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					The Cross Study of Nonlinear
     Modeling Methods

     Hans J. (Jochen) Scholl
   University at Albany / SUNY
              What has this topic to do with
                 Information Science?
   Why has it NOT to do with Information Science?
   The understanding of Information Science rests on the understanding
    and definition of “information”
      – Shannon’s engineering perspective (physical transmission)
      – Context / meaning of “information”
      – Buckland (“process” - “thing” - “knowledge”)
      – Quigley and Debons (just text answering to “NEOT” versus “WY”)
      – Buckland (“observation of phenomena that have the capacity to be
        informative”)
      – Norton (“fundamental link among all what we are, know, and do not
        know”)




MIT Field Trip, 4/20//2001             Hans J. (Jochen) Scholl              Slide 2
              What has this topic to do with
               Information Science? (more)
   Lipetz ( “facilitation of utilization of records”)
   Georgia Institute of Technology (1961)
      – “The science that investigates the properties and behaviors of information, the forces
        governing the flow of information, and the means of processing information for
        optimum accessibility and usability. The processes include the origination,
        interpretation, and use of information. The field is derive from or related to
        mathematics, logic, linguistics, psychology, computer technology, operations
        research, the graphic arts, communications, library science, and some other fields”
        (Shera & Cleveland)
   Paisley (“IS is not retrievology”)
   Borko’s list of nine application fields (…(6) system design, (7) analysis and
    evaluation, (8) pattern recognition, (9) adaptive (and self-organizing) systems)
   Otten and Debons (“Metascience - framework for all information-oriented
    sciences”)
   Skovira (“Pluralism in understanding of IS”)

MIT Field Trip, 4/20//2001                    Hans J. (Jochen) Scholl                  Slide 3
The Information Science Continuum


   Parent Disciplines                                  Metascience
   Mathematics
   Computer Science
   Linguistics
   OR
   Public Administration
   Psychology                  An Information Scientist is trained in
   Business Administration     and has a natural interest in cross
   ….                          studies and multi-method approaches
   Library Science


MIT Field Trip, 4/20//2001   Hans J. (Jochen) Scholl              Slide 4
       Research Methods and Tools
   It is all about models
   Traditional Research
      – Mathematical or linguistic models : rigorous versus flexible
      – Quantitative / qualitative
      – Underlying principle: "(1) the cause precedes the effect in time, (2) there is an empirical
          correlation between them, and (3) the relationship is not found to be the result of some third variable” (Babbie,
          1999)

      – Best applied to relatively simple, linear systems and when coping
        with relatively narrow / limited data spaces
   Computer-based experiments
      – Vast data spaces
      – Flexible AND
      – Rigorous

MIT Field Trip, 4/20//2001                                  Hans J. (Jochen) Scholl                                 Slide 5
    The Notion of Comparative Research
     Problem pi with i=1,…n and piP
     Methodology mj with j=1,…m and mjM
     Result rk with k=1,…r and rk R

     What rR found through mM when applied to explain a
     certain pP
     • correspond / are similar / are equal?
     • differ / contradict?
     • neither correspond nor contradict / complement ?

     What rR can be expected when combining certain mM to
     explain / triangulate a certain pP?
MIT Field Trip, 4/20//2001    Hans J. (Jochen) Scholl   Slide 6
    The More Specific Research Question
   What dynamic problems have been explained by means of which
    methodology?
   What where the findings in cases when more than one methodology
    was applied to a dynamic problem?
   What are the insights from comparing the findings?
   What are strengths and limitations of the methodologies used when
    applied to explain the dynamic problem at hand?
   What are potential benefits of multi-method research designs?
   Case in point: The Beer Distribution Game




MIT Field Trip, 4/20//2001          Hans J. (Jochen) Scholl        Slide 7
                             Usage of Terms
   Linearity
      – A relationship is linear if the effect on a dependent variable of a change of
        one unit in an independent variable is the same for all possible such changes
   Nonlinearity (ergo)
      – A relationship is nonlinear if the effect on a dependent variable of a change
        of one unit in an independent variable is NOT the same for all possible such
        changes
   Nonlinearity
      – If f is a nonlinear function or an operator, and x is a system input (either a function or
        variable), then the effect of adding two inputs, x1 and x2, first and then operating on
        their sum is, in general, not equivalent to operating on two inputs separately and then
        adding the outputs together; i.e. . Popular form: the whole is not necessarily equal to
        the sum of its parts. Dissipative nonlinear dynamic systems are capable of exhibiting
        self-organization and chaos. (Nonlinear Dynamics and Complex Systems Theory,
        Glossary of Terms - http://www.cna.org/isaac/Glossb.htm#Nonlinearity - access date
        04/09/2001)


MIT Field Trip, 4/20//2001                     Hans J. (Jochen) Scholl                    Slide 8
                     Usage of Terms (more)
   Nonlinearity
      – “a system is nonlinear if it contains a multiplication or division of variables or if it
        has a coefficient which is a function of a variable (Forrester, 1968)
   “Degree of (a system’s) nonlinearity
      – implies the number of policies in the system that are nonlinear (ibid.)
   Complexity in systems
      – multiple interconnected positive and negative feedback loops containing
        nonlinearity (ibid.)
   Complex systems
      – have seven characteristics: (1) counterintuitive, (2) insensitive to many parameter
        changes, (3) resistant to policy changes, (4) pressure or leverage points, (5)
        compensate for externally applied pressure, (6) short-term behavior may differ
        from long-term behavior (7) tendency to low performance (social systems)
        (Forrester, Urban Dynamics, 1969)


MIT Field Trip, 4/20//2001                      Hans J. (Jochen) Scholl                    Slide 9
                     Usage of Terms (more)
   Emergence
      – “… a product of coupled, context-dependent interactions (which) , and the
        resulting system, are nonlinear “ (Holland, Emergence, 1999)
   Nonlinearity
      – “The behavior of the overall system cannot be obtained by summing the
        behaviors of its constituent parts” (ibid.)
   Complexity
      – (generated) emergent system behavior based on simple laws




MIT Field Trip, 4/20//2001              Hans J. (Jochen) Scholl            Slide 10
                     Usage of Terms (more)
   Stanislaw Ulam reportedly said (something like) "Calling a science 'nonlinear' is
    like calling zoology 'the study of non-human animals’ (J.D. Meiss, sci.nonlinear FAQ )
   Nonlinearity
      – In geometry, linearity refers to Euclidean objects: lines, planes, (flat) three-
        dimensional space, etc.--these objects appear the same no matter how we examine
        them. A nonlinear object, a sphere for example, looks different on different scales--
        when looked at closely enough it looks like a plane, and from a far enough distance
        it looks like a point.
      – In algebra, we define linearity in terms of functions that have the property f(x+y) =
        f(x)+f(y) and f(ax) = af(x). Nonlinear is defined as the negation of linear. This
        means that the result f may be out of proportion to the input x or y. The result may
        be more than linear, as when a diode begins to pass current; or less than linear, as
        when finite resources limit Malthusian population growth. Thus the fundamental
        simplifying tools of linear analysis are no longer available (ibid)




MIT Field Trip, 4/20//2001                    Hans J. (Jochen) Scholl                 Slide 11
                     Usage of Terms (more)
   Complex Systems
      – are spatially and/or temporally extended nonlinear systems characterized
        by collective properties associated with the system as a whole--and that
        are different from the characteristic behaviors of the constituent parts.
      – While, chaos is the study of how simple systems can generate complicated
        behavior, complexity is the study of how complicated systems can
        generate simple behavior. An example of complexity is the
        synchronization of biological systems ranging from fireflies to neurons.
      – In these problems, many individual systems conspire to produce a single
        collective rhythm. (ibid.)




MIT Field Trip, 4/20//2001              Hans J. (Jochen) Scholl            Slide 12
      Agent-based Modeling (ABM)
                                                  Individual or agent as
                                                   unit of analysis
                                                  Behavior governed by
                                                   (few) rules
                                                  Global consequences of
 Boids’ Three Rules (Craig Reynolds)               individual interaction
 1.    Maintain a minimum distance from
       other objects in the environment,
                                                  Complex, nonlinear
 2.
       including other boids.
       Match velocities with boids in its
                                                   behavior
       neighborhood.
 3.    Move toward the perceived center of        Emergence
       mass of boids in its neighborhood.




MIT Field Trip, 4/20//2001                       Hans J. (Jochen) Scholl   Slide 13
             System Dynamics Modeling
                      (SDM)
                               X
             dX dt

               initial x                                                  Causal relationships between
               S
                                    dZ dt
                                                    Z
                                                                           system elements
                           B
                                                                          Stocks and flows
                                                 RminusZ
                                     R
                                                                          Feedback loop as unit of
                           Y                                               analysis
                                         dY dt

                                                                          Positive (that is, reinforcing
   Deterministic chaos: Lorenz’s weather equations
                                                                           feedback) and
                               Graph for Y                                Negative (that is,
    40
                                                                           counterbalancing or goal-
                                                                           seeking feedback)
     0
                                                                          Differential equations
   -40
                                                                          Pattern of complex / nonlinear
         0           10            20         30           40   50         behavior rooted in system
                                    Time (time)

     Y : base28001
                                                                           structure - endogenous behavior
     Y : base27999
     Y : base28

MIT Field Trip, 4/20//2001                                           Hans J. (Jochen) Scholl         Slide 14
Characteristics & Fields of Study
   Overlapping fields of study
      – Economics, ecology, biology, anthropology, psychology, sociology, economics,
        traffic simulations, military, model testing
      – Tragedy of the commons,deer management, predator/prey, beer game
   ABM
      –   Inductive / generative
      –   Individual / rule based
      –   Emergent system behavior
      –   More than one unique set of agents/rules could lead to similar emergent behavior
      –   Path from emergent behavior down to agent/rule level can be difficult
   SDM
      –   Deductive / analytical
      –   Aggregate
      –   Leverage / intervention points
      –   Causal relationships debatable - expert consensus



MIT Field Trip, 4/20//2001                    Hans J. (Jochen) Scholl                Slide 15
        Similarities and Differences
   According to Phelan, almost identical meaning and usage of terms
    such as system, emergence, dynamic, nonlinear, adaptive and
    hierarchy.
   Both theories also share a belief that there are universal principles
    underlying the behavior of all systems.
   “Confirmatory analysis” and “problem solving perspective”,
    “generating shared understanding and consensus one requires to
    improve the system” (SDM) as opposed to mainly exploratory research
    (ABM).
   Individual versus aggregate




MIT Field Trip, 4/20//2001          Hans J. (Jochen) Scholl        Slide 16
             Epistemological Aspects
   ABM modelers typically take positivist to extreme positivist positions
   SDM modelers range from positivist to constructivist positions
   However, as seen earlier, positivist positions suffered from a serious
    attack from within (deterministic chaos)




MIT Field Trip, 4/20//2001           Hans J. (Jochen) Scholl         Slide 17
                A Remarkable Beginning
   John H. Miller’s ANTs (Active, nonlinear tests)
      – A simulation model is subjected to automated testing by use of hill-
        climbing and genetic algorithms (mutation and crossover). Vast test
        spaces result
      – Sensitivity of a model’s variables to parameter changes in very wide test
        spaces (zillions of solutions) is uncovered which leads to a better
        assessment of model validity
      – World3 as case in point




MIT Field Trip, 4/20//2001               Hans J. (Jochen) Scholl             Slide 18
                       The Bullwhip Effect
   SD treatment
      – Forrester, Industrial Dynamics (1958)
            • Multi-echelon supply chain are “by virtue of policies, organization, and
              delays…naturally oscillatory”
            • Remedies
                  – Faster order handling
                  – Better information along the chain regarding consumer demand
                  – Modest and gradual inventory adjustments
      – Sterman, Misperceptions of Feedback (1989a & b)
            • Beer distribution game experiment
            • Simulation of an economy
      – Peter Senge, The Fifth Discipline (1990)
            • No strategy - pass on order rule




MIT Field Trip, 4/20//2001                       Hans J. (Jochen) Scholl                 Slide 19
                The Bullwhip Effect (more)
   Economics / Traditional Management Science Treatment
      – Lee et al, (1997)
            • Distorted information as cause and “rational decision-making”
                 – Demand signaling
                 – Order batching
                 – Price fluctuations
                 – Rationing and shortage gaming
            • Recommended remedies: (1) information sharing, (2) channel alignment, (3)
              improved operational efficiency
            • Strategic interaction among rational supply chain members




MIT Field Trip, 4/20//2001                  Hans J. (Jochen) Scholl               Slide 20
                The Bullwhip Effect (more)
   Agent-based Modeling Treatment
      – Kimbrough et al, (2001)
            • ABM implementation of the MIT (stationary input) and the Columbia (stochastic inputs)
              beer games
            • Algorithm
                  Initialization. A certain number of rules are randomly generated to form generation 0.
                  2) Pick the first rule from the current generation.
                  3) Agents play the beer game according to their current rules.
                  4) Repeat step 3, until the game period (say 35 weeks) is finished.
                  5) Calculate the total average cost for the whole team and assign fitness value to the current rule.
                  6) Pick the next rule from the current generation and repeat step 2, 3, and 4 until the performance of all the rules in the current
                        generation have been evaluated.
                  7) Use genetic algorithms to generate a new generation of rules and repeat steps 2 to 6 until the maximum number of generations is
                        reached

            • Experiments
                  –   Mimicking the MIT game -> pass-order rule found - Nash equilibrium
                  –   Stochastic demand input -> agents find better rules than pass-order - no bullwhip effect
                  –   Stochastic demand and stochastic lead time -> agents stiff find better rules and again - no
                      bullwhip effect




MIT Field Trip, 4/20//2001                                           Hans J. (Jochen) Scholl                                                 Slide 21
                The Bullwhip Effect (more)
   Areas of Agreement and Departure
      – Traditional research claims the rationality of (local) decision-making
            • March & Simon (1958) discussed the demands of such a proposition: (1) all alternatives
              of choice are given; (2) all consequences are known under certainty, risk, and uncertainty;
              (3) rational man has complete utility-ordering
            • Lee’s et al definition of rationality is not specified
            • Evidence for the lack of local rationality mounting (Sterman, Moxnes)
      – No disagreement on other areas (demand inflation, amplification, etc.)
      – ABM literature is silent about the causes of the bullwhip effect
      – All three strands agree on the remedies (except changing the mental models as
        proposed by SD)
      – ABM demonstrates the existence of better than pass-order solutions
      – ABM also confirms the “perceptional source” of the bullwhip effect




MIT Field Trip, 4/20//2001                         Hans J. (Jochen) Scholl                       Slide 22
                             Conclusion
   Certain similarities despite differences in basic concepts and
    understandings
   Dynamic modeling techniques may have a capacity to complement
    each other (as in the case of the beer game)
   Study of findings and research designs
   Understanding strengths and limitations of each modeling technique
   Potential for triangulation
   “Basic problem” cross study will continue
      – Predator/prey
      – Deer management
      – Tragedy of the commons
   Integrated research designs


MIT Field Trip, 4/20//2001          Hans J. (Jochen) Scholl        Slide 23
The Hawaiian International Conference on
       System Sciences (HICSS)
   According to MIS Quarterly (1997) the second most important conference in
    its field (after ICIS, and before IFIP, DSS, …, Cad.of Mgmt etc.)
   This year over 650 attendees (40 percent of whom came from overseas)
   85 percent of attendees present papers
   Nine main tracks, dozens of minitracks
   The 35th conference will be held next January, 7-10




MIT Field Trip, 4/20//2001             Hans J. (Jochen) Scholl           Slide 24
                              HI CS S
   Very productive
      – Over fifty percent of presented papers become journal articles of
        monographs
   Tracks of Special Interest
      – Complex Systems
      – Decision Technologies for Management




MIT Field Trip, 4/20//2001            Hans J. (Jochen) Scholl         Slide 25
    Decision Technologies for Management
                   Track
    Minitrack “Modeling Nonlinear Human and Natural Systems” (formerly
     Agent-based Modeling and System Dynamics) - the minitrack invites papers
      –   From an SD perspective
      –   From an Agent-based modeling perspective
      –   From other nonlinear modeling disciplines
      –   Highly welcome are papers which incorporate various modeling techniques




MIT Field Trip, 4/20//2001              Hans J. (Jochen) Scholl           Slide 26

				
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