01a Decision Making

8/8/2019 01a Decision Making

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2007 Pearson Education

Decision MakingDecision Making

Supplement ASupplement A


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Break-Even AnalysisBreak-Even Analysis

Break-even analysis is used to compareprocesses by finding the volume at which two

different processes have equal total costs.Break-even point is the volume at which

total revenues equal total costs.

Variable costs (c) are costs that varydirectly with the volume of output.

Fixed costs (F) are those costs that remainconstant with changes in output level.


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Q is the volume of customers or units,c is the unit variable cost, Fis fixedcosts andp is the revenue per unit

cQis the total variable cost.

Total cost =F+ cQ

Total revenue =pQ

Break-even is wherepQ= F+ cQ

(Total revenue = Total cost)

Break-Even AnalysisBreak-Even Analysis


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Break-Even Analysis cantell you

If a forecast sales volume is sufficientto break even (no profit or no loss)

How low variable cost per unit must beto break even given current prices andsales forecast.

How low the fixed cost need to be tobreak even.

How price levels affect the break-even

volume.


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Hospital ExampleHospital ExampleExample A.1Example A.1

A hospital is considering a new procedure to be offeredat $200 per patient. The fixed cost per year would be

$100,000, with total variable costs of $100 per patient.

Q = F / (p - c)Q = F / (p - c) = 100,000 / (200-100)= 100,000 / (200-100) = 1,000 patients= 1,000 patients

What is the break-even quantity for this service?


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400 400

300 300

200 200

100 100

0 0

Patients (Patients (QQ))

D

ollars

(in

thou

sands)

D

ollars

(in

thousands)

|| || || ||

500500 10001000 15001500 20002000

Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)

(Q) (100,000 + 100Q) (200Q)0 100,000 0

2000 300,000 400,000

Hospital ExampleHospital ExampleExample A.1Example A.1continuedcontinued


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(Q) (100,000 + 100Q) (200Q)

0 100,000 02000 300,000 400,000

400 400

300 300

200 200

100 100

0 0


D

ollars

(in

thou

sands)

D

ollars

(in

thousands)

|| || || ||

500500 10001000 15001500 20002000

(2000, 400)(2000, 400)

Total annual revenuesTotal annual revenues


(Q) (100,000 + 100Q) (200Q)

0 100,000 02000 300,000 400,000


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Total annual costsTotal annual costs


D

ollars

(in

thou

sands)

D

ollars

(in

thousands)

400 400

300 300

200 200

100 100

0 0

|| || || ||

500500 10001000 15001500 20002000

Fixed costsFixed costs

(2000, 400)(2000, 400)

(2000, 300)(2000, 300)


(Q) (100,000 + 100Q) (200Q)

0 100,000 02000 300,000 400,000



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D

ollars

(in

thousands)

D

ollars(in

thou

sands)

400 400

300 300

200 200

100 100

0 0

|| || || ||

500500 10001000 15001500 20002000


Break-even quantityBreak-even quantity

(2000, 400)(2000, 400)

(2000, 300(2000, 300))

ProfitsProfits

LossLoss


(Q) (100,000 + 100Q) (200Q)

0 100,000 02000 300,000 400,000


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D

ollars

(in

thousands)

D

ollars(in

thou

sands)

400 400

300 300

200 200

100 100

0 0

|| || || ||

500500 10001000 15001500 20002000


ProfitsProfits

LossLoss

Sensitivity AnalysisSensitivity AnalysisExample A.2Example A.2

Forecast = 1,500Forecast = 1,500

pQ (F+ cQ)

200(1500) [100,000 + 100(1500)]

$50,000


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Two Processes andTwo Processes andMake-or-Buy DecisionsMake-or-Buy Decisions

Breakeven analysis can be used to choosebetween two processes or between aninternal process and buying those services or

materials.

The solution finds the point at which the totalcosts of each of the two alternatives are

equal.The forecast volume is then applied to see

which alternative has the lowest cost for thatvolume.


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Breakeven forBreakeven for

Two ProcessesTwo ProcessesExample A.3Example A.3


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Q =Fm Fb

cb cm

Q =12,000 2,400

2.0 1.5

Breakeven forBreakeven for



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Q=Fm Fb

cb cm

Q= 19,200 saladsBreakeven forBreakeven for



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Preference MatrixPreference Matrix

A Preference Matrix is a table that allows you to ratean alternative according to several performance criteria.

The criteria can be scored on any scale as long as thesame scale is applied to all the alternatives beingcompared.

Each score is weighted according to its perceivedimportance, with the total weights typically equaling 100.

The total score is the sum of the weighted scores(weight score) for all the criteria. The manager cancompare the scores for alternatives against one another


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PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted Score

CriterionCriterion ((AA)) ((BB)) ((AA xx BB))Market potentialMarket potential

Unit profit marginUnit profit margin

Operations compatibilityOperations compatibility

Competitive advantageCompetitive advantage

Investment requirementInvestment requirementProject riskProject risk

Threshold scoreThreshold score = 800= 800

Preference MatrixPreference MatrixExample A.4Example A.4


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CriterionCriterion ((AA)) ((BB)) ((AA xx BB))

Market potentialMarket potential 3030

Unit profit marginUnit profit margin 2020

Operations compatibilityOperations compatibility 2020

Competitive advantageCompetitive advantage 1515

Investment requirementInvestment requirement 1010Project riskProject risk 55


Preference MatrixPreference MatrixExample A.4Example A.4continuedcontinued


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Market potentialMarket potential 3030 88

Unit profit marginUnit profit margin 2020 1010

Operations compatibilityOperations compatibility 2020 66

Competitive advantageCompetitive advantage 1515 1010

Investment requirementInvestment requirement 1010 22Project riskProject risk 55 44




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Market potentialMarket potential 3030 88 240240

Unit profit marginUnit profit margin 2020 1010 200200

Operations compatibilityOperations compatibility 2020 66 120120

Competitive advantageCompetitive advantage 1515 1010 150150

Investment requirementInvestment requirement 1010 22 2020Project riskProject risk 55 44 2020




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CriterionCriterion ((AA)) ((BB)) ((AA xx BB))Market potentialMarket potential 3030 88 240240





Weighted score =Weighted score = 750750




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Market potentialMarket potential 3030 88 240240





Weighted score =Weighted score = 750750



Score does not meet theScore does not meet the

threshold and is rejected.threshold and is rejected.


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Decision Theory

Decision theory is a general approach to decisionmaking when the outcomes associated with alternativesare often in doubt.

A manager makes choices using the following process:

1. List the feasible alternatives2. List the chance events (states of nature).3. Calculate thepayofffor each alternative

in each event.4. Estimate theprobabilityof each event.

(The total probabilities must add up to 1.)

5. Select the decision rule to evaluate thealternatives.


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Decision Rules

Decision Making Under Uncertainty is when you areunable to estimate the probabilities of events. Maximin: The best of the worst. A pessimistic approach.

Maximax: The best of the best. An optimistic approach.

MinimaxRegret: Minimizing your regret (also pessimistic)

Laplace: The alternative with the best weighted payoffusing assumed probabilities.

Decision Making Under Riskis when one is able toestimate the probabilities of the events. ExpectedValue: The alternative with the highest weighted

payoff using predicted probabilities.


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Clemens Model of Decision Analysis[adapted from Fig. 1.1]

Identify the decisionsituation &understand

objectives Identify alternatives

Decompose &

model the problemproblem structureuncertainty

preferences

Choose the bestalternative

Sensitivity analysis

Iterate or continuethe analysis?

Implement chosen

alternative


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OConnors Model

ID theDecision;

Set

boundariesfor analysis

IDAlternatives

DevelopObjectiveFunction

DevelopInfluenceDiagram

ConductSensitivityAnalysis

RefineInfluenceDiagram

Structure &ComputeDecision

Tree or RunM.C.

Simulation

Model DMsUtility

ComputeEVPI


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AlternativesAlternatives LowLow HighHigh

Small facilitySmall facility 200200 270270Large facilityLarge facility 160160 800800

Do nothingDo nothing 00 00

EventsEvents(Uncertain Demand)(Uncertain Demand)

MaxiMin DecisionExample A.6a.

1.1. Look at the payoffs for each alternative and identify theLook at the payoffs for each alternative and identify thelowest payoff for each.lowest payoff for each.

2.2. Choose the alternative that has the highest of these.Choose the alternative that has the highest of these.

(the maximum of the minimums)(the maximum of the minimums)


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MaxiMaxDecisionExample A.6b.

1.1. Look at the payoffs for each alternative and identify theLook at the payoffs for each alternative and identify thehighesthighest payoff for each. payoff for each.

2.2. Choose the alternative that has the highest of these.Choose the alternative that has the highest of these.

(the maximum of the maximums)(the maximum of the maximums)


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Laplace(Assumed equal probabilities)

Example A.6c.


(0.5)(0.5) (0.5)(0.5)

Small facilitySmall facility 200200 270270

Large facilityLarge facility 160160 800800


EventsEvents

200*0.5 + 270*0.5 = 235200*0.5 + 270*0.5 = 235

160*0.5 + 800*0.5 = 480160*0.5 + 800*0.5 = 480

Multiply each payoff by the probability ofMultiply each payoff by the probability ofoccurrence of its associated event.occurrence of its associated event.

Select the alternative with the highest weighted payoff.Select the alternative with the highest weighted payoff.


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MiniMax Regret

Example A.6d.





Look atLook at

eacheach

payoff and ask yourself,payoff and ask yourself,

If I end up here, doIf I end up here, do

I have any regrets?I have any regrets?

Your regret, if any, is the difference between that payoffYour regret, if any, is the difference between that payoffand what you could have had by choosing a differentand what you could have had by choosing a different

alternative, given the same state of nature (event).alternative, given the same state of nature (event).


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MiniMax RegretExample A.6d. continued





If you chose a smallIf you chose a smallfacility and demand isfacility and demand islow, you have zerolow, you have zeroregret.regret.

If you chose a large facility andIf you chose a large facility and

demand is low, you have a regret ofdemand is low, you have a regret of40. (The difference between the40. (The difference between the

160 you got and the 200 you could160 you got and the 200 you couldhave had.)have had.)


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MiniMax Regret

Example A.6d. continued





Alternatives LowAlternatives Low HighHigh

Small facility 0Small facility 0 530530

Large facility 40Large facility 40 00

Do nothing 200Do nothing 200 800800

EventsEvents

MaxRegretMaxRegret

530530

4040

800800

Regret MatrixRegret MatrixBuilding a largeBuilding a large

facility offers thefacility offers the

least regret.least regret.

E pected Val e


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Expected ValueDecision Making under Risk

Example A.7


((0.40.4)) ((0.60.6))

Small facilitySmall facility 200200 270270

Large facilityLarge facility 160160 800800


EventsEvents

200*0.4 + 270*0.6 = 242200*0.4 + 270*0.6 = 242

160*0.4 + 800*0.6 = 544160*0.4 + 800*0.6 = 544

Multiply each payoff by the probability ofMultiply each payoff by the probability ofoccurrence of its associated event.occurrence of its associated event.

Select the alternative with the highest weighted payoff.Select the alternative with the highest weighted payoff.


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Decision TreesDecision Treesare schematic modelsare schematic modelsof alternatives available along withof alternatives available along with

their possible consequences.their possible consequences.They are used in sequential decisionThey are used in sequential decision

situations.situations.Decision points are represented byDecision points are represented by

squares.squares.Event points are represented byEvent points are represented by

circles.circles.

Decision TreesDecision Trees


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= Event node= Event node

= Decision node= Decision node

1st1st

decisiondecisionPossiblePossible

2nd decision2nd decision

Payoff 1Payoff 1

Payoff 2Payoff 2

Payoff 3Payoff 3

Alternative 3Alternative 3



Payoff 1Payoff 1

Payoff 2Payoff 2

Payoff 3Payoff 3

EE11 & Probability& Probability

EE22& Probability& Probability




EE11&

Prob

ability

&Pr

obab

ility

Altern

ativ

e1

Alter

nativ

e1

Alterna

tive2

Alternat

ive2

Payoff 1Payoff 1

Payoff 2Payoff 2

1 2

Decision TreesDecision Trees


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Smallf

acili

ty

Sm

allf

acili

ty

Largefacility

Largefa

cility

1

Drawing the TreeDrawing the TreeExample A.8Example A.8


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Small

facilit

y

Small

facilit

y

Larg

efacility

Larg

efacility

Low demand [0.4]Low demand [0.4]

Dont expandDont expand

ExpandExpand

$200$200

$223$223

$270$270

Highdemand

Highdemand

[0.6]

[0.6]

1

2

Drawing the TreeDrawing the TreeExample A.8Example A.8continuedcontinued


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Small

facilit

y

Small

facilit

y

Largefacility

Largefacility

1

Lowde

mand

Lowde

mand

[0.4]

[0.4]



ExpandExpand

Do nothingDo nothing

AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800

Modest response [0.3]Modest response [0.3]

Sizable response [0.7]Sizable response [0.7]

$20$20

$220$220

Highdeman

d

Highdeman

d

[0.6]

[0.6

]

High demand [0.6]High demand [0.6]

2

3

Completed DrawingCompleted DrawingExample A.8Example A.8

S #S l i D i i #3


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Solving Decision #3Solving Decision #3

Example A.8Example A.8

Lowde

man

d

Lowde

mand

[0.4]

[0.4]

Small

facilit

y

Small

facilit

y

Larg

efacility

Largefacility



ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800



$20$20

$220$220

Highdema

nd

Highdeman

d

[0.6]

[0.6]


1

2

3

0.3 x $20 = $60.3 x $20 = $6

0.7 x $220 = $1540.7 x $220 = $154

$6 + $154 = $160$6 + $154 = $160

S #


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ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800

$160$160Lo

wde

man

d

Lowde

mand

[0.4]

[0.4]

Small

facilit

y

Small

facilit

y

Larg

efacility

Largefacility




$20$20

$220$220

Highdema

nd

Highdeman

d

[0.6]

[0.6]


1

2

3



$160$160

S l i D i i #2S l i D i i #2


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$160$160



$20$20

$220$220



Expanding has aExpanding has a

higher value.higher value.

Lowde

man

d

Lowde

mand

[0.4]

[0.4]

$160$160

Small

facilit

y

Small

facilit

y

Largefacility

Largefacility



ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800

Highdema

nd

Highdeman

d

[0.6]

[0.6]


1

2

3

$270$270

S l i D i i #1


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$470$470

x 0.4 = $80x 0.4 = $80

x 0.6 = $162x 0.6 = $162

$242$242

$160$160Lo

wde

mand

Lowdema

nd

[0.4]

[0.4]

$270$270

$160$160

Small

facilit

y

Smallf

acili

ty

Largefacility

Largefacility



ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800



$20$20

$220$220

Highdeman

d

Highdeman

d

[0.6][0.6]


1

2

3





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$242$242

$160$160Lo

wdema

nd

Lowdema

nd

[0.4]

[0.4]

$270$270

$160$160

Small

facilit

y

Smallf

acili

ty

Largefacility

Largefacility



ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800



$20$20

$220$220

Highdeman

d

Highdeman

d

[0.6][0.6]


1

2

3

x 0.6 = $480x 0.6 = $480

0.4 x $160 = $640.4 x $160 = $64

$544$544



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$160$160Lo

wdem

and

Lowdem

and

[0.4]

[0.4]

$270$270

$160$160

Small

facilit

y

Small

facilit

y

Largefacility

Largefacility

$242$242

$544$544



ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800



$20$20

$220$220

Highdemand

Highdemand

[0.6][0.6]


1

2

3



$544$544


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