DecisionDecision AnalysisAnalysis

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Johan Oscar Ong, ST, MT

Analytical Decision MakingAnalytical Decision Making

��Can Help Managers Can Help Managers ttoo: :

�� Gain deeper insight into the nature of Gain deeper insight into the nature of business relationshipsbusiness relationships

�� Find better ways to assess values in such Find better ways to assess values in such relationships; andrelationships; and

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

understanding, uncertainty thatunderstanding, uncertainty that surrounds surrounds business plans and actionsbusiness plans and actions

Steps to Steps to Analytical DMAnalytical DM

��Define problem and influencing factorsDefine problem and influencing factors

��Establish decision criteriaEstablish decision criteria

��Select decisionSelect decision--making tool (model)making tool (model)

��Identify and evaluate alternatives using Identify and evaluate alternatives using decisiondecision--making tool (model)making tool (model)

��Select best alternativeSelect best alternative

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��Select best alternativeSelect best alternative

��Implement decisionImplement decision

��Evaluate the outcomeEvaluate the outcome

ModelsModels

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

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

�� Are built for management problems and Are built for management problems and encourage management inputencourage management input

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encourage management inputencourage management input

�� Force a consistent and systematic approach to Force a consistent and systematic approach to the analysis of problemsthe analysis of problems

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

�� Help reduce the time needed in decision makingHelp reduce the time needed in decision making

Limitations of the ModelsLimitations of the Models

��TheThey y may be expensive and timemay be expensive and time--consuming to develop and testconsuming to develop and test

��OOftenften misused and misunderstood (and misused and misunderstood (and feared) because of their mathematical feared) because of their mathematical and logical complexityand logical complexity

TTend to downplay the role and value of end to downplay the role and value of

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��TTend to downplay the role and value of end to downplay the role and value of nonquantifiablenonquantifiable informationinformation

��OOftenften have assumptions that have assumptions that oversimplify the variables of the real oversimplify the variables of the real worldworld

The DecisionThe Decision--Making ProcessMaking Process

Problem Decision

Quantitative Analysis

LogicHistorical DataMarketing ResearchScientific Analysis

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Problem DecisionModeling

Qualitative Analysis

EmotionsIntuitionPersonal Experienceand Motivation

Rumors

66

��Decision treesDecision trees

��Decision Decision ttablesables

States of Nature

Outcomes

DisplayingDisplaying a Decision Problema Decision Problemw

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ttablesables

Decision Problem

Alternatives

TTypesypes of of DDecisionecision MModelsodels

��Decision making under Decision making under uncertaintyuncertainty

��Decision making under Decision making under risk risk

��Decision making under Decision making under certaintycertainty

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��Decision making under Decision making under certaintycertainty

Fundamentals of Decision TheoryFundamentals of Decision Theory

TermsTerms::

��AlternativeAlternative: course of action or choice: course of action or choice

��State of natureState of nature: an occurrence over : an occurrence over which the decision maker has no which the decision maker has no controlcontrol

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Symbols used in Symbols used in a a decision treedecision tree::

��A A decision nodedecision node from which one of from which one of several alternatives may be selectedseveral alternatives may be selected

��A A state of nature nodestate of nature node out of which one out of which one state of nature will occurstate of nature will occur

Decision TableDecision Table

States of Nature

Alternatives State 1 State 2

Alternative 1 Outcome 1 Outcome 2

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Alternative 1 Outcome 1 Outcome 2

Alternative 2 Outcome 3 Outcome 4

1010

Getz Products Decision TreeGetz Products Decision Tree

1Unfavorable market

Favorable market

Favorable marketA state of nature node

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2Unfavorable market

Favorable market

Construct small plant

A decision node

Decision Making under Decision Making under UncertaintyUncertainty

��MaximaxMaximax -- Choose the alternative that Choose the alternative that maximizes the maximum outcome for maximizes the maximum outcome for every alternative (Optimistic criterion)every alternative (Optimistic criterion)

��MaximinMaximin -- Choose the alternative that Choose the alternative that

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

��Equally likelyEqually likely -- chose the alternative chose the alternative with the highest average outcome.with the highest average outcome.

Example:Example:

States of NatureAlternatives Favorable

MarketUnfavorable

MarketMaximum

in RowMinimum in Row

Row Average

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

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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

Decision criteriaDecision criteria

�� The The maximaxmaximax choice is to construct a large choice is to construct a large plant. This is the plant. This is the maximummaximum of the of the maxmaximum imum number within each row or alternative.number within each row or alternative.

�� The The maximinmaximin choice is to do nothing. This is the choice is to do nothing. This is the maximaximum of the mum of the minminimum number within each imum number within each row or alternative.row or alternative.

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row or alternative.row or alternative.

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

Decision Making under RiskDecision Making under Risk

��Probabilistic decision situationProbabilistic decision situation

��States of nature have probabilities of States of nature have probabilities of occurrenceoccurrence

��Maximum Likelihood CriterionMaximum Likelihood Criterion

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��Maximum Likelihood CriterionMaximum Likelihood Criterion

��Maximize Expected Monitary Value Maximize Expected Monitary Value (Bayes Decision Rule)(Bayes Decision Rule)

Maximum LikelihoodMaximum Likelihood CriteriaCriteria

�� Maximum LikelihoodMaximum Likelihood: Identify most likely event, : Identify most likely event, ignore others, and pick act with greatest payoff.ignore others, and pick act with greatest payoff.

�� Personal decisions Personal decisions are are often made that way.often made that way.�� Collectively, other events may be more likely.Collectively, other events may be more likely.�� Ignores lots of information.Ignores lots of information.

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BayesBayes Decision RuleDecision Rule

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

�� Consider the FarConsider the Far--Fetched Lottery Fetched Lottery decision:decision:

ACTSACTS

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Would you gamble? Would you gamble?

EVENTSEVENTS ProbabilityProbability

ACTSACTS

GambleGamble Don’t GambleDon’t Gamble

HeadHead .5.5 +$10,000+$10,000 $0$0

TailTail .5.5 −−5,0005,000 00

The FarThe Far--Fetched Lottery DecisionFetched Lottery Decision

EVENTSEVENTSProbaProba--bilitybility

ACTSACTS

GambleGamble Don’t GambleDon’t Gamble

Payoff Payoff ×× Prob.Prob. Payoff Payoff ×× ProbProb

HeadHead .5.5 +$5,000+$5,000 $0$0

TailTail .5.5 −−2,5002,500 00

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Most people prefer not to gamble!Most people prefer not to gamble!

�� That That violatesviolates the the BayesBayes decision rule.decision rule.�� But the rule often indicates preferred choices even though it is But the rule often indicates preferred choices even though it is

not perfect.not perfect.

TailTail .5.5 −−2,5002,500 00

Expected Payoff:Expected Payoff: $2,500$2,500 $0$0

Expected Monetary ValueExpected Monetary Value

N: N: Number of states of natureNumber of states of naturek: Number of alternative decisionsk: 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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∑ == N

j jiji PXAEMV1

)(

Example:Example:

States of NatureAlternatives Favorable

MarketP(0.5)

UnfavorableMarket P(0.5)

Expectedvalue

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P(0.5)Construct $200,000 -$180,000 $10,000

Constructsmall plant

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

Do nothing $0 $0 $0

Best choice

large plant

Decision Making under CertaintyDecision Making under Certainty

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

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

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��A marketing research company A marketing research company requests $65000 for this informationrequests $65000 for this information

Questions:Questions:

��Should Getz hire the firm to make Should Getz hire the firm to make this study?this study?

��How much does this information How much does this information

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��How much does this information How much does this information worth?worth?

��What is the value of perfect What is the value of perfect information?information?

Expected Value With Perfect Expected Value With Perfect Information (Information (EVPI))

EVPI = Expected Payoff - Maximum expected payoff

under Certainty with no information

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

∑N

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jP.}){∑=

N

1j

iji X(Max

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

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

Expected Payoff under Ceratinty=

Example: Example: Expected Value of Expected Value of Perfect InformationPerfect Information

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Expected Value of Perfect Expected Value of Perfect InformationInformation

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

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EVPIEVPI = = EExpectedxpected VValuealue Under Certainty Under Certainty --MMax(ax(EMVEMV))

= = $100,000 $100,000 -- $40,000$40,000

= $60,000= $60,000

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

Ex: Toy ManufacturerEx: Toy Manufacturer

��How to choose among 4 types of How to choose among 4 types of tippitippi--toes?toes?

��Demand for tippiDemand for tippi--toes is uncertain:toes is uncertain:

Light demand: 25,000 units (10%)Light demand: 25,000 units (10%)

Moderate demand: 100,000 units Moderate demand: 100,000 units

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Moderate demand: 100,000 units Moderate demand: 100,000 units (70%)(70%)

Heavy demand: 150,000 units Heavy demand: 150,000 units (20%)(20%)

EventEvent(State of (State of nature)nature) ProbabilityProbability

ACT (choice)ACT (choice)

Gears and Gears and leverslevers

Spring Spring ActionAction

Weights and Weights and pulleyspulleys

Payoff Tablew

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LightLight 0.100.10 $25,000$25,000 --$10,000$10,000 --$125,000$125,000

ModerateModerate 0.700.70 400,000400,000 440,000440,000 400,000400,000

HeavyHeavy 0.200.20 650,000650,000 740,000740,000 750,000750,000

Maximum Expected Payoff Maximum Expected Payoff CriteriaCriteria

ACT (choice)ACT (choice)

Gears and Gears and leverslevers

Spring Spring ActionAction

Weights and Weights and pulleyspulleys

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

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Expected Expected PayoffPayoff

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

Maximum expected payoff occurs at Spring Action!

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

�� Decision tables are convenient for Decision tables are convenient for problems problems

wwithith one set of alternatives and states ofone set of alternatives and states of naturenature..�� With several sets of alternatives and states of With several sets of alternatives and states of

nature (sequential decisions), decision nature (sequential decisions), decision trees aretrees are

Decision TreesDecision Treesw

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nature (sequential decisions), decision nature (sequential decisions), decision trees aretrees areusedused!!

�� EMV criterion EMV criterion is the is the most most commonlycommonly usedused criterion criterion in decision tree analysis.in decision tree analysis.

Steps of Steps 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 Assign probabilities to the states of naturenature

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naturenature

��Estimate payoffs for each possible Estimate payoffs for each possible combination of alternatives and states of combination of alternatives and states of naturenature

��Solve the problem by computing Solve the problem by computing expected monetary values for each stateexpected monetary values for each state--ofof--nature nodenature node

Decision TreeDecision Tree

1

State 1

State 2

Outcome 1Outcome 1

Outcome 2Outcome 2

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2

State 1

State 2

Decision Node

Outcome 3Outcome 3

Outcome 4Outcome 4

State of Nature Node

Ex1:Ex1:Getz Products Decision Getz Products Decision TreeTree

Payoffs

$200,000

-$180,0001

Unfavorable market (0.5)

Favorable market (0.5)

Favorable market (0.5)EMV for node 1 = $10,000

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$100,000

-20,000

0

2Unfavorable market (0.5)

Favorable market (0.5)

Construct small plant

EMV for node 2 = $40,000

A More Complex Decision TreeA More Complex Decision Tree

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

��Conduct a survey for $10000?Conduct a survey for $10000?

��Build a large or small plant or not Build a large or small plant or not

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��Build a large or small plant or not Build a large or small plant or not build?build?

Ex1:Ex1:Getz Products Decision Getz Products Decision TreeTree

1$1

06,4

00 2

3

$190,000

-$190,000

$90,000

-$30,000

-$10,000

$190,000

Fav. Mkt (0.78)

Fav. Mkt (0.78)

Fav. Mkt (0.27)

Unfav. Mkt (0.22)

Unfav. Mkt (0.22)

$106,400

$63,600

-$87,400

1st decision point

2nd decision point

$49,200

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14

7

$49,

200

$40,

000

$2,4

00

5

6

$190,000

-$190,000

$90,000

-$30,000

-$10,000

$200,000

-$180,000

$100,000

-$20,000

$0

Fav. Mkt (0.27)

Fav. Mkt (0.27)

Fav. Mkt (0.5)

Fav. Mkt (0.5)

Unfav. Mkt (0.73)

Unfav. Mkt (0.73)

Unfav. Mkt (0.5)

Unfav. Mkt (0.5)

-$87,400

$2,400

$10,000

$40,000

Resulting DecisionResulting Decision

��EMV of conducting the survey=$49,200EMV of conducting the survey=$49,200

��EMV of not conducting the EMV of not conducting the survey=$40,000survey=$40,000

So Getz should conduct the survey!So Getz should conduct the survey!

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BIS 517BIS 517--Aslı Sencer ErdemAslı Sencer Erdem 3535

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

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

Ex2: Ponderosa Record Ex2: Ponderosa Record CompanyCompany

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

��Alternative1: test market 5000 units Alternative1: test market 5000 units and if favorable, market 45000 units and if favorable, market 45000 units nationallynationally

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nationallynationally

��Alternative2: Market 50000 units Alternative2: Market 50000 units nationallynationally

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

Ex2: PonderosaEx2: Ponderosa--costs, pricescosts, prices

�� Fixed payment to group: $5000Fixed payment to group: $5000

�� Production cost:Production cost: $5000 and $0.75/cd$5000 and $0.75/cd

�� Handling, distribution: $0.25/cdHandling, distribution: $0.25/cd

�� Price of a cd: $2/cdPrice of a cd: $2/cd

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Cost of producing 5,000 cd’s Cost of producing 5,000 cd’s =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 cd’sCost of producing 45,000 cd’s

=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 cd’sCost of producing 50,000 cd’s

=5,000+5,000+(0.25+0.75)50,000=$60,000=5,000+5,000+(0.25+0.75)50,000=$60,000

Ex2: PonderosaEx2: Ponderosa--Event ProbabilitiesEvent Probabilities

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

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P(failure|test result is favorable)=0.2P(failure|test result is favorable)=0.2

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

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

Decision Tree for Ponderosa Decision Tree for Ponderosa Record CompanyRecord Company

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Backward ApproachBackward Approachw

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Sensitivity AnalysisSensitivity Analysis

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

Question:Question:

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Question:Question:

--How does $1000 payoff change with How does $1000 payoff change with respect to a change inrespect to a change in

�� success probability (0.8 currently)?success probability (0.8 currently)?�� earnings of success ($90,000 currently)?earnings of success ($90,000 currently)?�� test marketing cost ($15,000 currently)?test marketing cost ($15,000 currently)?

Application Areas of Decision Application Areas of Decision TheoryTheory

Investments in Investments in

research and developmentresearch and developmentplant and equipmentplant and equipmentnew buildings and structuresnew buildings and structures

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new buildings and structuresnew buildings and structures

Production and Inventory controlProduction and Inventory control

Aggregate PlanningAggregate Planning

MaintenanceMaintenance

Scheduling, etc.Scheduling, etc.

ReferencesReferences

�� Lapin L.L., Whisler W.D., Quantitative Decision Making, Lapin L.L., Whisler W.D., Quantitative Decision Making, 7e, 2002.7e, 2002.

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

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

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Management, 8e, 2003.Management, 8e, 2003.

�� Anderson,Anderson, DD..RR..,, SweeneySweeney DD..J,J, WilliamsWilliams TT..AA..,, StatisticsStatisticsforfor BusinessBusiness andand Economics,Economics, 88ee,, 20022002..

�� Taha,Taha, HH..,, OperationsOperations Research,Research, 19971997..

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