Decision Theory Ppt(Mba3)2011

© 2008 Prentice Hall, Inc. A – 1

OperationsResearchOperationsResearch Decision-Making Decision-Making Theory and ToolsTheory and Tools


OutlineThe Decision Process in OperationsFundamentals of Decision MakingDecision Tables

Decision Making under UncertaintyDecision Making Under RiskDecision Making under CertaintyExpected Value of Perfect Information (EVPI)

Decision TreesA More Complex Decision Tree

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Decision analysisDecision analysis allows us to select a decision from a set of

possible decision alternatives when uncertainties regarding the

future exist.

The goal is to optimize the resulting payoff in terms of a decision

criterion. For evaluating and choosing among alternatives

Considers all the possible alternatives and possible outcomes


6.1 Introduction to Decision AnalysisMaximizing expected profit is

a common criterion when

probabilities can be assessed.

4

• Maximizing the decision

maker’s utility function is the

mechanism used when risk is

factored into the decision

making process.


Decision Making.Decisions are processes by which a manager seeks to

achieve some desired state. They are means rather than ends. Making a decision involves making a choice between the alternatives. Decisions could be a) engineering or scientific or b) management

Decision making is the sequential process of thought and deliberation that results in a decision.

The process of decision making is same in both the types of decisions and involves a) defining the problem b) gathering facts related to the problem c) comparing these with right or wrong criteria based on knowledge and experience and then taking the best course of action

Management decision making a more of an art than a science.


Management decisions are tough because management problems are wider in scope and they are related to human behavior which is most unpredictable.

Management decisions could be either a) programmed or b) Non programmed.

While Programmed decisions are repetitive and routine in nature and provide solutions to structured problems the Non programmed decisions are of non routine or unique in nature and attempt to provide solutions to complex and unstructured problems Top Broad, unstructured, infrequent, uncertaintyTop Broad, unstructured, infrequent, uncertainty

Middle Both structured and unstructured Middle Both structured and unstructured Lower Frequent, structured, repetitive,Lower Frequent, structured, repetitive, routine, certainty routine, certainty

Programmed decisionsProgrammed decisions

Un Programmed decisionsUn Programmed decisions

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Decision theory is an area of study of discrete mathematics, related to and of interest to practitioners in all branches of science, engineeringand in all human social activities.

It is concerned with how real or ideal decision-makers make or should make decisions, and how optimal decisions can be reached.


The decision processa

Identify & defineIdentify & defineThe problemThe problem

Develop Develop alternativesalternatives

Evaluate Evaluate alternativesalternatives

Select Select alternativesalternatives

Evaluate Evaluate & control& control

Implement Implement decisiondecision

Certainty Risk Certainty Risk UncertaintyUncertainty

GatherGather InformationInformation

Re

vis

eR

ev

ise


PowerPoint presentation to PowerPoint presentation to accompany Operations accompany Operations Management, 6E (Heizer & Management, 6E (Heizer & Render)Render)

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ProblemProblem DecisionDecision

Quantitative Quantitative AnalysisAnalysis

LogicLogicHistorical DataHistorical DataMarketing ResearchMarketing ResearchScientific AnalysisScientific AnalysisModelingModeling

Qualitative AnalysisQualitative Analysis

EmotionsEmotionsIntuitionIntuitionPersonal ExperiencePersonal Experience and Motivationand MotivationRumorsRumors


The Decision Process in The Decision Process in OperationsOperations

1.1. Clearly define the problems and the Clearly define the problems and the factors that influence itfactors that influence it

2.2. Develop specific and measurable Develop specific and measurable objectivesobjectives

3.3. Develop a modelDevelop a model

4.4. Evaluate each alternative solutionEvaluate each alternative solution

5.5. Select the best alternativeSelect the best alternative

6.6. Implement the decision and set a Implement the decision and set a timetable for completiontimetable for completion


AdvantagesAre less expensive and disruptive than

experimenting with the real world systemAllow operations managers to ask “What if”

types of questionsAre built for management problems and

encourage management inputForce a consistent and systematic approach to

the analysis of problemsRequire managers to be specific about

constraints and goals relating to a problemHelp reduce the time needed in decision

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Limitations of ModelsTheymay be expensive and time-consuming to

develop and testare often misused and misunderstood (and

feared) because of their mathematical and logical complexity

tend to downplay the role and value of non quantifiable information

often have assumptions that oversimplify the variables of the real world

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Factors influencing decision makingIndividual differences influence the decision making

process. The four individual differences which have a significant impact of the decision making process are

1. Values: Values are the guidelines that a person uses when confronted with a situation in which a choice has to be made. Values are acquired early in life and are a basic part of individual’s thought. Value judgment is involved at every stage in the process of decision making. They are reflected in the decision maker’s behavior before making the decision, in making the decision and in putting the decision into effect.

2. Personality : Decision makers are influenced by many psychological forces both conscious and subconscious. These are strongly reflected in decision making under uncertainty. Personality traits of the decision maker combine with situational and interact ional variables influence the decision making process..


3. Propensity for risk : (Risk taking capacity ) This is a specific aspect of personality which strongly influences the process of making decision.

4. Potential for dissonance : Traditionally researchers have focused much of their attention on the forces and influences on the decision maker before a decision is made.

Utility of the alternatives is the criterion for decision making. Value of the decision is dependent on the utility. Recently Behavioral scientists have focused their attention on post decision anxiety or cognitive dissonance experienced by the decision maker. Such anxiety is related to lack of consistency or harmony among individual’s various cognitions (attitudes, beliefs and so on) Individuals are likely to use one or more of the following to reduce their dissonancea. Seek information that supports their decision.b. selectively perceive information that supports the decision c. adopt a less favorable view of the foregone alternatives.d. Exaggerate the importance of positive aspects of the decision


Fundamentals of Fundamentals of Decision MakingDecision Making

1.1. Terms:Terms:

a.a. AlternativeAlternative – a – a course of action or course of action or strategy that may be chosen by the strategy that may be chosen by the decision makerdecision maker

b.b. State of nature – an occurrence or State of nature – an occurrence or a situation over which the decision a situation over which the decision maker has little or no controlmaker has little or no control


Decision Table

A-A-1616

States of NatureStates of Nature

AlternativesAlternatives State 1State 1 State 2State 2

Alternative 1Alternative 1 Outcome 1Outcome 1 Outcome 2Outcome 2

Alternative 2Alternative 2 Outcome 3Outcome 3 Outcome 4Outcome 4


6.2 Payoff Table AnalysisPayoff Tables

Payoff table analysis can be applied when: There is a finite set of discrete decision alternatives. The outcome of a decision is a function of a single future

event.

In a Payoff table - The rows correspond to the possible decision alternatives. The columns correspond to the possible future events. Events (states of nature) are mutually exclusive and

collectively exhaustive. The table entries are the payoffs.

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Fundamentals of Fundamentals of Decision MakingDecision Making

2.2. Symbols used in a decision tree:Symbols used in a decision tree:

.a.a – – decision node from which one decision node from which one of several alternatives may be of several alternatives may be selected selected

.b.b – – a state-of-nature node out of a state-of-nature node out of which one state of nature will occurwhich one state of nature will occur


Decisions under uncertainty3. Uncertainty : The decision maker (dm)

has absolutely no knowledge of the probability of outcome of each alternative.

When no information exists the personality characteristics of the decision maker become more important for determining which decision is made. The following five characteristics describe what most of the dm’s do.

a. Optimistic Decisionsb. Pessimistic Decisionsc. Realistic decisions.d. Regret minimizing Decisions.e. Insufficient Reasoner


2.Decision making under risk:-2.Decision making under risk:-The decision maker has some probabilistic estimate of the outcome of each decision. Condition of risk occurs when the decision maker has enough information to allow the use of probability in evaluating the alternatives. Probability of occurrence of an is event is the expectancy of event happening.

Several states of nature may occurSeveral states of nature may occur

Each has a probability of occurringEach has a probability of occurring


Decisions with risk Probability can be assigned based ona. Logic or deduction: This is Objective

probability. This reflects the historical evidence. Ex. Getting head/tail for a tossed coin. Or getting a number on rolling dice etc.

b. Past experience is with empirical evidence.c. Subjective estimate due to intelligence or

intuition.When the decision maker has access to

probability information, the criterion for decision making is to maximize s the expected value of the decision.


Decision Making Under CertaintyThe consequence of every alternative is

knownUsually there is only one outcome for each

alternative

• State of nature is known, The decision maker has a complete knowledge of the outcome of each alternative.

• This seldom occurs in reality


Decision Making Under Uncertainty - The Maximin Criterion

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Decision Making Under Uncertainty

Probabilities of the possible outcomes are not known

Decision making methods:1. Maximax2. Maximin3. Criterion of realism/The hurwiczcriterion4. Equally likely/Criterion of rationality./the

laplace criterion5. Minimax regret/The savage criterion


Decision Making Under UncertaintyMaximax - Choose the alternative that

maximizes the maximum outcome for every alternative (Optimistic criterion)

Maximin - Choose the alternative that maximizes the minimum outcome for every alternative (Pessimistic criterion)

Equally likely or Criterion of rationality/laplace criterion - chose the alternative with the highest average outcome.

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Decision Making Under Uncertainty

4.The hurwitz criterion/Criterion of realism:this criterion represents that the decision

making should not be done by completely optimistic or completely pessimistic and it is a mixture of both.It introduced the cofficient of optimism to measure the degree of optimisim.It is represented by aplha(α)which lies b/w 0 and 1.This coefficient ranges from complete pessimistic (0) to complete optimistic(1) attitude about future.


Decision Making Under Uncertainty5.The savage criterion/Minimax regret:-It is based on the opportunity loss concept,

which selects the course of actions that minimizes the maximum regret. It is also known as minimax regret because after taking wrong alternative decision, which results loss,the decision maker feels regret.


Criteria of Decision makinga. Optimistic Decisions The DM think optimistically

about the event that influence decisions. They choose the alternative that maximizes the outcome

b. Pessimistic Decisions They believe that worst possible outcome will occur no matter what they do. They estimate the worst outcomes associated with each alternative and select the best of these worst outcomes.

c. Realistic Decisions. They take the middle path neither optimistic nor pessimistic.

d. Regret minimizing Decisions. They want to minimize the dissonance they experience after the fact.

e. Insufficient Reason Decisions. These are also

called eqi-probable decision maker. They assume that all the possible outcomes have equal chance of occurring.


Example - Decision Making Under UncertaintyA firm has two options for expanding production of a A firm has two options for expanding production of a product: (1) construct a large plant; or (2) construct a small product: (1) construct a large plant; or (2) construct a small plant. Whether or not the firm expands, the future market for plant. Whether or not the firm expands, the future market for the product will be either favorable or unfavorable. the product will be either favorable or unfavorable.

If a large plant is constructed and the market is favorable, If a large plant is constructed and the market is favorable, then the result is a profit of $200,000. If a large plant is then the result is a profit of $200,000. If a large plant is constructed and the market is unfavorable, then the result is constructed and the market is unfavorable, then the result is a loss of $180,000. a loss of $180,000.

If a small plant is constructed and the market is favorable, If a small plant is constructed and the market is favorable, then the result is a profit of $100,000. If a small plant is then the result is a profit of $100,000. If a small plant is constructed and the market is unfavorable, then the result is constructed and the market is unfavorable, then the result is a loss of $20,000. Of course, the firm may also choose to “do a loss of $20,000. Of course, the firm may also choose to “do nothing”, which produces no profit or loss.nothing”, which produces no profit or loss.


Example - Maximax

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States of NatureStates of NatureAlternativesAlternativesFavorableFavorable

MarketMarketUnfavorableUnfavorable

MarketMarketConstructConstructlarge plantlarge plant

$200,000$200,000 -$180,000-$180,000

ConstructConstructsmall plantsmall plant

$100,000$100,000 -$20,000-$20,000

$0$0 $0$0Do Do nothingnothing

Maximax decision is to construct large plant.Maximax decision is to construct large plant.


Example - Maximin

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MinimumMinimumin Rowin Row

-$180,000-$180,000

-$20,000-$20,000

$0$0

Maximin decision is to do nothing.Maximin decision is to do nothing.

(Maximum of minimums for each alternative)(Maximum of minimums for each alternative)




$200,000$200,000 -$180,000-$180,000


$100,000$100,000 -$20,000-$20,000



Example - Decision Making Under Uncertainty

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States of Nature Alternatives Favorable

Market Unfavorable

Market Maximum

in Row Minimum in Row

Row Average

Construct large plant

$200,000 -$180,000 $200,000 -$180,000 $10,000

Construct small plant

$100,000 -$20,000 $100,000 -$20,000 $40,000

Do nothing $0 $0 $0 $0 $0

MaximaxMaximax MaximinMaximin Equally Equally

likelylikely


Decision Making Under UncertaintyDecision Making Under UncertaintyStates of NatureStates of Nature

FavorableFavorable UnfavorableUnfavorable MaximumMaximum MinimumMinimum RowRowAlternativesAlternatives MarketMarket MarketMarket in Rowin Row in Rowin Row AverageAverage

ConstructConstruct large plantlarge plant $200,000$200,000 -$180,000-$180,000 $200,000$200,000 -$180,000-$180,000 $10,000$10,000

ConstructConstructsmall plantsmall plant $100,000$100,000 -$20,000 -$20,000 $100,000$100,000 -$20,000 -$20,000 $40,000$40,000

Do nothingDo nothing $0$0 $0$0 $0$0 $0$0 $0$0

1.1. Maximax choice is to construct a large plantMaximax choice is to construct a large plant2.2. Maximin choice is to do nothingMaximin choice is to do nothing3.3. Equally likely choice is to construct a small plantEqually likely choice is to construct a small plant

MaximaxMaximax MaximinMaximin Equally Equally likelylikelyProbability Probability unknownunknown unknownunknown


Criterion of RealismUses the coefficient of realism (α) to estimate the decision maker’s optimism

0 < α < 1

α x (max payoff for alternative)+ (1- α) x (min payoff for alternative)

= Realism payoff for alternative


Criterion of Realism

Alternatives

Outcomes (Demand) Realism Payoff

High Moderate

Low α x (max payoff )+ (1- α) x (min payoff

Large plant

200,000 100,000 -120,000 .45x2ooooo)+(1-.45)x(-12oooo)=24000

Small plant

90,000 50,000 -20,000 29500

No plant 0 0 0 0


Suppose α = 0.45

Choose small plant

AlternativesRealism Payoff

Large plant 24,000

Small plant 29,500

No plant 0


Minimax Regret CriterionRegret or opportunity loss measures

much better we could have done Regret = (best payoff) – (actual payoff)

Alternatives

Outcomes (Demand)

High Moderate Low

Large plant 200,000 100,000 -120,000

Small plant 90,000 50,000 -20,000

No plant 0 0 0

The best payoff for each outcome is highlighted


Alternatives

Outcomes (Demand)

High(Best payoff- actual payoff)

200,000

Moderate

(Best payoff- actual

payoff)1000,00

Low

(Best payoff- actual payoff)

0

Large plant

(200000-200000)=0

(100000-100000)=0

(0-(1200000)=120,000

Small plant

(200000-90000)=11

0,000

(100000-50000)=50,0

00

(0-(200000)=20,000

No plant

(200000-0)=200,000

(100000-100,000)=o

(0-0)=0

Regret ValuesMax

Regret

120,000

110,000

200,000


We want to minimize the amount of regret we might experience, so chose small plant


TOM BROWN INVESTMENT DECISION

Tom Brown has inherited $1000.He has to decide how to invest the

money for one year.A broker has suggested five potential

investments.GoldJunk BondGrowth StockCertificate of DepositStock Option Hedge

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TOM BROWNThe return on each investment depends on

the (uncertain) market behavior during the year.

Tom would build a payoff table to help make the investment decision

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TOM BROWN - Solution

Select a decision making criterion, and apply it to the payoff table.

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S1 S2 S3 S4

D1 p11 p12 p13 p14

D2 p21 p22 p23 P24

D3 p31 p32 p33 p34

S1 S2 S3 S4

D1 p11 p12 p13 p14

D2 p21 p22 p23 P24

D3 p31 p32 p33 p34

Criterion

P1P2P3

• Construct a payoff table.

• Identify the optimal decision.

• Evaluate the solution.


The Payoff TableThe Payoff Table

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Decision States of Nature

Alternatives Large Rise Small Rise No Change Small Fall Large Fall

Gold -100 100 200 300 0Bond 250 200 150 -100 -150Stock 500 250 100 -200 -600C/D account 60 60 60 60 60Stock option 200 150 150 -200 -150

The states of nature are mutually exclusive and collectively exhaustive.

Define the states of nature.

DJA is down more than 800 points

DJA is down [-300, -800]

DJA moveswithin [-300,+300]

DJA is up [+300,+1000]

DJA is up more than1000 points


The Payoff TableThe Payoff Table

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Determine the set of possible decision alternatives.


The Payoff Table

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The stock option alternative is dominated by the

bond alternative

250 200 150 -100 -150

-150


TOM BROWN - The Maximin CriterionTo find an optimal decision

Record the minimum payoff across all states of

nature for each decision.

Identify the decision with the maximum “minimum

payoff.”

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The Maximin Criterion Minimum

Decisions Large Rise Small rise No Change Small Fall Large Fall Payoff

Gold -100 100 200 300 0 -100Bond 250 200 150 -100 -150 -150Stock 500 250 100 -200 -600 -600C/D account 60 60 60 60 60 60

The Maximin Criterion Minimum

Decisions Large Rise Small rise No Change Small Fall Large Fall Payoff

Gold -100 100 200 300 0 -100Bond 250 200 150 -100 -150 -150Stock 500 250 100 -200 -600 -600C/D account 60 60 60 60 60 60

The optimal decision


=MAX(H4:H7)

* FALSE is the range lookup argument in the VLOOKUP function in cell B11 since the values in column H are not in ascending order

=VLOOKUP(MAX(H4:H7),H4:I7,2,FALSE)

=MIN(B4:F4)Drag to H7


To enable the spreadsheet to correctly identify the optimal maximin decision in cell B11, the labels for cells A4 through A7 are copied into cells I4 through I7 (note that column I in the spreadsheet is hidden).

I4

Cell I4 (hidden)=A4Drag to I7


Decision Making Under Uncertainty - The Minimax Regret Criterion

• The Minimax Regret Criterion This criterion fits both a pessimistic

and a conservative decision maker approach.

The payoff table is based on “lost opportunity,” or “regret.”

The decision maker incurs regret by failing to choose the “best” decision.

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The Minimax Regret CriterionTo find an optimal decision, for each state of

nature: Determine the best payoff over all decisions. Calculate the regret for each decision alternative

as the difference between its payoff value and this best payoff value.

For each decision find the maximum regret over all states of nature.

Select the decision alternative that has the minimum of these “maximum regrets.”

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TOM BROWN – Regret Table

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The Payoff TableDecision Large rise Small rise No change Small fall Large fallGold -100 100 200 300 0Bond 250 200 150 -100 -150Stock 500 250 100 -200 -600C/D 60 60 60 60 60


Let us build the Regret Table

The Regret TableDecision Large rise Small rise No change Small fall Large fallGold 600 150 0 0 60Bond 250 50 50 400 210Stock 0 0 100 500 660C/D 440 190 140 240 0


Investing in Stock generates no regret when the market exhibits

a large rise



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The Regret Table MaximumDecision Large rise Small rise No change Small fall Large fall RegretGold 600 150 0 0 60 600Bond 250 50 50 400 210 400Stock 0 0 100 500 660 660C/D 440 190 140 240 0 440


Investing in gold generates a regret of 600 when the market

exhibits a large rise


500 – (-100) = 600


=MAX(B$4:B$7)-B4Drag to F16

=VLOOKUP(MIN(H13:H16),H13:I16,2,FALSE)

=MIN(H13:H16)

=MAX(B14:F14)Drag to H18

Cell I13 (hidden) =A13Drag to I16


RiskRisk Each possible state of nature has an Each possible state of nature has an

assumed probabilityassumed probability

States of nature are mutually exclusiveStates of nature are mutually exclusive

Probabilities must sum to 1Probabilities must sum to 1

Determine the expected monetary value Determine the expected monetary value (EMV) for each alternative(EMV) for each alternative



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Let us build the Regret Table



Investing in Stock generates no regret when the market exhibits

a large rise



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Investing in gold generates a regret of 600 when the market

exhibits a large rise


500 – (-100) = 600


=MAX(B$4:B$7)-B4Drag to F16

=VLOOKUP(MIN(H13:H16),H13:I16,2,FALSE)

=MIN(H13:H16)

=MAX(B14:F14)Drag to H18

Cell I13 (hidden) =A13Drag to I16


Decision Making Under Uncertainty - The Maximax CriterionThis criterion is based on the best possible scenario.

It fits both an optimistic and an aggressive decision maker.

An optimistic decision maker believes that the best possible outcome will always take place regardless of the decision made.

An aggressive decision maker looks for the decision with the highest payoff (when payoff is profit).

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TOM BROWN - The Maximax Criterion

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The Maximax Criterion MaximumDecision Large rise Small rise No change Small fall Large fall PayoffGold -100 100 200 300 0 300Bond 250 200 150 -100 -150 200Stock 500 250 100 -200 -600 500C/D 60 60 60 60 60 60



TOM BROWN - Insufficient Reason Sum of Payoffs

Gold 600 DollarsBond 350 DollarsStock 50 DollarsC/D 300 Dollars

Based on this criterion the optimal decision alternative is to invest in gold.

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Decision Making Under Decision Making Under Uncertainty – Uncertainty – Spreadsheet Spreadsheet

templatetemplatePayoff Table

Large Rise Small Rise No Change Small Fall Large FallGold -100 100 200 300 0Bond 250 200 150 -100 -150Stock 500 250 100 -200 -600C/D Account 60 60 60 60 60d5d6d7d8Probability 0.2 0.3 0.3 0.1 0.1

Criteria Decision PayoffMaximin C/D Account 60Minimax Regret Bond 400Maximax Stock 500Insufficient Reason Gold 100EV Bond 130EVPI 141

RESULTS


Decision Making Under Risk

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• The probability estimate for the

occurrence of

each state of nature (if available) can

be incorporated in the search for the

optimal decision.

• For each decision calculate its

expected payoff.


Decision Making Under RiskWhere probabilities of outcomes are available

Expected Monetary Value (EMV) uses the probabilities to calculate the average payoff for each alternative

EMV (for alternative i) =

∑(probability of outcome) x (payoff of outcome)


Decision Making Under RiskExpected Monetary value(EMV):It is a

value of average pay off as follows

Here,the decision maker selects the course of action which yields the optinal EMV.

Probability of payoffProbability of payoffEMVEMV AA VV PP VV

VV PP VV VV PP VV VV PP VV

ii iiii

ii

NN NN

(( (( ))

(( )) (( )) (( ))

)) ==NN

== **

== ** ++ ** ++ ++ **

11

11 11 22 22

Number of states of Number of states of naturenatureValue of PayoffValue of Payoff

Alternative iAlternative i

......


Expected Opportunity LossEOLEOL is the cost of not picking the best

solutionEOLEOL = Expected Regret

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Expected Opportunity Loss (EOL)How much regret do we expect based on the probabilities?

EOL (for alternative i) = ∑(probability of outcome) x (regret of outcome)


Decision Making Under RiskB.Expected Opportunity loss(EOL):-This

approach is to minimize the expected opportunity loss. It is the difference b/w the highest pay-off and actual profit obtained for course of action taken.

Probability of payoffProbability of payoffEOLEOL PiPiii

LijLij

))

==NN

== **11

Number of states of Number of states of naturenature

Opportunity loss due to state of nature and course of action


EMV ExampleEMV Example

1.1. EMV(EMV(AA11) = (.5)($200,000) + (.5)(-$180,000) = $10,000) = (.5)($200,000) + (.5)(-$180,000) = $10,000

2.2. EMV(EMV(AA22) = (.5)($100,000) + (.5)(-$20,000) = $40,000) = (.5)($100,000) + (.5)(-$20,000) = $40,000

3.3. EMV(EMV(AA33) = (.5)($0) + (.5)($0) = $0) = (.5)($0) + (.5)($0) = $0


FavorableFavorable UnfavorableUnfavorable Alternatives Alternatives Market Market MarketMarket

Construct large plant (A1)Construct large plant (A1) $200,000$200,000 -$180,000-$180,000

Construct small plant (A2)Construct small plant (A2) $100,000$100,000 -$20,000-$20,000

Do nothing (A3)Do nothing (A3) $0$0 $0$0

ProbabilitiesProbabilities .50.50 .50.50

Table A.3Table A.3


EMV ExampleEMV Example

1.1. EMV(EMV(AA11) = (.5)($200,000) + (.5)(-$180,000) = $10,000) = (.5)($200,000) + (.5)(-$180,000) = $10,000

2.2. EMV(EMV(AA22) = (.5)($100,000) + (.5)(-$20,000) = $40,000) = (.5)($100,000) + (.5)(-$20,000) = $40,000

3.3. EMV(EMV(AA33) = (.5)($0) + (.5)($0) = $0) = (.5)($0) + (.5)($0) = $0







Best Option

Table A.3Table A.3


Example - Expected Value


© 2001 by Prentice Hall, Inc., Upper Saddle River, © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458N.J. 07458

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Suppose: Probability of favorable market = 0.5Suppose: Probability of favorable market = 0.5 Probability of unfavorable market = 0.5 Probability of unfavorable market = 0.5




$200,000$200,000 -$180,000-$180,000


$100,000$100,000 -$20,000-$20,000


Expected Expected ValueValue

$10,000$10,000

$40,000$40,000

$0$0

Decision is to “Construct small plant”.Decision is to “Construct small plant”.


Decision Making Under RiskDecision Making Under Risk

1.1. EMV(EMV(AA11) = (0.3)($200,000) + (0.7)(-$180,000) = -$66,000) = (0.3)($200,000) + (0.7)(-$180,000) = -$66,000

2.2. EMV(EMV(AA22) = (0.3)($100,000) + (0.7)(-$90,000) = -$33,000) = (0.3)($100,000) + (0.7)(-$90,000) = -$33,000

3.3. EMV(EMV(AA33) = (0.3)($0) + (0.7)($0) = $0) = (0.3)($0) + (0.7)($0) = $0






ProbabilitiesProbabilities 0.30.3 0.70.7

From Table A.3From Table A.3

If A3 is excluded, The preferable option is If A3 is excluded, The preferable option is A2A2


Decision Making Under Risk (2)Decision Making Under Risk (2)

In some cases the states of nature expected are certain, however the In some cases the states of nature expected are certain, however the values of each states are uncertain. values of each states are uncertain.

States of DemandStates of Demand

Seasonal TicketSeasonal Ticket Occasional Occasional Alternatives Prob. Market Alternatives Prob. Market Prob. Market Prob. Market

Sell 100 tickets early (A1) Sell 100 tickets early (A1) 0.7 0.7 $200,000 $200,000 0.30.3 $50,000 $50,000

Sell 100 tickets later (A2) Sell 100 tickets later (A2) 0.7 0.7 $150,000 $150,000 0.30.3 $300,000 $300,000

Do nothing (A3) Do nothing (A3) $0$0 $0 $0

1.1. EMV(EMV(AA11) = (0.7)($200,000) + (0.3)($50,000) = $155,000) = (0.7)($200,000) + (0.3)($50,000) = $155,000

2.2. EMV(EMV(AA22) = (0.7)($150,000) + (0.3)($300,000) = $195,000) = (0.7)($150,000) + (0.3)($300,000) = $195,000

3.3. EMV(EMV(AA33) = (0)($0) + (0)($0) = $0) = (0)($0) + (0)($0) = $0 The preferable option is A2The preferable option is A2

Case: Selling 100 tickets each time early or later in markets.Case: Selling 100 tickets each time early or later in markets.


Expected Monetary ValueExpected Monetary ValueEMV (Alternative i) =EMV (Alternative i) = (Payoff of 1(Payoff of 1stst state of state of

nature) x (Probability of 1nature) x (Probability of 1stst state of nature)state of nature)

++ (Payoff of 2(Payoff of 2ndnd state of state of nature) x (Probability of 2nature) x (Probability of 2ndnd state of nature)state of nature)

+…++…+ (Payoff of last state of (Payoff of last state of nature) x (Probability of nature) x (Probability of last state of nature)last state of nature)


TOM BROWN - The Expected Value Criterion

75

The Expected Value Criterion ExpectedDecision Large rise Small rise No change Small fall Large fall ValueGold -100 100 200 300 0 100Bond 250 200 150 -100 -150 130Stock 500 250 100 -200 -600 125C/D 60 60 60 60 60 60Prior Prob. 0.2 0.3 0.3 0.1 0.1

EV = (0.2)(250) + (0.3)(200) + (0.3)(150) + (0.1)(-100) + (0.1)(-150) = 130



EOL ExampleEOL Example







Table A.3Table A.3


Computing EOL - The Opportunity Loss Table

State of Nature

Alternative Favorable Market($)

UnfavorableMarket ($)

Large Plant 200,000 - 200,000 0 - (-180,000)Small Plant 200,000 - 100,000 0 -(-20,000)Do Nothing 200,000 - 0 0-0Probabilities 0.50 0.50

PowerPoint presentation to PowerPoint presentation to accompany Operations Management, accompany Operations Management, 6E (Heizer & Render)6E (Heizer & Render)

© 2001 by Prentice Hall, Inc., Upper © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458Saddle River, N.J. 07458A-A-7777


The Opportunity Loss Table - continued

State of NatureAlternative Favorable Market

($)UnfavorableMarket ($)

Large Plant 0 180,000Small Plant 100,000 20,000Do Nothing 200,000 0Probabilities 0.50 0.50




The Opportunity Loss Table - continuedAlternative EOLLarge Plant (0.50)*$0 +

(0.50)*($180,000)$90,000

Small Plant (0.50)*($100,000)+ (0.50)(*$20,000)

$60,000

Do Nothing (0.50)*($200,000)+ (0.50)*($0)

$100,000




CertaintyCertainty

Is the cost of perfect information Is the cost of perfect information worth it?worth it?

Determine the expected value of Determine the expected value of perfect information (EVPI)perfect information (EVPI)


Perfect InformationPerfect Information would tell us with

certainty which outcome is going to occurHaving perfect information before making a

decision would allow choosing the best payoff for the outcome


Expected Value of Expected Value of Perfect InformationPerfect Information

EVPI is the difference between the payoff EVPI is the difference between the payoff under certainty and the payoff under riskunder certainty and the payoff under risk

EVPI = –EVPI = –Expected value Expected value

with perfect with perfect informationinformation

Maximum Maximum EMVEMV

Expected value with Expected value with perfect information perfect information (EVwPI)(EVwPI)

== (Best outcome or consequence for 1(Best outcome or consequence for 1stst state state of nature) x (Probability of 1of nature) x (Probability of 1stst state of nature) state of nature)

++ Best outcome for 2Best outcome for 2ndnd state of nature) state of nature) x (Probability of 2x (Probability of 2ndnd state of nature) state of nature)

++ … … + Best outcome for last state of nature) + Best outcome for last state of nature) x (Probability of last state of nature)x (Probability of last state of nature)


6.4 Expected Value of Perfect Information

The gain in expected return obtained from knowing with certainty the future state of nature is called:

Expected Value of Perfect Expected Value of Perfect

Information (EVPI)Information (EVPI)

83


Expected Value of Perfect Information (EVPI)EVPIEVPI places an upper bound on what one

would pay for additional information

EVPIEVPI is the expected value with perfect information minus the maximum EMV

PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render)

© 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

A-

84


Expected Value With Perfect Information (EVwPI)

The expected payoff of having perfect information before making a decision

EVwPI = ∑ (probability of outcome)

x ( best payoff of outcome)


Expected Value of Perfect Information (EVPI)The amount by which perfect information

would increase our expected payoffProvides an upper bound on what to pay for

additional information

EVPI = EVwPI – EMV

EVwPI = Expected value with perfect information

EMV = the best EMV without perfect information


Alternatives

Demand

High Moderate Low

Large plant 200,000 100,000 -120,000

Small plant 90,000 50,000 -20,000

No plant 0 0 0

Probability 0.3 0.5 0.2

Max payoff for state of nature:-1.High -----2000002.Moderate-----1000003.low----------0


Alternatives

Demand

High Moderate Low

Large plant 200,000 100,000 -120,000

Small plant 90,000 50,000 -20,000

No plant 0 0 0


Max payoff for state of nature

200000 100000 0

EVWPI 200000*o.3+100000*0.5+0*0.2=110000.


Alternatives

Demand

High Moderate Low EMV

Large plant

200,000*0.3=60000

100,000*0.5=50000

-120,000

*0.2=-24000

(60000+50000+(-24000)=86000

Small plant

90,000*0.3

50,000*0.5 -20,000*0.2

48000

No plant

0*0.3 0*0.5 0*0.2 o



Expected Value of Perfect InformationEVPI = EVwPI – EMV

= $110,000 - $86,000 = $24,000

The “perfect information” increases the expected value by $24,000

Would it be worth $30,000 to obtain this perfect information for demand?


Example - EVUC



A-

91

Best outcome for Favorable Market = $200,000

Best outcome for Unfavorable Market = $0

States of NatureAlternativesFavorable

MarketUnfavorable

MarketConstructlarge plant

$200,000 -$180,000

Constructsmall plant

$100,000 -$20,000

$0 $0Do nothing


Expected Value of Perfect Information



A-

92

State of NatureAlternative

Probabilities

Construct alarge plantConstruct a small plant

Do nothing

200,000 -$180,000

$0

Favorable Market ($)

Unfavorable Market ($)

0.50 0.50

EMV

$40,000$100,000

$20,000

$0 $0

$20,000



EVPIEVPI = EVUC - max(EVEV) = ($200,000*0.50 + 0*0.50) - $40,000 = $60,000

Thus, you should be willing to pay up to $60,000 to learn whether the market will be favorable or not.



A-

93

Suppose: Probability of favorable market = 0.5 Probability of unfavorable market = 0.5




Now, you should be willing to pay up to $54,000 to learn whether the market will be favorable or not.



A-

94

Now suppose: Probability of favorable market = 0.7 Probability of unfavorable market = 0.3


Expected Value of Perfect InformationEVPIEVPI = expected value with perfect

information - max(EMVEMV)

= $200,000*0.50 + 0*0.50 - $40,000

= $60,000



A-

95





AA--

9966

State of NatureAlternative

Probabilities

Construct aConstruct alarge plantlarge plant

Construct a Construct a small plantsmall plant

Do nothingDo nothing

200,000200,000 -$180,000-$180,000

$0$0

Favorable Favorable Market ($)Market ($)

Unfavorable Unfavorable Market ($)Market ($)

0.500.50 0.500.50

EMVEMV

$40,000$40,000$100,0$100,00000

$20,00$20,0000

$0$0 $0$0

$20,000$20,000




Thus, you should be willing to pay up to $60,000 to learn whether the market will be favorable or not.



AA--

9977

Suppose: Probability of favorable market = 0.5Suppose: Probability of favorable market = 0.5 Probability of unfavorable market = 0.5 Probability of unfavorable market = 0.5




Now, you should be willing to pay up to $54,000 to learn whether the market will be favorable or not.



AA--

9988

Now suppose: Probability of favorable market = Now suppose: Probability of favorable market = 0.70.7 Probability of unfavorable market = Probability of unfavorable market = 0.30.3


Expected Value of Perfect InformationEVPIEVPI = expected value with perfect

information - max(EMVEMV)

= $200,000*0.50 + 0*0.50 - $40,000

= $60,000



AA--

9999


TOM BROWN - EVPI

100

The Expected Value of Perfect Information Decision Large rise Small rise No change Small fall Large fallGold -100 100 200 300 0Bond 250 200 150 -100 -150Stock 500 250 100 -200 -600C/D 60 60 60 60 60Probab. 0.2 0.3 0.3 0.1 0.1

If it were known with certainty that there will be a “Large Rise” in the market

Large rise

... the optimal decision would be to invest in...

-100

250

50

0 60

Stock

Similarly,…


TOM BROWN - EVPI

101

The Expected Value of Perfect Information Decision Large rise Small rise No change Small fall Large fallGold -100 100 200 300 0Bond 250 200 150 -100 -150Stock 500 250 100 -200 -600C/D 60 60 60 60 60Probab. 0.2 0.3 0.3 0.1 0.1

-100

250

50

0 60

Expected Return with Perfect information = ERPI = 0.2(500)+0.3(250)+0.3(200)+0.1(300)+0.1(60) = $271

Expected Return without additional information = Expected Return of the EV criterion = $130

EVPI = ERPI - EREV = $271 - $130 = $141


Decision Trees Graphical display of decision process Used for solving problems

With 1 set of alternatives and states of nature, decision tables can be used also

With several sets of alternatives and states of nature (sequential decisions), decision tables cannot be used

EMV is criterion most often used



AA--

110022


Characteristics of a decision tree

A Decision Tree is a chronological representation of the decision process.

The tree is composed of nodes and branches.

103

A branch emanating from a state of nature (chance) node corresponds to a particular state of nature, and includes the probability of this state of nature.

Decision node

Chance node

Decision 1

Cost 1Decision 2Cost 2

P(S2)

P(S1)

P(S3 )

P(S2)

P(S1)

P(S3 )

A branch emanating from a decision node corresponds to a decision alternative. It includes a cost or benefit value.


Decision TreesDecision Trees1.1. Define the problemDefine the problem

2.2. Structure or draw the decision treeStructure or draw the decision tree

3.3. Assign probabilities to the states of Assign probabilities to the states of naturenature

4.4. Estimate payoffs for each possible Estimate payoffs for each possible combination of decision alternatives and combination of decision alternatives and states of naturestates of nature

5.5. Solve the problem by working backward Solve the problem by working backward through the tree computing the EMV for through the tree computing the EMV for each state-of-nature nodeeach state-of-nature node


AA--

110055

ProcessProcess


Decision TheoryTerms:Alternative: Course of action or choice.State of nature: An occurrence over

which the decision maker has no control.

Symbols used in decision tree: A decision node from which one of several

alternatives may be selected. A state of nature node out of which one

state of nature will occur.AA--

110066


Decision Tree

A-A-107107

11

22

State 1State 1

State 2State 2

State 1State 1

State 2State 2

Alternativ

e 1

Alternativ

e 1

Alternative 2

Alternative 2

Decision Decision NodeNode

Outcome 1Outcome 1Outcome 1Outcome 1




State of Nature NodeState of Nature Node


Decision TreesDecision Trees Information in decision tables can be Information in decision tables can be

displayed as decision treesdisplayed as decision trees

A decision tree is a graphic display of the A decision tree is a graphic display of the decision process that indicates decision decision process that indicates decision alternatives, states of nature and their alternatives, states of nature and their respective probabilities, and payoffs for respective probabilities, and payoffs for each combination of decision alternative each combination of decision alternative and state of natureand state of nature

Appropriate for showing sequential Appropriate for showing sequential decisionsdecisions


Decision Tree ExampleDecision Tree Example

Favorable marketFavorable market

Unfavorable marketUnfavorable market

Favorable marketFavorable market

Unfavorable marketUnfavorable market

Construct Construct small plantsmall plant

Do nothing

Do nothing

A decision nodeA decision node A state of nature nodeA state of nature node

Construct

Construct

large plant

large plant

Figure A.1Figure A.1


Decision Tree Example

A-A-110110

A firm can build a large plant or small plant initially (for A firm can build a large plant or small plant initially (for a new product). Demand for the new product will be a new product). Demand for the new product will be high or low initially. The probability of high demand is high or low initially. The probability of high demand is 0.6. (The probability of low demand is 0.4.) 0.6. (The probability of low demand is 0.4.)

If they build “small” and demand is “low”, the payoff is If they build “small” and demand is “low”, the payoff is $40 million. If they build “small” and demand is “high”, $40 million. If they build “small” and demand is “high”, they can do nothing and payoff is $45 million, or they they can do nothing and payoff is $45 million, or they can expand. If they expand, there is a 30% chance the can expand. If they expand, there is a 30% chance the demand drops off and the payoff will be $35 million, demand drops off and the payoff will be $35 million, and a 70% chance the demand grows and the payoff is and a 70% chance the demand grows and the payoff is $48 million. $48 million.

If they build “large” and demand is “high”, the payoff If they build “large” and demand is “high”, the payoff is $60 million. If they build “large” and demand is is $60 million. If they build “large” and demand is “low”, they can do nothing and payoff is -$10 million, “low”, they can do nothing and payoff is -$10 million, or they can reduce prices and payoff is $20 million. or they can reduce prices and payoff is $20 million. Determine the best decision(s) using a decision tree.Determine the best decision(s) using a decision tree.


Decision Tree Example



Three decisions:Three decisions: 1. Build “Large” or “Small” plant initially.1. Build “Large” or “Small” plant initially.

2. If build “Small” and demand is “High”, then “Expand” 2. If build “Small” and demand is “High”, then “Expand” or or “Do nothing”.“Do nothing”.

3. If build “Large” and demand is “Low”, then decide to 3. If build “Large” and demand is “Low”, then decide to “Reduce prices” or “Do nothing”.“Reduce prices” or “Do nothing”.

Two states of nature:Two states of nature: 1. Demand is “High” (0.6) or “Low” (0.4) initially.1. Demand is “High” (0.6) or “Low” (0.4) initially.

2. If build “Small”, demand is “High”, and decision is 2. If build “Small”, demand is “High”, and decision is “Expand”, then demand “Grows” (0.7) or demand “Expand”, then demand “Grows” (0.7) or demand “Drops” “Drops” (0.3).(0.3).


Decision Tree



Build small

Build small

Build large

Build large High (0.6)High (0.6)

Low (0.4)

Low (0.4)

High (0.6)

High (0.6)

Low (0.4)

Low (0.4)

Expand

Expand



Reduce pricesReduce prices

Demand grows (0.7)Demand grows (0.7)

Demand drops (0.3)Demand drops (0.3)

$48$48

$35$35

$45$45

$40$40

$60$60

$20$20

-$10-$10

11

33

22


Decision Tree



Build small

Build small

Build large


Low (0.4)

Low (0.4)

High (0.6)

High (0.6)

Low (0.4)

Low (0.4)

Expand

Expand






$48$48

$35$35

$45$45

$40$40

$60$60

$20$20

-$10-$10

11

33

22


Decision Tree Solution



Work right to left (from end back to Work right to left (from end back to beginning).beginning).

Start with Decision 3:Start with Decision 3:““Reduce prices” or “Do nothing”.Reduce prices” or “Do nothing”.

Choose “Reduce prices” (20 > -10).Choose “Reduce prices” (20 > -10).


Decision Tree



Build small

Build small

Build large


Low (0.4)

Low (0.4)

High (0.6)

High (0.6)

Low (0.4)

Low (0.4)

Expand

Expand






$48$48

$35$35

$45$45

$40$40

$60$60

$20$20

-$10-$10

11

33

22

$20$20


Decision Tree Solution



Consider Decision 2: “Expand” or “Do Consider Decision 2: “Expand” or “Do nothing”. nothing”.

To compare outcomes we need expected To compare outcomes we need expected value if we “Expand”: (48*0.7) + (35*0.3) = value if we “Expand”: (48*0.7) + (35*0.3) = 44.144.1

Choose “Do nothing” (45 > 44.1).Choose “Do nothing” (45 > 44.1).


Decision Tree



Build small

Build small

Build large


Low (0.4)

Low (0.4)

High (0.6)

High (0.6)

Low (0.4)

Low (0.4)

Expand

Expand






$48$48

$35$35

$45$45

$40$40

$60$60

$20$20

-$10-$10

11

33

22

$44.1$44.1

$45$45

$20$20

$45$45


Decision Tree



Build small

Build small

Build large


Low (0.4)

Low (0.4)

High (0.6)

High (0.6)

Low (0.4)

Low (0.4)

Expand

Expand






$48$48

$35$35

$45$45

$40$40

$60$60

$20$20

-$10-$10

11

33

22

$44.1$44.1

$45$45

$20$20

$45$45

$44$44

$43$43


Decision Tree Final Solution



Decisions:Decisions:

1. Build “Large”.1. Build “Large”.

2. If demand is “Low”, then “Reduce 2. If demand is “Low”, then “Reduce prices”.prices”.

Expected payoff = $44 million.Expected payoff = $44 million.




AA--

112200

AdvantagesAdvantages




AA--

112211

DisadvantagesDisadvantages


Decision Tree ExampleDecision Tree Example= (.5)($200,000) + (.5)(-$180,000)= (.5)($200,000) + (.5)(-$180,000)EMV for node 1

= $10,000

EMV for node 2= $40,000 = (.5)($100,000) + (.5)(-$20,000)= (.5)($100,000) + (.5)(-$20,000)

PayoffsPayoffs

$200,000$200,000

-$180,000-$180,000

$100,000$100,000

-$20,000-$20,000

$0$0

Construct la

rge plant

Construct la

rge plant

Construct Construct

small plantsmall plantDo nothing

Do nothing

Favorable market Favorable market (.5)(.5)

Unfavorable market Unfavorable market (.5)(.5)1





Decision Table ExampleDecision Table Example

State of NatureState of Nature

AlternativesAlternatives Favorable MarketFavorable Market Unfavorable MarketUnfavorable Market

Construct large plantConstruct large plant $200,000$200,000 –$180,000–$180,000

Construct small plantConstruct small plant $100,000$100,000 –$ 20,000–$ 20,000

Do nothingDo nothing $ 0$ 0 $ 0 $ 0

Table A.1Table A.1


Decision Tree ExampleDecision Tree Example= (.5)($200,000) + (.5)(-$180,000)= (.5)($200,000) + (.5)(-$180,000)EMV for node 1

= $10,000

EMV for node 2= $40,000 = (.5)($100,000) + (.5)(-$20,000)= (.5)($100,000) + (.5)(-$20,000)

PayoffsPayoffs

$200,000$200,000

-$180,000-$180,000

$100,000$100,000

-$20,000-$20,000

$0$0

Construct la

rge plant

Construct la

rge plant

Construct Construct

small plantsmall plantDo nothing

Do nothing







In-Class ExerciseIn-Class Exercise Two suppliers deliver a product to us. Supplier Two suppliers deliver a product to us. Supplier

1 charges $ 575 for the part. The part seldom 1 charges $ 575 for the part. The part seldom fails but its probability of failing is 0.1. The fails but its probability of failing is 0.1. The amount that we loose if part fails is $100. amount that we loose if part fails is $100.

Supplier 2 charges $ 550 for the same part. The Supplier 2 charges $ 550 for the same part. The probability of having a good part for this probability of having a good part for this supplier is 0.8. The amount that we loose if a supplier is 0.8. The amount that we loose if a part fails is $460. part fails is $460.

Find the expected monetary value of defective Find the expected monetary value of defective part from supplier 1?part from supplier 1?

Find the expected monetary value of defective Find the expected monetary value of defective part from supplier 2?part from supplier 2?

Find the total expected monetary value for each Find the total expected monetary value for each supplier?supplier?


BGD plans to do a commercial development on a property.

Relevant data Asking price for the property is 300,000 dollars. Construction cost is 500,000 dollars. Selling price is approximated at 950,000 dollars. Variance application costs 30,000 dollars in fees and

expenses There is only 40% chance that the variance will be

approved. If BGD purchases the property and the variance is denied,

the property can be sold for a net return of 260,000 dollars. A three month option on the property costs 20,000 dollars,

which will allow BGD to apply for the variance. 126

BILL GALLEN DEVELOPMENT BILL GALLEN DEVELOPMENT COMPANYCOMPANY


BILL GALLEN DEVELOPMENT COMPANYA consultant can be hired for 5000 dollars.The consultant will provide an opinion about

the approval of the application P (Consultant predicts approval | approval granted)

= 0.70 P (Consultant predicts denial | approval denied) =

0.80

BGD wishes to determine the optimal strategyHire/ not hire the consultant now,Other decisions that follow sequentially.

127


Construction of the Decision Tree

Initially the company faces a decision about

hiring the consultant.

After this decision is made more decisions follow regarding Application for the variance. Purchasing the option. Purchasing the property.

128

BILL GALLEN - SolutionBILL GALLEN - Solution


Let us consider the decision

to not hire a consultant

Do not h

ire consulta

nt

Hire consultant

Cost = -5000

Cost = 0

Do nothing

0Buy land-300,000Purchase option

-20,000

Apply for variance

Apply for variance

-30,000

-30,000

0

3


BILL GALLEN - The Decision Tree

130

Approved

Denied

0.4

0.6

12

Approved

Denied

0.4

0.6

-300,000 -500,000 950,000

Buy land Build Sell

-50,000

100,000

-70,000

260,000Sell

Build Sell950,000-500,000

120,000Buy land and apply for variance

-300000 – 30000 + 260000 =

-300000 – 30000 – 500000 + 950000 =

Purchase option andapply for variance


60

Do not hire consultant

Hire consultantCost = -5000

Cost = 0

Do nothing

0

Buy land-300,000Purchase option

-20,000

Apply for variance

Apply for variance

-30,000

-30,000

0

61

12

-300,000 -500,000 950,000

Buy land Build Sell

-50,000

100,000

-70,000

260,000Sell

Build Sell950,000-500,000

120,000Buy land and apply for variance

-300000 – 30000 + 260000 =

-300000 – 30000 – 500000 + 950000 =

Purchase option andapply for variance

This is where we are at this stage

Let us consider the decision to hire a consultant


BILL GALLEN – The Decision Tree

132

Do not hire consultant

0

Hire consultant

-5000 Predict

Approval

Predict

Denial

0.4

0.6

-5000

Apply for variance

Apply for variance

Apply for variance

Apply for variance

-5000

-30,000

-30,000

-30,000

-30,000

Let us consider the decision to hire a consultant

Done

Do Nothing

Buy land

-300,000Purchase option-20,000

Do Nothing

Buy land

-300,000Purchase option-20,000


Approved

Denied

Consultant predicts an approval

?

?

Build Sell950,000-500,000

260,000Sell

-75,000

115,000


Approved

Denied

?

?

Build Sell950,000-500,000

260,000Sell

-75,000

115,000

The consultant serves as a source for additional information

about denial or approval of the variance.


?

?

Approved

Denied

Build Sell950,000-500,000

260,000Sell

-75,000

115,000

Therefore, at this point we need to calculate theposterior probabilities for the approval and denial

of the variance application


22Approved

Denied

Build Sell950,000-500,000

260,000Sell

-75,000

27

25

115,000

23 24

26

The rest of the Decision Tree is built in a similar manner.

Posterior Probability of (approval | consultant predicts approval) = 0.70Posterior Probability of (denial | consultant predicts approval) = 0.30

?

?

.7

.3


The Decision Tree Determining the Optimal Strategy

Work backward from the end of each branch.

At a state of nature node, calculate the expected value of the node.

At a decision node, the branch that has the highest ending node value represents the optimal decision.

137


BILL GALLEN - The Decision Tree Determining the Optimal Strategy

138

22Approved

Denied

27

2523 24

26

-75,000

115,000115,000

-75,000

115,000

-75,000

115,000

-75,000

115,000

-75,00022

115,000

-75,000

(115,000)(0.7)=80500

(-75,000)(0.3)= -22500

-22500

80500

80500

-22500

80500

-22500

58,000?

?0.30

0.70

Build Sell950,000-500,000

260,000Sell

-75,000

115,000

With 58,000 as the chance node value,we continue backward to evaluate

the previous nodes.


Predicts approvalHire

Do nothing

.4

.6

$10,000

$58,000

$-5,000

$20,000

$20,000

Buy land; Apply for variance

Predicts denial

Denied

Build,Sell

Sell land

Do not

hire

$-75,000

$115,000

.7

.3

Ap

pro

ved


THANK YOU

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