Stuff we’ll need for the Midterm James Burns Fall 2010.
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Transcript of Stuff we’ll need for the Midterm James Burns Fall 2010.
Stuff we’ll need for the Midterm
James Burns
Fall 2010
The Adjacency Matrix
1 2 3 4
1 || 0 1 0 0 ||
2 || 0 0 1 0 ||
3 || 0 1 0 1 ||
4 || 0 0 0 0 ||
Also known as the Square Ternary MatrixBe able to convert it to a causal loop
diagramBe able to convert the CLD to a SDFBe able to write the rate equations
associated with the SFD Assumes rates are multiplicative functions
of their antecedents
The Pension Fund ProblemWhat sectors did you find?What stocks?What rates?
Employees RetireesNew Hires Retire rate Deaths
Fund
Deposits Withdrawals
Growth
SalaryGrow rate
Pension Fund Problem
Fund SectorSalary Sector
Employee/Retiree Sector
NH Rate Norm
Grow Rate Norm
Dep NormWithdraw Norm
Grwth Norm
Employment timeRetirement time
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
FeedbackName two typesWhich 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?
Stock SAcquisition Rate
AR
Adjustment forStock AS Desired Stock S*
Stock AdjustmentTime SAT
Loss Rate
Variables XU
Behaviorally, it is..Stock S
1,000
750
500
250
0
0 10 20 30 40 50 60 70 80 90 100Time (Month)
Stock S : stock3Stock S : stock2
How can we fix this problem?
Here DAR = AS + LR
Stock SAcquisition Rate
AR
Adjustment forStock AS Desired Stock S*
Stock AdjustmentTime SAT
Loss Rate
Variables XU
Desired AcquisitionRate DAR
What is AR equal to???Acquisition RateWhat else?
What is wrong with this picture?
20
16.66
13.33
10
2 22
22 2 2 2 2 2 2 2 2 2 2
1 1
11
11
1 1 1 1 1 1 1 1 1
0 1 2 3 4 5 6 7 8 9 10Time (Year)
Acquisition Rate AR : bdscm2 Units/Year1 1 1 1 1 1 1 1
Loss Rate LR : bdscm2 Units/Year2 2 2 2 2 2 2 2 2
Supply LineSL
Stock S
Order RateOR
AcquisitionRate AR
Loss RateLR
IndicatedOrders IO
Adjustmentfor SupplyLine ASL Desired
Supply LineSL*
Adjustmentfor Stock
AS
ExpectedLoss Rate
EL
AcquisitionLag AL
++
+
+
+
-
-
-
+
B B
Supply LineControl
Stock Control
StockAdjustmentTime SAT
Supply LineAdjustmentTime SLAT
-
-
ExpectedAcquisition
Lag EAL
+
+
DesiredAcquisitionRate DAR +
+
DesiredStock S*
<InitialDesiredStock>
<Input>+
+
+
ExogenousVariables U
EndogenousVariables X
Stock Management Structure ABOVEYOU WON’T BE TESTED ON THIS!!
Seeing the World AnewAs wholesSeeing 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 runWhen 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 stockgrowing action slowing action
BalancingReinforcing
VENSIMKnow how to create CLD’sKnow how to create SFDsKnow how to use the toolsKnow how to use the output icons
—print/plot/etcKnow how to use the control
panel
VENSIMHow 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 RatiosWhat do we use them for??What impact do they have on
dimensional consistency of an equation?
Why do they make sense?
Dimensionless RatiosHow as a dimensionless ratio used in
the natural gas model?
Construct equations for this model
RabbitsNet Rabbit Birth rate
Effect of resourcesCarrying capacity
Normal Rabbit Growth Rate
B
R
What kind of behavior is this?
Rabbits
1,00040
00
0 20 40 60 80 100Time (Month)
Rabbits : rab1Net Rabbit Birth rate : rab1
Dimensionality ConsiderationsRigorously, 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
Population
birth rate normal
births crowdingmultiplier
births food multiplier
births deathsbirths material multiplier
births pollution multiplier
<Time>
death rate normal
deathscrowdingmultiplier deaths food multiplier
deaths material multiplier
deaths pollution multiplier
crowding
land areapopulation
density normalbirths
crowdingmult tab
deathscrowdingmult tab
food ratio
food coefficientfood coefficient 1
food crowding multiplier
food percapita normal
food per capita potential
food pollutionmultiplier
switch time 7<Time>
foodpollutionmult tab
<pollution ratio>
<capital ratio agriculture>
food per capitapotential tab
<foodcrowdingmult tab>
<Time>
capital agriculture fraction indicated
births foodmult tab
deaths foodmult tab
capital agriculturefraction indicated tab
<material standard ofliving>
deathsmaterialmult tab
birthspollutionmult tab
births materialmult tab
<materialstandard of
living>
deaths pollutionmult tab
<pollution ratio>
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 ratiosFood 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 pictureQuality of Life
Quality of Life Normal
Pollution Ratio
Food Ratio
MSL Ratio
Crowding ratio
Pollution Multiplier
Food Multiplier
MSL Multiplier
Crowding Multiplier
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 lookupsTable lookups use _____ ______
between data points, by default
Comment about Table LookupsTo find the ordinate value
corresponding to a particular abscissa value that is given, let b = ordinate desired, a given abscissa. Then
b = bi + (a – ai)*(bi+1 – bi) / (ai+1 – ai)
Where a has been determined to lie between abscissas ai and ai+1
DelaysWhere 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 3rd-order exponential delays?Why 1st-order exponential delays?
Some Flow Delays that we’ve already looked at
Pop 0-15
Pop 16-45
Pop 46-60
Pop 61-75
Unprovenreserves
Provenreserves
Crude oil
Refined oilproducts
birth rate
r 15to16
r46to46
r60to61
death rate
discovery rate
extraction rate
refinery rate
consumptioin rate
Cascaded Coflow -- "Hines"
Hines 1996characteristicof new stuff
Avgcharacteristicnew material
Change incharacteristic
of new material
dilution time ofnew Material
New materialMaterialmaturing
Time tomature
Materialflowing in
Maturematerial
Old material
Materialaging
Materialflowing out
Time to age Time to flowout
Avgcharacteristic ofMature material
Change incharacteristic ofmature material
Maturematerial
dilution time
Avg Characteristicof Old Material
Change incharacteristicof old material
Old MaterialDilution Time
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 MethodEuler for models with discrete eventsRK4 for models with oscillation
Dynamic Test InputsPurpose
Reveal inherent behavior Create extreme conditions
Examples Pulse Step Ramp—one we didn’t look at Exponential growth Noise—randomness
Extreme ConditionsPurpose
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 TestingPurpose
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 EliminationPurpose
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 AnalysisPurpose
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 bottomNumerical
Numerical values change, but behavior “looks” the same
Behavior mode Shift from s-shaped growth to oscillation
Policy Policy conclusions change
Policy EvaluationPurpose
Develop effective policies Identify conditions for effectiveness Identify weakness in formulation of existing
policiesTools
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 WarmingHow 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….
STABLEUNSTABLE
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 ModelName 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
Work in ProcessInventory
InventoryProduction Rate
Shipment RateProduction StartRate
Customer OrderRate
Order Fulfillment
demandForecasting
ProductionScheduling
B
WIP Control
B
Inventory Control
B
Stockout
Three Balancing LoopsStock 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?
InventoryWork in Process
InventoryProduction StartRate
Production Rate
ManufacturingCycle Time
Production
An Order Fulfillment Structure
InventoryShipment Rate
InventoryCoverage
Customer OrderRate
Desired ShipmentRate
Order FulfillmentRatio
MaximumShipment Rate
Table for OrderFulfillment
Desired InventoryCoverage
Safety StockCoverage
Minimum OrderProcessinig Time
InventoryAdjustment Time
What is the Desired Shipment Rate here?
InventoryShipment Rate
InventoryCoverage
Customer OrderRate
Desired ShipmentRate
Order FulfillmentRatio
MaximumShipment Rate
Table for OrderFulfillment
Desired InventoryCoverage
Safety StockCoverage
Minimum OrderProcessinig Time
InventoryAdjustment Time
A production starts structure
Work in Process InventoryProduction RateProduction Start
Rate
Adjustment forWIP
Desired ProductionStart Rate
ManufacturingCycle Time
Desired WIPWIP Adjustment
Time
DesiredProduction
ExpectedOrder Rate
Desired Inventory
Adjustment forInventory
InventoryAdjustment Time
What is the equation for Adjustment for WIP?
Work in Process InventoryProduction RateProduction Start
Rate
Adjustment forWIP
Desired ProductionStart Rate
ManufacturingCycle Time
Desired WIPWIP Adjustment
Time
DesiredProduction
ExpectedOrder Rate
Desired Inventory
Adjustment forInventory
InventoryAdjustment Time
What is the equation for Desired WIP?
Work in Process InventoryProduction RateProduction Start
Rate
Adjustment forWIP
Desired ProductionStart Rate
ManufacturingCycle Time
Desired WIPWIP Adjustment
Time
DesiredProduction
ExpectedOrder Rate
Desired Inventory
Adjustment forInventory
InventoryAdjustment Time
What is the equation for Desired Production?
Work in Process InventoryProduction RateProduction Start
Rate
Adjustment forWIP
Desired ProductionStart Rate
ManufacturingCycle Time
Desired WIPWIP Adjustment
Time
DesiredProduction
ExpectedOrder Rate
Desired Inventory
Adjustment forInventory
InventoryAdjustment Time
What is the equation for Desired Production Start Rate?
Work in Process InventoryProduction RateProduction Start
Rate
Adjustment forWIP
Desired ProductionStart Rate
ManufacturingCycle Time
Desired WIPWIP Adjustment
Time
DesiredProduction
ExpectedOrder Rate
Desired Inventory
Adjustment forInventory
InventoryAdjustment Time
What structure was used to create a Demand Forecast?
The Demand Forecast structure
ExpectedOrder Rate
Change inExp Orders
Time to AverageOrder Rate
CustomerOrder Rate
+
+-
- +
+
Chapter 19
In the model which follows, what is the equation for LABOR?
LaborQuit RateHiring Rate
Avg Duration ofEmployment
In the model which follows, what is the equation for Quit Rate?
LaborQuit RateHiring Rate
Avg Duration ofEmployment
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