a large system, it may not be possible to perform validating experiments. You cannot, for example, test conclusions about global strategic war by trying them even once. . It may not be possible to observe the phenomena in its desired environment. This is true of the thrust of rocket motors for use in outer-planetary space . When any of these difficulties occur, as they do daily in the attempts to tackle previously untouched, unmanageable problems, some form of simulation is the obvious tool to be tried.
There are many advantages to the use of computer simulation models. They may have different advantages in relation to the different objectives for using the model. These advantages could be grouped into the following six areas:
THE NATURE OF A COMPUTER SIMULATION MODEL
(1) They impose a logical discipline which forces precise statements of problems and objectives and requires that the system being described be explicitly divided into its major components and major interrelationships among these components. Thus, it is possible to identify components and relationships that may have been previously missed or ignored even before a simulation is run. (2) While simulations do not give answers directly, they can provide novel and critical insights into system behavior. Sometimes these insights may be counter to what was expected. Further, these insights can provide the bases for experimenting more deeply in certain directions and suggest new research possibilities. (3) Simulations provide a framework within which experiments can be conducted. The sensitivity of the system to changes in the magnitudes of its variables and to changes in relationships among the variables can be observed. Critical variables and significant relationships can be confirmed or rejected. Factors having negligible influence on final outputs can be identified. The impact of current policies on future system behavior as well as the influence of potential policies can be tested. The model can be used to answer “what if’ questions of two types: (a) “what if we set the values of the critical and controllable parameters at certain levels; (b) What if certain variables which are not very controllable take on certain values? (4) A simulation model cannot and does not eliminate risk. Risk is inherent in policymaking. However, the nature of various risks may be clarified, and adequate and inadequate options for minimizing risks may be delineated. Thus, policies may be formulated with more knowledge of the risks they entail. (5) Simulation may be used as an educational device for teaching both policymakers and technicians. Theoretical analysis skills can be refined and rational thinking can be stimulated. (6) The development and implementation of simulation models may lead to more “open” communications regarding the system among all interested parties. Different points of view are frequently uncovered and agreements and disagreements focused more sharply. LIMITATION, MISUSES AND VALIDITY
OF SIMULATION MODELS
For all their potential utility, simulation models are subject to a number of sources of error. If the limitations of modeling are clearly recognized, faulty conclusions can be avoided and the simulation technique can be employed to the greatest advantage. Some limitations that have been mentioned with respect to simulation models are: (1) SimpZification of the reaZ system. -A simulation model is always a simplification of the real system it represents. This simplification takes place in many ways-by making assumptions, by including only the critical variables in the model, by incorporating only the important relationships in the model, by performing greater aggregation, and by other methods. There is always danger, however, that oversimplification or inaccurate simplification may occur. (2) Dynamic behavior of the real system.-Every system contains a certain degree of random and uncertain behavior, exhibits delays and has a number of nonlinear relationships among its variables. One can’t be sure how many of these dynamic factors can be excluded from a model and still have a valid representation. (3) Data collection.-A simulation model needs data in order to assign values to its variables and parameters. Sometimes the required data is available in the correct form.
and DENNIS LITTLE
When such data is unavailable the model-builder has to obtain the necessary values through empirical studies, from actual events and by educated guesses. Regardless of how obtained, the reliability and validity of data should never be taken for granted. (4) Zntungibk factors.-All systems contain intangibles such as political opinions, and other human attitudes and values. These are difficult-if not impossible-to incorporate directly into the simulation model. Usually, the model includes intangibles indirectly by such techniques as increasing or decreasing the values of certain variables over time, by incorporating more or fewer time delays, by strengthening or weakening particular relationships, and similar ways. The modeler, is rarely, if ever sure that this implicit treatment of political and human factors is realistic and accurate. (5) Experimentation.-Experimentation is the process of designing sets of computer runs to determine the sensitivity of a simulation model to potential changes in system variables, assumptions and relationships. A great deal of experimentatiocan be performed or very little of it. Further, it can be done efficiently or inefficiently. However, no standard techniques exist for insuring that experimentation is done completely and efficiently on large-scale, complex simulation models. (6) Practical considerations.-In developing and implementing simulations, there are a number of practical considerations to contend with. These include such items as available time on the computer, deadlines as to when the results are needed, adequacy of the computer facilities to be used, availability of required numbers and types of skills, and so on. Rarely does one have enough of these items. If one is forced to make “tradeoffs” among these items, the risk of error is increased. In addition to being aware of the limitations of models, policymakers should also know the different ways in which simulation models can be misused. A business executive has pointed out three common misuses of models as follows [ 181 : 1. Sometimes work with a model becomes a substitute for good, hard thinking about assumptions and alternative courses of action. It becomes an unimaginative ritual just as the annual planning cycle becomes the rite of fall. 2. If many alternatives are tested with the model, the one that finally is selected sometimes takes on vaunted status because it has been so rigorously tested. Thereafter, it may be followed too rigidly under changed conditions. 3. In many organizations, planning is an advocacy process. In such settings, models are sometimes used to justify, rather than to explore, the implications of actions.
The construction of a simulation model is an attempt to make a mental model of a system explicit and dynamic. The question often asked is, “how does one know if the explicit and dynamic model that was developed is a valid representation of the system, is measuring the correct things, and is useful?” Dennis Meadows, author of Limits to Growth and head of the Systems Dynamics Group at Dartmouth College has listed three criteria for judging the validity of a simulation model: 1. Each assumption in the model should be consistent with direct measurements or observations of the real-world system: no assumption or parameter without real-world meaning should be added merely to improve mathematical convenience or historical fit. 2. When the total model is used to simulate historical time periods, the behavior of each variable should resemble the historical behavior modes of corresponding elements in the real world. When the system is simulated into the future each variable should follow an understandable path within a reasonable range of values. 3. The model should be sufficiently simple so that the reasons for its behavior can be comprehended and abstracted as generally applicable principles for dealing with the real world system.
THE NATURE OF A COMPUTER SIMULATION MODEL Ultimately, the model should no longer be needed because its basic constituent should become part of the mental models of its users [ 191. Validation
in at least
These are: (1)
Degree to which model
to which model
past system conforms
(3) Degree to which model accurately forecasts (4) Degree to which model is found acceptable
using historical and relevant
as it unfolds.
to other model-builders. (5) Degree to which model is found acceptable to those who will use it (for example the policymakers). (6) Degree to which model yields opposite results when opposite values are assigned to the variables and opposite relationships are postulated and opposite assumptions are made. All of these methods contain flaws. No one method can claim it does complete validation. Each simulation model should be judged by reference to its own end purpose and the feasible alternative approaches. One model-builder talked about validation as follows: Models cannot be judged in the abstract, but only with regard to some purpose that we want them to fulfill. Before we can meaningfully judge and evaluate particular models, we must first be able to specify what it is that we want them to be able to do. Only then can we look at particular models to judge how well in fact they do it, or look at modeling techniques to judge what potential they have for doing it [ 201.
Jay Forrester made the following comments
with respect to validation
The validity and usefulness of dynamic models should be judged, not against an imaginary perfection, but in comparison with the mental and descriptive models which we would otherwise use. We should judge the formal models by their clarity of structure and compare this clarity to the confusion and incompleteness so often found in a verbal description. We should judge the models by whether or not the underlying assumptions are more clearly exposed than in the veiled background of our thought processes. We should judge the models by the certainty with which they show the correct time-varying consequences of the statements made in the models compared to the unreliable conclusions we often reach in extending our mental image of system structure to its behavioral implications. We should judge the models by the ease of communicating their structure compared to the difficulty in conveying a verbal description.
One useful test of a simulation model is to simultaneously determine how useful, usable and used the model appears to be. A model can be considered useful if it shows promise of attaining the objectives initially established for it. A simulation model can be considered usable if it is understandable and plausible to both technicians and policymakers, economic to run on a computer, and accessible to those who wish to use it. If a simulation model is useful and usable, it stands a good chance of being used, especially if the potential users receive the proper training. SUMMARY
A model is a vehicle for arriving at a concise and structured view of a system. It is an intellectual tool for distinguishing the possible from the impossible. It is also an analogy. Mental models are formed through our experiences, knowledge and intuition. Physical models are constructed from concrete, tangible materials. Symbolic models use symbols in its construction. Mathematical symbolic models use mathematical representation to
MARVIN KORNBLUH and DENNIS LITTLE
describe a system. Mathematical models are constructed Simulation models are usually a special class of mathematical
by formulating equations. models. They are dynamic in
the sense that they involve changes in the state of the system through time. They may be deterministic or probabilistic and linear or non-linear. The Monte-Carlo procedure is the repeated running of a probabilistic model to produce a distribution of outputs. A simulation model is always aggregated to some degree and may permit individuals to interact directly with it through a computer system. This is called gaming. Computers are very useful in simulation because they can replicate experiments quickly and can combine a number of components and relationships into a single experimental run. Simulation models have a number of advantages including imposing a logical discipline, providing critical insights, providing a framework for experimentation, clarifying risks, providng a tool for education and training, and facilitating open communications. Simulation models may also oversimplify reality, fail to treat intangibles correctly, perform poor experimentation, and possess insufficient resources for their development. All methods for validating simulation models contain flaws. No one method can claim complete validation. Each simulation model should be judged by reference to its own end purpose and the feasible alternative approaches. The Phases of Model Development The actual development of a computer simulation model is a process. It “is both art and science. Inspiration leads, then pieces of evidence, and many sources of information are needed to put together a good model.”  It is a process that calls for delineating a set of distinct and logical steps and moving through them in sequence. Each step is dependent upon the previous step. Dennis Meadows listed nine steps that he followed in building his global model known as World 3  : 1. General verbal description of the system within which the problem is observed. 2. Precise specification of the model’s purpose in terms of the dynamic system behavior to be explained. 3. Definition of the model’s time horizon. 4. Identification of the major elements necessary to represent the relevant aspects of the system. 5. Postulation of the model’s structure; conceptualization of causal relationships and feedback loops. 6. Estimation of the model’s parameters; quantification of causal assumptions. 7. Evaluation of the model’s sensitivity and utility through computer simulation. 8. Experimentation by means of further simulation with possible further policies. 9. Communication of results. In a more can be reduced the simulation
aggregated to three; model
in the model-building
of the simulation
of the simulation
CONCEPTUALIZATION OF THE SIMULATION MODEL
The conceptualization of a simulation aspects of the system such as: (1) (2) (3) (4) (5)
The The The The The
critical system components and attributes. principal decisions made. important relationships among the system components. problems the system appears to have. areas of system behavior where little knowledge is available.
of the essential
(6) The variables of the system that are not controllable. (7) The environment of the system. (8) The constraints present with respect to system behavior. (9) The random and uncertain elements in the system. (10) The stability of system behavior. (11) The trade-offs that the system usually makes. (12) The manner in which system effectiveness can be measured. Analysis of these system aspects leads to the formulation of the objectives of the simulation model. These objectives usually involve the increase of system understanding, the prediction of future system trends and the setting of guidelines for policymaking. After the model-building objectives have been formulated, the system is divided into meaningful and convenient (for analysis) parts, often called sectors or subsystems. This actoring results in several submodels which can be separately studied and subsequently reintegrated into the total model. Then the major attributes of the system variables are deduced and specific cause and effect interactions are identified. By this time, a specific simulation modeling technique should have been selected such as systems dynamics or econometrics (described further on). In addition, the time horizon over which to generate the state (system) history is chosen along with appropriate time intervals with which to move along this horizon. For example, for a 100 year history, five year intervals might be chosen. Another important step in model conceptualization is data collection. Values for the variables and the parameters in the equations of the simulation model are needed. It is possible to estimate the data requirements for the model and decide on the source and methods of data collection even if the precise forms of the model equations are not yet established. Data collection methods usually involve one or more of the following: (1) (2) (3) (4) (5)
Statistical data reflecting past system behavior Educated guesses from people familiar with system behavior Personal observations of system behavior Specially designed experiments duplicating system behavior Measurements obtained from sampling system behavior.
Current data values are converted into future data values usually by statistical projections or subjective judgments. The sources of data are public (Federal, state, and local governments, academic institutions) and private (households, businesses, academic institutions). A further factor with respect to data collection is the extent to which data will be aggregated, that is, individual items grouped together and treated as larger items in the models. Data may be available in the desired level of aggregation or it may be necessary to artificially group data. about system behavior are After data collection is well along, the assumptions reviewed for clarity and accuracy. An assumption implies that some facets of system behavior are not apparent and visible and it is necessary to postulate what this behavior would be. Collected data sometimes reveal unanticipated trends. This may call for revisions of initial assumptions. At this point, formulation of the actual equations that will comprise the simulation model can begin. After appropriate equations have been formulated, initial testing of the model starts. This involves:
(1) Checking numerical calculations. (2) Reviewing the model and checking to insure that the rationale for its construction is still valid. This is known as verifying the model. The final steps in model conceptualization make all necessary corrections revealed by the testing activity and document the conceptualization. Normally this documentation takes the form of detailed reports which describe the rationale for model conceptualization, the detailed structure and characteristics of the model, and a compilation of the testing results. IMPLEMENTATION
OF THE SIMULATION
The second phase, entitled model implementation, translates the conceptual model into a computerized working model. This phase first calls for the preparation of detailed flow charts. A flow chart, as employed in computer simulation, is simply a “graphical representation of a sequence of machine operations using symbols to represent the operations such as compute, substitute, compare, go to, if, read, write, etc.”  The next step in this phase revolves around computers. The computer system on which the model will be run is selected and/or assigned. In addition, computer programming specifications, indicating the nature and the magnitude of the programming of the computer is carried out. A computer program is a logical sequence of instructions which directs the actions of the computer system. The programming specifications are used as a guide in the preparation of the computer instructions. There are several special purpose simulation languages available to facilitate this translation  After the computer programming is completed, final testing is performed. This involves: (1) done. (2) closely (3) logical
the model to determine
if the computer
has been correctly
Running the model using time series (chronological) data and determining how the results approximate the past performance of the system. Running the model over future time periods and determining if the results appear and reasonable.
Model implementation also involves what is called the “design of experiments”. This is a process whereby the states of the system are successively changed and the model outputs are compared to determine the effects of these changes. The model is repeatedly run with different values assigned to the variable and parameters, under alternative assumptions, and with changed relationships among the variables. As with the first phase of model development, this phase is also documented. The flow charts, the computer programs and the results of the computer tests and experimental runs are recorded. ANALYSIS
The final phase in the development of a simulation model is the analysis of the results obtained from the simulation model. Outputs from the various computer runs are studied and interpreted and conclusions are drawn. Conclusions typically involve providing answers to the following types of questions: (1) What are the principal conditions established?
effects of the system interactions
under the alternative
(2) What are the likely trends in system behavior? (3) Did any alternative policies improve system behavior or adversely affect it? (4) What might happen to system behavior if certain variables assumed particular values? If desired, the simulation can be re-run a large number of times in order to obtain a better statistical representation of the initial results and to examine a still larger number of alternatives. In most cases, the conclusions from the simulation model are translated into recommendations for action. Some of the conclusions reached may be method oriented rather than substantive. For example, it may be felt that the simulation model is still inadequate in certain ways and should be improved or updated. There are various ways to perform this task. Some of the more common ones include: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Inserting new variables into the model. Deleting some existing variables from the model. Inserting new relationships among the variables comprising the model. Deleting some existing relationships among the variables of the model. Further aggregation of some parts of the model. Disaggregating some parts of the model. Modifying the assumptions. Trying to obtain actual or more realistic data for the variables. Introducing unlikely but possible events on a probabilistic basis. Changing some variables into parameters (arbitrary constants).
It is important to understand the effect that a model can have on the policymaking process. Since every model is a simplification of the real system and emphasizes certain aspects of the system and not others, different models may lead to different results and different conclusions. If the policymaker recognizes the major steps in the model-building process, and knows the critical parameters and data sources, he can suggest appropriate changes to the model (perhaps more in accord with his views) and properly interpret the model outputs.
SUMMARY The development of a simulation model is a process. The number of steps in the model building process can be reduced, in broad terms, to three. These three are model conceptualization, model implementation, and analysis of model results. The first phase gathers data, identifies the major system components and relates them properly through the formulation of equations. The second phase utilizes computers to run the model and tests alternative options through the process of experimental design. The final phase interprets the model outputs and draws conclusions based upon these interpretations. It also improves and updates the model if necessary. Policy Oriented Simulation Models Many techniques have been employed to construct policy oriented simulation models for complex (socio-economic) systems. Three approaches in particular seem to be quite prevalent: Input-Output Analysis, Econometrics, and Systems Dynamics. Their major structural features, processing steps, assumptions, and criticisms will be reviewed in this chapter.
Input-output analysis reflects a general theory of production based on the idea of economic interdependence. As it is most frequently used, it divides regions, such as a national or world economy into a specified number of interdependent industries or sectors. An industry is composed of firms producing a similar product or products and is regarded as a distinct process of production. Each industry obtains the outputs of other industries in certain fixed proportions and combines and inputs them into its own productive process. For example, the auto industry buys certain amounts of output from the household industry (labor), the steel industry and other industries, combines them and inputs them into the auto production process. In addition, each industry sells and distributes its outputs to other industries in some fixed proportions. Further, each industry uses some of its own output as subsequent input. In this manner, the economy creates an intricate set of interdependencies of industries. The application of the input-output technique is based on three major assumptions: (1) The total output of an industry is consumed as input by all industries for the time period under consideration. (2) The inputs bought by each industry have usually been made dependent only on the industry’s level of output. For instance, twice as much output will call for twice as much input. (3) The ratio of an industry’s input to its output, once established, is fixed. This ratio is known as the production coefficient or the input-output number. Initial production measurements, called coefficients, are established and placed in the boxes of a square table called an input-output or Leontief matrix  . These coefficients show how the output of each industry is distributed among other industries and sectors. The entries in the table show, for example, how much of the output of the steel industry is used by the automobile manufacturing industry and how much of its output is used in transportation services that are used by the steel and other industries. Also shown are the ultimate demand: inventory accumulation, exports, government and private purchases and capital formation. Inputs in the form of payments from such sources into the economy are also represented. Today there are input-output tables listing several hundred industries and thousands of coefficients. They require a computer to store and handle them. If an industry expands its output, due to increased demand, all industries supplying inputs to that expanded industry will also expand. Further, the expansion of these latter industries would call for more inputs into their production processes. These effects continue for a number of cycles with additional inputs and outputs, gradually diminishing. A similar routine is followed when an industry contracts its output. When changes in technology, government spending, and similar factors occur, their influence on industrial outputs are estimated and appropriate coefficient changes made.  Input-output models are used to study the level or nature of the aggregate demand that would be required to achieve full employment and for making forecasts of the requirements of each industrial sector. They can also be used to study the effects of public programs (such as public works or space) on employment in industry. When this policy model is used for long-term forecasting, the factors in the model are changed to reflect technological developments. The criticisms of the input-output approach relate to the fact that its model is
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essentially static, linear, and incapable one critic put it  :
adapting to technological
Because proportionality is assumed between the output of an industry and its input requirements, there is a problem relative to the determination of demand for capital goods industries. The demand for capital goods generally depends more on the rate of change of production in the industries that purchase these capital goods, than on their actual present level of production. Thus one cannot really assume proportionality for these particular I-O relationships. . Because of this [linear assumption], it is impossible for I-O analysis to account for the effects of bottlenecks (constraints in the amount of available capacity, resources or manpower), on input availabilities and relative prices. Such constraints cause important substitution effects to occur in the I-O relationships, that are not accounted for in the model, and thus can invalidate results.
This type of policy oriented simulation modeling This is also known as statistical economics, empirical ics. This approach relies heavily on empirical data mathematics and statistical analysis. The process contains five essential steps:
is based on econometrics techniques. economics and quantitative economand is a blend of economic theory, of develping an econometric model
(1) The specification of what we want to measure. For example, we may want to predict the level of investment in a given year. (2) The specification of the economic variables which influence the value of the factor we are measuring and predicting. We might say, for instance, that investment decisions are influenced by such variables as gross national product, relative prices, and interest rates, and so forth. (3) The collection and observation of relevant data. (4) The derivation of equations based on statistical and theoretical relationships among the relevant variables. For example, equations that can plausibly predict investment levels, based on past, current, and anticipated relationships. (5) Analysis of the empirically derived results including their implications. It is the fourth step that changes a mental model into a mathematical model. This mathematical model can take the form of a set of simultaneous equations. Simultaneous means that a number of equations must be jointly formulated and solved to derive the l values for the variables in the equations. Economic theory contributes heavily to this formulation of empirically derived equations. Initial data for the equations come from the historical and observed measurements. Data is often arranged in a format called a “time series.” This means that data are obtained for successive periods of time. The time period for which predictions are made from the model is called the prediction period or the forecast period. One author amplified this by stating  : During a typical period there are changes in some of the economic phenomena being studied such as prices, outputs, sales, inventories, interest rate, investment, planned investment for the future, consumption, government purchase, tax rates, and subsidies, or sometimes changes in more fundamental economic realities such as consumer tastes, technological knowledge, and known available natural resources. But there are also underlying features of the economy that do not change during the same period. . The features of the problem being studied that do change during a period will be called “variables”, and the whole complex of features that do not change will be called economic structure or often simply the structure. Numerical constants characterizing the structure are called structural parameters. Some parameters of the structure and some variables are observable, and some are not.. . . It is clear that we cannot tell which are the variables and
which are the parameters discussed.
of the structure,
until we know what problem
and what period
Two men who are regarded as the founders of the econometric approach to modeling are Jan Tinberger of the Netherlands and Lawrence R. Klein of the United States. Tinberger shared the nobel prize with Rognar Frisch of Norway in 1969. Klein was a leader in the construction of econometric models of the United States economy. Two major assumptions have governed econometric modeling. First, is that the formulated equations do in fact utilize the historical data appropriately. While econometricians can never be sure that their equations truly correspond to reality, they can and do apply statistical techniques to determine the consistency of formulated equations with sets of observed data. The second important assumption is that the future will behave in a manner depicted by the formulated equations. It is, of course, not possible to know for sure whether an equation will describe future behavior. Some of the features [of the economy] that do not change during one period may change during another. For example, the effective Federal income tax rate in the United States was constant (at a level of zero) from 1873 through 1912, but it has been changed ever few years since then [ 301. SYSTEM DYNAMICS
System dynamics modeling, developed by Professor Forrester of M.I.T. is a methodology that deals with deterministic, dynamic, non-linear, closed boundary systems. Its initial application in 1961 was to the study of the behavior of industrial systems where the short-term dynamics of production rates and inventory levels were analyzed . Forrester expanded his system dynamics techniques in Principles of Systems in 1968 . More recently he has applied his modeling methods to longer term problems of the city  and to the problems of world growth . Currently, Forrester is developing a dynamic model of the United States economy. Dennis Meadows, an ex-student of Forrester has developed a similar world model in his Limits to Growth (popular summary)  and Dynamics of Growth in a Finite World (technical version) . System dynamics is based on principles borrowed from engineering-especially feedback concepts. It makes possible a representation of decision policies and information flow. The major concepts of this methodology can be organized and sequenced as follows: (1) All systems that change through time can be represented by varying levels and rates. (2) A level represents an accumulation within a system. This could be people, dollars, pollution, natural resources and almost anything tangible or intangible. It is analogous to a storage device or facility. It also provides an indicator of the condition or state of a system. (3) A rate is a flow from one area to another of what has been accumulated. Rates of flow cause, and control changes to levels. A rate of flow need not be constant-it can vary. These flows symbolize activities within the system. (4) Decision rules control system activities-that is rates of flow. Decision rules are called policies by Forrester. A policy describes how available information is used to generate decision. It defines what a decision maker does (or should do) when he receives specific kinds of information. As one user of system dynamics put it  : A policy
how goals are set, what information
are used for making
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and the nature of the response to available system and to various personal and political
and past conditions
(5) The environment, once determined, is considered constant during a particular set of time periods being simulated. (6) According to Forrester, feedback loops are the basic building blocks of a system. A simple feedback loop is illustrated in Fig. 2 below as a closed path connecting a decision point (decision rules which control rate of flow), a system level and the environment. Available information is the basis for a current decision that causes action to be taken. This action, in turn, alters the level of some system variables. (7) There are often additional delays or distortions appearing sequentially in a feedback loop. (8) There are two types of feedback. The “goal seeking” or negative feedback has a goal or desired value for a level. If the level departs from this value the rate of flow is modified to bring the level back to its desired value much like a thermostat. Conversely, positive feedback loops contribute to either persisitent growth or continuous decline of levels-frequently past what is desired. (9) A system dynamics model consists of multiple positive and negative feedback loops linked together-frequently in complicated manner. Sometimes the different types of feedback loops dampen extreme fluctuations of system variables. Sometimes, feedback loops exhibit “exponential growth” where there is, in each succeeding time interval, greater and greater increases in a level. Examples of this type of growth are seen in cell division, the chain reaction of an atomic explosion, and in the multiplication of rabbits. (10) Level equations and rate equations are developed to quantify the system activities, interrelationships, and flows. (11) Data for the equations are obtained by some combination of available data and educated guesses. (12) The system is simulated under alternative policies (decision rules), levels, and environments, and resulting system behavior described.
While critics have sharply attacked certain assumptions responded favorably to the methodology itself .
of system dynamics, many have
A great asset of the method is that it forces comprehensive consideration of the system rather than singling out a particular facet and trying to understand it alone. Forrester has made us aware that interrelations in complex systems often tend to hide ultimate causes far from the point where results are seen and has shown that simulation technique gives us a feasible approach to understanding such systems.
has been applied to such disparate areas as solid waste generation,
Fig. 2. Simple feedback
MARVIN KORNBLUH and DENNIS LITTLE
narcotic addiction, commodity production, research and development, merchant shipbuilding, and sports and recreation. The major criticisms of the approach have included: (1) The sparing use of measured, supportive, empirical data. The values for many of the variables have been obtained from intuitive judgments and theoretical constructs. (2) The exclusion of future unprecedented events such as scientific discoveries, revolutions, abrupt reversals of political policies and technological advancements. (3) System dynamics models are more easily created than verified. They do little more than reflect the sincere opinions of their builders. Assumptions of the model structure are not sufficiently justified through comparison of model behavior with post history and through intensive discussions with experienced systems personnel. (4) Overconcentration on the mechanistic view of socio-economic systems. The approach implicitly assumes that people and institutions show little fundamental change in behavior with the passage of time. It’s simply “more or less” behavior rather than different behavior. (5) The nature of the equations are such that the approach does not adequately handle events that occur at random. PROBABILISTIC
The Futures Group, a private organization in Glastonbury, Connecticut has recently devised a new technique which tries to capitalize on the strengths of system dynamics and another technique entitled cross-impact analysis. Cross impact analysis attempts to capture the interrelationships among events. This technique, when performed on a computer, allows the consideration of a large number of events and the determination of sequential and indirect (second and third order) affects that are not usually apparent in a purely intuitive analysis. Probabilistic system dynamics adds to the two aforementioned techniques “a consideration of the interactions between the events and the model. These new interactions are of two types: 1) the impacts of the events on the model (model structure, parameter values, etc.) and 2) the impacts of model variables on event probabilities. This new technique has been applied to the study of Japanese national development policies.”  SUMMARY
Three approaches are prevalent in constructing policy oriented simulation modelsinput-output analysis, econometrics, and system dynamics. Input-output analysis shows the relationships between the inputs and outputs of a specified number of industries or sectors within an economy. Each industry obtains the outputs of other industries in certain fixed proportions and combines and inputs them into its own productive process. Also, each input uses some of its own output as subsequent input. In this manner, an intricate set of interdependencies of industries is structured for analysis. Econometrics constructs equations to study the behavior of various economic units in the activities of producing, exchanging and consuming economic goods and services. Economic units are households, firms, governments, and so on. Highly aggregative measures are used as variables such as national income, total employment, and the price level. The derivation of equations is based on statistical relationship among relevant historical data. System dynamics is based on the traditional management process, feedback theory which deals with how decisions are made and the way they are embedded in information channels, and the use of computer simulation techniques. The approach is to construct equations
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which represent levels or accumulations within a system and rates of flow which transfers accumulations from one area to another. Sets of decision rules-called policies-control the rates of flow. Many feedback loops are utilized. They either help attain desired values for levels (negative feedback) or contribute to persistent growth or continuous decline of levels (positive feedback). References and Footnotes 1. Jay W. Forrester, Principles of Systems, Wright-Allen Press, Inc., Cambridge, Mass., 1968, p. l-l. 2. Forest W. Horton, Jr., Systems Approach and Systems Analysis, in Forest W. Horton, Jr., ed., Reference Guide to Advanced Management Methods, American Management Association, Inc., New York, 1972, p. 293. 3. Ibid., pp. 293-294. 4. Jay W. Forrester, op. cit., pp. 1-5. 5. C. West Churchman, The Systems Approach, Dalecort Press, Inc., New York, 1968, Chapter 3. 6. Forest W. Horton, Jr., Models, in Forest W. Horton, Jr., ed. Reference Guide to Advanced Management Methods, American Management Association, Inc., New York, 1972, p. 182. 7. John Henize, A Framework for the Evaluation of Large-scale Social System Models, paper presented at the Workshops on Modeling Large Scale Systems at National and Regional Levels, Brookings Institution, Washington, D.C., Feb. 10-12, 1975. 8. Harvey M. Wagner, Prireiples of Operations Research with Applications to Managerial Decision, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971, pp. 10-l 1. 9. Alphonse Chapanis, Men, Machines and Models,Amer. Psycho/. 16, 115 (March 1961). 10. Geoffrey Gordon, Sysrem Simulation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969, p. 5. 11. Jay W. Forrester, op. cit., p. 3-1. 12. Ibid., pp. 3-2 and 3-3. 13. Roger L. Sisson, Introduction to Decision Models, in A Guide to Models in Governmental Planning and Operations, Washington, D.C. U.S. Environmental Protection Agency, Washington Environmental Research Center (Contract No. 68-01-0788) Aug. 1974, Chapt. 1, pp. 11-12. 14. Dennis L. Little, Models and Simulation-Some Definitions, Institute for the Future, Middletown, Conn. April 1970, p. 5. 15. Theodore J. Gordon, Tools and Techniques, in Albert Somit, ed., Political Science and the Study of the Fufure, The Dryden Press, Hinsdale, Ill., 1974, p. 104. 16. R. F. Barton, A Primer on Simulation and Gaming, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1970, p. 20. 17. H. Morgenthaler, in Forest W. Horton, Jr., ed., Reference Guide to Advanced Management Merhods, American Management Association, Inc., New York. 1972, p. 273. 18. John S. Hammond, III, Do’s and Dont’s of Computer Models for Planning, Harvard Business Review, Boston, Mass., March-April 1974, p. 121. 19. Dennis L. Meadows, er al., Dynamics of Growth in a Finite World, Wright-Allen Press, Inc., Cambridge, Mass., 1974, p. 24. 20. John Henize, A Framework for the Evaluation of Large-scale Social System Models, paper presented at the Workshops on Modeling Large Scale Systems at National and Regional Levels, Brookings Institute, Washington, D.C., Feb. 10-12, 1975, p. 19. 21. Jay W. Forrester, op. cit., 3-3. 22. L. R. Klein, The Econometric Experience, paper presented at the Workshops on Modeling Large Scale Systems at National and Regional Levels, Brookings Institute, Washington, D.C., Feb. 10-12, p. 2. 23. Dennis L. Meadows, etal., op. cit., p. 5. 24. Chester L. Meek, Glossary of Computing Terminology, CCM Information Corp., New York, 1972, p. 94. 25. A good overview of three special purpose simulation languages, DYNAMO, GPSS, and SIMSCRIPT are covered in Geoffrey Gordon, System Simulation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. 26. W. W. Leontief is considered the inventor of the input-output methodology. He was awarded the Nobel Prize for economics in 1973 for his pioneering work. 27. For an interesting explanation and new application of the input-output method by Leontief
28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.
himself see, W. W. Leontief, Environmental Repercussions and the Economic Structure: An Input-Output Approach, Review of Economics and Statistics 52, (1971). John Henize, op. cit., p. 11. Carl F. Christ, Economic Models and Methods, John Wiley and Sons, Inc., New York, 1966, p. 11. Ibid., p. 11. J. W. Forrester, Industrial Dynamics, M.I.T. Press, Cambridge, Mass., 1961. J. W. Forrester, Principles of Systems, Wright-Allen Press, Inc., Cambridge, Mass., 1968. J. W. Forrester, Urban Dynamics, Wright-Allen Press, Inc., Cambridge, Mass., 1969. J. W. Forrester, World Dynamics, Wright-Allen Press, Inc., Cambridge, Mass., 1971. John Henize, op. cit., p. 17. Dennis L. Meadows and Donnella H. Meadows, Jorgen Randers and William W. Behrens, III., eds., Limits to Growth, Universe Books, New York, 1972. Dennis L. Meadows, et al., Dynamics of Growth in a Finite World, Wright-Allen Press, Inc., Cambridge, Mass., 1974. Statement by Wesley H. Long in John Henize, op. cit., p. 17. John C. Stover, Energy Policy Modeling with Probabilistic System Dynamics: A Japanese Case Study, paper presented at the 1974 Summer Computer Simulation Conference, Houston, Tex., The Futures Group, Glastonbury, Corm., 1974.
Received December 19 75