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Outcomes
DisplayingDisplaying a Decision Problema Decision Problem
Decision treesDecision trees
DecisionDecision ttablesables
Alternatives
States of Nature
Decision Problem
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TTypes ofypes of DDecisionecision MModelsodels
Decision making underDecision making under uncertaintyuncertainty
Decision making underDecision making under riskrisk
Decision making underDecision making under certaintycertainty
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Fundamentals of Decision TheoryFundamentals of Decision Theory
TermsTerms:: ternat veternat ve: course o act on or c o ce: course o act on or c o ce
State of natureState of nature: an occurrence over: an occurrence overwhich the decision maker has no controlwhich the decision maker has no control
Symbols used inSymbols used in aa decision treedecision tree::
alternatives may be selectedalternatives may be selected
AAstate of nature nodestate of nature node out of which oneout of which onestate of nature will occurstate of nature will occur
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Getz Products Decision TreeGetz Products Decision Tree
Favorable market
1
2
Unfavorable market
Favorable market
Construct
small plant
A decision node
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Expected Monetary ValueExpected Monetary Value
N:N: Number of states of natureNumber of states of nature
N
k: Number of alternative decisionsk: Number of alternative decisionsXij: Value of Payoff for alternative iin stateof naturej, i=1,2,...,k and j=1,2,...,N.Pj: Probability of state of naturej
j jiji 1
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Example:Example:
a es o a ureAlternatives Favorable
MarketP(0.5)
UnfavorableMarket P(0.5)
Expectedvalue
Construct $200,000 -$180,000 $10,000
Construct -
large plant
small plant, , ,
Do nothing $0 $0 $0
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Example:Example: Expected Value ofExpected Value ofPerfect InformationPerfect Information
State of N ature
Alternative Favorable Unfavorable
Construct alarge plant
Construct asmall plant
200,000 -$180,000
Market ($) Market ($)
$40,000$100,000 -$20,000
$10,000
Probabilities
o no ng
0.50 0.50
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Expected Value of PerfectExpected Value of PerfectInformationInformation
Expected Value Under CertaintyExpected Value Under Certainty==(($200,000*0.50 + 0*0.50$200,000*0.50 + 0*0.50)= $100,000)= $100,000
MMax(ax(EMVEMV))= Max{10,000, 40,000, 0}=$40,000= Max{10,000, 40,000, 0}=$40,000
EVPIEVPI == EExpectedxpected VValuealue Under CertaintyUnder Certainty -- MMax(ax(EMEM== ,, -- ,,
= $60,000= $60,000
So Getz should not be willing to pay more than $60,00
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Graphical display of decision processGraphical display of decision process, i.e., alternativ, i.e., alternative
Decision TreesDecision Trees
, , ., , .
Decision tables are convenient forDecision tables are convenient for problemsproblems
wwith one set of alternatives and states ofith one set of alternatives and states of naturenature..
With several sets of alternatives and states of natureWith several sets of alternatives and states of nature(sequential decisions), decision(sequential decisions), decision trees aretrees are usedused!!
decision tree analysis.decision tree analysis.
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Softwares for Decision TreeSoftwares for Decision TreeAnalysisAnalysis
DPLDPL
Tree PlanTree Plan
SupertreeSupertree
Analysis with less effort.Analysis with less effort.Full color presentations for managersFull color presentations for managers
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Steps ofSteps of Decision TreeDecision Tree AnalysisAnalysis
Define the problemDefine the problem Structure or draw the decision treeStructure or draw the decision tree
Assign probabilities to the states of natureAssign probabilities to the states of nature
Estimate payoffs for each possibleEstimate payoffs for each possiblecombination of alternatives and states ofcombination of alternatives and states ofnaturenature
monetary values for each statemonetary values for each state--ofof--naturenaturenodenode
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Decision TreeDecision Tree
State 1 1
2
State 2
State 1
u comeu come
Outcome 2Outcome 2
Outcome 3Outcome 3
DecisionNode
Outcome 4Outcome 4
State of Nature Node
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Ex1:Ex1:Getz Products Decision TreeGetz Products Decision Tree
Payoffs
Favorable market (0.5)
EMV for node 1 = $10,000
,
-$180,000
$100,000
-
1
2Unfavorable market 0.5
Unfavorable market (0.5)
Favorable market (0.5)
Construct
small plant ,
0
EMV for node 2 = $40,000
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A More Complex Decision TreeA More Complex Decision Tree
Lets say Getz Products has twoLets say Getz Products has twosequential decisions to make:sequential decisions to make:
Conduct a survey for $10000?Conduct a survey for $10000?
Build a large or small plant or notBuild a large or small plant or notbuild?build?
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Ex1:Ex1:Getz Products Decision TreeGetz Products Decision Tree
00
2 -
Fav. Mkt (0.78)
Unfav. Mkt (0.22)
$106,4001st decision
point
2nd decision point
14
00
$106,
4
$2
,400
3
5
Fav. Mkt (0.78)
Fav. Mkt (0.27)
Fav. Mkt (0.27)
Unfav. Mkt (0.22)
Unfav. Mkt (0.73)
Unfav. Mkt (0.73)
$63,600
-$87,400
$2,400
$49,200
7
$49,
2
$40,
000
6Fav. Mkt (0.5)
Fav. Mkt (0.5)
Unfav. Mkt (0.5)
Unfav. Mkt (0.5)
$10,000
$40,000
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Resulting DecisionResulting Decision
EMV of conducting the survey=$49,200EMV of conducting the survey=$49,200
EMV of not conducting the survey=$40,00EMV of not conducting the survey=$40,00
So Getz should conduct the survey!So Getz should conduct the survey!
If the survey results are favourable, buildIf the survey results are favourable, buildlarge plant.large plant.
If the survey results are infavourable, buildIf the survey results are infavourable, buildsma p ant.sma p ant.
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Ex2: Ponderosa Record CompanyEx2: Ponderosa Record Company
Decide whether or not to market theDecide whether or not to market therecordings of a rock group.recordings of a rock group.
Alternative1: test market 5000 unitsAlternative1: test market 5000 unitsand if favorable, market 45000 unitsand if favorable, market 45000 unitsnationallynationally
nationallynationally
Outcome is a complete success (allOutcome is a complete success (allare sold) or failureare sold) or failure
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Ex2: PonderosaEx2: Ponderosa--costs, pricescosts, prices
Fixed payment to group: $5000Fixed payment to group: $5000
.. Handling, distribution: $0.25/cdHandling, distribution: $0.25/cd
Price of a cd: $2/cdPrice of a cd: $2/cd
Cost of producing 5,000 cdsCost of producing 5,000 cds=5,000+5,000+(0.25+0.75)5,000=$15,000=5,000+5,000+(0.25+0.75)5,000=$15,000
Cost of producing 45,000 cdsCost of producing 45,000 cds=0+5,000+ 0.25+0.75 45,000= 50,000=0+5,000+ 0.25+0.75 45,000= 50,000
Cost of producing 50,000 cdsCost of producing 50,000 cds
=5,000+5,000+(0.25+0.75)50,000=$60,000=5,000+5,000+(0.25+0.75)50,000=$60,000
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Ex2: PonderosaEx2: Ponderosa--Event ProbabilitiesEvent Probabilities
Without testing P(success)=P(failure)=0.5Without testing P(success)=P(failure)=0.5
With testingWith testing
P(success|test result is favorable)=0.8P(success|test result is favorable)=0.8
P(failure|test result is favorable)=0.2P(failure|test result is favorable)=0.2
..
P(failure|test result is unfavorable)=0.8P(failure|test result is unfavorable)=0.8
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Decision Tree for Ponderosa RecordDecision Tree for Ponderosa RecordCompanyCompany
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Backward ApproachBackward Approach
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Optimal Decision PolicyOptimal Decision Policy
Precision Tree provides excell addPrecision Tree provides excell add--ins.ins.
Test marketTest market
If the market is favorable, market nationallyIf the market is favorable, market nationally
Else, abortElse, abort
Risk ProfileRisk Profile
. .. .
$35,000 with probability 0.4$35,000 with probability 0.4
--$55,000 with probability 0.1$55,000 with probability 0.1
--$15,000 with probability 0.5$15,000 with probability 0.5
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Application Areas of DecisionApplication Areas of DecisionTheoryTheory
Investments inInvestments in
research and developmentresearch and development
plant and equipmentplant and equipment
new buildings and structuresnew buildings and structures
Production and Inventory controlProduction and Inventory control
MaintenanceMaintenance
Scheduling, etc.Scheduling, etc.
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ReferencesReferences
Lapin L.L., Whisler W.D., Quantitative Decision Making, 7e,Lapin L.L., Whisler W.D., Quantitative Decision Making, 7e,2002.2002.
Heizer J., Render, B., Operations Management, 7e, 2004.Heizer J., Render, B., Operations Management, 7e, 2004.
Render, B., Stair R. M., Quantitative Analysis forRender, B., Stair R. M., Quantitative Analysis forManagement, 8e, 2003.Management, 8e, 2003.
Anderson,Anderson, DD..RR..,, SweeneySweeney DD..J,J, WilliamsWilliams TT..AA..,, StatisticsStatisticsBusinessBusiness andand Economics,Economics, 88ee,, 20022002..
Taha,Taha, HH..,, OperationsOperations Research,Research, 19971997..
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