Decision AnalysisPart 1

Graduate Program in Business Information Systems

Aslı Sencer

Analytical Decision Making

Can Help Managers to: Gain deeper insight into the nature of

business relationships Find better ways to assess values in such

relationships; and See a way of reducing, or at least

understanding, uncertainty that surrounds business plans and actions

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Steps to Analytical DM

Define problem and influencing factors Establish decision criteria Select decision-making tool (model) Identify and evaluate alternatives using

decision-making tool (model) Select best alternative Implement decision Evaluate the outcome

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Models

Are less expensive and disruptive than experimenting with the real world system

Allow operations managers to ask “What if” types of questions

Are built for management problems and encourage management input

Force a consistent and systematic approach to the analysis of problems

Require managers to be specific about constraints and goals relating to a problem

Help reduce the time needed in decision making

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Limitations of the Models

They may be expensive and time-consuming to develop and test

Often misused and misunderstood (and feared) because of their mathematical and logical complexity

Tend to downplay the role and value of nonquantifiable information

Often have assumptions that oversimplify the variables of the real world

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The Decision-Making Process

Problem Decision

Quantitative Analysis

LogicHistorical DataMarketing ResearchScientific AnalysisModeling

Qualitative Analysis

EmotionsIntuitionPersonal Experience and MotivationRumors

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Decision trees Decision

tables

Decision Problem

Alternatives

States of Nature

Outcomes

Displaying a Decision Problem

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Types of Decision Models

Decision making under uncertainty Decision making under risk Decision making under certainty

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Fundamentals of Decision Theory

Terms: Alternative: course of action or choice State of nature: an occurrence over

which the decision maker has no control

Symbols used in a 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

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Decision Table

States of Nature

Alternatives State 1 State 2

Alternative 1 Outcome 1 Outcome 2

Alternative 2 Outcome 3 Outcome 4

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Getz Products Decision Tree

1

2Unfavorable market

Unfavorable market

Favorable market

Favorable market

Construct small plant

Construct

large plant

Do nothing

A decision node

A state of nature node

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Decision Making under Uncertainty

Maximax - 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 - chose the alternative with the highest average outcome.

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Example:

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

$0 $0 $0 $0 $0 Maximax Maximin Equally

likely

Do nothing

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Decision criteria

The maximax choice is to construct a large plant. This is the maximum of the maximum number within each row or alternative.

The maximin choice is to do nothing. This is the maximum of the minimum number within each row or alternative.

The equally likely choice is to construct a small plant. This is the maximum of the average outcomes of each alternative. This approach assumes that all outcomes for any alternative are equally likely.

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Decision Making under Risk

Probabilistic decision situation States of nature have probabilities of

occurrence

Maximum Likelihood Criterion Maximize Expected Monitary Value

(Bayes Decision Rule)

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Maximum Likelihood Criteria

Maximum Likelihood: Identify most likely event, ignore others, and pick act with greatest payoff. Personal decisions are often made that way. Collectively, other events may be more likely. Ignores lots of information.

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Bayes Decision Rule

It is not a perfect criterion because it can lead to the less preferred choice.

Consider the Far-Fetched Lottery decision:

Would you gamble?

EVENTS Probability

ACTS

Gamble Don’t Gamble

Head .5 +$10,000 $0

Tail .5 -5,000 0

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The Far-Fetched Lottery Decision

Most people prefer not to gamble! That violates the Bayes decision rule. But the rule often indicates preferred choices even

though it is not perfect.

EVENTSProba-bility

ACTS

Gamble Don’t Gamble

Payoff × Prob. Payoff × Prob

Head .5 +$5,000 $0

Tail .5 -2,500 0

Expected Payoff: $2,500 $0

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N

j jiji PXAEMV1

)(

Expected Monetary Value

N: Number of states of naturek: Number of alternative decisionsXij: Value of Payoff for alternative i in state of nature j, i=1,2,...,k and j=1,2,...,N.Pj: Probability of state of nature j

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Example:

States of NatureAlternatives Favorable

MarketP(0.5)

UnfavorableMarket P(0.5)

Expectedvalue

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

Constructsmall plant

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

Do nothing $0 $0 $0

Best choice

large plant

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Decision Making under Certainty

What if Getz knows the state of the nature with certainty?

Then there is no risk for the state of the nature!

A marketing research company requests $65000 for this information

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Questions:

Should Getz hire the firm to make this study?

How much does this information worth?

What is the value of perfect information?

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Expected Value With Perfect Information (EVPI)

jP.}){

N

1jiji X(Max

EVPI = Expected Payoff - Maximum expected payoff under Certainty with no information

Let N: Number of states of nature and k: Number of actions,

EVPI places an upper bound on what one would pay for additional information

Maximum expected payoff with no information=Max {EMVi; i=1,..,k}

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Expected Payoff under Ceratinty=

Example: Expected Value of Perfect Information

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

$10,000

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Expected Value of Perfect Information

Expected Value Under Certainty =($200,000*0.50 + 0*0.50)= $100,000

Max(EMV)= Max{10,000, 40,000, 0}=$40,000

EVPI = Expected Value Under Certainty - Max(EMV) = $100,000 - $40,000 = $60,000

So Getz should not be willing to pay more than $60,000

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Ex: Toy Manufacturer

How to choose among 4 types of tippi-toes?

Demand for tippi-toes is uncertain:Light demand: 25,000 units (10%)Moderate demand: 100,000 units (70%)Heavy demand: 150,000 units (20%)

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Event(State of nature) Probability

ACT (choice)

Gears and levers

Spring Action

Weights and pulleys

Light 0.10 $25,000 -$10,000 -$125,000

Moderate 0.70 400,000 440,000 400,000

Heavy 0.20 650,000 740,000 750,000

Payoff Table

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Maximum Expected Payoff Criteria

ACT (choice)

Gears and levers

Spring Action

Weights and pulleys

Expected Payoff

$412,500 $455,500 $417,000

Maximum expected payoff occurs at Spring Action!

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Graphical display of decision process, i.e., alternatives, states of nature, probabilities, payoffs.

Decision tables are convenient for problems

with one set of alternatives and states of nature. With several sets of alternatives and states of nature

(sequential decisions), decision trees are used!

EMV criterion is the most commonly used criterion in decision tree analysis.

Decision Trees

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Softwares for Decision Tree Analysis

DPL Tree Plan Supertree

Analysis with less effort.Full color presentations for managers

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Steps of Decision Tree Analysis

Define the problem Structure or draw the decision tree Assign probabilities to the states of nature Estimate payoffs for each possible

combination of alternatives and states of nature

Solve the problem by computing expected monetary values for each state-of-nature node

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Decision Tree

1

2

State 1

State 2

State 1

State 2

Alternative 1

Alternative 2

Decision Node

Outcome 1Outcome 1

Outcome 2Outcome 2

Outcome 3Outcome 3

Outcome 4Outcome 4

State of Nature Node

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Ex1:Getz Products Decision Tree

Payoffs

$200,000

-$180,000$100,000

-20,000

0

1

2Unfavorable market (0.5)

Unfavorable market (0.5)

Favorable market (0.5)

Favorable market (0.5)

Construct small plant

Construct

large plant

Do nothing EMV for node 2 = $40,000

EMV for node 1 = $10,000

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A More Complex Decision Tree

Let’s say Getz Products has two sequential decisions to make:

Conduct a survey for $10000? Build a large or small plant or not

build?

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Ex1:Getz Products Decision Tree

1 4

7

$49,

200

$106

,400

$40,

000

$2,4

00

2

3

5

6

$190,000

-$190,000

$90,000

-$30,000

-$10,000

$190,000

-$190,000

$90,000-$30,000-$10,000

$200,000

-$180,000

$100,000

-$20,000$0

Surv

ey

No survey

Large plant

Small plantNo plant

Large plant

Small plantNo plant

Large plant

Small plantNo plant

Fav. Mkt (0.78)

Fav. Mkt (0.78)

Fav. Mkt (0.27)

Fav. Mkt (0.27)

Fav. Mkt (0.5)

Fav. Mkt (0.5)

Unfav. Mkt (0.22)

Unfav. Mkt (0.22)

Unfav. Mkt (0.73)

Unfav. Mkt (0.73)

Unfav. Mkt (0.5)

Unfav. Mkt (0.5)

$106,400

$63,600

-$87,400

$2,400

$10,000

$40,000

Sur. Res. Neg. (.55)

Sur. Res.

Pos. (.45)

1st decision point

2nd decision point

$49,200

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Resulting Decision

EMV of conducting the survey=$49,200 EMV of not conducting the survey=$40,000So Getz should conduct the survey!

If the survey results are favourable, build large plant.If the survey results are infavourable, build small plant.

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Ex2: Ponderosa Record Company

Decide whether or not to market the recordings of a rock group.

Alternative1: test market 5000 units and if favorable, market 45000 units nationally

Alternative2: Market 50000 units nationally

Outcome is a complete success (all are sold) or failure

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Ex2: Ponderosa-costs, prices

Fixed payment to group: $5000 Production cost: $5000 and $0.75/cd Handling, distribution: $0.25/cd Price of a cd: $2/cd

Cost of producing 5,000 cd’s =5,000+5,000+(0.25+0.75)5,000=$15,000

Cost of producing 45,000 cd’s=0+5,000+(0.25+0.75)45,000=$50,000

Cost of producing 50,000 cd’s=5,000+5,000+(0.25+0.75)50,000=$60,000

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Ex2: Ponderosa-Event Probabilities

Without testing P(success)=P(failure)=0.5

With testingP(success|test result is favorable)=0.8P(failure|test result is favorable)=0.2

P(success|test result is unfavorable)=0.2P(failure|test result is unfavorable)=0.8

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Decision Tree for Ponderosa Record Company

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Backward Approach

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Optimal Decision Policy

Precision Tree provides excell add-ins. Optimal decision is:

Test market If the market is favorable, market nationally Else, abort

Risk Profile Possible outcomes for the opt. soln.$35,000 with probability 0.4-$55,000 with probability 0.1-$15,000 with probability 0.5

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Risk Profilefor Ponderosa Record Co.

Risk Profile For Ponderosa Record Company

0

0.1

0.2

0.3

0.4

0.5

0.6

-70000 -60000 -50000 -40000 -30000 -20000 -10000 0 10000 20000 30000 40000 50000

Expected Value, $

Pro

ba

bil

ity

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Sensitivity Analysis

The optimal solution depends on many factors. Is the optimal policy robust?

Question:-How does $1000 payoff change with respect

to a change in success probability (0.8 currently)? earnings of success ($90,000 currently)? test marketing cost ($15,000 currently)?

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Application Areas of Decision Theory

Investments in research and developmentplant and equipmentnew buildings and structures

Production and Inventory controlAggregate PlanningMaintenanceScheduling, etc.

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References

Lapin L.L., Whisler W.D., Quantitative Decision Making, 7e, 2002.

Heizer J., Render, B., Operations Management, 7e, 2004.

Render, B., Stair R. M., Quantitative Analysis for Management, 8e, 2003.

Anderson, D.R., Sweeney D.J, Williams T.A., Statistics for Business and Economics, 8e, 2002.

Taha, H., Operations Research, 1997.

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