Decision Trees Taha Latest_1

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Outcomes

DisplayingDisplaying a Decision Problema Decision Problem

Decision treesDecision trees

DecisionDecision ttablesables

Alternatives

States of Nature

Decision Problem

BIS 517BIS 517--Asl Sencer ErdemAsl Sencer Erdem


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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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