Taylor Introms10 Ppt 12

7/30/2019 Taylor Introms10 Ppt 12

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12-1Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall

Decision Analysis

Chapter 12


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Components of Decision Making

Decision Making without Probabilities

Decision Making with Probabilities

Decision Analysis with Additional Information

Utility

Chapter Topics

Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall


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Table 12.1 Payoff Table

A state of nature is an actual eventthat may occur in the future.

Apayoff tableis a means of organizing a decision situation,

presenting the payoffs from different decisions given the various

states of nature.

Decision Analysis

Components of Decision Making



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Decision Analysis

Decision Making Without Probabilities


Figure 12.1


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Decision-Making Criteria

maximax maximin minimax

minimax regret Hurwicz equal likelihood

Decision Analysis


Table 12.2



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Table 12.3 Payoff Table Illustrating a Maximax Decision

In themaximaxcriterionthe decision maker selects the decision

that will result in the maximum of maximum payoffs; anoptimisticcriterion.


Maximax Criterion



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Table 12.4 Payoff Table Illustrating a Maximin Decision

In the maximincriterion the decision maker selects the decision

that will reflect the maximum of the minimumpayoffs; a

pessimisticcriterion.


Maximin Criterion



8/6112-8Table 12.6 Regret Table Illustrating the Minimax Regret Decision

Regretis the difference between the payoff from the best

decision and all other decision payoffs.

The decision maker attempts to avoid regretby selecting the

decision alternative that minimizes the maximum regret.


Minimax Regret Criterion



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TheHurwiczcriterion is a compromise between the maximaxand maximin criterion.

Acoefficient of optimism, , is a measure of the decisionmakers optimism.

The Hurwicz criterion multiplies the best payoff by and theworst payoff by 1- ., for each decision, and the best result isselected.

Decision Values

Apartment building $50,000(.4) + 30,000(.6) = 38,000

Office building $100,000(.4) - 40,000(.6) = 16,000

Warehouse $30,000(.4) + 10,000(.6) = 18,000


Hurwicz Criterion



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The equal likelihood( or Laplace) criterion multiplies thedecision payoff for each state of nature by an equal weight, thus

assuming that the states of nature are equally likelyto occur.

Decision Values

Apartment building $50,000(.5) + 30,000(.5) = 40,000

Office building $100,000(.5) - 40,000(.5) = 30,000

Warehouse $30,000(.5) + 10,000(.5) = 20,000


Equal Likelihood Criterion



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Adominantdecision is one that has a better payoff than anotherdecision under each state of nature.

The appropriate criterion is dependent on the risk personality

and philosophy of the decision maker.

Criterion Decision (Purchase)

Maximax Office building

Maximin Apartment building

Minimax regret Apartment buildingHurwicz Apartment building

Equal likelihood Apartment building


Summary of Criteria Results



12/6112-12Exhibit 12.1


Solution with QM for Windows (1 of 3)



13/6112-13Exhibit 12.2





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Exhibit 12.3





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Solution with Excel

Exhibit 12.4Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall


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Expected valueis computed by multiplying each decision

outcome under each state of nature by the probability of itsoccurrence.

EV(Apartment) = $50,000(.6) + 30,000(.4) = 42,000

EV(Office) = $100,000(.6) - 40,000(.4) = 44,000

EV(Warehouse) = $30,000(.6) + 10,000(.4) = 22,000

Table 12.7


Expected Value



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The expected opportunity lossis the expected value of the

regret for each decision. The expected value and expected opportunity loss criterion

result in the same decision.

EOL(Apartment) = $50,000(.6) + 0(.4) = 30,000EOL(Office) = $0(.6) + 70,000(.4) = 28,000EOL(Warehouse) = $70,000(.6) + 20,000(.4) = 50,000

Table 12.8


Expected Opportunity Loss



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Exhibit 12.5

Expected Value Problems

Solution with QM for Windows



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Exhibit 12.6


Solution with Excel and Excel QM (1 of 2)



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Solution with Excel and Excel QM (2 of 2)

Copyright 2010 Pearson Education, Inc. Publishing as Prentice HallExhibit 12.7

D i i ki i h P b bili i


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The expected value of perfect information (EVPI) is the

maximum amount a decision maker would payfor additional

information.

EVPI equals the expected value given perfect information

minus the expected value without perfect information.

EVPI equals the expected opportunity loss (EOL) for the best

decision.


Expected Value of Perfect Information


D i i M ki i h P b bili i


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Table 12.9 Payoff Table with Decisions, Given Perfect Information


EVPI Example (1 of 2)




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Decision with perfect information:

$100,000(.60) + 30,000(.40) = $72,000

Decision without perfect information:EV(office) = $100,000(.60) - 40,000(.40) = $44,000

EVPI = $72,000 - 44,000 = $28,000EOL(office) = $0(.60) + 70,000(.4) = $28,000


EVPI Example (2 of 2)




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Exhibit 12.8


EVPI with QM for Windows




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A decision tree is a diagram consisting of decision nodes

(represented as squares), probability nodes (circles), and

decision alternatives (branches).

Table 12.10 Payoff Table for Real Estate Investment Example


Decision Trees (1 of 4)




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Figure 12.2 Decision Tree for Real Estate Investment Example






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The expected value is computed at each probability node:

EV(node 2) = .60($50,000) + .40(30,000) = $42,000

EV(node 3) = .60($100,000) + .40(-40,000) = $44,000

EV(node 4) = .60($30,000) + .40(10,000) = $22,000

Branches with the greatest expected value are selected.




D i i M ki ith P b biliti


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Figure 12.3 Decision Tree with Expected Value at Probability Nodes






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12-29Exhibit 12.9


Decision Trees with QM for Windows




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Decision Trees with Excel and TreePlan (1 of 4)


Exhibit 12.10

D i i n M kin ith Pr b biliti


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12-31Exhibit 12.11




Decision Making ith Probabilities


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12-32Exhibit 12.12






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12-33Exhibit 12.13






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Sequential Decision Trees (1 of 4)

Asequential decision treeis used to illustrate a situationrequiring a series of decisions.

Used where a payoff table, limited to a single decision, cannot

be used.

Real estate investment example modified to encompass a ten-

year period in which several decisions must be made:




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Figure 12.4 Sequential Decision Tree






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Decision is to purchase land; highest net expected value

($1,160,000).

Payoff of the decision is $1,160,000.




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12-37Figure 12.5 Sequential Decision Tree with Nodal Expected Values




Sequential Decision Tree Analysis


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Exhibit 12.14


Solution with QM for Windows




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12-39Exhibit 12.15


Solution with Excel and TreePlan




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Bayesian analysis uses additional information to alter the

marginal probability of the occurrence of an event. In real estate investment example, using expected value

criterion, best decision was to purchase office building withexpected value of $444,000, and EVPI of $28,000.

Table 12.11


Bayesian Analysis (1 of 3)




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Aconditional probabilityis the probability that an event willoccur given that another event has already occurred.

Economic analyst provides additional information for real estate

investment decision, forming conditional probabilities:

g = good economic conditionsp = poor economic conditions

P = positive economic report

N = negative economic report

P(P g) = .80 P(N G) = .20

P(P p) = .10 P(N p) = .90






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Aposterior probabilityis the altered marginal probabilityof anevent based on additional information.

Prior probabilities for good or poor economic conditions in real

estate decision:

P(g) = .60; P(p) = .40 Posterior probabilities by Bayes rule:

(g P) = P(P G)P(g)/[P(P g)P(g) + P(P p)P(p)]

= (.80)(.60)/[(.80)(.60) + (.10)(.40)] = .923 Posterior (revised) probabilities for decision:

P(g N) = .250 P(p P) = .077 P(p N) = .750






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Decision Trees with Posterior Probabilities (1 of 4)

Decision tree with posterior probabilities differ from earlierversions in that:

Two new branches at beginning of tree represent report

outcomes.

Probabilities of each state of nature are posterior

probabilities from Bayes rule.




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Figure 12.6 Decision Tree with Posterior Probabilities






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EV (apartment building) = $50,000(.923) + 30,000(.077)

= $48,460

EV (strategy) = $89,220(.52) + 35,000(.48) = $63,194




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Figure 12.7 Decision Tree Analysis






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Table 12.12 Computation of Posterior Probabilities


Computing Posterior Probabilities with Tables




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Computing Posterior Probabilities with Excel

Exhibit 12.16




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The expected value of sample information(EVSI) is the

difference between the expected value with and without

information:

For example problem, EVSI = $63,194 - 44,000 = $19,194

The efficiencyof sample information is the ratio of the

expected value of sample information to the expected value of

perfect information:

efficiency = EVSI /EVPI = $19,194/ 28,000 = .68


Expected Value of Sample Information




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Table 12.13 Payoff Table for Auto Insurance Example


Utility (1 of 2)




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Expected Cost (insurance) = .992($500) + .008(500) = $500Expected Cost (no insurance) = .992($0) + .008(10,000) = $80

Decision should be do notpurchase insurance, but people

almost always dopurchase insurance.

Utility is a measureof personal satisfaction derived from money.

Utiles are unitsof subjective measures of utility.

Risk avertersforgo a high expected value to avoid a low-

probability disaster. Risk takerstake a chance for a bonanza on a very low-

probability event in lieu of a sure thing.

ec s on nalys s w th dd t onal n o at on

Utility (2 of 2)


Decision Analysis


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States of Nature

DecisionGood Foreign Competitive

ConditionsPoor Foreign Competitive

Conditions

ExpandMaintain Status Quo

Sell now

$ 800,0001,300,000

320,000

$ 500,000-150,000

320,000

y

Example Problem Solution (1 of 9)


Decision Analysis


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y


a. Determine the best decision without probabilities using the 5criteria of the chapter.

b. Determine best decision with probabilities assuming .70

probability of good conditions, .30 of poor conditions. Use

expected value and expected opportunity loss criteria.

c. Compute expected value of perfect information.

d. Develop a decision tree with expected value at the nodes.

e. Given following, P(P g) = .70, P(N g) = .30, P(P p) = 20,

P(N p) = .80, determine posterior probabilities using Bayesrule.

f. Perform a decision tree analysis using the posterior probability

obtained in part e.


Decision Analysis


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Step 1 (part a): Determine decisions without probabilities.Maximax Decision: Maintain status quo

Decisions Maximum Payoffs

Expand $800,000

Status quo 1,300,000 (maximum)Sell 320,000

Maximin Decision: Expand

Decisions Minimum Payoffs

Expand $500,000 (maximum)

Status quo -150,000

Sell 320,000

y



Decision Analysis


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Minimax Regret Decision: ExpandDecisions Maximum Regrets

Expand $500,000 (minimum)

Status quo 650,000

Sell 980,000

Hurwicz ( = .3) Decision: Expand

Expand $800,000(.3) + 500,000(.7) = $590,000

Status quo $1,300,000(.3) - 150,000(.7) = $285,000

Sell $320,000(.3) + 320,000(.7) = $320,000

y



Decision Analysis


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Equal Likelihood Decision: ExpandExpand $800,000(.5) + 500,000(.5) = $650,000

Status quo $1,300,000(.5) - 150,000(.5) = $575,000

Sell $320,000(.5) + 320,000(.5) = $320,000

Step 2 (part b): Determine Decisions with EV and EOL.

Expected value decision: Maintain status quo

Expand $800,000(.7) + 500,000(.3) = $710,000

Status quo $1,300,000(.7) - 150,000(.3) = $865,000

Sell $320,000(.7) + 320,000(.3) = $320,000

y



Decision Analysis


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Expected opportunity loss decision: Maintain status quoExpand $500,000(.7) + 0(.3) = $350,000

Status quo 0(.7) + 650,000(.3) = $195,000

Sell $980,000(.7) + 180,000(.3) = $740,000

Step 3 (part c): Compute EVPI.

EV given perfect information = 1,300,000(.7) + 500,000(.3) =

$1,060,000

EV without perfect information = $1,300,000(.7) - 150,000(.3) =$865,000

EVPI = $1.060,000 - 865,000 = $195,000

y



Decision Analysis


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Step 4 (part d): Develop a decision tree.

y



Decision Analysis


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Step 5 (part e): Determine posterior probabilities.P(g P) = P(P g)P(g)/[P(P g)P(g) + P(P p)P(p)]

= (.70)(.70)/[(.70)(.70) + (.20)(.30)] = .891

P(p P) = .109

P(g N) = P(N g)P(g)/[P(N g)P(g) + P(N p)P(p)]

= (.30)(.70)/[(.30)(.70) + (.80)(.30)] = .467

P(p N) = .533

y



Decision Analysis


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Step 6 (part f): Decision tree analysis.

y




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Taylor Introms10 Ppt 12