Homework due next Homework due next Tuesday, September 22Tuesday, September 22

p. 156 # 5-7, 5-8, 5-9p. 156 # 5-7, 5-8, 5-9

Please use complete Please use complete sentences to answer any sentences to answer any

questions and make. Include questions and make. Include any tables you are asked to any tables you are asked to

make.make.

Chapter 5: Decision-making Chapter 5: Decision-making ConceptsConcepts

Quantitative Decision Making with Quantitative Decision Making with Spreadsheet Applications 7Spreadsheet Applications 7thth ed. ed.

By Lapin and WhislerBy Lapin and Whisler

Section 5-7: Decision Tree AnalysisSection 5-7: Decision Tree AnalysisSome slides are from Business Statistics: Some slides are from Business Statistics:

A Decision-Making ApproachA Decision-Making Approach

66thth Edition found at Edition found at www.clt.astate.edu/asyamil/groebner6ed/ppt/ch18ppln.ppt www.clt.astate.edu/asyamil/groebner6ed/ppt/ch18ppln.ppt

The Bayes Decision RuleThe Bayes Decision Rule Takes into account all the information about the Takes into account all the information about the

chances for various payoffs.chances for various payoffs.

EventEvent (level (level of of demandemand)d)

ProbabilitProbabilityy

ActAct (Choice of Movement) (Choice of Movement)

Gears & LeversGears & Levers Spring ActionSpring Action Weights & Weights & PulleysPulleys

PayoffPayoff Payoff Payoff x Probx Prob

PayoffPayoff Payoff Payoff x Probx Prob

PayoffPayoff Payoff Payoff x Probx Prob

LightLight .10.10 $$25,0025,0000

$2500$2500 --$10,00$10,0000

-$1000-$1000 --$125,00$125,0000

--$12,50$12,5000

ModerModerateate

.70.70 400,00400,0000

280,00280,0000

440,0440,00000

308,00308,0000

400,00400,0000

280,0280,00000

HeavyHeavy .20.20 650,00650,0000

130,00130,0000

740,0740,00000

148,00148,0000

750,00750,0000

150,0150,00000

ExpecteExpected d

Payoff:Payoff:

$412,50$412,5000

$455,00$455,0000

$417,50$417,5000

Other Decision CriteriaOther Decision Criteria

Maximin Payoff Criterion – choose Maximin Payoff Criterion – choose the best of the worst outcomes.the best of the worst outcomes.

Maximum Likelihood Criterion – focus Maximum Likelihood Criterion – focus on the most likely event to the on the most likely event to the exclusion of all others.exclusion of all others.

The Criterion of Insufficient Reason – The Criterion of Insufficient Reason – every event has the same every event has the same probability.probability.

Table vs. TreeTable vs. Tree

Payoff table: simple decisionsPayoff table: simple decisions Decisions made at different points in Decisions made at different points in

time with uncertain events occurring time with uncertain events occurring between decisions.between decisions.

Tree gives more flexibility.Tree gives more flexibility. Tree shows every possible course of Tree shows every possible course of

action and all possible outcomes.action and all possible outcomes.

Decision TreeDecision Tree

AA decision tree decision tree is a picture of all the is a picture of all the possible courses of action and the possible courses of action and the consequent possible outcomes. consequent possible outcomes. A box is used to indicate the point at A box is used to indicate the point at

which a decision must be made, which a decision must be made, The branches going out from the box The branches going out from the box

indicate the alternatives under indicate the alternatives under considerationconsideration

A circle represents an event (usually has A circle represents an event (usually has a probability)a probability)

The branches going out from the circle The branches going out from the circle represent outcomes of the event.represent outcomes of the event.

Sample Decision TreeSample Decision Tree

Large factory

Small factory

Average factory

Strong Economy

Stable Economy

Weak Economy

Strong Economy

Stable Economy

Weak Economy

Strong Economy

Stable Economy

Weak Economy

Add Probabilities and Add Probabilities and PayoffsPayoffs

Large factory

Small factory

Decision

Average factory

Uncertain Events(States of Nature)

Strong Economy

Stable Economy

Weak Economy

Strong Economy

Stable Economy

Weak Economy

Strong Economy

Stable Economy

Weak Economy

(continued)

PayoffsProbabilities

200

50

-120

40

30

20

90

120

-30

(.3)

(.5)

(.2)

(.3)

(.5)

(.2)

(.3)

(.5)

(.2)

Decision Tree AnalysisDecision Tree Analysis Each node is evaluated in terms of its Each node is evaluated in terms of its

expected payoff.expected payoff. Event forksEvent forks: expected payoffs are computed.: expected payoffs are computed. Act forksAct forks: the greatest value is brought back.: the greatest value is brought back.

The decision tree is The decision tree is folded backfolded back by by maximizing expected payoff.maximizing expected payoff. Inferior acts are Inferior acts are prunedpruned from the tree. from the tree. The pruned tree indicates the The pruned tree indicates the best course of best course of

actionaction, the one maximizing expected payoff. , the one maximizing expected payoff. The process works backward in time.The process works backward in time.

Fold Back the TreeFold Back the Tree

Large factory

Small factory

Average factory

Strong Economy

Stable Economy

Weak Economy

Strong Economy

Stable Economy

Weak Economy

Strong Economy

Stable Economy

Weak Economy

200

50

-120

40

30

20

90

120

-30

(.3)

(.5)

(.2)

(.3)

(.5)

(.2)

(.3)

(.2)

EV=200(.3)+50(.5)+(-120)(.2)=61

EV=90(.3)+120(.5)+(-30)(.2)=81

EV=40(.3)+30(.5)+20(.2)=31

(.5)

Make the DecisionMake the Decision

Large factory

Small factory

Average factory

Strong Economy

Stable Economy

Weak Economy

Strong Economy

Stable Economy

Weak Economy

Strong Economy

Stable Economy

Weak Economy

200

50

-120

40

30

20

90

120

-30

(.3)

(.5)

(.2)

(.3)

(.5)

(.2)

(.3)

(.5)

(.2)

EV=61

EV=81

EV=31

Maximum

EV=81