ch13 the art of modelling with spreadsheet

8/20/2019 Ch13 The Art of Modelling with Spreadsheet

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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

*ECISION ANAL+SIS

CHAPTE! ,-

POWE!POINT


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INTRODUCTION

• Many business problems contain n&ertainele#ents that are impossible to ignorewithout losing the essence of the situation.

•

In this chapter, we introuce some basicmethos for analy!ing ecisions a"ecte byuncertainty.

Chapter ,- Cop%right / 01,- 2ohn Wile% 3Sons4 In&.

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UNC#RT$IN %$R$M#T#R&


-

• Now, we broaen our 'iewpoint to inclue n&ertaininpts(parameter 'alues sub)ect to uncertainty.

• Uncertain parameters become *nown only after a ecisionis mae.

•

+hen a parameter is uncertain, we treat it as if it coul ta*eon two or more 'alues, epening on inuences beyon ourcontrol.

• These inuences are calle states of natre, or moresimply, states.

• In many instances, we can list the possible states, an foreach one, the corresponing 'alue of the parameter.

• -inally, we can assign probabilities to each of the states sothat the parameter outcomes form a probability istribution.


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%$O-- T$/0#& $ND D#CI&ION CRIT#RI$

• -or each action1state combination, the entryin the table is a measure of the economicresult.

•

Typically, the payo"s are measure inmonetary terms, but they nee not be pro2t2gures.

• They coul be costs or re'enues in other

applications, so we use the more generalterm payof .


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/#NC3M$R4 CRIT#RI$

• The Ma6i#a6 pa%o7 &riterion see*s thelargest of the ma5imum payo"s among theactions.

•

The #a6i#in pa%o7 &riterion see*s thelargest of the minimum payo"s among theactions.

• The #ini#a6 regret &riterion see*s the

smallest of the ma5imum regrets among theactions.


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INCOR%OR$TIN6 %RO/$/I0ITI#&

• +e can immeiately translate this informationinto probability istributions for the payo"scorresponing to each of the potential

actions.• +e use the notation EP to represent an

e5pecte payo" 7e.g., an e5pecte pro2t8.

• Note that the e5pecte payo" calculation

ignores no information9 all outcomes anprobabilities are incorporate into the result.


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U&IN6 TR##& TO MOD#0 D#CI&ION&

• $ pro$a$ilit% tree epicts one or moreranom factors

• The noe from which the branches emanate iscalle a &han&e node, an each branch

represents one of the possible states thatcoul occur.

• #ach state, therefore, is a possible resolutionof the uncertainty represente by the chancenoe.

• #'entually, we:ll specify probabilities for eachof the states an create a probabilityistribution to escribe uncertainty at thechance noe.


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&IM%0# %RO/$/I0IT TR##


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T3R## C3$NC# NOD#& IN T#0#6R$%3IC-ORM


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D#CI&ION TR##&

• Decision1tree moels o"er a 'isual tool thatcan represent the *ey elements in a moel forecision ma*ing uner uncertainty an helporgani!e those elements by istinguishing

between ecisions 7controllable 'ariables8 anranom e'ents 7uncontrollable 'ariables8.

• In a de&ision tree, we escribe the choicesan uncertainties facing a single ecision1

ma*ing agent.• This usually means a single ecision ma*er,

but it coul also mean a ecision1ma*inggroup or a company.


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R#%R#NTIN6 D#CI&ION&

• In a ecision tree, we represent ecisions ass;uare noes 7bo5es8, an for each ecision,the alternati'e choices are represente asbranches emanating from the ecision noe.

• These are potential actions that are a'ailableto the ecision ma*er.

• In aition, for each uncertain e'ent, thepossible alternati'e states are represente asbranches emanating from a chance noe,labele with their respecti'e probabilities.


,,


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D#CI&ION TR##&9 RI&4 %RO-I0#&

• The istribution associate with a particular actionis calle its ris= pro>le.

• The ris* pro2le shows all the possible economicoutcomes an pro'ies the probability of each9 It is

a probability istribution for the principal output ofthe moel.

• This form reinforces the notion that, when some ofthe input parameters are escribe in probabilisticterms, we shoul e5amine the outputs in

probabilistic terms.• $fter we etermine the optimal ecision, we can

use a probability moel to escribe the pro2toutcome.


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D#CI&ION TR##& -OR $ RI#& O- D#CI&ION&

• Decision trees are especially useful in situations wherethere are multiple sources of uncertainty an a se;uenceof ecisions to ma*e.

• -or e5ample, suppose that we are introucing a newprouct an that the 2rst ecision etermines which

channel to use uring test1mar*eting.• +hen this ecision is implemente, an we ma*e an

initial commitment to a mar*eting channel, we can beginto e'elop estimates of eman base on our test.

• $t the en of the test perio, we might reconsier ourchannel choice, an we may ecie to switch to another

channel.• Then, in the full1scale introuction, we attain a le'el of

pro2t that epens, at least in part, on the channel wechose initially.


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#=$M%0#

• In the following e5ample, we ha'e epicte7in telegraphic form8 a situation in which wechoose our channel initially, obser'e the test

mar*et, reconsier our choice of a channel,an 2nally obser'e the eman uring full1scale introuction.


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D#CI&ION TR## +IT3 >U#NTI$0D#CI&ION&


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%RINCI%0#& -OR /UI0DIN6$ND $N$0


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RO00/$C4 %ROC#DUR# -OR $N$0


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T3# CO&T O- UNC#RT$INT

• $n action must be chosen beore learninghow an uncertain e'ent will unfol.

• The situation woul be much more

manageable if we coul learn about theuncertain e'ent 2rst an then choose anaction.


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IM%#R-#CT F&. %#R-#CT IN-ORM$TION

• +hen we ha'e to ma*e a ecision beforeuncertainty is resol'e, we are operating withimperfect information 7uncertain *nowlege8about the state of nature.

•+hen we can ma*e a ecision afteruncertainty is resol'e, we can respon toperfect information about the state of nature.

• Our probability assessments of e'entoutcomes remain unchange, an we are still

ealing with e5pecte 'alues.


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#=%#CT#D F$0U# O- %#R-#CT IN-ORM$TION7EVPI)

• The e5pecte payo" with perfect informationmust always be at least as goo as thee5pecte payo" from following the optimalpolicy in the original problem, an it will

usually be better.• The EVPI measures the i"erence, or the gain

ue to perfect information.• The calculation of EVPI can also be

represente with a tree structure, where we

re'erse the se;uence of ecision an chancee'ent in the tree iagram, )ust as we i inthe calculations.


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D#CI&ION TR## -OR T3# #F%IC$0CU0$TION


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U&IN6 D#CI&ION TR## &O-T+$R#

• It is often iGcult to create a layout for thecalculations that is tailore to the features ofa particular e5ample.

• -or that reason, it ma*es sense to ta*ea'antage of software that has beenesigne e5pressly for representing ecisiontrees in #5cel.

• *e&ision Tree is a tool containe in $nalytic

&ol'er %latform for constructing an analy!ingecision tree.


0-


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D#CI&ION TR## M#NU


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D#-$U0T INITI$0 TR## %RODUC#D / D#CI&ION TR##


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D#T$I0& -OR T3# -IR&T D#CI&ION NOD#


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#=%$ND#D INITI$0 TR## DI$6R$M


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NOD# +INDO+ -OR T3# -IR&T #F#NTNOD#


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-IR&T #F#NT NOD# %RODUC#D /D#CI&ION TR##


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#=%$ND#D DI$6R$M +IT3 COND #F#NTNOD# CO%I#D


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-U00 DI$6R$M


-,


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N&ITIFIT $N$0&I& +IT3 TR##%0$N

• $ ecision1tree analysis retains the propertiesof a spreasheet.

• The wor*sheet prouce by Decision Tree

contains inputs, formulas, an outputs, )ust asin any well1esigne moel.

• Thus, we can perform sensiti'ity analyses inthe usual ways.


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N&ITIFIT $N$0&I& -OR T3# #=$M%0#MOD#0


--


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MINIMI


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0OC$TION O- T3# M$=IMI


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?M$=IMI


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#=%ON#NTI$0 UTI0IT -UNCTION

• $lthough there are many ways of con'ertingollars to utils, one straightforwar methouses an e6ponential tilit% fn&tion9U a J b e5p 7JD/R8

where D is the 'alue of the outcome inollarsK U is the utility 'alue, or the 'alue ofan outcome in utilsK an a, b, an R represent parameters of the utility function.

%arameters a an b are essentially scalingparametersK R inuences the shape of thecur'e an is *nown as the ris= toleran&e.


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$N$0&I& +IT3 UTI0ITI#&

• To carry out the analysis, we use this functionto con'ert each monetary outcome fromollars to utils, an then we etermine theaction that achie'es the ma5imum e5pecte

utility.• $lthough Decision Tree allows the e5ibility of

setting three i"erent parameters, we usuallya'ise setting a b ?.

• This choice ensures that the function passes

through the origin, so that our remaining tas*is 2ning a 'alue of R that captures theecision ma*er:s preferences.


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6R$%3 O- UTI0IT -UNCTION -OR T3##=$M%0#


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U&IN6 TR## %0$N +IT3 #=%ON#NTI$0 UTI0IT-UNCTION

• In Decision Tree, it is necessary to specify the threeparameters in the e5ponential utility function.

• These three 'alues must be entere in the tas*

pane on the Moel tab, along with esignating the

'alue for Certainty #;ui'alents to be the#5ponential Utility -unction.

• $fter the user esignates the use of #5ponentialUtility -unction, Decision Tree isplays aitional

calculations in columns /, -, an . Immeiatelybelow the monetary payo"s the isplay shows thesame 2gures con'erte to utils.


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MODI-IC$TION O- T3# #=$M%0# MOD#0 -OR #=%ON#NTI$0UTI0ITI#&


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• $ ecision tree is a speciali!e moel for recogni!ing the role ofuncertainties in a ecision1ma*ing situation.

• Trees help us istinguish between ecisions an ranom e'ents,an more importantly, they help us sort out the se;uence inwhich they occur.

• %robability trees pro'ie us with an opportunity to consier the

possible states in a ranom en'ironment when there are se'eralsources of uncertainty, an they become components of ecisiontrees.

• The *ey elements of ecision trees are ecisions an chancee'ents. $ ecision is the selection of a particular action from agi'en list of possibilities.

• $ chance e'ent gi'es rise to a set of possible states, an eachaction1state pair results in an economic payo".

• In the simplest cases, these relationships can be isplaye in apayo" table, but in comple5 situations, a ecision tree tens tobe a more e5ible way to represent the relationships anconse;uences of ecisions mae uner uncertainty.

&UMM$R

Chapter ,- Cop%right / 01,- 2ohn Wile% 3Sons4 In&. 50


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&UMM$R 7CONT:D8

• The choice of a criterion is a critical step in sol'ing a ecisionproblem when uncertainty is in'ol'e.

• There are benchmar* criteria for optimistic an pessimisticecision ma*ing, but these are somewhat e5treme criteria. Theyignore some a'ailable information, incluing probabilities, inorer to simplify the tas* of choosing a ecision.

• The more common approach is to use probability assessmentsan then to ta*e the criterion to be ma5imi!ing the e5pectepayo", which in the business conte5t translates into ma5imi!inge5pecte pro2t or minimi!ing e5pecte cost.

• Using the rollbac* proceure, we can ientify those ecisionsthat optimi!e the e5pecte 'alue of our criterion. -urthermore,we can prouce information in the form of a probability

istribution to help assess the ris* associate with any ecisionin the tree.

• Decision Tree is a straightforwar spreasheet program thatassists in the structuring of ecision trees an in the calculationsre;uire for a ;uantitati'e analysis.

Chapter ,- Cop%right / 01,- 2ohn Wile% 3Sons4 In&. 5-


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ch13 the art of modelling with spreadsheet

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