Chapter Two Decision Businesses Analysis.pdf

ADVICE TO ALL EMPLOYEES

1. Build a home earlier. Be it rural home or urban home. Building a house at 50 is not an achievement. Don't get used to government houses. This comfort is so dangerous. Let all your family have good time in your house.

2. Go home. Don't stick at work all the year. You are not the pillar of your department. If you drop dead today, you will be replaced immediately and operations will continue. Make your family a priority.

3. Don't chase promotions. Master your skills and be excellent at what you do. If they want to promote you, that's fine if they don't, stay positive to your personal.
development.

4. Avoid office or work gossip. Avoid things that tarnish your name or reputation. Don't join the bandwagon that backbites your bosses and colleagues. Stay away from negative gatherings that have only people as their agenda.

5. Don't ever compete with your bosses. You will burn your fingers. Don't compete with your colleagues, you will fry your brain.

6. Ensure you have a side business. Your salary will not sustain your needs in the long run.

7. Save some money. Let it be deducted automatically from your payslip.

8. Borrow a loan to invest in a business or to change a situation not to buy luxury. Buy luxury from your profit.

9. Keep your life,marriage and family private. Let them stay away from your work. This is very important.

10. Be loyal to yourself and believe in your work. Hanging around your boss will alienate you from your colleagues and your boss may finally dump you when he leaves.

11. Retire early. The best way to plan for your exit was when you received the employment letter. The other best time is today. By 40 to 50 be out.

12. Join work welfare and be an active member always. It will help you a lot when any eventuality occurs.

13.Take leave days utilize them by developing yr future home or projects..usually what you do during yr leave days is a reflection of how you'll live after retirement..If it means you spend it all holding a remote control watching series on Zee world, expect nothing different after retirement.

14. Start a project whilst still serving or working. Let your project run whilst at work and if it doesn't do well, start another one till it's running viably. When your project is viably running then retire to manage your business. Most people or pensioners fail in life because they retire to start a project instead of retiring to run a project.

15. Pension money is not for starting a project or buy a stand or build a house but it's money for your upkeep or to maintain yourself in good health. Pension money is not for paying school fees or marrying a young wife but to look after yourself.

16. Always remember, when you retire never be a case study for living a miserable life after retirement but be a role model for colleagues to think of retiring too.

17. Don't retire just because you are finished or you are now a burden to the company and just wait for your day t

1. DECISION ANALYSIS
CHAPTER TWO
02/04/2023 DECISION ANALYSIS1

2. INTRODUCTION
▪Decisionanalysiscanbeusedtodevelopanoptimal
strategywhenadecisionmakerisfacedwithseveral
decisionalternativesandanuncertainorrisk-filled
patternoffutureevents.
▪Decisiontheoryisananalyticandsystematic
approachtothestudyofdecision-making.
▪Agooddecisionisonethatisbasedonlogicand
considersallavailabledataandpossible
alternatives,andthequantitativeapproach
describedinthischapter.
02/04/2023 DECISION ANALYSIS2

3. CONT’D
Makingadecisionrequiresanenumerationof
feasibleandviablealternatives,theconsequences
associatedwithdifferentalternatives,andthe
measureofeffectivenessbywhichthemostpreferred
alternativeisidentified.
Itprovidesamethodofnaturaldecision-making
whereindataconcerningtheoccurrenceofdifferent
outcomesmaybeevaluatedtoenablethedecision-
makertoidentifysuitablealternatives.
02/04/2023 DECISION ANALYSIS3

4. CONT’D
Decisionmodelsusefulinhelpingdecision-makers
makethebestpossibledecisionsareclassified
accordingtothedegreeofcertainty;
•completecertainty
•completeuncertainty
•riskorprobabilisticproblems.
02/04/2023 DECISION ANALYSIS4

5. SOME IMPORTANT TERMINOLOGIES
Thedecisionmakeristheindividualorgroup
responsibleformakingthedecision(orsequenceof
decisions)underconsideration.
ListofAlternatives:asetofmutuallyexclusiveand
collectivelyexhaustivedecisionsthatareavailableto
thedecisionmaker.
02/04/2023 DECISION ANALYSIS5

6. CONT’D
StatesofNature:thesetofpossiblefutureconditions,
orevents,beyondthecontrolofthedecisionmaker.
Thisinformationmaybeintheformofjustsubjective
estimatesbasedontheexperienceorintuitionofan
individual,ortheremaybesomedegreeofhard
evidence.
Payoffs:thepayoffsmightbeprofits,revenues,costs,
orothermeasuresofvalue.Thenumberofpayoffs
dependsonthenumberofalternative/state-of-nature
combinations.
02/04/2023 DECISION ANALYSIS6

7. CONT’D
DegreeofCertainty:theapproachoftenusedbya
decision-makerdependsonthedegreeofcertainty
thatexists.
oneextremeiscompletecertaintyandtheotheris
completeuncertainty.Betweenthesetwoextreme,
thereisarisk.
DecisionCriteria:thedecisionmaker’sattitudetoward
thedecisionaswellasthedegreeofcertaintythat
surroundsadecision.Forexample;maximizethe
expectedpayoffs.
02/04/2023 DECISION ANALYSIS7

8. CONT’D
ThePayoffTable:apayofftableisadevicethata
decisionmakercanusetosummarizeinformation
relevanttoaparticulardecision.
Itincludes:
✓Listofalternative
✓Possiblefuturestateofnature
✓Thepayoffsassociatedwitheachofthe
alternative/state-of-naturecombinations.
✓Probabilities
02/04/2023 DECISION ANALYSIS8

9. THE PAYOFF TABLE
Where:
Ai=theithalternative
Sj=thejthstatesofnature
Pi=probabilityundereachstateofnature
Vij=thevalueorpayoffthatwillberealizedif
alternativeiischosenandeventjoccur.
02/04/2023 DECISION ANALYSIS9
State of Nature
Alternatives
S1 S2 S3
P1 P2 P3
A1 V11 V12 V13
A2 V21 V22 V23
A3 V31 V32 V33

10. DECISION-MAKING PROCESS
1.Identificationofthevariouspossibleoutcomes,calledthestate
ofnatureorevents,Ei’sforthedecisionproblem.Theeventsare
beyondthecontrolofthedecision-maker.
2.Identificationofallthecoursesofaction,Aj’s,orthestrategies
thatareavailabletothedecisionmaker.Thedecision-maker
hascontroloverthechoiceofthese.
3.Determinationofthepayofffunctionwhichdescribesthe
consequenceresultingfromthedifferentcombinationsofthe
actsandevents.ThepayoffmaybedesignedasVij’s.The
payoffresultingfromi
th
eventsandj
th
strategy.
4.Choosingfromamongthevariousalternativesonthebasisof
somecriterion,whichmayinvolvetheinformationgiveninstep3
onlyorwhichmayrequireandincorporatesomeadditional
information.
02/04/2023 DECISION ANALYSIS10

11. EXAMPLE
SupposeMr.Abemelekarealestatedevelopermustdecideonaplanfor
developingacertainpieceofproperty.Aftercarefulconsideration,Mr.
Abemelekhasleftwiththefollowinglistofacceptablealternatives.
✓Residentialproposal
✓Commercialproposal#1
✓Commercialproposal#2
Themainfactorthatwillinfluencetheprofitabilityofthedevelopmentis
whetherornotashoppingcenterbuilt,andthesizeoftheshoppingcenter,if
oneisbuilt.Supposethatdeveloperviewsthepossibilitiesas:
✓No-shoppingcenter
✓Medium–sizeshoppingcenter
✓Largeshoppingcenter
02/04/2023 DECISION ANALYSIS11

12. PAYOFF TABLE
02/04/2023 DECISION ANALYSIS12
State of Nature
Alternatives
No SC MS SC LS SC
Residential 400,000 1,600,0001,200,000
Commercial #1600,000 500,000 1,400,000
Commercial #2 -100,000 400,000 1,500,000

13. DECISION MAKING WITHOUT PROBABILITIES
Inthissectionweconsiderapproachestodecision-making
thatdonotrequireknowledgeoftheprobabilitiesofthe
statesofnature.
Theseapproachesareappropriateinsituationsinwhichthe
decisionmakerhaslittleconfidenceinhisorherabilityto
assesstheprobabilities,orinwhichasimplebest-caseand
worst-caseanalysisisdesirable.
Becausedifferentapproachessometimesleadtodifferent
decisionrecommendations,thedecisionmakermust
understandtheapproachesavailableandthenselectthe
specificapproachthat,accordingtothejudgmentofthe
decisionmaker,isthemostappropriate.
02/04/2023 DECISION ANALYSIS13

14. DECISION MAKING WITHOUT PROBABILITIES
There are several criteria for making decisions making
without probabilities
1.Maximax(optimistic)
2.Maximin(pessimistic)
3.Criterionofrealism(Hurwicz)
4.Equallylikely(principleofinsufficientreason/
Laplace)
5.Minimaxregret
02/04/2023 DECISION ANALYSIS14

15. OPTIMISTIC APPROACH
Theoptimisticapproach(MaxiMax)evaluateseach
decisionalternativeintermsofthebestpayoffthat
canoccur.
Foraprobleminwhichmaximumprofitisdesired,the
optimisticapproachwouldleadthedecisionmakerto
choosethealternativecorrespondingtothelargest
profit.
Whereas,forproblemsinvolvingminimization,this
approachleadstochoosingthealternativewiththe
smallestpayoff.
02/04/2023 DECISION ANALYSIS15

16. CONT’D
Themaximaxcriterionisthedecisioncriterionforthe
eternaloptimist.Hereishowthiscriterionworks:Identifythe
maximumpayofffromanystateofnatureforeachdecision
alternative.Findthemaximumofthesemaximumpayoffsand
choosethecorrespondingdecisionalternative.
02/04/2023 DECISION ANALYSIS16
State of Nature
Alternatives
No SC MS SC LS SC Max. in
Row
Residential 400,0001,600,0001,200,0001,600,000
Commercial #1600,000500,0001,400,0001,400,000
Commercial #2 -100,000400,0001,500,0001,500,000

17. CONSERVATIVE APPROACH
Themaximin(pessimistic)criterionchoosestheaction
withthe“best”worstoutcome.Themaximincriterion
alwayschoosesthedecisionalternativethatprovides
thebestguaranteeforitsminimumpossiblepayoff.
02/04/2023 DECISION ANALYSIS17
State of Nature
Alternatives
No SC MS SC LS SC Min. in
Row
Residential 400,0001,600,0001,200,000400,000
Commercial #1600,000500,0001,400,000500,000
Commercial #2 -100,000400,0001,500,000-100,000

18. MINIMAX REGRET APPROACH
Indecisionanalysis,regretisthedifferencebetweenthe
payoffassociatedwithaparticulardecisionalternativeand
thepayoffassociatedwiththedecisionthatwouldyieldthe
mostdesirablepayoffforagivenstatenature.Thisiswhy
regretisoftenreferredtoasopportunityloss.
Asitsnameimplies,undertheminimaxregretapproachto
decisionmakingonewouldchoosethedecisionalternativethat
minimizesthemaximumstateofregretthatcouldoccuroverall
possiblestatesofnature.Thisapproachisneitherpurely
optimisticnorpurelyconservative.
02/04/2023 DECISION ANALYSIS18

19. CONT’D
Anapproachthattakesallpayoffsintoaccount.To
usethisapproach,itisnecessarytodevelopan
opportunitylosstablethatreflectsthedifference
betweeneachpayoffandthebestpossiblepayoffin
acolumn(i.e.,givenastateofnature).
02/04/2023 DECISION ANALYSIS19

20. CONT’D
02/04/2023 DECISION ANALYSIS20
Opportunity Loss Table State of Nature
Alternatives
No SC MS SC LS SC
Residential 200,000 0 300,000
Commercial #1 0 1,100,000100,000
Commercial #2 700,0001,200,000 0
Original Payoff Table State of Nature
Alternatives
No SC MS SC LS SC
Residential 400,0001,600,0001,200,000
Commercial #1600,000500,0001,400,000
Commercial #2 -100,000400,0001,500,000

21. CONT’D
02/04/2023 DECISION ANALYSIS21
State of Nature
Alternatives
No SC MS SC LS SC Max Loss
Residential 200,000 0 300,000300,000
Commercial #1 0 1,100,000100,0001,100,000
Commercial #2 700,0001,200,000 0 1,200,000
Sincetheobjectiveistominimizemaximumlossthe
decision-makerswillchoosearesidentialalternative.

22. PRINCIPLE OF INSUFFICIENT REASON/
EQUAL LIKELIHOOD/ LAPLACE
Considers all the payoffs for each alternative
Find the average payoff for each alternative
Select the alternative with the highest average
02/04/2023 DECISION ANALYSIS22
State of Nature
Alternatives
No SC MS SC LS SC Raw
Average
Residential 400,0001,600,0001,200,0001066,666.67
Commercial #1600,000500,0001,400,000833,333.3
Commercial #2 -100,000400,0001,500,000600,000

23. THE HURWITZ CRITERION
Theapproachoffersthedecisionmakeracompromise
betweenthemaximaxandthemaximincriteria.
Requiresthedecisionmakertospecifyadegreeof
optimism,intheformofacoefficientofoptimismα,
withpossiblevaluesofαrangingfrom0to1(0<<
1).
Theclosertheselectedvalueofαisto1,themore
optimisticthedecisionmakeris,andthecloserthe
valueofαisto0,themorepessimisticthedecision
makeris.
02/04/2023 DECISION ANALYSIS23

24. CONT’D
If=1,thenthedecisionmakerissaidtobe
completelyoptimistic,
If=0,thenthedecisionmakeriscompletely
pessimistic.Giventhisdefinition,ifiscoefficientof
optimism,
1-iscoefficientofpessimism.
TheHurwitzcriterionrequiresthatforeach
alternative,themaximumpayoffismultipliedby
andtheminimumpayoffbemultipliedby1-.
02/04/2023 DECISION ANALYSIS24

25. CONT’D
If = 0.4 for the above example,
A1=(0.4x1600000)+(0.6x400000)=880,000
A2=(0.4x1400000)+(0.6x500000)=860,000
A3=(0.4x1500000)–(0.6x100000)=540,000
02/04/2023 DECISION ANALYSIS25
State of Nature
Alternatives
No SC MS SC LS SC
Residential 400,000 1,600,0001,200,000
Commercial #1600,000 500,000 1,400,000
Commercial #2 -100,000 400,000 1,500,000

26. DECISION MAKING WITH PROBABILITIES
•Inmanydecision-makingsituations,wecanobtain
probabilityassessmentsforthestatesofnature.
•Decisionmakingwhenthereareseveralpossible
statesofnatureandweknowtheprobabilities
associatedwitheachpossiblestate
•Mostpopularmethodistochoosethealternativewith
thehighestExpectedMonetaryValue(EMV)
02/04/2023 DECISION ANALYSIS26

27. EXPECTED MONETARY VALUE (EMV)
TheEMVapproachprovidesthedecisionmakerwith
avaluewhichrepresentsanaveragepayoffforeach
alternative.Thebestalternativeis,then,theonethat
hasthehighestEMV.Theaverageorexpected
payoffofeachalternativeisaweightedaverage:
EMV (alternative i)= (payoff of first state of nature)
x (probability of first state of nature)
+ (payoff of second state of nature)
x (probability of second state of nature)
+ … + (payoff of last state of nature)
x (probability of last state of nature)
02/04/2023 DECISION ANALYSIS27

28. CONT’D
EMV (A1) = 0.20(400000) + 0.50(1600000) + 0.30(1200000) =
1,240,000,* Max
EMV (A2) = 0.20(6) + 0.50(5) + 0.30(14) = 790,000
EMV (A3) = 0.20(-1) + 0.50(4) + 0.30(15) = 630,000
02/04/2023 DECISION ANALYSIS28
State of Nature
Alternatives
No SC MS SC LS SC
Expected
Payoff Probability
0.2 0.5 0.3
Residential 400,0001,600,0001,200,0001,240,000
Commercial #1600,000500,000 1,400,000 790,000
Commercial #2 -100,000400,000 1,500,000 630,000

29. EXPECTED OPPORTUNITY LOSS (EOL)
EOListhecostofnotpickingthebestsolution
•Firstconstructanopportunitylosstable
•Foreachalternative,multiplytheopportunitylossby
theprobabilityofthatlossforeachpossibleoutcome
andaddthesetogether
•MinimumEOLwillalwaysresultinthesamedecision
asMaximumEMV
•MinimumEOLwillalwaysequalEVPI
02/04/2023 DECISION ANALYSIS29

30. CONT’D
EOL(A1)=0.20(2)+0.50(0)+0.30(3)=130,000*Minimum
EOL(A2)=0.20(0)+0.50(11)+0.30(1)=580,000
EOL(A3)=0.20(7)+0.50(12)+0.30(0)=740,000
TheEOLapproachresultedinthesamealternativeastheEMVapproach
(Maximizingthepayoffsisequivalenttominimizingtheopportunitylosses).
02/04/2023 DECISION ANALYSIS30
State of Nature
Alternatives
No SC MS SC LS SC
Probability
0.2 0.5 0.3
Residential 200,000 0 300,000
Commercial #1 0 1,100,000 100,000
Commercial #2 700,000 1,200,000 0

31. EXPECTED VALUE OF PERFECT INFORMATION
(EVPI)
TheEVPIisthemeasureofthedifferencebetweenthecertainty
payoffsthatcouldberealizedunderaconditioninvolvingrisk.
IfthedecisionmakerknowsthatS1willoccur,A2wouldbe
chosenwithapayoffof$600,000.Similarly,forS2
$1600,000(forA1),andforS3,$1500,000(withA3)would
bechosen.
Hence,theexpectedpayoffundercertainty(EPC)wouldbe:
EPC=0.20(600,000)+0.50(1,600,000)+0.30(1,500,000)
=1,370,000
02/04/2023 DECISION ANALYSIS31

32. CONT’D
Thedifferencebetweenthisfigureandtheexpected
payoffunderrisk(i.e.,theEMV)istheexpectedvalue
ofperfectinformation.Thus:
EVPI=EPC–EMV
=1,370,000–1,240,000=130,000
TheEOLindicatestheexpectedopportunitylossdueto
imperfectinformation,whichisanotherwayofsaying
theexpectedpayoffthatcouldbeachievedbyhaving
perfectinformation.
02/04/2023 DECISION ANALYSIS32

33. DECISION TREES
Decisiontree,likeaprobabilitytree,iscomposedof
squares,circles,andlines:
Thesquaresindicatedecisionpointsandcircles
representchanceevents(circlesandsquaresare
callednodes)
Thelines(branches)emanatingfromsquares
representalternatives.Thelinesfromcirclesrepresent
statesofnature
Thetreeisreadfromrighttoleft.
02/04/2023 DECISION ANALYSIS33

34. FOLDING BACK A DECISION TREE
•Foridentifyingthebestdecisioninthetree
•Workfromrighttoleft
•Calculatetheexpectedpayoffateachoutcome
node
•Choosethebestalternativeateachdecisionnode
(basedonexpectedpayoff)
02/04/2023 DECISION ANALYSIS34

35. CONT’D
02/04/2023 DECISION ANALYSIS35

36. CONT’D
02/04/2023 DECISION ANALYSIS36

37. EXERCISE
WarrenBuffyisanenormouslywealthyinvestorwhohasbuilthisfortunethroughhislegendary
investingacumen.Hecurrentlyhasbeenofferedthreemajorinvestmentsandhewouldliketo
chooseone.Thefirstoneisaconservativeinvestmentthatwouldperformverywellinanimproving
economyandonlysufferasmalllossinaworseningeconomy.Thesecondisaspeculativeinvestment
thatwouldperformextremelywellinanimprovingeconomybutwoulddoverybadlyina
worseningeconomy.Thethirdisacountercyclicalinvestmentthatwouldlosesomemoneyinan
improvingeconomybutwouldperformwellinaworseningeconomy.Warrenbelievesthatthereare
threepossiblescenariosoverthelivesofthesepotentialinvestments:(1)animprovingeconomy,(2)
astableeconomy,and(3)aworseningeconomy.Heispessimisticaboutwheretheeconomyis
headed,andsohasassignedpriorprobabilitiesof0.1,0.5,and0.4,respectively,tothesethree
scenarios.Healsoestimatesthathisprofitsundertheserespectivescenariosarethosegiveninthe
followingtable.
Heestimatedapayoffvalueof30million,5million,and-10millionunderimprovingeconomy,
stableeconomy,andworseningeconomyrespectivelyinhisconservativeinvestment.Inhis
speculativeinvestmentdecision,hisestimatedpayoffvalueis40million,10million,and-30million
underanimprovingeconomy,stableeconomy,andworseningeconomyrespectively.Furthermore,he
estimatedapayoffvalueof-10million,0,and15millioninhiscountercyclicalinvestmentin
improvingeconomy,stableeconomy,andworseningeconomyrespectively.
02/04/2023 DECISION ANALYSIS37

38. REQUIRED
Which investment should Warren make under each of the following
criteria?
1.Maximax
2.Maximin
3. Maximum likelihood criterion
4.Hurwitz Criterionif α= .4
5.Minimaxregret
5.Construct the decision tree
02/04/2023 DECISION ANALYSIS38

39. PAY OFF TABLE FOR REAL ESTATE
INVESTMENT
02/04/2023 DECISION ANALYSIS39
State of Nature
Alternatives
Good Economic
Condition
Poor Economic
Condition
Probability
0.6
Appartement Building 50,000 30,000
Office Building 100,000 -40,000
Warehouse 30,000 10,000

40. RISK ANALYSIS AND SENSITIVITY ANALYSIS
Riskanalysishelpsthedecisionmakerrecognize
thedifferencebetweentheexpectedvalueofa
decisionalternativeandthepayoffthatmayactually
occur.Sensitivityanalysisalsohelpsthedecision
makerbydescribinghowchangesinthestate-of-
natureprobabilitiesand/orchangesinthepayoffs
affecttherecommendeddecisionalternative.
02/04/2023 DECISION ANALYSIS40

41. EXAMPLE
State of Nature
Strong Demand Weak Demand
Alternatives/Prob. P1= .8 P2 = .2
Small Complex (d1) 8 7
Medium Complex (d2) 14 5
Large Complex (d3) 20 -9
02/04/2023 DECISION ANALYSIS41
PAYOFFTABLEFORTHEABCCONDOMINIUMPROJECT
($MILLIONS)

42. RISK ANALYSIS
Adecisionalternativeandastateofnaturecombineto
generatethepayoffassociatedwithadecision.The
riskprofileforadecisionalternativeshowsthe
possiblepayoffsalongwiththeirassociated
probabilities.
02/04/2023 DECISION ANALYSIS42

43. CONT’D
Areviewoftheriskprofileassociatedwithanoptimal
decisionalternativemaycausethedecisionmakerto
chooseanotherdecisionalternativeeventhoughthe
expectedvalueoftheotherdecisionalternativeisnotas
good.
Forexample,theriskprofileforalternative(d2)showsa
0.8probabilityfora$14millionpayoffanda0.2
probabilityfora$5millionpayoff.Becausenoprobability
ofalossisassociatedwithdecisionalternatived2itwould
bejudgedlessriskythand3.Asaresult,adecisionmaker
mightpreferthed2eventhoughithasanexpectedvalue
of$2millionlessthanthed3.
02/04/2023 DECISION ANALYSIS43

44. SENSITIVITY ANALYSIS
SAcanbeusedtodeterminehowchangesinthe
probabilitiesforthestatesofnatureorchangesinthe
payoffsaffecttherecommendeddecisionalternative.
Inmanycases,theprobabilitiesforthestatesof
natureandthepayoffsarebasedonsubjective
assessments.
Sensitivityanalysishelpsthedecisionmaker
understandwhichoftheseinputsarecriticaltothe
choiceofthebestdecisionalternative.
02/04/2023 DECISION ANALYSIS44

45. CONT’D
Oneapproachtosensitivityanalysisistoselect
differentvaluesfortheprobabilitiesofthestatesof
natureandthepayoffsandthenresolvethedecision
analysisproblem.Iftherecommendeddecision
alternativechanges,weknowthatthesolutionis
sensitivetothechangesmade.
02/04/2023 DECISION ANALYSIS45

46. CONT’D
ThebestalternativeforABC,therealstatedeveloper
willselectbasedonEMVisthelargecomplex.
EMV A1: = 0.8(8) + 0.2(7) = 7.8
A2: = 0.8(14) + 0.2(5) = 12.2
A3: = 0.8(20) + 0.2(-9) = 14.2* maximum
Oneapproachtosensitivityanalysisistoselect
differentvaluesfortheprobabilitiesofthestatesof
natureandthepayoffsandthenresolvethedecision
analysisproblem.
02/04/2023 DECISION ANALYSIS46

47. CONT’D
Forthespecialcaseoftwostatesofnature,a
graphicalprocedurecanbeusedtodeterminehow
changesfortheprobabilitiesofthestatesofnature
affecttherecommendeddecisionalternative.
Todemonstratethisprocedure,weletPdenotethe
probabilityofstateofnatureS1;thatis,P(S1)=P.
Withonlytwostatesofnature,theprobabilityofstate
ofnatureS2isP(S2)=1-P(S1)=1-P.
02/04/2023 DECISION ANALYSIS47

48. EXPECTEDVALUEFORTHEABCDECISION
ALTERNATIVESASAFUNCTIONOFP
02/04/2023 DECISION ANALYSIS48

49. CONT’D
Conclusion:decisionalternatived1providesthe
largestexpectedvalueforP≤0.25,decision
alternatived2providesthelargestexpectedvalue
for0.25≤P≤0.70,anddecisionalternatived3
providesthelargestexpectedvalueforP≥0.70.
02/04/2023 DECISION ANALYSIS49

50. COMPUTING BRANCH PROBABILITIES
WITH BAYS' THEOREM
•Allowsprobabilityvaluestoberevisedbasedon
newinformation(fromasurveyortestmarket)
•Priorprobabilitiesaretheprobabilityvaluesbefore
newinformation
•Revisedprobabilitiesareobtainedbycombiningthe
priorprobabilitieswiththenewinformation
02/04/2023 DECISION ANALYSIS50

51. CONT’D
Thestepsusedtodevelopthistableareasfollows:
Step1.Incolumn1enterthestatesofnature.Incolumn2enterthe
priorprobabilitiesforthestatesofnature.Incolumn3enterthe
conditionalprobabilitiesofafavourablemarketresearchreport(F)
giveneachstateofnature.
Step2.Incolumn4computethejointprobabilitiesbymultiplyingthe
priorprobabilityvaluesincolumn2bythecorrespondingconditional
probabilityvaluesincolumn3.
Step3.Sumthejointprobabilitiesincolumn4toobtainthe
probabilityofafavourablemarketresearchreport,P(F).
Step4.Divideeachjointprobabilityincolumn4byP(F)=0.77to
obtaintherevisedorposteriorprobabilities,P(S1/F)andP(S1/F).
02/04/2023 DECISION ANALYSIS51

52. CONT’D
02/04/2023 DECISION ANALYSIS52
IntheABCproblemweassumethatthefollowing
assessmentsareavailablefortheseconditional
probabilities:
Market Research
State of Nature Favourable, FUnfavourable, U
Strong demand, S1P(F/S1)= 0.90P(U/S1)= 0.10
Weak demand, S2P(F/S2)= 0.25P(U/S2)= 0.75

53. CONT’D
BranchProbabilitiesforTheABCCondominiumProjectBased
OnAFavourableMarketResearchReport
02/04/2023 DECISION ANALYSIS53
State of
Nature
Prior
Probabilities
Conditional
Probabilities
Joint
Probabilities
Posterior
Probabilities
Sj P(Sj) P(F/Sj) P(F ∏Sj) P(Sj/F)
S1 0.8 0.90 0.72 0.94
S2 0.2 0.25 0.05 0.06
1 P(F) = 0.77 1
Notethattheprobabilityofobtaininganfavourablemarketresearch
reportisP(F)=0.77.Ifanfavourablereportisobtained,theposterior
probabilityofastrongmarketdemand,S1is0.94andofaweak
marketdemand,S2,is0.06.

54. CONT’D
BranchprobabilitiesfortheABCcondominiumprojectbased
onanunfavourablemarketresearchreport
02/04/2023 DECISION ANALYSIS54
State of
Nature
Prior
Probabilities
Conditional
Probabilities
Joint
Probabilities
Posterior
Probabilities
Sj P(Sj) P(U/Sj) P(U ∏Sj) P(Sj/U)
S1 0.8 0.10 0.08 0.35
S2 0.2 0.75 0.15 0.65
1 P(U) = 0.23 1
Notethattheprobabilityofobtaininganunfavourablemarketresearch
reportisP(U)=0.23.Ifanunfavourablereportisobtained,the
posteriorprobabilityofastrongmarketdemand,S1is0.35andofa
weakmarketdemand,S2,is0.65.

55. DECISION-MAKING WITH UTILITIES
Thusfar,whenapplyingBayes’decisionrule,wehaveassumed
thattheexpectedpayoffinmonetarytermsistheappropriate
measureoftheconsequencesoftakinganaction.However,in
manysituationsthisassumptionisinappropriate.
Thetermutilityisthemeasureofpreferenceforvarious
alternativesintermsofrelativevalueformoney.Theutilityofa
givenalternativeisuniquetotheindividualdecision-makersand
unlikeasimplemonetaryamount,canincorporateintangible
factorsorsubjectivestandardsfromtheirownvaluesystems.
02/04/2023 DECISION ANALYSIS55

56. CONT’D
Theutilityprovidesawayofincorporatingthe
decisionmaker’sattitudetowardriskinarrivingata
decisionandhencemeasuresthetruevalueofan
outcome.
•AnalternativetoEMV
•Peopleviewriskandmoneydifferently,soEMVis
notalwaysthebestcriterion
•Utilitytheoryincorporatesaperson’sattitudetoward
risk
•Autilityfunctionconvertsaperson’sattitudetoward
moneyandrisksintoanumberbetween0and1
02/04/2023 DECISION ANALYSIS56

57. CONT’D
Monetaryvalueisnotalwaysatrueindicatorofthe
overallvalueoftheresultofadecision
TheoverallvalueofadecisioniscalledUTILITY
Rationalpeoplemakedecisionstomaximizetheir
utility
02/04/2023 DECISION ANALYSIS57

58. CONT’D
Utilityassessmentassignstheworstoutcomeautility
of0,andthebestoutcome,autilityof1
Astandardgambleisusedtodetermineutilityvalues
Whenyouareindifferent,theutilityvaluesareequal
02/04/2023 DECISION ANALYSIS58

59. GENERAL PROCEDURES
Step1.Developapayofftableusingmonetaryvalues
Step2.Identifythebestandworstpayoffvaluesinthe
tableandassigneachautility,withU(bestpayoff)>
U(worstpayoff)
Step3.ForeveryothermonetaryvalueMintheoriginal
payofftable,dothefollowingtodetermineitsutility:
a.Definethelotterysuchthatthereisaprobabilitypof
thebestpayoffandaprobability(1-p)oftheworst
payoff
02/04/2023 DECISION ANALYSIS59

60. CONT’D
b.Determinethevalueofpsuchthatthedecisionmakeris
indifferentbetweenaguaranteedpayoffofMandthelottery
definedinstep3(a)
c.CalculatetheutilityofMasfollows:
U(M)=pU(bestpayoff)+(1-p)U(worstpayoff)
Step4.Converteachmonetaryvalueinthepayofftabletoa
utility
Step5.Applytheexpectedutilityapproachtotheutility
tabledevelopedinstep4andselectthedecisionalternative
withthehighestexpectedutility
02/04/2023 DECISION ANALYSIS60

61. EXAMPLE CONT’D
PAYOFF TABLE FOR SWOFFORD, INC.
02/04/2023 DECISION ANALYSIS61
Decision
Alternative
State of Nature
Prices Go Ups S1
P = .3
Prices Stable S2
P = .5
Prices go Down S3
P = .2
Investment A, d1 30000 20000 -50000
Investment B, d2 50000 -20000 -30000
Investment C, d3 0 0 0
EMV A1: = 0.3(30000) + 0.5(20000) + .2(-50,000)= 9000
A2: = 0.3(50000) + 0.5(-20000) + .2(-30,000)= 2000
A3: = 0.3(0) + 0.5(0) + .2(0) = 0

62. CONT’D
Best Payoff = 50, 000 10
Worst Payoff = -50, 000 0
02/04/2023 DECISION ANALYSIS62
Monetary Value Indifference
Value of P
Utility
50,000 Doesn’t apply 10
30,000 .95 9.5
20,000 .90 9
0 .75 7.5
-20,000 .55 5.5
-30,000 .40 4.0
-50,000 Doesn’t apply 0

63. CONT’D
UTILITY TABLE FOR SWOFFORD, INC.
02/04/2023 DECISION ANALYSIS63
Decision
Alternative
State of Nature
Prices Go Ups S1
P = .3
Prices Stable S2
P = .5
Prices go Down S3
P = .2
Investment A, d1 9.5 9.0 0
Investment B, d2 10 5.5 4
Investment C, d3 7.5 7.5 7.5
EU A1: = 0.3(9.5) + 0.5(9) + .2(0)= 7.35
A2: = 0.3(10) + 0.5(5.5) + .2(4)= 6.55
A3: = 0.3(7.5) + 0.5(7.5) + .2(7.5) = 7.5

64. LINKS
https://www.solver.com/
https://treeplan.com/
02/04/2023 DECISION ANALYSIS64

65. END
02/04/2023 DECISION ANALYSIS65