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


A production starts structure

Work in Process InventoryProduction RateProduction Start

Rate

Adjustment forWIP

Desired ProductionStart Rate


Desired WIPWIP Adjustment

Time

DesiredProduction

ExpectedOrder Rate

Desired Inventory

Adjustment forInventory


What is the equation for Adjustment for WIP?


Rate

Adjustment forWIP




Time

DesiredProduction

ExpectedOrder Rate

Desired Inventory



What is the equation for Desired WIP?


Rate

Adjustment forWIP




Time

DesiredProduction

ExpectedOrder Rate

Desired Inventory



What is the equation for Desired Production?


Rate

Adjustment forWIP




Time

DesiredProduction

ExpectedOrder Rate

Desired Inventory



What is the equation for Desired Production Start Rate?


Rate

Adjustment forWIP




Time

DesiredProduction

ExpectedOrder Rate

Desired Inventory



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

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