© 2007 Pearson Education Decision Making Supplement A.

© 2007 Pearson Education

Decision MakingDecision Making

Supplement ASupplement A


Break-Even AnalysisBreak-Even Analysis

Break-even analysis is used to compare processes 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 vary directly with the volume of output.

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


“Q” is the volume of customers or units, “c” is the unit variable cost, F is fixed costs and p is the revenue per unit

cQ is the total variable cost.Total cost = F + cQTotal revenue = pQBreak-even is where pQ = F + cQ

(Total revenue = Total cost)

Break-Even AnalysisBreak-Even Analysis


Break-Even Analysis can tell you…

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

How low variable cost per unit must be to break even given current prices and sales forecast.

How low the fixed cost need to be to break even.

How price levels affect the break-even volume.


Hospital ExampleHospital ExampleExample A.1Example A.1

A hospital is considering a new procedure to be offered at $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?


400 –400 –

300 –300 –

200 –200 –

100 –100 –

0 –0 –

Patients (Patients (QQ))

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500500 10001000 15001500 20002000

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

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

0 100,000 02000 300,000 400,000

Hospital ExampleHospital ExampleExample A.1Example A.1 continuedcontinued



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

0 100,000 02000 300,000 400,000

400 –400 –

300 –300 –

200 –200 –

100 –100 –

0 –0 –


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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


Total annual costsTotal annual costs


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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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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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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


Application A.1


Application A.1Solution

TR = pQTR = pQ TC = F + cQTC = F + cQQQ



TC = F + cQTC = F + cQTR = pQTR = pQQQ



TR = pQTR = pQQQ TC = F + pQTC = F + pQ

pQ = F + cQpQ = F + cQ


Two Processes and Two Processes and Make-or-Buy Decisions Make-or-Buy Decisions

Breakeven analysis can be used to choose

between two processes or between an internal process and buying those services or materials.

The solution finds the point at which the total costs of each of the two alternatives are equal.

The forecast volume is then applied to see which alternative has the lowest cost for that volume.


Breakeven for Breakeven for Two ProcessesTwo Processes

Example A.3Example A.3


Q =Fm – Fb

cb – cm

Q =12,000 – 2,400

2.0 – 1.5Breakeven forBreakeven for

Two ProcessesTwo ProcessesExample A.3Example A.3


Q =Fm – Fb

cb – cm

Q = 19,200 saladsBreakeven for Breakeven for Two ProcessesTwo Processes

Example A.3Example A.3


Application A.2

FFmm – F – Fbb

c cbb – –

ccm m

==Q =Q = $300,000 – $0$300,000 – $0 $9 – $7$9 – $7

= = $150,000$150,000


Preference MatrixPreference Matrix

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

The criteria can be scored on any scale as long as the same scale is applied to all the alternatives being compared.

Each score is weighted according to its perceived importance, 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 can compare the scores for alternatives against one another or against a predetermined threshold.


PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted ScoreCriterionCriterion ((AA)) ((BB)) ((AA x x BB))

Market potentialMarket potentialUnit profit marginUnit profit marginOperations compatibilityOperations compatibilityCompetitive advantageCompetitive advantageInvestment requirementInvestment requirementProject riskProject risk

Threshold score Threshold score = 800= 800

Preference MatrixPreference MatrixExample A.4Example A.4



Market potentialMarket potential 3030Unit profit marginUnit profit margin 2020Operations compatibilityOperations compatibility 2020Competitive advantageCompetitive advantage 1515Investment requirementInvestment requirement 1010Project riskProject risk 55


Preference MatrixPreference MatrixExample A.4Example A.4 continuedcontinued



Market potentialMarket potential 3030 88Unit profit marginUnit profit margin 2020 1010Operations compatibilityOperations compatibility 2020 66Competitive advantageCompetitive advantage 1515 1010Investment requirementInvestment requirement 1010 22Project riskProject risk 55 44





Market potentialMarket potential 3030 88 240240Unit profit marginUnit profit margin 2020 1010 200200Operations compatibilityOperations compatibility 2020 66 120120Competitive advantageCompetitive advantage 1515 1010 150150Investment requirementInvestment requirement 1010 22 2020Project riskProject risk 55 44 2020






Weighted score =Weighted score = 750750






Weighted score =Weighted score = 750750



Score does not meet the Score does not meet the threshold and is rejected.threshold and is rejected.



Application A.3

Repeat this process for each alternative — pick the one with the largest weighted scoreRepeat this process for each alternative — pick the one with the largest weighted score

The concept of a weighted scoreThe concept of a weighted score


Decision Theory

Decision theory is a general approach to decision making when the outcomes associated with alternatives are 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 the payoff for each alternative

in each event.4. Estimate the probability of each event.

(The total probabilities must add up to 1.)5. Select the decision rule to evaluate the

alternatives.


Decision Rules

Decision Making Under Uncertainty is when you are unable to estimate the probabilities of events. Maximin: The best of the worst. A pessimistic approach. Maximax: The best of the best. An optimistic approach. Minimax Regret: Minimizing your regret (also pessimistic) Laplace: The alternative with the best weighted payoff

using assumed probabilities.

Decision Making Under Risk is when one is able to estimate the probabilities of the events. Expected Value: The alternative with the highest weighted

payoff using predicted probabilities.


AlternativesAlternatives LowLow HighHigh

Small facilitySmall facility 200200 270270Large facilityLarge facility 160160 800800Do nothingDo nothing 00 00

EventsEvents(Uncertain Demand)(Uncertain Demand)

MaxiMin DecisionExample A.6 a.

1.1. Look at the payoffs for each alternative and identify the Look at the payoffs for each alternative and identify the lowest 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)





MaxiMax Decision Example A.6 b.

1.1. Look at the payoffs for each alternative and identify the Look at the payoffs for each alternative and identify the ““highesthighest” 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)


Laplace(Assumed equal probabilities)

Example A.6 c.

AlternativesAlternatives LowLow HighHigh(0.5)(0.5) (0.5) (0.5)


EventsEvents

200*0.5 + 270*0.5 = 235200*0.5 + 270*0.5 = 235160*0.5 + 800*0.5 = 480 160*0.5 + 800*0.5 = 480

Multiply each payoff by the probability of Multiply each payoff by the probability of occurrence 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.


MiniMax Regret Example A.6 d.




Look at Look at eacheach payoff and ask yourself, payoff and ask yourself, “If I end up here, do “If I end up here, do I have any regrets?”I have any regrets?”

Your regret, if any, is the difference between that payoff Your regret, if any, is the difference between that payoff and what you could have had by choosing a different and 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).


MiniMax Regret Example A.6 d. continued




If you chose a small If you chose a small facility and demand is facility and demand is low, you have zero low, you have zero regret.regret.

If you chose a large facility and If you chose a large facility and demand is low, you have a regret of demand is low, you have a regret of 40. (The difference between the 40. (The difference between the 160 you got and the 200 you could 160 you got and the 200 you could have had.) have had.)


MiniMax Regret Example A.6 d. continued




Alternatives LowAlternatives Low HighHigh

Small facility 0Small facility 0 530530Large facility 40Large facility 40 00Do nothing 200Do nothing 200 800800

EventsEvents

MaxRegret MaxRegret 530 530 40 40 800 800

Regret MatrixRegret Matrix

Building a large Building a large facility offers the facility offers the least regret.least regret.


Expected ValueDecision Making under Risk

Example A.7

AlternativesAlternatives LowLow HighHigh((0.40.4)) ( (0.60.6))


EventsEvents

200*0.4 + 270*0.6 = 242200*0.4 + 270*0.6 = 242160*0.4 + 800*0.6 = 544 160*0.4 + 800*0.6 = 544

Multiply each payoff by the probability of Multiply each payoff by the probability of occurrence 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.


Example A.7

Expected Value AnalysisExpected Value Analysis


Application A.4


Application A.4

840 – 840 = 0840 – 840 = 0

840 – 370 = 470840 – 370 = 470

840 – 25 = 830840 – 25 = 830

1150 – 440 = 7101150 – 440 = 710

1150 – 220 = 9301150 – 220 = 930

1150 – 1150 = 01150 – 1150 = 0 670 – (-25) = 695670 – (-25) = 695

670 – 670 = 0670 – 670 = 0

670 – 190 = 480670 – 190 = 480 710710

930930

830830

What is the minimax regret solution?What is the minimax regret solution?


Application A.5


Decision TreesDecision Trees are schematic models are schematic models of alternatives available along with of alternatives available along with their possible consequences.their possible consequences.

They are used in sequential decision They are used in sequential decision situations.situations.

Decision points are represented by Decision points are represented by squares. squares.

Event points are represented by Event points are represented by circles.circles.

Decision TreesDecision Trees


= Event node= Event node

= Decision node= Decision node

1st1stdecisiondecision

PossiblePossible2nd 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




EE 11 &

Pro

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Altern

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Altern

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Alternative 2

Alternative 2

Payoff 1Payoff 1

Payoff 2Payoff 2

1 2




After drawing a decision tree, we solve it by working from right to left, starting with decisions farthest to the right, and calculating the expected payoff for each of its possible paths.

We pick the alternative for that decision that has the best expected payoff.

We “saw off,” or “prune,” the branches not chosen by marking two short lines through them.

The decision node’s expected payoff is the one associated with the single remaining branch.


Smal

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Smal

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Large facility

Large facility

1

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


Smal

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Smal

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Large facility

Large facility

Low demand [0.4]Low demand [0.4]

Don’t expandDon’t expand

ExpandExpand

$200$200

$223$223

$270$270

High demand

High demand

[0.6][0.6]

1

2

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


Smal

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Smal

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Large facility

Large facility

1

Low dem

and

Low dem

and

[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

High demand

High demand

[0.6][0.6]

High demand [0.6]High demand [0.6]

2

3

Completed DrawingCompleted DrawingExample A.8Example A.8


Solving Decision #3Solving Decision #3 Example A.8Example A.8

Low dem

and

Low dem

and

[0.4]

[0.4]

Smal

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Smal

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Large facility

Large facility



ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800



$20$20

$220$220

High demand

High demand

[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



ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800

$160$160Low d

emand

Low dem

and

[0.4]

[0.4]

Smal

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Smal

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Large facility

Large facility




$20$20

$220$220

High demand

High demand

[0.6][0.6]


1

2

3


$160$160


$160$160



$20$20

$220$220


Expanding has a Expanding has a higher value.higher value.

Low dem

and

Low dem

and

[0.4]

[0.4]

$160$160

Smal

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Smal

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Large facility

Large facility



ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800

High demand

High demand

[0.6][0.6]


1

2

3

$270$270


$470$470

x 0.4 = $80x 0.4 = $80

x 0.6 = $162x 0.6 = $162

$242$242

$160$160Low d

emand

Low dem

and

[0.4]

[0.4]

$270$270

$160$160

Smal

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Smal

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Large facility

Large facility



ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800



$20$20

$220$220

High demand

High demand

[0.6][0.6]


1

2

3




$242$242

$160$160Low d

emand

Low dem

and

[0.4]

[0.4]

$270$270

$160$160

Smal

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Smal

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Large facility

Large facility



ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800



$20$20

$220$220

High demand

High demand

[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


$160$160Low d

emand

Low dem

and

[0.4]

[0.4]

$270$270

$160$160

Smal

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Smal

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Large facility

Large facility

$242$242

$544$544



ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800



$20$20

$220$220

High demand

High demand

[0.6][0.6]


1

2

3


$544$544


Application A.6 Application A.6

OM Explorer Solution OM Explorer Solution


Solved Problem 1Solved Problem 1

250 –250 –

200 –200 –

150 –150 –

100 –100 –

50 –50 –

0 –0 –

Total revenuesTotal revenues

Total costsTotal costs

Units (in thousands)Units (in thousands)

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11 22 33 44 55 66 77 88

Break-evenBreak-evenquantityquantity

3.13.1

$77.7$77.7


Solved Problem 4Solved Problem 4

Bad times [0.3]Bad times [0.3]

Normal times [0.5]Normal times [0.5]

Good times [0.2]Good times [0.2]

One liftOne lift

Two liftsTwo lifts

Bad times [0.3]Bad times [0.3]

Normal times [0.5]Normal times [0.5]

Good times [0.2]Good times [0.2]

$256.0$256.0

$225.3$225.3

$256.0$256.0

$191$191

$240$240

$240$240

$151$151

$245$245

$441$441

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