ch14 powell and baker

8/20/2019 Ch14 Powell and Baker

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MANAGEMENT

SCIENCEThe Art of Modeling with Spreadsheets

STEPHEN G. POWELL

ENNETH !. "AE!

Co#pati$le with Anal%ti& Sol'er Platfor#(O)!TH E*ITION

MONTE CA!LO SIM)LATION

CHAPTE! +,

POWE!POINT


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INTRODUCTION

• Monte Carlo si#-lation is an important andfexible technique or modeling situations in whichuncertaint is a !e actor"

• #naltic $ol%er &latorm pro%ides the capabilit to

implement 'onte Carlo simulation in spreadsheetmodels. • $imulation can describe not onl what the

outcomes o a gi%en decision could be( but also the probabilities with which these outcomes will occur"

• In act( the result o a simulation is the entirepro$a$ilit% distri$-tion o outcomes"

• In a sense( simulation is an ad%anced orm osensiti%it analsis in which we attach a probabilitto each possible outcome"

Chapter +, Cop%right /0+1 2ohn Wile% 3Sons4 In&.

/


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INTRODUCTION

• )e oten wish to determine the probabilit o a particularset o outcomes"

• $uch *tail probabilities+ are oten suitable measures othe ris! associated with a decision"

• )hile decision trees pro%ide a simple means or anal,ing

decisions with uncertaint and ris!( simulation is the toolo choice when there are a large number o uncertainties(especiall when these are represented b continuousdistributions"

• $imulation is also a practical method when the underlingmodel is complex"

• -owe%er( it is important to reali,e that( .ust as withdecision trees( the result o a simulation is a pro$a$ilit%distri$-tion or each outcome"

• #nal,ing these distributions and extracting managerialinsights is an important part o the art o simulation"


1


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/$$/NTI#0 $T/&$ IN # $I'U0#TION


,

1" $tart with a base case model and determine which othe input parameters to represent as uncertain"

2" De%elop probabilit distributions or those inputs"

3" Ta!e random samples rom those inputs and calculate

the resulting output( repeating the process until aclear picture o the output distribution emerges"

4" Create a histogram o the outcomes and interpret it"

• $imulation pro%ides two essential pieces o

inormation5 mean values 6also called expected%alues7 and tail probabilities 6e"g"( the probabilit o apositi%e pro8t7"


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'OD/0IN9 TI&5 CR/#TIN9 $I'U0#TION 'OD/0$

• :eginners to simulation modeling oten 8nd itdi;cult to build an initial spreadsheet model" Thisma be because a simulation model mustcorrectl e%aluate a large or e%en in8nite numbero di


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$/N$ITI=IT> #N#0>$I$

• The base?case model should be thoroughlexplored( using parametric sensiti%it(tornado charts or other methods( beoreunderta!ing a simulation analsis"

• )e can thin! o simulation as a sophisticatedapproach to sensiti%it analsis"

• )hereas sensiti%it analsis is a necessar8rst step( and can oten re%eal unexpected

relationships in the model( a simulationanalsis is required to anal,e the combinede


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$&/CI@>IN9 &RO:#:I0IT> DI$TRI:UTION$5/NT/RIN9 T-/ NOR'#0 DI$TRI:UTION U$IN9RI$A $O0=/R

• Con%ert our base?case model into a simulation model breplacing our 8xed 6deterministic7 assumptions withprobabilit distributions"

1" $elect #naltic $ol%er&latormB$imulation'odelBDistributionsBCommonBNormal( which opensthe window shown at rightwith a normal distributionwith a mean o and astandard o 1"

2" /nter the appropriate

parameters"3" Clic! on the $a%e and Close

icon"


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/#'&0/ O@ $I'U0#TION 'OD/0


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$&/CI@>IN9 OUT&UT$

• The second step in setting up a simulationmodel is to de8ne the model outputs so that#naltic $ol%er &latorm can sa%e these%alues during a simulation run"

1" &lace the cursor on the cell containing theoutput ormula"

2" $elect #naltic $ol%er &latormB$imulation'odel BResultsBOutputBIn Cell" This

selection adds the unction &siOutput67 to theormula alread in the cell("

3" Repeat the abo%e process or other outputcells"


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$/TTIN9 $I'U0#TION R#'/T/R$

E #naltic $ol%er &latorm allows the user to con8gure asimulation model b choosing %alues or a number oparameters" These options can be

displaed b selecting theOptions icon and choosing the$imulation tab"

'ost o these options cansael be let at their deaultsettings"

The number o trials in #naltic$ol%er &latorm is the numbero times model outputs arecalculated or di


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#N#0>FIN9 $I'U0#TION OUT&UT$

• #naltic $ol%er &latorm can perorm simulations in either amanual or an automatic mode"

1" In manual mode( we run a single simulation b selecting#naltic $ol%er &latormB$ol%e #ctionB$imulateBRun Once" – This will cause #naltic $ol%er &latorm to sample rom each o

the input probabilit distributions( calculate the resulting %aluesor the output cell or cells( and repeat or the number o trials"

– In this mode( #naltic $ol%er &latorm will not run a simulationwhen we enter a parameter or ta!e an other action that resultsin the spreadsheet being recalculated 6including pressing @G7"

2" In automatic mode( select #naltic $ol%er &latormB$ol%e#ctionB$imulateBInteracti%e" – The lightbulb icon turns ellow( signiing automatic simulation is

on"

– #naltic $ol%er &latorm stores simulation results or each outputcell in the cell itsel"

– : double?clic!ing on an output cell we can displa the results in%arious ormats"


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/#'&0/ O@ OUT&UT5 @OR/C#$T)INDO)


+/


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$U''#R> O@ T-/ $I'U0#TION &ROC/$$

• $electing uncertain parameters

• $electing probabilit distributions

• $electing output6s7

• Running a simulation

• #nal,ing outputs


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#N#0>TIC $O0=/R TI&5 /NT/RIN9DI$TRI:UTION$


+,

1" -ighlight the target cell"

2" $elect #naltic $ol%er &latormB$imulation 'odelBDistributions" This sequence displas six categories o distributions5 Common(#d%anced( /xotic( Discrete( Custom and Certi8ed" -ighlight ancategor and the speci8c distributions in that categor are

displaed graphicall" # total o 4H distributions is a%ailable"3" $elect a particular distribution and a probabilit distribution

window" /ach probablit distribution window depicts thedistribution in the orm o a &D@ 6probabilit distribution unction7( aCD@ 6cumulati%e distribution unction7( or a Re%erse CD@" It alsoallows the user to input the parameters o the distribution( such as

the mean and standard de%iation( either as numbers or as cellreerences"

4" Clic! on $a%e to enter the distribution in the target cell" 6&robabilitdistributions can also be entered into cells b tping the rele%antormulas directl"7


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#N#0>TIC $O0=/R TI&5 D/@ININ9 OUT&UT C/00$


+5

1" -ighlight the target cell"

2" $elect #naltic $ol%er &latormB$imulation'odelBResultsBOutputBIn Cell"

3" To create a separate cell with the distribution o the

target cell( highlight the target cell and select#naltic $ol%er &latormB$imulation'odelBResultsBOutputBReerred Cell"

4" #naltic $ol%er &latorm also allows the user to

record %arious aspects o the distribution o a cell onthe spreadsheet" $elect #naltic $ol%er&latormB$imulation 'odelBResultsB$tatisticsB'ean"


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#N#0>TIC $O0=/R TI&5 #N#0>FIN9 OUT&UT$

1" Double?clic! on the output cell( which opens theoutput window that contains 8%e tabs5

1" @requenc

2" Cumulati%e @requenc3" Re%erse Cumulati%e @requenc

4" $ensiti%it" $catter &lots

2" To a%oid opening the output window and searchingor speci8c statistical results b capturing themdirectl in cells on the spreadsheet( select #naltic

$ol%er &latorm B$imulation'odelBResultsBRangeB&ercentile( and clic! on cell"


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$I'U0#TION $/N$ITI=IT>


+7

• To answer sensiti%it questions with a simulation

model( we need to run a simulation in #naltic$ol%er &latorm once or each %alue o the

parameter we wish to test" This is done in two

steps"

– @irst we de8ne the range o %alues or the inputparameter using a &si$im&aram unction( a!in tothe &si$en&aram unction or deterministic

sensiti%it analsis" – Then we create a table 6Report7 or chart o %alues

or speci8c statistics o an output cell b runningsimulations or each %alue o the input"


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/#'&0/ O@ 'U0TI&0/ $I'U0#TION$ R/&ORT)INDO)


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#N#0>TIC $O0=/R TI&5 $I'U0#TION $/N$ITI=IT>

1" Create and run a simulation model with at least oneoutput cell"

2" De8ne the sensiti%it range or the input parameterb reerencing the unction &si$im&aram6lower limit(upper limit7"

3" &lace the cursor on the Output cell6s7"4" $elect #naltic $ol%er &latorm B#nalsisBReportsB

$imulationB&arameter #nalsis" This sequence opensthe 'ultiple $imulations Report window"

" Choose the output cell6s7 rom the drop?down list at

the top o the window"H" $elect one or more statistics o the output cell6s7 bplacing chec! mar!s appropriatel"

J" $elect the input parameter cell6s7 rom the listpro%ided"


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#N#0>TIC $O0=/R TI&5 $I'U0#TION $/N$ITI=IT>6CONTKD7

L" $elect one o the three options rom the pull?downmenu5

1" =ar #ll $elected &arameters $imultaneousl

2" =ar #ll $elected &arameters One at a Time3" =ar Two $elected &arameters Independentl

G" $peci the number o 'a.or #xis &oints 6and 'inor#xis &oints i necessar or a two?dimensional table7"#naltic $ol%er &latorm will di%ide the range or theinput parameter speci8ed in the &si$im&aramunction into the number o %alues speci8ed here(

and run one simulation or each o these %alues"1" Clic! on OA"


/0


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$/0/CTIN9 UNC/RT#IN R#'/T/R$

• $ome degree o uncertaint surrounds the true %alueo every parameter in a model 6with ew exceptions7"

• $electing which parameters to treat as uncertain ismore art than science"

• It is essential to carr out a deterministic analsis withthe model beore considering simulation"

• &erorming a sensiti%it analsis not onl tests themodel and describes possible outcomes( it pro%ides asense as to whether or not the simulation is needed"

• # tornado chart can help determine which parameters

ha%e a signi8cant impact on the outcome"• 'ore inormation is required to assign a separate

range o %ariation to each parameter( but the resultsare more meaningul"


//


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$/0/CTIN9 &RO:#:I0IT> DI$TRI:UTION$

• Once we ha%e selected a set o uncertainparameters( the next step is to choose aprobabilit distribution or each one"

• :ut which tpe o distribution should we choose5

discrete( uniorm( normal( triangular( or perhapssomething elseM

• #nd once we ha%e chosen a tpe o distribution(how do we choose its speci8c parameters 6such asthe mean and standard de%iation or the normal

distribution7M• )hile #naltic $ol%er &latorm pro%ides do,ens o

tpes o distributions( most business analsts useonl a small handul o them"


/1


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/'&IRIC#0 D#T# #ND UD9'/NT#0 D#T#

• /mpirical data consists o numerical obser%ationsrom experience( such as monthl sales or thepast our ears or dail stoc! returns o%er thepre%ious ear"

• udgmental data are estimates made b expertsin the 8eld or b the decision ma!ers most closelin%ol%ed in the analsis"

• )e can learn to as! decision ma!ers orprobabilit estimates such as the mean( theminimum( or the 1th and Gth percentilesneeded or tornado?chart analsis"


/,


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/'&IRIC#0 D#T# #0ON/ #R/ $/0DO'$U@@ICI/NT

• In most cases( unless we are doing scienti8cresearch( no empirical data at all will be a%ailable"6udgmental data( on the other hand( are usualla%ailable"7

• /%en i empirical data are a%ailable( the inormation

ma be biased or otherwise inappropriate or thepurposes at hand"

• /%en i appropriate empirical data are a%ailable( itrequires .udgment to determine whether thedistribution that pro%ides the best 8t to the gi%en

empirical data is appropriate in the model"• In man cases( the results o interest depend on the

mean and %ariance o an uncertain parameter( butnot on the speci8c orm o the probabilitdistribution"


/5


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$I /$$/NTI#0 DI$TRI:UTION$

1" The "erno-lli distribution is used in situations where anuncertain parameter can ta!e on one o onl two possible%alues"

2" The integer -nifor# distribution5 )e oten wish to model arandom outcome that ta!es on a small number o discrete%alues with equal probabilities"

3" The $ino#ial distribution is used or the number ooutcomes on repeated trials"

4" The -nifor# distribution describes an outcome that isequall li!el to all anwhere between a minimum and amaximum %alue"

" The triang-lar distribution is a more fexible amil ocontinuous distributions5 these distributions are speci8ed bthree parameters5 the minimum( maximum( and most li!el%alues"

H" The nor#al distribution is a smmetric distribution( usuallspeci8ed b its mean and standard de%iation"


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# :/RNOU00I DI$TRI:UTION


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#N INT/9/R UNI@OR' DI$TRI:UTION


/8


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# :INO'I#0 DI$TRI:UTION


/9


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# UNI@OR' DI$TRI:UTION


10


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# TRI#N9U0#R DI$TRI:UTION


1+


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# NOR'#0 DI$TRI:UTION


1/


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@ITTIN9 DI$TRI:UTION$ TO D#T#

E #naltic $ol%er &latorm pro%ides a tool or 8ttingcontinuous or discrete distributions to sample data"

-ighlight the data and select

#naltic $ol%er&latormBToolsB@it"

This sequence brings up the @itOptions window in which we

speci the location o the dataand choose to 8t continuous

distributions to the data"

&ress the @it button( and

#naltic $ol%er &latorm 8tseach o the continuous

distributions in turn to this dataset and presents them in ordero goodness?o?8t"


11


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/#'&0/5 @IT O&TION$ )INDO)


1,


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/N$URIN9 &R/CI$ION IN OUT&UT$5 $I'U0#TION/RROR

• /%er time we run a simulation( we are perormingan experiment"

• )ith an simulation result( there is somedi


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/N$URIN9 &R/CI$ION IN OUT&UT$5 'OD/0/RROR

• $imulation error is not the onl source o error inour modeling e


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&R/CI$ION =/R$U$ #CCUR#C>

• #n estimate based on a larger sample is more precise.

• )hile it is important to ensure an appropriatele%el o precision in our results( there is atrade?o< between the precision o the resultsand the time it ta!es to get them"

• Thus( an e


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#N /&/RI'/NT#0 '/T-OD

• The simplest approach to determining theprecision o a simulation estimate is toexperiment with multiple independent runs"

• )e must ensure that di


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&R/CI$ION U$IN9 T-/ '$/


,0

• # more sophisticated approach to measuring the precision ina simulation estimate relies on the mean standard error6'$/7"

• # con8dence inter%al is constructed around the estimatedmean %alue b adding and subtracting a multiple o the '$/"

• The larger the multiple( the wider the con8dence inter%al andthe higher the probabilit that the true mean %alue will liewithin the con8dence inter%al"

• The '$/ declines roughl with the square root o the numbero trials( so as we increase the number o trials( we increase

the precision o our estimates( but not in a linear ashion"

• # good wa to use the '$/ is to determine the acceptableerror beore running a simulation"


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$I'U0#TION /RROR IN # D/CI$ION CONT/T

• $ometimes analsts de%ote excessi%e e


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INT/R&R/TIN9 $I'U0#TION OUTCO'/$

• )hen we run a simulation with( sa( 1(trials( the raw result is simpl a collection o1( %alues or each outcome cell"

• )e rarel ha%e to wor! with the raw data

directl"• )e use #naltic $ol%er &latorm to displa

and summari,e the results or us"• 'ost oten( that summar ta!es the orm o a

histogram( or requenc chart( but there areother was o summari,ing output data"

Chapter +, Cop%right /0+1 2ohn Wile% 3Sons4 In&. ,/


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$I'U0#TION R/$U0T$

• )hen we double clic! on an output cell aterrunning a simulation( the $imulation Resultswindow opens"

• )e can show the mean %alue or the simulationoutcomes b selecting 'ar!ers in the tas!pane" )e then clic! on the double?plus icon(select 'ean under Tpe( and enter 'ean in theDescription window"

• )e can calculate and displa a tail probabilitb entering a lower or upper cut?o< %alueunder $tatistics Chart $tatistics"

Chapter +, Cop%right /0+1 2ohn Wile% 3Sons4 In&. ,1


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T-/ $I'U0#TION R/$U0T$ )INDO)

Chapter +, Cop%right /0+1 2ohn Wile% 3Sons4 In&. ,,


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T-/ $I'U0#TION R/$U0T$ )INDO) $-O)IN9 T-/'/#N#ND # T#I0 &RO:#:I0IT>



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DI$&0#>IN9 R/$U0T$ ON T-/ $&R/#D$-//T

• In most cases( we reer to the $imulation Resultswindow to anal,e the results o a simulation.

• $ometimes( especiall when we must run asimulation man times( it is more con%enient to

record the results directl on the spreadsheet"• #naltic $ol%er &latorm pro%ides a number o

special unctions or this purpose"

• The most commonl used measure o the resultso a simulation is the mean" Rather than open the$imulation Results window to 8nd the mean( wecan displa it directl on the spreadsheet usingthe &si'ean67 unction"



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DI$&0#>IN9 R/$U0T$ ON T-/ $&R/#D$-//T6CONTKD7

• Other statistics can be captured on thespreadsheet. $ome o the most commonstatistics are5 – The mean and standard de%iation 6select

#naltic $ol%er &latormB$imulation'odelBResultsB$tatistics7"

– The %alue at ris! and the conditional %alue atris! 6select #naltic $ol%er &latormB$imulation'odelBResults B'easures7"

– The minimum and maximum 6#naltic $ol%er&latormB$imulation 'odelBResultsBRange7"



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)-/N TO $I'U0#T/ #ND )-/N NOT TO$I'U0#T/

• Occasionall we ma go to the trouble oconducting a simulation onl to disco%er thatthe e


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$U''#R>

• $imulation shows us how uncertaint in the inputs infuencesthe outputs o our analsis"

• 0i!e optimi,ation( simulation can be seen as a sophisticatedorm o sensiti%it analsis"

• In /xcel( simulation can be carried out con%enientl using#naltic $ol%er &latorm( which pro%ides all the probabilitmodels needed to express the uncertainties in ourassumptions( and automates the repetiti%e process osampling rom these distributions" @inall( it pro%idesextensi%e methods or displaing and anal,ing the results"

• $imulation is a powerul tool when used appropriatel( but itshould ne%er be used beore an appropriate sensiti%it

analsis is carried out on a deterministic %ersion o the model"• )hat?i analsis( in%ol%ing use o Data $ensiti%it and Tornado

Charts( unco%ers those input parameters that ha%e thebiggest impact on the outcomes"

• These should be the ocus o an uncertaint analsis"



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$U''#R>

• /%er simulation analsis in%ol%es our ma.oracti%ities5 – $electing uncertain parameters

– $electing probabilit distributions

– $nsuring precision in the outcomes – Interpreting outcome distributions

• )hile simulation is more sophisticated than simplespreadsheet modeling( it is one o the most widelused o the ad%anced management science tools"

• Oten( the biggest challenge with simulation istranslating the results into a orm that managerscan understand and act upon"

Chapter +, Cop%right /0+1 2ohn Wile% 3Sons4 In&. 50


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ch14 powell and baker

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