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4 Macro-Level Formal Models T his chapter presents modeling approaches for representing the behavior of humans in groups and organizations. It discusses system dynamics models first, followed by a discussion of several approaches to organizational modeling. System Dynamics Models What Is System Dynamics Modeling? System dynamics modeling is a method of modeling the dynamic b Â ehavior of complex systems by breaking down these systems into sim- pler interÂconnected components (âblocksâ) connected together via links or âwiresâ that connect one blockâs outputs to another blockâs inputs. This breaking down or recursive modeling continues until simple blocks can be defined in terms of well-understood interactions between the blockâs inputs, outputs, and its âinternal state.â Within any given block, this state is defined by the associated state variables, which are usually related by a set of differential equations that underlie the dynamics of that block. To provide a quick illustration of the basic concepts involved, if oneÂ were to model the dynamics of two cars traveling down a straight road, one behind the other, one might specify four blocks: one for each car and one for each driver. Each car would have (a) two states: a speed and a â he T use of differential equations reflects the history of system dynamics modeling and its roots in electrical and mechanical engineering and control systems theory. 122
MACRO-LEVEL FORMAL MODELS 123 position/location down the road; (b) a single input (or control) of accelera- tion, determined by the driverâs application of the gas or brake pedal; and (c) a single output, the position/location down the road. Simple differential equations, based on the laws of physics (and the vehicle Âacceleration/braking d Â ynamics) would then be used to define the relation of the input (control) of the driverâs use of the gas pedal or brake to the carâs output, the position down the road. The second car would be modeled similarly. The trailing car driver would be likewise modeled as a block, with perhaps two inputs, distance and closing speed to the front car, and a single output, gas/brake pedal usage. The differential equations or âcontrol lawâ relating driver inputs to driver outputs would be specified by well-understood manual control dynamics (see, for example, McRuer and Krendel, 1974). The lead driver could be modeled in âopen-loopâ fashion, as a block with no input but with a randomly varying output of gas pedal pressure, leading to ran- dom speed behavior. By specifying each individual blockâs behavior (via the inputs, the outputs, and the differential equations underlying the Âinternal dynamics) and by linking up the appropriate inputs to the appropriate outputs of the four-block system, one then has a general system dynamics representation of the dynamics of the two-car, two-driver âsystem.â The fundamental power of this approach lies in four areas: 1. System dynamics concepts are tightly bound to the twin notions of (1) the dynamic behavior of systems over time and (2) feedback and cross-connectivity between different elements of the system. Dynamic behavior can evolve simply because of a systemâs internal dynamics and its initial conditions (e.g., a frictionless swing set to infinite harmonic oscillation by an initial offset from the vertical). But the dynamic behavior is considerably more interesting when it is driven by the dynamics of yet some other system (e.g., some- one pumping the swing ever higher and eliciting nonlinear swing behaviors), through a cross-coupling or feedback loop involving real physics or abstract information. And when these loops are contaminated by noise (an erratic âpumperâ), time delays (a slow- to-respond pumper), and/or distortion in the form of frequency- or amplitude-selective feedback channels, then the opportunity exists for often unanticipated and sometime surprising behaviors across the system as a whole. These are often the characteristics of com- â Two states suffice for a simple kinematic representation of the longitudinal (fore-aft) control of vehicle location; additional states would be added for finer grained representation of the situation if one were interested in modeling the effect of the detailed dynamics of the brake calipers, for example. The approach would be the same, however, via the introduction of yet another block placed between the driverâs brake pedal and the block representing the vehicle kinematics.
124 BEHAVIORAL MODELING AND SIMULATION plex human-machine and human-human systems that modelers are dealing with. 2. The use of blocks, which can be made up of subblocks ad infini- tum, so that any level of detail can be examined in a given model, within practical computational limits. Literally millions of state variables can be introducedâin a structured mannerâto allow the finest grained examination of the impact of very small com- ponents (e.g., O-ring brake failure) on overall system behavior (e.g., a 20-car pileup on the Los Angeles freeway). In essence, this approach provides one means of modeling the âbutterfly effect,â as an alternative to chaos theory, which models how small changes in the initial state (or initial conditions) of a nonlinear system can lead to large changes of the system state (or system trajectory) at some later point in time. The systems dynamics approach takes a bottom-up building block approach, which is appealing in its dependence on well-understood domain-specific theory and laws, whereas chaos theory takes a broader systems level view that, if more abstract, is well grounded mathematically. 3. The use of interconnected blocks ensures that the fundamentals of feedback are (nearly) always present. In the example above, the driving behavior of the lead driver clearly will affect the behavior of the trailing driver. Thus, subtle interactions can be accounted for, as one element of the system accounts for and accommodates to others. It is often these feedback loops that give rise to unantici- pated âemergentâ behaviors (pilot-induced oscillations in aircraft handling, stock market crashes, etc.). 4. The use of blocks with âinternalsâ that can be elaborated as the need arises. Generally, differential equations serve as the basis for a blockâs dynamics, but it is straightforward to elaborate, via either the addition of subordinate blocks as just described or the addi- tion of, for example, nonlinear characteristics (e.g., a limit on the acceleration obtainable via a fully pressed-down gas pedal in the above example). However, any such nonlinear additions often tend â he term âbutterfly effectâ was introduced by one of the pioneers of chaos theory, Edward T Lorenz, in a paper given by him in 1972 to the American Association for the Advancement of Science in Washington, D.C., entitled Predictability: Does the Flap of a Butterflyâs Wings in Brazil Set Off a Tornado in Texas? â ee later comments on the limits to the system dynamics approach of building, from the S ground up, models that seem plausible at each level, until they are actually run and compared with dramatically different real-world results. â nd to explore the impact of the trailing driverâs behavior on the lead driverâs, one would A merely need to add in a rear-view mirror into the model of the lead driver, and postulate the dynamics of lead driver behavior as a function of, say, trailing driver tailgating activity, thus fully âclosing the loopâ between the two drivers.
MACRO-LEVEL FORMAL MODELS 125 to make the theoretical analysis of such systems intractable, so that system dynamics analysts must then rely on simulation execution and analysis in order to understand or predict system behavior. A specialized version of system dynamics modeling, and the main focus of this section, focuses on a fairly explicit representation of the system states, called âstocksâ (entities that accumulate or deplete over time) and their associated âflowsâ (the rates of change of stocks) (Forrester, 1968). In essence, Forrester transformed the generic nth order differential equations characterizing general system dynamics theory into n first-order differential equations that are intuitively simple to understand and, via the associated programming language Dynamo, into a transparent graphic representa- tion of the key interrelationships among variables (Richardson and Pugh, 1981). Using Dynamo to implement these first-order relations, it becomes a relatively simple exercise in computational model development by the nonÂspecialist who may not have been schooled in differential equations and their specification or solution. Feedback and interconnections are intro- duced by defining how the level of one stock controls the flow of another. Nonlinearity is introduced via simple limits on stock levels and flow rates. A simple example is given in Box 4-1, which illustrates how two states (birth rate and death rate) define the flow of a third state (net growth rate). This is a simple open-loop example with no feedback, but it is not a diffi- cult exercise to close the loop, for example, by postulating how population growth rate might influence economic growth rate, which could induce consumer confidence and, through that, cause birth rates to increase. An example showing this level of loop closure is given in Figure 4-1, which illustrates one component of a larger system dynamics model of the spread of an epidemic (Sage and Armstrong, 2000). The three state vari- ables (stocks) are X1, the population susceptible to infection (susceptible population), X2, the population that is actually infected (infected popula- tion), and X3, the population that has developed an immunity to the infec- tion (immune population). Note that boxes are used to represent these states graphically. The associated flows are LR (loss of immunity rate), IR (infection rate), and RR (recovery rate). Note that the valve symbols are used to indicate how the flows control the stock levels, via the following intuitive graphic analogy: flow into a block increases the stock level, while â lthough A Jay Forresterâs name is the one most closely associated with the system dynamics concept, his work owes much to the electrical engineering pioneers at Bell Laboratories work- ing with feedback circuits and notions of system stability in the 1920s and 1930s (see, e.g., Black, 1977); the discipline of cybernetics developed at the Massachusetts Institute of Tech- nology by Norbert Weiner and colleagues during the 1940s and 1950s (Weiner, 1948); and, more recently, practitioners who have done much to popularize its application to important problems in the social sciences, most notably Richardson and colleagues (see, e.g., Richardson and Pugh, 1981; Richardson, 1991).
126 BEHAVIORAL MODELING AND SIMULATION BOX 4-1 The Equation, Variables, and Mathematical Representations for Birth and Death Used in Population Modeling Description of variables: b(t) : Average birth rate per unit person in the population at time t D(t) : Average death rate per unit person in the population at time t mn(t) : Expected value Mathematical representation of birth rate, death rate, and average rate of popula- tion growth: b(t)mn(t) : Total average birth rate D(t)mn(t) : Total average death rate dÂµn (t ) = [ Î² (t ) â â (t )] Âµn (t ) : Average rate of population growth (the difference dt between the total average birth rate and death rate) X1 Susceptible Population IR(t) ) Infection Rate X22 x LR(t) ) Infected Infected Loss of Immunity Population population Rate RR(t) ) Recovery Rate X3 Immune Population FIGURE 4-1â Example of a system dynamics model that shows the partial system dynamics description for propagation of 4-1.eps epidemic. a potential SOURCE: Adapted from Sage and Armstrong (2000, p. 235).
MACRO-LEVEL FORMAL MODELS 127 flow out decreases it. The diagram captures the following qualitative and, for the mathematically inclined, quantitative notions: â¢ For the states: â The susceptible population X1 will increase as the recovered lose immunity (LR) and decrease as the susceptibles become infected (IR). Or n d(X1)/dt = LR â IR â The infected population X2 will increase as the susceptibles become infected (IR) and decrease as the infected recover (RR). Or n d(X2)/dt = IR â RR â The immune population X3 will increase as the infected recover (RR) and decrease as the immune lose immunity (LR). Or n d(X3)/dt = RR â LR â¢ For the flows (not illustrated for simplicity): â The infection rate (IR) increases both as the susceptibles (X1) increase and as the infected (X2) increases, due to the net- worked nature of spreading infections. Or10 n IR = a*X1*X2 â The recovery rate (RR) is directly proportional to the infected (X2). Or n RR = b*X2 â Likewise, the loss of immunity rate (LR) is directly propor- tional to the infected (X3). Or n LR = b*X3 Note the complete loop closure relating the three states, and the potential for continuing growth and decay of an infected population over time. Note also the potential for nonlinear behavior over time, because of the fundamental nonlinearity introduced via the infection rate equation (IR = a*X1*X2). The structure of system dynamics models can be characterized by four hierarchical levels, as shown in Figure 4-2.11 All interactions and impacts â ot N explicitly shown is how the flows are influenced by the stock levels. â ote N that in this set of equations and in subsequent sets, the asterisk (*) is not meant to represent a convolution operation or function composition, but rather a simple multiplication, in line with DYNAMO code conventions, as well as FORTRAN syntax, which was a popular computational language at the time of DYNAMOâs introduction. â )/dt is used to denote the first-order derivative of the associated variable. d( 10âThe constants (a,b,c) are chosen on the basis of underlying knowledge of dynamics of infection, recovery, etc. 11â his description borrows heavily from Sage and Armstrong (2000, p. 237). T
128 BEHAVIORAL MODELING AND SIMULATION Closed Boundary Around a System Rate and Level Variables as Basic Structural Elements Level Variables Representing Rate Variables Representing Accumulations Within Activity Within Feedback Loops Feedback Loops Detection of Control or Goals or Observed Discrepancy Policy Action Objectives Conditions Between Goals Based on the and Observed Discrepancy Conditions FIGURE 4-2â The four hierarchical levels of system dynamics modeling. 4-2.eps SOURCE: Sage and Armstrong (2000, p. 237). in the system dynamics model take place inside a boundary. Within this boundary, variables are chosen to represent the key states that define overall system behavior. A derivative variable is chosen to control a flow into the state or level variable, which integrates or accumulates this level. Informa- tion concerning the level is used to control the rate variable (state feedback to the same associated state). In other words, we define a rate variable as the time derivative of a level or state variable and determine rate variables as functions of level variables. Some useful readings on system dynamics modeling methodology are Roberts, Anderson, Deal, Garet, and Shaffer (1983); Sterman (2000); Ogata (2003); and Karnopp, Margolis, and Rosenberg (2006). A more detailed description of system dynamics modeling and the equations it uses is available in Sage (1977) and Sage and Armstrong (2000). Comprehen- sive approaches to modeling complex projectsâincluding industrial and m Â ilitaryâare described by Williams (2002).
MACRO-LEVEL FORMAL MODELS 129 State of the Art in System Dynamics Modeling Early History of System Dynamics Jay W. Forrester created this focused version of system dynamics in the mid- to late 1950s at the Massachusetts Institute of Technologyâs Sloan School of Management, basing it on the more traditional modeling used at the time, implementing differential equation models on analog com- puters. Forrester brought these concepts to the digital domain, codified them in the stocks and flows paradigm described above, and used this approach to model highly complex systems such as organizations and the urban environment (Forrester, 1961; see also Forrester, 1969). This novel approach of developing computational dynamic models of hitherto u Â nmodeled Âphenomena led to the founding of the System Dynamics Group at the Massachusetts Institute of Technology in the early 1960s (see http:// web.mit.edu/sdg/www/what_is_sd.html). Forrester wrote several books on system dynamics methodology that provide the foundations of the field. The first was Industrial Dynamics (Forrester, 1961), providing a computational foundation for understand- ing the dynamics of organizations and processes in industry. Forrester then published Urban Dynamics (1969), which was the first nonÂcorporate application of system dynamics (Radzicki, 1997). Shortly thereafter For- rester published World Dynamics (1971) in which he applied system dynamics methodology to the behavior of the highly interrelated forces of global dynamics (Sage and Armstrong, 2000). Forresterâs student, Dennis Meadows, and colleagues expanded on World Dynamics in The Limits to Growth (Meadows, Meadows, Randers, and Behrens, 1972) and a follow- up, Beyond the Limits (1992) (Radzicki, 1997). The Malthusian projections that came from these early models not only alienated the growth-oriented policy makers of the West, but also brought severe criticism from many of the academics in the field (e.g., economists), because of the glaring mis- match between model âpredictionsâ and what was actually occurring on the world stage. This became more apparent as time went on, and it is fair to say that this failure to meet empirical validation standards considerably dampened the initial enthusiasm that met the system dynamics viewpoint toward understanding the complex interrelations of complex systems.12 12â owever, system dynamics modeling has been applied to several other areas, including H software project dynamics (Abdel-Hemid and Madnick, 1991), organizational learning (Senge, Kleiner, Roberts, Ross, and Smith, 1994; Morecroft and Sterman, 1994), agriculture (Elmahdi, Malano, and Khan, 2006), health care management (Rohleder, Bischak, and Baskin, 2007), and transportation (Springael, Kunsch, and Brans, 2002).
130 BEHAVIORAL MODELING AND SIMULATION More Recent Applications of System Dynamics Modeling More recently, there has been a resurgence of interest in system Âdynamics modeling, most particularly in public policy and business areas. Stermanâs text on Business Dynamics (2000) presents a number of case studies that demonstrate successful applications across a number of areas, including global warming, the war on drugs, reengineering the supply chain of a major computer firm, developing a marketing strategy in the automobile industry, and planning process improvements in the petrochemicals indus- try. The Department of Defense (DoD) has also taken a keen interest in this approach, particularly for modeling diplomatic, information, military, and economic (DIME) actions, and political, military, economic, social, infor- mation, and infrastructure (PMESII) interactions. It is not our intent here to survey all of these efforts, but merely to provide a few illustrative examples to indicate the potential of system dynamics modeling in this area. For example, Robbinsâ Stabilization and Reconstruction Operations Model (SROM) (Robbins, Deckro, and Wiley, 2005) analyzes the orga- nizational hierarchy, dependencies, interdependencies, exogenous drivers, strengths, and weaknesses of a countryâs PMESII systems using a complex set of interdependent system dynamics representations. SROM models a country system in a holistic manner as a national model, which, as shown in Figure 4-3, is then defined in terms of its n regional submodels that interact with each other and the national model. Each regional submodule contains six functional submodels: the demographics submodel, the insurgent and coalition military submodel, critical infrastructure, law enforcement, indig- enous security institutions, and public opinion. Each submodel is comprised of approximately 600 model parameters, 90 random variables, 80 states (stocks), and 190 rates of change (flows). National Sub-Model Region 1 Region 2 Region N Sub-Module Sub-Module Sub-Module FIGURE 4-3â Top-level nation SROM. SOURCE: Robbins et al. (2005, p. 19). 4-3.eps
MACRO-LEVEL FORMAL MODELS 131 Figure 4-4 shows a portion of the critical infrastructure model of SROM. The model captures a sequence of influences among variables, start- ing from the power supply at an electrical substation. The generated power is fed into an industrial water plant, which produces water consumed by oil field work. An oil field produces crude oil to be refined by a refinery. Finally, refined fuel is used to generate power, which in turn is supplied to various power substations, thus forming a closed loop. SROM has been demonstrated in modeling and analysis of Iraqi recon- struction and recruiting efforts (Robbins et al., 2005). Parameters were set to reflect prevailing conditions in Iraq on May 1, 2003, including â¢ Regional makeup (governorates) â¢ Regional population â¢ Population subgroup distribution â¢ Population support for coalition â¢ Oil and gas infrastructure â¢ Power infrastructure â¢ Transportation infrastructure â¢ Economicâregional gross domestic product Robbins (2005) claims that the SROM allows analysts to more precisely investigate the multifaceted process that is nation building: â[Because] the complexities of nation-building involve many different but interrelated systems and institutions, understanding the significance of the dynamic relationships between these systems and institutions is paramount to operational success. The system dynamics model proposed in this study allows decision-makers and analysts to investigate different sets of decision approaches at a sub-national, regional levelâ (p. 135). The Pre-Conflict Anticipation and Shaping (PCAS) program (Popp et al., 2006) was an attempt to evaluate alternative DIME/PMESII model- ing efforts to predict nation-state collapse and to anticipate instabilities that might lead to conditions necessitating military intervention. One of the approaches, led by Nazli Choucri, developed a âstate stability modelâ using a system dynamics approach; a high-level view of the model is given in Figure 4-5. Power Industrial Oil Oil Power Substation Water Plant Field Refinery Generators Industrial Refined Power Crude Water Fuel FIGURE 4-4â SROM infrastructure model. SOURCE: Robbins, Deckro, and Wiley (2005). 4-4.eps
132 BEHAVIORAL MODELING AND SIMULATION + Military Capability + Dissident + + Institutional â + Capacity Social Anti-Regime Cohesion Activity â â + â â + Population + + â External â Resources Regime Force and Violence + State â + Institutional + â Capacity + + GNP Civic Capacity and Social + Liberties + + Regime + + Legitimacy 4-5.eps FIGURE 4-5â High-level view of system dynamics implementation of state stability model. redrawn SOURCE: Popp (2005). According to Popp (2005, p. 18), it âshows loads, demands and stresses on state and the causal dependencies; shows feedback loops, tipping points and unintended consequences; [and] shows the internal and lateral pressures that can lead to conflict.â By looking at the loads (demands) placed on the system (nation-state) and evaluating those demands in terms of the systemâs capabilities, an assessment of stability can be made based on how much demands exceed capacity. Finally, OâBrienâs Integrated Crisis Early Warning System (ICEWS) is a new program at DARPA/IPTO aimed at following on from the PCAS exploration just described. According to the announcement of the research program, its goal âis to develop a comprehensive, integrated, automated, generalizable, and validated system to monitor, assess, and forecast national, sub-national, and international crises in a way that supports decisions on how to allocate resources to mitigate them. ICEWS will provide Combat- ant Commanders (COCOMs) with a powerful, systematic capability to anticipate and respond to stability challenges in the Area of Responsibility (AOR); allocate resources efficiently in accordance to the risks they are designed to mitigate; and track and measure the effectiveness of resource allocations toward end-state stability objectives, in near-real timeâ (see
MACRO-LEVEL FORMAL MODELS 133 http://www.arpa.mil/ipto/solicitations/open/07-10_PIP.pdf [accessed July 2007]). Environments for System Dynamics Modeling The earliest computer-based system dynamics simulations were created by Richard Bennett, who developed the SIMPLE (Simulation of Industrial Management Problems with Lots of Equations) compiler in 1958 (Forrester, 1989). In 1959, Phyllis Fox and Alexander Pugh used the SIMPLE compiler to form the DYNAMO simulation package, which was used as the standard system dynamics language for over 30 years (Radzicki, 1997). There are several computer-based simulators that are used to model system dynamics problems. The DYNAMO system dynamics simula- tion language is described in Richardson and Pugh (1981) and a per- sonal Â computerâbased language, STELLA, is discussed in Richmond and Â Peterson (1992). Other software packages that are used for system d Â ynamics modelÂing include Powersim, Vensim, MapSys, Simile, and Evo- luciÃ³n. The tradition of easy model development is also carried on via the Ptolemy systems modelÂing language developed by Buck, Ha, Lee, and Messerschmitt (1994). Relevance, Limitations, and Future Directions The relevance of the system dynamics approach to the problems addressed by this panel is manifest both by the early work by Forrester and colleagues in attempting to model organizations, cities, nations, and overall world dynamics and by the current resurgence in interest by DoD in retackling these very hard problems, in recognition of the âsoftâ nature of warfare now dominating current conflicts. The fundamental appeal of this methodology is due to the strengths noted earlier: â¢ System dynamics concepts provide a means of representing critical dynamic behavior of systems over time, as well as feedback, and cross-connectivity between different elements of the system. â¢ The use of blocks that can be made up of subblocks ad infinitum, so that any level of detail can be examined. â¢ The use of interconnected blocks that ensures that the fundaÂ mentals of feedback are (usually) always present, enabling emer- gent behavior. â¢ The use of blocks with internals that can be elaborated as the analysis need arises, in terms of both resolution and modeling fundamentals.
134 BEHAVIORAL MODELING AND SIMULATION One of the major limitations of the system dynamics approach is that its strong grounding in a mathematical description of the organizational dynamics (namely, first-order differential equations) tends to preclude par- ticipation by researchers and modelers who are more linguistically and semantically oriented, for example, those working in causal networks, expert systems, or the like. Attempting to bring these different communities together is not a trivial task, as evidenced by the experience of the PCAS program, and attempting to integrate across these different methodologies is likewise problematic, as described in Chapter 8. Another limitation is verification and validation, since these models are particularly easy to build by making simple assumptions about struc- tures, feedback path, and parameter values, without ever relying on ârealâ data.13 As noted by Sage and Armstrong with respect to the urban modeling effort of Forrester: âForresterâs interest in modeling the city is a somewhat abstract one in that he does not fit the data and parameters for his city to any particular city. Effort is primarily directed at discovering the essential features of the city and expressing relationships between these features in mathematical terms as difference equationsâ (Sage and Armstrong, 2000, p. 253). A system dynamics model must have both behavioral and structural validity (Quadrat-Ullah, 2005). Forrester and Senge (1980) presented some tests for determining if a model has structural validity: â¢ Boundary adequacy: whether the important concepts and struc- tures for addressing the policy issue are endogenous to the model. â¢ Structure verification: whether the model structure is consistent with relevant descriptive knowledge of the system being modeled. â¢ Parameter verification: whether the parameters in the model are consistent with relevant descriptive and numerical knowledge of the system. â¢ Dimensional consistency: whether each equation in the model dimensionally corresponds to the real system. â¢ Extreme conditions: whether the model exhibits a logical behavior when selected parameters are assigned extreme values. 13â r, O as one of the report reviewers so aptly noted, âExpressing a social relationship as a differential equation (or any other kind of equation for that matter) does not make it so. There are such things as accounting identities, but mathematically exact descriptions of social or h Â uman processes generally do not exist.â We agree, but, of course, this is not a shortÂcoming that is specific to computational models built on system dynamics concepts; it is a general issue with any âmodelâ that can be reduced to executable software. Adequate verification and validation is always a critical issue for any modeling paradigm, as we discuss at length in Chapter 8.
MACRO-LEVEL FORMAL MODELS 135 Finally, there are a number of potential directions for future research and development (R&D) efforts, including bridging the gap to models and simulations that are not so formally mathematically defined, improv- ing model composability from smaller component libraries (Davis and A Â nderson, 2004), and ensuring that the difficult problem of verification and validation does not outstep the progress being made in developing develop- ment environments that are easy to use. Organizational Modeling An organization consists of a number of individuals who must work together to achieve a goal. Corporations, governmental bureaus, religious organizations, the Armed Forces, divisions, squads, and teams are all orga- nizations; they are everywhere and each of us can be members of many organizations. A fundamental aspect of an organization is that the orga- nizational task requires the efforts of many individuals who must work together to accomplish this overall task. The big task is broken down into smaller subtasks or jobs which must then be coordinated in order to achieve the organizational goal. Each organization is the context or structure for the individuals to achieve their own smaller tasks. Individuals are linked through the organizational structure. What Is Organizational Modeling? Organization theory is a study of the structure, behavior, and perfor- mance of the organization (Scott, 1998) in order to describe, explain, and predict. Basic questions include: Under what circumstances is decentraliza- tion better than centralization? When should an organization be highly formalized with many rules and when should it be more informal? When should the information and communications follow the hierarchy, and when should there be many cross-hierarchy exchanges? When should tasks be grouped together by task specialization and when by purposeâall for better performance? There are many ways to describe an organization. One generally thinks of an organization in terms of its task assignment and its hierarchy of command and control. Another more basic description is: Who does what, when, and where?âthe four Ws of an organization. The âwhoâ is the individualâthe task assignment is the âwhatââthe âwhenâ introduces the time of actionâand the âwhereâ is the location. This is a rather complete description of an organization, leaving out only the how (with what resources and knowledge) and the why (with what goals). Beyond a few individuals, it is difficult to think about an organization at this level, without the use of dynamic network analysis models, so we introduce
136 BEHAVIORAL MODELING AND SIMULATION organizational properties, such as decentralization and formalization, or rules for how decisions are made and the information communicated, and the behavioral patterns or routines that are repeated. In information- p Â rocessing terms, the Ws take on a slightly different aspect: who talks to whom about what (communication networks, which may be hierarchical) and who decides what to do (decision making or command structure). In modern information-intensive organizations, the information-processing view of an organization is a frame for both describing an organization and designing it (Burton and Obel, 2004). Organizational design is the complement of organization theory in which one specifies what the organization should be, beginning with the purpose of the organization and then specifying the tasks and coordination mechanisms or communications and decision-making structures. The focus goes beyond what is or has been to what might be and then what should be (Burton, 2003). A good design requires a good understanding of organiza- tion theory, as the theory indicates what is feasible and not feasible in the circumstances. Organizational design can be the specification of what the organization should be: its hierarchy, its formalization, its decentralization, its communications, and its coordination and control mechanismsâan information-processing view. Or the term âorganizational designâ may describe the process of finding a good design and the issues of change or redesign. Organizational design is used both as a noun for what the design should be and as a verb for the process of determining the design. We dis- cuss both below. In the social and managerial sciences, the research on organizations is deeper in organization theory than organizational design, although the opposite tends to be true in engineering. In general, however, the focus has been on the âwhat isâ description of organizations and explaining what has happenedâto enhance understanding of how organizations behave. There are theories of bureaucracy, routines as rules and patterns, decentraliza- tion, coordination, and control; all yield hypotheses for confirmation or rejection. For the most part, these hypotheses have been examined empiri- cally. Researchers have used field data and, to a much lesser extent, lab experimental data to test the hypotheses and add to the understanding of organizations. In addition, some researchers take an ethnographic approach in which they gather more detailed data about an organization, describe it in great depth, and in doing so generate emergent hypotheses and theories. For both approaches, there is an emphasis on the data gathered from orga- nizations using an inductive approach for understanding. There has been a smaller effort on formal mathematical modeling of organizations using a deductive approach, in which the analysis of the models yields insights and hypotheses that can be tested using field or lab data. This includes optimization approaches, in which the structure of the
MACRO-LEVEL FORMAL MODELS 137 organization is optimized to meet the demands of the mission and tasks to be performed (Pattipati, Meirina, Pete, Levchuk, and Kleinman, 2002). Simulation or computational models offer a third approach (Axelrod, 1997). Simulation modeling is distinctively different from both approaches described above yet also has characteristics of both. First, a simulation model of an organization, which includes its structure and agents, generates behavioral and performance data on the organization, which can be ana- lyzed as if they were field data.14 These are frequently called virtual experi- ments. Agent-based models explicitly model both the agents or individuals and the decision-making structure of the organization, which includes the communication and authority links among the agents. In these experi- ments, the simulation model parameters can be varied beyond what can be observed from field or lab data to explore what might be; for example, new structures and decision procedures can be created, and even the infor- mation-processing characteristics of the agents (human or machine) can be varied. In both situations, the simulation models generate a larger set of possibilities from which to gain insight and understanding. Second, simu- lation models can be similar to mathematical models, but they are more complex and not amenable to closed-form solutions. Here, the simulation model can be used to explore and generate hypotheses for further investiga- tion in the field or lab. Simulation models free one from the constraints of mathematical m Â odels in which closed-form equilibrium solutions are required. Simula- tion models free one from the size and scale restrictions of lab experiments and from the limitations of field data, which necessarily are historical and limited to what did happenânot what could have happened. For action, we are interested in the alternatives available and what might happenâwhich is broader than what has happened in the past. 14â e W emphasize âas ifâ for two reasons: First, the simulation-generated data can be Âprocessed and analyzed via the same methods and toolsets used for real-world data. This is clearly an advantage both in terms of economical reuse of methods and software already developed for real-world data, and in terms of ease of comparing processed and analyzed data collected from the two domains (simulated and real-world). This latter case is particularly important, since it is often impossible to compare, for example, single-time histories of organizational âstateâ recorded from real and virtual experiments (because of ânoise,â for example), whereas it is possible to compare processed data, obtained from time- or ensemble-averaged statistics calculated over many âruns,â both virtual and real. The second reason for the emphasis on âas ifâ is not so positive. Because simulation- generated data can be made to look so much like real data, they are often confounded, and researchers can be led to overinterpret the results of a simulation, coming to conclusions as if they had been looking at real data generated by real-world experiments (or at real-world data generated by an experiment which grew out of a hypothesis created by a simulation- based virtual experiment), rather than at data generated by a simulation that has not been adequately validated.
138 BEHAVIORAL MODELING AND SIMULATION State of the Art in Organizational Modeling Here, we focus on simulation or computational organizational models. A number of books contain overviews and examples of many models in this area (Carley and Prietula, 1994; Carley and Gasser, 1999; Lomi and Larsen, 2001). Some models consider organization theory questions; others are more oriented to organizational design questions; and some can be used for both purposes. We begin with the theory models and then consider the design models, with comments when the models can be used both ways. Organization Theory Models There are numerous organization simulations or computational orga- nizational models; here we review a few of them. Most, but not all, are agent-based models in which the organization is represented as agents that are linked together by communication or authority structures or both. The earliest computational organizational model was a behavioral theory of the firm in which the organization was modeled in terms of goals, expectations, and choice (Cyert and March, 1963). Simple systems were used to demonstrate how nonrational behavior could generate behavior similar to that observed in real organizations. This was then extended in the now canonical model, the garbage can model of organizational choice (Cohen, March, and Olsen, 1972). This was a simple Fortran program in which basic matching and accumulation functions were combined to show how variations in the problem access, salience of problems, and energy of the participants altered the level of work and the quality of outcomes. The Lin and Carley models look at organizations as networks of com- munication linkages among agents, such that agents learn only from the information that they get from the outside world or that is provided to them by another agent in the organization (Lin and Carley, 2003; Lin, Zhao, Ismail, and Carley, 2006). Using these models, they investigated questions of crisis response. They conducted a âmatched-setâ validation experiment, in which they compared the behavior of 69 real-world organizations faced with industrial crises with the behavior of the simulated versions of those same 69 companies. Using what-if analysis, they were then able to show that the type of decision making employed by the organizationâfor exam- ple, following standard operating procedures or following the dictates of historically based experienceâoften led organizations to false conclusions about their performance. This work was generalized and extended to produce the OrgAhead model. OrgAhead is a multiagent model of organizational design and the examination of the impact of learning and strategic adaptation on that design (Carley and Svoboda, 1996). In this model, learning occurs at the
MACRO-LEVEL FORMAL MODELS 139 operational and structural levels, using experiential and expectation-based learning models. From a technical standpoint, the model uses simulated annealing15 to alter the communication and authority lines and number of agents. The agents are information-processing units with a simple learning component. OrgAhead can be thought of as an operationalized grounded theory. The basis for OrgAhead is the body of research, both empirical and theoretical, on organizational learning and organizational design. The model has built into it several theories of different aspects of organiza- tional behavior. From the information-processing tradition comes a view of organizations as information processors composed of collections of intel- ligent individuals, each of whom is boundedly rational and constrained in actions, access to information by the current organizational design (rules, procedures, authority structure, communication infrastructure, etc.), and his or her own cognitive capabilities. Organizations are seen as capable of changing their design (DiMaggio and Powell, 1983; Romanelli, 1991; Stinchcombe, 1965) and as needing to change if they are to adapt to changes in the environment or the available technology (Finne, 1991). Dif- ferent organizational designs are seen as better suited to some environments or tasks than others (Hannan and Freeman, 1977; Lawrence and Lorsch, 1967). Aspects of the model have been tuned to reflect the findings of various empirical studies related to these theories. The set of theories that are unified into a single computational theory of organizational behavior interact in complex fashions to determine the overall level of organizational performance. Harrison and Carroll (1991) investigated the effect of turnover on organizational culture for different prototypical organizations and poli- cies. Their model is stated as a set of mathematical functions, which are then simulated and yield data that are analyzed as if they were field data. The model is essentially a cultural diffusion model operating at the group level. On the basis of âvirtual experimentsâ conducted with the model and a follow-on analysis of the resulting simulation-based data, they found that some employee turnover can help stabilize the culture of the organiza- tion, suggesting that some previously held truths about turnover are not general. An alternative information diffusion model is Construct, developed by Carley to examine the coevolution of structure and culture that results from individual information exchange and the formation and dissolution 15â imulated annealing is a technique to find a good solution to an optimization problem by try- S ing random variations of the current solution. A worse variation is accepted as the new solution with a probability that decreases as the computation proceeds. The slower the cooling schedule, or rate of decrease, the more likely the algorithm is to find an optimal or near-Âoptimal solution (see http://www.nist.gov/dads/HTML/simulatedAnnealing.html Â[accessed August 2007]).
140 BEHAVIORAL MODELING AND SIMULATION of social networks (Carley, 1991). Construct has been used to examine the impact of new technologies on the workplace (Carley and Schreiber, 2002), performance under diverse leadership styles (Schreiber and Carley, 2004), and the emergence of organizational vulnerabilities (Carley, 2004). NK models, originally suggested by Kauffman, are simple optimiza- tion models, often operationalized using genetic algorithms, in which N is the number of actors and K is degree of connectedness among the actors (Kauffman and Weinberger, 1989). NK models have been applied to organization theory questions of adaptation (Levinthal, 1997), search and stability (Rivkin and Siggelkow, 2003), modularity and innovation (Ethiraj and Levinthal, 2004), imitation and benchmarking (Rivkin, 2000), and other basic questions about organizations. The explicit modeling of rugged landscapes permits one to understand the limitations of organization expla- nations that implicitly assume smooth performance surfaces. It also yields greater insights into the persistence of variety among organizations. The SimVision model (earlier called VDT) is a project organization model (Levitt, Thomsen, Kunz, Jin, and Nass, 1999) which explicitly m Â odels the project tasks (similar to a critical path method network) and the hierarchical organization structure. In essence, this model is the merger of Gantt chart technology with a limited information-processing model for the agents. The project tasks are linked by the project network, and each task is assigned directly to an agent in the hierarchy. SimVision has been used as a laboratory for organization experiments.16 For example, ÂCarroll, Burton, Levitt, and Kiviniemi (2006) found that âfast trackingâ or concurrent engi- neering of projects quickly leads to increased coordination demands that do not reduce total project time; additional personnel can also increase project time as they require time to manage; and decentralization increases coordi- nation demands. Earlier, Kim and Burton (2002) found that decentraliza- tion reduces project time but may also decrease quality. Long, Burton, and Cardinal (2002) demonstrated that three simultaneous control approaches are better than any single control approach. These Âstudies began with orga- nizational questions and observations of real organizations as base models. The simulation experimental manipulations (âvirtual experimentsâ) went beyond real-world observations to investigate plausible conditions of what could happen for a better understanding of potential outcomes. Field obser- 16â n I the studies cited here it must be remembered that the conclusions drawn from Âanalysis of the simulation-based data (in turn generated by virtual experiments in the simulation domain) are not to be confounded with conclusions drawn from an analysis of homologous real-world data. This is in keeping with our earlier footnote regarding how simulation-based data can be analyzed as if it were real-world data. It often can, but the fundamental issue still remains regarding the validity of applying the simulation-based conclusions to real-world organizational behavior. Naturally, the more validated the model, the more likely one is to be correct in cross-applying oneâs conclusions.
MACRO-LEVEL FORMAL MODELS 141 vations and generalizations are limited in their applicability and should be used with caution in the design of future organizations. Simulation Âstudies provide deeper insight into what is possible and what is desirable for organizational redesign and change. ÂSimVision can also be applied as an organizational design model. Organizational Design Models The term âorganizational designâ is used both to mean the design of the organization and the process of design. The two meanings are different but closely related. In a special issue of Organization Science, Dunbar and Starbuck (2006) focus on the process of organizational design in its many facets. The articles give insight into how design can be accomplished and the challenges encountered. SimVision was applied to investigate organization theory questions. But it was originally created as an organizational design tool to help p Â roject managers optimize projects and project management implemen- tation (Levitt, 2004) This included avoiding unforeseen bottlenecks and finding options to compress project time. One of the insights is that project managers adapted quite well to minor variations from the normal base case but less well when there were large changes in requirements. The simula- tions were extremely useful in helping project managers reframe the project and redesign the project. Pattipati and colleagues (Pattipati et al., 2002; Levchuk, Levchuk, Luo, Pattipati, and Kleinman, 2002a, 2002b; Levchuk, Levchuk, ÂMeirina, Pattipati, and Â Kleinman, 2004) have used multiobjective optimization algorithms to develop organizational designs optimized to meet mission requirements for military command and control organizations, focusing specifically on Joint Task Force command teams. These designs specify both structure and process by specifying roles in the organization defined in terms of control of resources, responsibility for tasks, and requirements for coordination. Designs are then tested in simulations of organizational performance and finally tested in field experiments in which military officers play the roles that were designed using the model. Studies have shown that optimized organizational designs based on the model result in performance that exceeds that observed under more traditional designs suggested by military subject matter experts (Entin, 1999). A key find- ing of this work is that sufficient training is essential for the officers to function effectively in the innovative organizational structures developed using the model. Carroll, Gormley, Bilardo, Burton, and Woodman (2006) describe an organizational design process at the National Aeronautics and Space Administration (NASA), where SimVision and other organizational design
142 BEHAVIORAL MODELING AND SIMULATION tools were used as decision aids in creating a new organization. The chal- lenge was to create an organization that had multiple functional experts, was geographically disperse, and had severe resource constraints in which project time and quality were paramount. The design team began with the construction of the design structure matrix; it gave a good beginning but generated questions as well as answers. Next, they used OrgConâan expert system organizational diagnosis and design toolâto model the proposed organization at a high level in terms of structural properties, such as formal- ization and decentralization. One purpose of this modeling was to identify âmisfitsâ (Burton and Obel, 2004) that suggested a need for change; they found few of them. But many questions remained. Then they created a SimVision of the proposed design to obtain greater detail and better under- standing of how the organization would actually work. Using variations in the design, they confirmed that the design developed with the aid of the tools was reasonable. Perhaps most importantly, the usual organizational design approach would have resulted in an organization that would have failed to meet the goals and would have incurred delays and unanticipated costs. The results indicate that the tools can make a difference and lead to better designs; furthermore, the theory-based notion of organizational misfits aids in the process. It can be a bridge between theory and design and theory and practice, as managers find the identification of misfits and their correction both intuitive and practical. NASA had been accustomed to using simulations in engineering design but not in organizational design. Nonetheless, the culture was amenable to the application of such tools for organizational design. Similarly, OrgAhead was built to explore the relative effectiveness of different organizational designs. For example, it was used to determine the adaptability and performance characteristics of different designs under consideration by the Naval Strategic Studies Group. Construct, referred to earlier, has also been used to evaluate various organizational designs under different turnover regimes. Moreover, when data are collected on the who, what, where, and how of organizations, such data can first be assessed for points of vulnerability in ORA and then Construct can be applied to the same empirical description of the real organization to forecast its behavior in terms of information diffusion and performance with or without turn- over (Carley, Diesner, Reminga, and Tsvetovat, 2005). Levis and Wagenhals (2000) and the subsequent work with Shin, Kim, Bienvenu, and Shin led to the development of a Petri net model for design- ing and assessing organizational architectures (Bienvenu, Shin, and Levis, 2000; Wagenhals, Shin, Kim, and Levis, 2000). Modeling agents, their resources, and the decision process, this overall approach makes possible the fine tuning of detailed designs of core groups in organizations. This approach has been used consistently to evaluate command and control
MACRO-LEVEL FORMAL MODELS 143 structures. The key advantage of this approach is that designs can be opti- mized to the specific communication and timing requirements. Relevance, Limitations, and Future Directions The relevance of organizational models to the requirements outlined in Chapter 2 is obvious. Representative tasks, such as designing effective orga- nizations and disrupting adversary organizations, are clear candidates for the use of such models. If it were possible to accurately assess the probable effectiveness of various organizational options before implementing them, much effort could be saved and many potentially catastrophic mistakes avoided. Limitations of such models as they now exist include requirements for data that may be totally unavailable or unavailable in appropriate formats and structures, the need for culturally appropriate information on which to base assumptions and algorithms, especially for non-Western organiza- tions, and technical issues requiring further development and refinement of the models themselves. R&D requirements include better methods for obtaining and using organizational performance data to provide leaders and managers with b Â etter tools for restructuring their organizations as necessary. The vast majority of current model-based organizational design methods are static. That is, they use prior performance data about the organization to develop future designs, but they do not use âstreamingâ performance data as it comes in to understand or modify the organizationâs structure and processes in real time. Organizational models that could accept and use real-time data could provide a tool for making organizations more flexible and able to adapt to changing conditions and missions more quickly. An additional area in need of research is the ability to combine models at different levels of granularity and detail to represent large organiza- tions, as well as the advantages and drawbacks of including more or less detail. Including detail for all of the individuals in a large organization can quickly lead to intractable size and computational infeasibility, but system- level models may not be able to represent the detail that leads to emergent behavior. For example, system dynamics models could be developed at the level of the entire organization, with individual agents developed to repre- sent key individuals or groups in the organization. Data could flow in both directions between the detailed agent-based models and the organization- level system model. Challenges and existing approaches for developing such integrated multilevel models are discussed in Chapter 8. Finally, innovative experimentation approaches are needed to advance the state of the art in organizational modeling. Systematic controlled experi- ments are not feasible for organizations of any sizeâteam experiments
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