Stuff we’ll need for the Midterm James Burns Fall 2010

The Adjacency Matrix ||

Also known as the Square Ternary Matrix  Be able to convert it to a causal loop diagram  Be able to convert the CLD to a SDF  Be able to write the rate equations associated with the SFD  Assumes rates are multiplicative functions of their antecedents

The Pension Fund Problem  What sectors did you find?  What stocks?  What rates?

Be able to ….  Delineate what structures will product exponential growth and exponential goal-seeking  Explain why what is going on within any single firm contributes to the hockey stick phenomenon

Feedback  Name two types  Which type produces exponential growth?  Which type produces exponential goal seeking?  What is the discernment rule for distinguishing one type from another?

What about delays?  Cause ____ and ____ when ____ moves are applied Cause oscillation and overshoot when aggressive moves are applied

What is the behavioral problem with this structure?

Behaviorally, it is..

How can we fix this problem?

Here DAR = AS + LR

What is AR equal to???  Acquisition Rate  What else?

What is wrong with this picture?

Stock Management Structure ABOVE  YOU WON’T BE TESTED ON THIS!!

Seeing the World Anew  As wholes  Seeing ourselves as part of the whole, part of the system  Coping with Complexity mandates systems thinking  Today, we are creating complexity at a frenetic pace

When is dynamic complexity present?  When there are dramatically different effects in the short vs. the long run  When an action has one set of consequences locally and a very different set of consequences in another part of the system  When obvious interventions produce non-obvious consequences

The first Archetype: Limits to Growth  Senge often says structures of which we are unaware hold us ____.  All growth eventually ____.  Which archetype illustrates this??  Most managers react to the slowing growth by pushing harder on the _____ loop  Instead, concentrate on the balancing loop-- changing the _____ factor

Structure state of stock growing action slowing action Balancing Reinforcing

VENSIM  Know how to create CLD’s  Know how to create SFDs  Know how to use the tools  Know how to use the output icons—print/plot/etc  Know how to use the control panel

VENSIM  How do we determine what data files (sets) will appear plotted on our univariate plots?  How can we re-define a parameter (or a set of parameters) to a different value (different values) without using the equation editor to actually edit the values?

Dimensionless Ratios  What do we use them for??  What impact do they have on dimensional consistency of an equation?  Why do they make sense?

Dimensionless Ratios  How as a dimensionless ratio used in the natural gas model?

Construct equations for this model

What kind of behavior is this?

Dimensionality Considerations  Rigorously, all models must be ________ _______  What ever units you use for stocks, the associated rates must have those units divided by ______  Explain what the SYNTHESIM tool does in VENSIM

What if Dimensionless Ratios Don’t give us the effect we want?  Is there another way to pull in information?  Let’s look at the Forrester World Model

What we see here is the use of table functions— Dimensionless Multipliers  Birth Rate = Birth Rate Normal * Population * Births Material Multiplier * Births Pollution Multiplier * Births Food Multiplier * Births Crowding Multiplier The last four multipliers are dimensionless table functions

Establishing units for un- quantified variables  How did Forrester do this in his world model?

More ratios  Food ratio = Food/ Food normal  Again, Food normal is the amount of food available in the year 1970, in Food units  Crowding ratio = Population density normal/Population density  again, Population density normal is the population density in the year 1970, say

Explain this picture

What does it take to create a table lookup function in VENSIM?  Do table lookups ever have connectors (arrows) directed toward them?  What point do we generally expect to see on a table lookup function?  Why?  How is the table lookup used in the function it impacts?

More about table lookups  Table lookups use _____ ______ between data points, by default

Comment about Table Lookups  To find the ordinate value corresponding to a particular abscissa value that is given, let b = ordinate desired, a given abscissa. Then b = b i + (a – a i )*(b i+1 – b i ) / (a i+1 – a i ) Where a has been determined to lie between abscissas a i and a i+1

Delays  Where do they appear?  Name some delays aging populations, mail delays, perception delays, shipping delays, appearance delays, adjustment delays, scheduling delays and queue delays  Name two delay types

Why 3 rd -order exponential delays?  Why 1 st -order exponential delays?

Some Flow Delays that we’ve already looked at

Comment about delays The modeler must ask… How do physical processes in the actual system create lagged behavior? How much dis-aggregation is necessary to represent the delay accurately

Simulation Time Step  Should be between.5 and.25 of the shortest time constant (delay) in the model  Look at all of the time constants  Adjustment time  Perception time  Delivery delay time  Construction time  Lifetime  Find smallest  Set simulation time step appropriately

Integration Method  Euler for models with discrete events  RK4 for models with oscillation

Dynamic Test Inputs  Purpose  Reveal inherent behavior  Create extreme conditions  Examples  Pulse  Step  Ramp—one we didn’t look at  Exponential growth  Noise—randomness

Extreme Conditions  Purpose  Reveal weaknesses  Generate insight  Methods  Remove contents of stock with PULSE function  Cut off inflows or outflows  Artificially force variables to 0 or to infinity

Partial Model Testing  Purpose  Divide and Conquer  Develop understanding of subsystems  Test response of subsystems to driving data  Methods  Cut & paste structures into a new model  Use data variables or test inputs to drive behavior

Feedback Elimination  Purpose  Identify feedback loops that are causing behavior  Methods  Sever flow connections  Replace variables with constants or test inputs  Insert 0*… in equations  Flatten lookups

Parameter Sensitivity Analysis  Purpose  Link behavior to feedback loop structure  Identify leverage points  Search for equilibria  Methods  Vary parameters and initial conditions  Stretch and shift lookup table shapes

Types of Sensitivity  Insensitive  Pendulum always comes to rest at bottom  Numerical  Numerical values change, but behavior “looks” the same  Behavior mode  Shift from s-shaped growth to oscillation  Policy  Policy conclusions change

Policy Evaluation  Purpose  Develop effective policies  Identify conditions for effectiveness  Identify weakness in formulation of existing policies  Tools  Sensitivity Analysis  Optimization  Gaming

Integration – IGNORE!!  When we used the RK4 integration algorithm, we found what, exactly?  What did RK4 assume in terms of step size?  Does RK4 like small step sizes?  What is the problem with small step sizes?

Global Warming  How much warming is likely over the next century?  What changes in climate patterns, rainfall, growing season, storm incidence and severity, and sea level might ensue?  How much damage would these changes cause to humanity?

All the models show the climate system to possess enormous inertia  The implication here is that if we had shut off all GHG emissions in the year 2000, TEMPERATURES WOULD CONTINUE TO RISE FOR ANOTHER 25 YEARS and then fall very slowly  This was an extreme condition test, of the type we talked about yesterday

Would you describe the global warming system as….  STABLE  UNSTABLE

 Warming reduces the winter snow cover and shrinks the highly reflective polar ice caps, thus increasing heat absorption and leading to further melting, less snow cover and still greater absorption. This positive loop will cause much greater warming at the poles than in the tropics and more warming in the winter than summer

 This, in turn releases more methane and carbon dioxide into the atmosphere from decayed biomass in the frozen tundra, resulting in still another positive feedback loop ALL THE MODELS AGREE THAT STABILIZING THE GHG EMISSIONS WILL NOT STABILIZE TEMPERATURES OR THE CLIMATE ANYTIME SOON

Barry Richmond’s Terrorism Model  Name some characteristic archetypes

 In addition to the escalation archetype, what other archetype comes to mind when you consider Barry Richmond’s model of terrorism

Chapter 18

How many balancing loops are there in the policy structure for inventory management?

Overview Production Model

Three Balancing Loops  Stock out loop regulates shipments as inventory varies  Inventory and WIP Control Loops adjust production starts to move the levels of inventory and WIP toward their desired levels

In the Production Structure below, what is the equation for Production Rate?

An Order Fulfillment Structure

What is the Desired Shipment Rate here?

A production starts structure

What is the equation for Adjustment for WIP?

What is the equation for Desired WIP?

What is the equation for Desired Production?

What is the equation for Desired Production Start Rate?

What structure was used to create a Demand Forecast?

The Demand Forecast structure

Chapter 19

In the model which follows, what is the equation for LABOR?

In the model which follows, what is the equation for Quit Rate?

In the equation which follows, the purpose of using the MAX(, ) Function is??  Desired Vacancies = MAX (0, Expected tom to fill vacancies * Desired Hiring rate)  The purpose of using the MAX function is

What impact did the ‘flexible work week’ have on the oscillations caused by step function?  it helped to subdue the oscillations  it increased the oscillations initially and dampened it later  flexible work week had no impact on the oscillations  flexible work is a fictional, not possible in real world  flexible work week cut off the oscillations altogether

Referring to Chapter 19 of Business Dynamics by John Sterman, Business cycles are caused by….  Personal Income Tax rate in the economy  Interest rate fixed by the Fed  Workforce shortage  Technological advances  Inventory-Workforce interactions