chapter 13, sterman: modeling decision making powerpoints by: james burns

Chapter 13, Sterman: Chapter 13, Sterman: Modeling Decision MakingModeling Decision Making

Powerpoints by: James BurnsPowerpoints by: James Burns

Modeling Decision MakingModeling Decision Making

This chapter explores the formulation This chapter explores the formulation of the decision rules representing the of the decision rules representing the behavior of the agents.behavior of the agents.

PrinciplesPrinciples

All model structures consist of two All model structures consist of two parts:parts:– Assumptions about the physical and Assumptions about the physical and

institutional environmentinstitutional environment– Assumptions about the decision Assumptions about the decision

processes of the agentsprocesses of the agents

Supply LineSL

Stock SOrder Rate OR Acquisition Rate AR Loss Rate LR

IndicatedOrders IO

Adjustmentfor SupplyLine ASL Desired

Supply LineSL*

Adjustmentfor Stock

AS

ExpectedLoss Rate

EL

Acquisition Lag AL

+

+

+

+

+

-

-

-

+

B B

Supply LineControl

Stock Control

StockAdjustmentTime SAT

Supply LineAdjustmentTime SLAT

-

-

ExpectedAcquisition

Lag EAL

+

+

DesiredAcquisitionRate DAR +

+

Average Lifetime L

-

DesiredStock S*

<InitialDesiredStock>

<Input>+

+

+

The physical/institutional The physical/institutional structure…structure…

Includes the model boundary and Includes the model boundary and stock and flow structures of people, stock and flow structures of people, material, money, information, and so material, money, information, and so forth that characterize the systemforth that characterize the systemForrester’s Urban Dynamics sought Forrester’s Urban Dynamics sought to understand why America’s large to understand why America’s large cities continued to decay despite cities continued to decay despite massive amounts of aid and massive amounts of aid and numerous renewal programsnumerous renewal programs

The decision processes of the The decision processes of the agents…agents…

Refer to the decision rules that Refer to the decision rules that determine the behavior of the actors determine the behavior of the actors in the systemin the system

In Urban Dynamics, these included In Urban Dynamics, these included decision rules governing migration decision rules governing migration and constructionand construction

Actually portraying the physical and Actually portraying the physical and ……

Institutional structure of a system is Institutional structure of a system is relatively straightforward.relatively straightforward.

Representing the decision rules of Representing the decision rules of actors is …actors is …

Subtle and challengingSubtle and challenging

To be useful simulation models must To be useful simulation models must mimic the behavior of the real mimic the behavior of the real decision makers so that they respond decision makers so that they respond appropriately, not only for conditions appropriately, not only for conditions observed in the past but also for observed in the past but also for circumstances never yet circumstances never yet encounteredencountered

Decisions and Decision RulesDecisions and Decision RulesModelers must make a sharp Modelers must make a sharp distinction between decisions and distinction between decisions and decision rulesdecision rulesDecision rules are the policies and Decision rules are the policies and protocols specifying how the decision protocols specifying how the decision maker processes available maker processes available informationinformationDecisions are the outcome of this Decisions are the outcome of this processprocess

More Decisions and Decision RulesMore Decisions and Decision Rules

It is not sufficient to model a particular It is not sufficient to model a particular decision.decision.

Modelers must detect and represent the Modelers must detect and represent the guiding policy that yields the stream of guiding policy that yields the stream of decisionsdecisions

Every rate in the stock and flow structure Every rate in the stock and flow structure constitutes a decision point, andconstitutes a decision point, and– The modeler must specify precisely the The modeler must specify precisely the

decision rule determining the ratedecision rule determining the rate

Every Decision Rule…Every Decision Rule…

Can be thought of as an information Can be thought of as an information processing procedureprocessing procedure

The inputs to the decision process The inputs to the decision process are various types of information or are various types of information or cuescues– The cues are then interpreted by the The cues are then interpreted by the

decision maker to yield the decisiondecision maker to yield the decision– Decision rules may not use all available Decision rules may not use all available

informationinformation

Cues in the Department Store CaseCues in the Department Store CaseCues used to revise prices in the Cues used to revise prices in the department store case include wholesale department store case include wholesale costs, inventory turnover, and competitor costs, inventory turnover, and competitor pricespricesDepartment store pricing decisions do not Department store pricing decisions do not depend on interest rates, required rates of depend on interest rates, required rates of return, store overhead, trade-offs of return, store overhead, trade-offs of holding costs against the risk of stock-holding costs against the risk of stock-outs, estimates of the elasticity of outs, estimates of the elasticity of demand, or any sophisticated strategic demand, or any sophisticated strategic reasoning.reasoning.

This gets back to a strategic This gets back to a strategic modeling question…modeling question…

Is our model a descriptive model or is Is our model a descriptive model or is it a prescriptive one?it a prescriptive one?

Recall:Recall:– Descriptive models…tell it like it actually Descriptive models…tell it like it actually

isis– Prescriptive models…tell is like it should Prescriptive models…tell is like it should

bebe

What determines what information What determines what information gets used?gets used?

Mental models of the decision Mental models of the decision makersmakers

Organizational, political, personal, Organizational, political, personal, and other factors, influence the and other factors, influence the selection of cues from the set of selection of cues from the set of available informationavailable information

The cues (information) used is not The cues (information) used is not necessarily processed optimallynecessarily processed optimally

According to Nobel Laureate Gary According to Nobel Laureate Gary Becker…Becker…

All human behavior can be viewed as All human behavior can be viewed as involving participants who maximize involving participants who maximize their utility from a stable set of their utility from a stable set of preferences and accumulate an preferences and accumulate an optimal amount of informationoptimal amount of information

In Becker’s view…In Becker’s view…

Not only do people make optimal Not only do people make optimal decisions given the information they decisions given the information they have, but they also invest exactly the have, but they also invest exactly the optimal time and effort in the optimal time and effort in the decision process, ceasing their decision process, ceasing their deliberations when the expected gain deliberations when the expected gain to further effort equals the costto further effort equals the cost

Five Formulation FundamentalsFive Formulation Fundamentals

The Baker Criterion: The inputs to all The Baker Criterion: The inputs to all decision rules in models must be decision rules in models must be restricted to information actually restricted to information actually available to the real decision makersavailable to the real decision makers

Senator Howard Baker: What did he Senator Howard Baker: What did he (Nixon) know and when did he know (Nixon) know and when did he know it??it??

In modeling decision rules…In modeling decision rules…

Must ask, “What did they know and Must ask, “What did they know and when did they know it?”when did they know it?”

To properly mimic the behavior of a To properly mimic the behavior of a real system, a model can use as an real system, a model can use as an input to a decision only those input to a decision only those sources of information actually sources of information actually available to and used by the decision available to and used by the decision makers in the real systemmakers in the real system

The principle that decisions in The principle that decisions in models must be based on available models must be based on available

information has three corollariesinformation has three corollaries

First, no one knows with certainty First, no one knows with certainty what the future will bringwhat the future will bringSecond, perceived and actual Second, perceived and actual conditions often differconditions often differThird, modelers cannot assume Third, modelers cannot assume decision makers know with certainty decision makers know with certainty the outcomes of contingencies they the outcomes of contingencies they have never experiencedhave never experienced

The decision rules of a model The decision rules of a model should conform to managerial should conform to managerial

practicepractice

All variables and relationships should have All variables and relationships should have real world counterparts and meaningreal world counterparts and meaning

The units of measure in all equations must The units of measure in all equations must balance without the use of arbitrary balance without the use of arbitrary scaling factorsscaling factors

Decision making should not be assumed to Decision making should not be assumed to conform to any prior theory but should be conform to any prior theory but should be investigated firsthandinvestigated firsthand

Homework: Homework:

Examine and respond to the Examine and respond to the Challenge questions on pages 520 to Challenge questions on pages 520 to 522522

A Library of Common FormulationsA Library of Common Formulations

Of rate equationsOf rate equations

Are presented nextAre presented next

Are the building blocks from which Are the building blocks from which more realistic and complex more realistic and complex structures can be derivedstructures can be derived

Formulating Rate EquationsFormulating Rate Equations

Fractional Increase RateFractional Increase Rate

Fractional Decrease RateFractional Decrease Rate

Adjustment to a goalAdjustment to a goal


RRII = g * S = g * S

Here, RHere, RI I is an input rate, g is some is an input rate, g is some fraction (<1) and S is the stock that fraction (<1) and S is the stock that accumulates Raccumulates RI I

ExamplesExamplesBirth rate = birth rate normal * PopulationBirth rate = birth rate normal * Population

Interest Due = Interest Rate * Debt Interest Due = Interest Rate * Debt OutstandingOutstanding


These examples all generate first-These examples all generate first-order, ________ loops.order, ________ loops.

By themselves, these rates create By themselves, these rates create exponential growthexponential growth

It’s never a good practice for these It’s never a good practice for these rates to be anything other than non-rates to be anything other than non-negativenegative


RROO = g * S = g * S

Here, RHere, RO O is an output rate, g is some is an output rate, g is some fraction (<1) and S is the stock that fraction (<1) and S is the stock that is depleted by Ris depleted by RO O

ExamplesExamplesDeath rate = death rate normal * PopulationDeath rate = death rate normal * Population

Death rate = Population / Average LifetimeDeath rate = Population / Average Lifetime


Left to themselves these rates Left to themselves these rates generate exponential decaygenerate exponential decay

Left to themselves, these rates Left to themselves, these rates create first-order, negative feedback create first-order, negative feedback loopsloops

Adjustment to a goalAdjustment to a goal

RRII = Discrepancy / AT = (S* - S) / AT = Discrepancy / AT = (S* - S) / AT

ExamplesExamples– Change in Price = (Competitors price – Change in Price = (Competitors price –

Price) / Price Adjustment timePrice) / Price Adjustment time– Net Hiring Rate = (Desired Labor – Net Hiring Rate = (Desired Labor –

Labor) / Hiring DelayLabor) / Hiring Delay– Bldg heat loss = (outside temp – inside Bldg heat loss = (outside temp – inside

temp) / temp adjustment timetemp) / temp adjustment time

Adjustment to a GoalAdjustment to a GoalGenerates exponential goal-seeking Generates exponential goal-seeking behaviorbehaviorIs also considered a first-order, negative Is also considered a first-order, negative feedback loopfeedback loopOften the actual state of the system is not Often the actual state of the system is not known to decision makers who rely instead known to decision makers who rely instead on perceptions or beliefs about the state on perceptions or beliefs about the state of the systemof the system– In these cases, the gap is the difference In these cases, the gap is the difference

between the desired and the perceived state of between the desired and the perceived state of the systemthe system

More Formulating Rate EquationsMore Formulating Rate Equations

The Stock Management Structure: The Stock Management Structure: Rate=Normal Rate + adjustmentsRate=Normal Rate + adjustments

Flow = Resource * ProductivityFlow = Resource * Productivity

Y = Y * Effect of X1 on Y * Effect of Y = Y * Effect of X1 on Y * Effect of X2 on Y* … * Effect of Xn on YX2 on Y* … * Effect of Xn on Y

Stock Management StructureStock Management StructureRate = Normal Rate + AdjustmentsRate = Normal Rate + Adjustments

If the input rate is RIf the input rate is RII = (S* - S) / AT, and = (S* - S) / AT, and the output rate is Rthe output rate is ROO , then the steady , then the steady state equilibrium will be S = S* - Rstate equilibrium will be S = S* - RO O * AT* ATTo prevent this the stock management To prevent this the stock management structure adds the expected outflow to the structure adds the expected outflow to the stock adjustment to prevent the steady stock adjustment to prevent the steady state error:state error:Inflow = Expected outflow + Adjustment Inflow = Expected outflow + Adjustment for Stock for Stock

Flow = Resource * ProductivityFlow = Resource * Productivity

The flows affecting a stock frequently The flows affecting a stock frequently depend on resources other than the depend on resources other than the stock itselfstock itself

The rate is determined by a resource The rate is determined by a resource and the productivity of that resourceand the productivity of that resource

Rate = Resource * Productivity, orRate = Resource * Productivity, or

Rate = Resource/Resources Required Rate = Resource/Resources Required per Unit Producedper Unit Produced

ExamplesExamples

Production = Labor Force * Average Production = Labor Force * Average ProductivityProductivity

Y = Y * Effect of X1 on Y * Effect of Y = Y * Effect of X1 on Y * Effect of X2 on Y* … * Effect of Xn on YX2 on Y* … * Effect of Xn on Y

These are called MULTIPLICATIVE EFFECTSThese are called MULTIPLICATIVE EFFECTSExamples:Examples:Rate = Normal Fractional Rate * Stock * Effect of Rate = Normal Fractional Rate * Stock * Effect of X1 on Rate * … * Effect of Xn on RateX1 on Rate * … * Effect of Xn on RateBirth Rate = Birth Rate Normal * Population * Birth Rate = Birth Rate Normal * Population * Effect of Material on Birth Rate * Effect of Effect of Material on Birth Rate * Effect of Pollution on Birth Rate * Effect of Crowding on Pollution on Birth Rate * Effect of Crowding on Birth Rate * Effect of Food on Birth RateBirth Rate * Effect of Food on Birth Rate

Recall, Forrester’s world2 Model…Recall, Forrester’s world2 Model…

A reference year of 1970 was definedA reference year of 1970 was defined

Normal fractional birth rate was the Normal fractional birth rate was the world average in the reference yearworld average in the reference year

All of the effects were normalized to All of the effects were normalized to their 1970 values, making those their 1970 values, making those normalized values equal to 1normalized values equal to 1

Multiplicative effectsMultiplicative effects

Create nonlinearitiesCreate nonlinearities

Forrester really believes the effects Forrester really believes the effects are multiplicativeare multiplicative

As an alternative consider additive As an alternative consider additive effects:effects:

Y = Y* + Effect of X1 on Y + Effect Y = Y* + Effect of X1 on Y + Effect of X2 on Y + … + Effect of Xn on Yof X2 on Y + … + Effect of Xn on Y

Example:Example:Change in wage = Fractional Change Change in wage = Fractional Change in Wage * Wagein Wage * WageFractional Change in Wage = Change Fractional Change in Wage = Change in Wage from Labor Availability + in Wage from Labor Availability + Change in Wage from Inflation + Change in Wage from Inflation + change in Wage from Productivity + change in Wage from Productivity + Change in Wage from Profitability + Change in Wage from Profitability + Change in Wage from EquityChange in Wage from Equity

Multiplicative or Additive, Multiplicative or Additive, WHICH???WHICH???

Linear formulations are common because Linear formulations are common because such formulations are simplesuch formulations are simple

Multiplicative formulations are generally Multiplicative formulations are generally preferable and sometimes requiredpreferable and sometimes required

The actual relationship between births and The actual relationship between births and food, crowding, or pollution is typically food, crowding, or pollution is typically complex and nonlinearcomplex and nonlinear

Multiplicative or Additive, Multiplicative or Additive, WHICH???WHICH???

Both are approximations to the Both are approximations to the underlying, true nonlinear function: underlying, true nonlinear function: Y = f(X1, X2, …, Xn)Y = f(X1, X2, …, Xn)

Each approximation is centered on a Each approximation is centered on a particular operating point given by particular operating point given by the reference point Y* = f(X1*, X2*, the reference point Y* = f(X1*, X2*, …, Xn*)…, Xn*)

Both additive and multiplicative Both additive and multiplicative approximations…approximations…

Will be reasonable in the Will be reasonable in the neighborhood of the operating point neighborhood of the operating point but increasingly diverge from the but increasingly diverge from the true, underlying function as the true, underlying function as the system moves away from itsystem moves away from it

Additive vs. MultiplicativeAdditive vs. MultiplicativeAdditive assumes the effects of each input Additive assumes the effects of each input are strongly separableare strongly separableStrong separability is clearly incorrect in Strong separability is clearly incorrect in extreme conditionsextreme conditionsIn the birth rate example, births must be In the birth rate example, births must be zero when food per capita is zero no zero when food per capita is zero no matter how favorable the other conditions matter how favorable the other conditions areareThe additive formulation can never The additive formulation can never capture thiscapture this


Fuzzy MIN FunctionFuzzy MIN Function

Fuzzy MAX FunctionFuzzy MAX Function

Floating goalsFloating goals

Fuzzy MIN FunctionFuzzy MIN Function

A rate or auxiliary is determined by A rate or auxiliary is determined by the most scarce of several resourcesthe most scarce of several resources

Production = MIN(Desired Production = MIN(Desired Production, Capacity)Production, Capacity)

Generally, Y = MIN(X, Y*), where Y* is Generally, Y = MIN(X, Y*), where Y* is the capacity of the processthe capacity of the process

Problems with the MIN FunctionProblems with the MIN Function

The sharp discontinuity created by The sharp discontinuity created by the MIN function is often unrealisticthe MIN function is often unrealistic

Often the capacity constraint is Often the capacity constraint is approached gradually due to physical approached gradually due to physical characteristics of the systemcharacteristics of the system

A fuzzy MIN function will accomplish A fuzzy MIN function will accomplish this for us so that there is not sharp this for us so that there is not sharp discontinuitydiscontinuity

Fuzzy MAX FunctionFuzzy MAX Function

Analogous to fuzzy MIN functionAnalogous to fuzzy MIN function

Hiring Rate = MAX(0, Desired Hiring Hiring Rate = MAX(0, Desired Hiring Rate) prevents Hiring Rate from ever Rate) prevents Hiring Rate from ever gong negativegong negative

Useful in situations where decision Useful in situations where decision makers want to keep a variable Y at makers want to keep a variable Y at its desired rate even as X falls to its desired rate even as X falls to zerozero

Fuzzy MIN and MAX FunctionsFuzzy MIN and MAX Functions

I couldn’t find any in VENSIMI couldn’t find any in VENSIM

Therefore, you must set this up using Therefore, you must set this up using a TABLE functiona TABLE function

Floating goalsFloating goals

The goal moves toward the actual The goal moves toward the actual state of the system while the actual state of the system while the actual state of the system moves toward state of the system moves toward the goal.the goal.

Floating GoalFloating Goal

State of thesystem

Net Changein State

DesiredState ofSystem

Net Changein Desired

State

-

-

+

+

StateAdjustment

Time

GoalAdjustment

Time

B

StateAdjustment

R

Floating GoalSpiral

B

GoalAdjustment

Initial DesiredState of System

Initial State ofSystem

State of thesystem

Net Changein State

DesiredState ofSystem

Net Changein Desired

State

-

-

+

+

StateAdjustment

Time

GoalAdjustment

Time

B

StateAdjustment

R

Floating GoalSpiral

B

GoalAdjustment

Initial DesiredState of System

Initial State ofSystem

Performance and Goal

1,000

750

500

250

0

0 5 10 15 20 25 30 35 40 45 50Time (Week)

State of the system : inivsdes1 UnitsDesired State of System : inivsdes1 Units


Nonlinear Weighted AverageNonlinear Weighted Average

Modeling Search: Hill-Climbing Modeling Search: Hill-Climbing OptimizationOptimization

Resource AllocationResource Allocation

Nonlinear Weighted AverageNonlinear Weighted Average


Decision makers must optimize a system Decision makers must optimize a system but lack knowledge of the system but lack knowledge of the system structure that might help them identify the structure that might help them identify the optimal operating pointoptimal operating pointExamples: A firm wants to Examples: A firm wants to – maximize profitmaximize profit– Minimize costsMinimize costs– Maximize the mix of labor and capitalMaximize the mix of labor and capital

Can do this in simulated real time using a Can do this in simulated real time using a variant of floating goalsvariant of floating goals

To find the optimal mix of labor and To find the optimal mix of labor and capital…capital…

The model adjusts the mix in the The model adjusts the mix in the right direction, toward a desired right direction, toward a desired state.state.

This is called hill-climbingThis is called hill-climbing

Hill ClimbingHill ClimbingState of

System SChange in

State ofSystem

DesiredState S*

Effect of ExternalPressures onDesired State

-+

+

StateAdjustment

Time

B

StateAdjustment

+

R

Goal Rev ision

ExternalPressures X

Sensitivity toExternal

Pressures

Increase inExternalPressure

Decrease inExternalPressure

+

-

Time forDecrease in

Pressure

Time forIncrease in

Pressure

State ofSystem S

Change inState ofSystem

DesiredState S*

Effect of ExternalPressures onDesired State

-+

+

StateAdjustment

Time

B

StateAdjustment

+

R

Goal Rev ision

ExternalPressures X

Sensitivity toExternal

Pressures

Increase inExternalPressure

Decrease inExternalPressure

+

-

Time forDecrease in

Pressure

Time forIncrease in

Pressure


I have taught entire courses in hill-I have taught entire courses in hill-climbing optimizationclimbing optimization

My favorite—Powell’s method—also My favorite—Powell’s method—also the one used in Vensimthe one used in Vensim– Doesn’t require first-partial derivatives Doesn’t require first-partial derivatives

of the objective function, as many of the objective function, as many methods domethods do

– Is fast, giving quadratic convergenceIs fast, giving quadratic convergence– Uses conjugate directions of searchUses conjugate directions of search

Problems with Hill-climbing Problems with Hill-climbing Optimization MethodsOptimization Methods

Converges to local optimaConverges to local optima

Must start it from a number of different Must start it from a number of different points in the search space to ensure that a points in the search space to ensure that a global optimum is foundglobal optimum is found

But that is NOT WHAT IS GOING ON HEREBut that is NOT WHAT IS GOING ON HERE—THE SIMPLE TECHNIQUE USED HERE IS —THE SIMPLE TECHNIQUE USED HERE IS JUST A VARIANT OF THE 1JUST A VARIANT OF THE 1STST ORDER ORDER NEGATIVE FEEDBACK GOAL SEEKING NEGATIVE FEEDBACK GOAL SEEKING STRUCTURESTRUCTURE

Example—setting priceExample—setting price

Price DecisionsPrice Decisions

Price

Change inPrice

IndicatedPrice

Effect ofDemand/Supply

Balance on Price

-+

+

PriceAdjustment

Time

B

PriceAdjustment

+

Demand

Supply

SupplyElasticity

DemandElasticityR

PriceDiscov ery

-

ReferenceDemand +

Demand/Supply Balance

+

+Sensitivity of Price to

Demand/SupplyBalance

ReferenceSupply

+

+

-

B

DemandResponse

B

SupplyResponse

Change inReferenceDemand

DemandCurve Shift

Time

InitialReferenceDemand

ReferencePrice -

<ReferencePrice>

-Price

Change inPrice

IndicatedPrice

Effect ofDemand/Supply

Balance on Price

-+

+

PriceAdjustment

Time

B

PriceAdjustment

+

Demand

Supply

SupplyElasticity

DemandElasticityR

PriceDiscov ery

-

ReferenceDemand +

Demand/Supply Balance

+

+Sensitivity of Price to

Demand/SupplyBalance

ReferenceSupply

+

+

-

B

DemandResponse

B

SupplyResponse

Change inReferenceDemand

DemandCurve Shift

Time

InitialReferenceDemand

ReferencePrice -

<ReferencePrice>

-

Price Adjustment in Hill Climbing Price Adjustment in Hill Climbing FashionFashion

Price

200

170

140

110

80

-2 -1 0 1 2 3 4 5 6 7 8 9 10Time (Period)

Price : price1 $/unit

Price vs. Indicated Price

200

170

140

110

80

-2 -1 0 1 2 3 4 5 6 7 8 9 10Time (Period)

Price : price1 $/unitIndicated Price : price1 $/unit

Demand vs. supply

125

116.25

107.5

98.75

90

-2 -1 0 1 2 3 4 5 6 7 8 9 10Time (Period)

Demand : price1 Units/PeriodSupply : price1 Units/Period

Resource AllocationResource Allocation

Common PitfallsCommon Pitfalls

All outflows require First-Order All outflows require First-Order ControlControl

Avoid IF..THEN..ELSE FormulationsAvoid IF..THEN..ELSE Formulations

Disaggregate Net FlowsDisaggregate Net Flows

All outflows require First-Order All outflows require First-Order ControlControl

Real stocks such as inventories, Real stocks such as inventories, personnel, cash and other resources personnel, cash and other resources cannot become negativecannot become negative

Outflow rates must be formulated so Outflow rates must be formulated so these stocks remain nonnegative these stocks remain nonnegative even under extreme conditionseven under extreme conditions

Do so requires all outflows to have Do so requires all outflows to have first-order controlfirst-order control

First-Order ControlFirst-Order ControlMeans the outflows are governed by a Means the outflows are governed by a first-order negative feedback loop that first-order negative feedback loop that shuts down the flow as the stock drops to shuts down the flow as the stock drops to zerozero

Examples:Examples:– Outflow = MIN (Desired Outflow, Maximum Outflow = MIN (Desired Outflow, Maximum

Outflow)Outflow)– Outflow = Stock / Residence timeOutflow = Stock / Residence time– Maximum Outflow = Stock / Minimum Maximum Outflow = Stock / Minimum

Residence timeResidence time

Avoid IF..THEN..ELSE Avoid IF..THEN..ELSE FormulationsFormulations

Sterman doesn’t like these because Sterman doesn’t like these because they introduce sharp discontinuities they introduce sharp discontinuities into your models, discontinuities that into your models, discontinuities that are often inappropriate.are often inappropriate.Individual decisions are rarely Individual decisions are rarely either/oreither/orIn many cases the decision is a In many cases the decision is a compromise or weighted average of compromise or weighted average of competing pressurescompeting pressures

More on IF..THEN..ELSE More on IF..THEN..ELSE FormulationsFormulations

They create conditional statements They create conditional statements that are often difficult to understand, that are often difficult to understand, especially when the conditions are especially when the conditions are complex or nested with otherscomplex or nested with others

Disaggregate Net FlowsDisaggregate Net Flows

SummarySummary

chapter 13, sterman: modeling decision making powerpoints by: james burns

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