2 decision making

© 2011 Lew Hofmann

Decision MakingDecision Making

© 2011 Lew Hofmann

Overview

• Break-Even Analysis

• Preference Matrices

• Payoff Tables (Decision Tables)

• Decision Trees

© 2011 Lew Hofmann

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. (EG: material costs, labor, etc.)

• Fixed costs (F) are those costs that remain constant with changes in output level. (EG: Insurance, rent, property taxes, etc.)

© 2011 Lew Hofmann

Break-Even Analysis

• Gives you a comparison of Revenues and Total Costs over a range of operations/output.• Assumes all changes are linear• Fixed Costs (F) are assumed to be level and

constant as output changes.• Variable Costs (c) are assumed to change linearly

with output.• Revenues are assumed to change linearly with

output.

• In reality, no changes are linear, but the technique can still be helpful.

© 2011 Lew Hofmann

Break-Even GraphD

olla

rs

Volume of Output (Q)

Fixed Costs

Total Costs

Total Revenues

Break-Even Point

Loss

Profits

© 2011 Lew Hofmann

Break-Even Analysis in the real world.

• Fixed costs increase incrementally as output capacity increases. • As capacity increases, periodic expansion of plant

and equipment is required, insurance cost and taxes increase…

• Variable Cost increase is curvilinear as output production increases. • As you purchase greater quantities of materials,

you usually get quantity discounts.• Revenue increase is curvilinear as output

increases.• Quantity discounts are given to larger sales.

© 2011 Lew Hofmann

The Complications of Non-linearity

Dol

lars

Volume of Output (Q)

Fixed Costs

Variable Costs

© 2011 Lew Hofmann

• Q is the volume in units• c is the variable cost per unit• F is the total fixed costs• p is the revenue per unit• cQ is the total variable cost.

(Variable cost per unit x Volume)

• Total cost = F + cQ (Fixed costs + total Variable costs)

• Total revenue = pQ (Revenue per unit x Volume)

• Break even is where Total Revenue = Total costs: pQ = F + cQ

Break-Even AnalysisBreak-Even Analysis(You don’t need the formula for exams.)

© 2011 Lew Hofmann

Break-Even Analysis can tell you…

...if a forecast sales volume is sufficient to make

a profit, or at least cover your costs.

...how low your variable cost per unit must be to

break even, given current product price and

sales-volume forecast.

...what the fixed cost need to be to break even.

...how price levels affect the break-even volume.

© 2011 Lew Hofmann

Hospital ExampleHospital Example

A hospital is considering a new procedure to be offered, billed at $200 per patient. The fixed cost (F) per year is…

$100,000, with variable costs at $100 per patient.

How many patients do they need to cover their costs? (I.E. what is the break-even level for this service?)

QQ = = FF / (/ (pp - - cc) = ) = 100,000100,000 / ( / (200200--100100) = 1,000 patients) = 1,000 patients

Where Q = total # of patients; F = fixed costs; p = revenue per unit; c = variable costs per patient

© 2011 Lew Hofmann

Using Excel Solver

• Select the Break-Even solver model on the L-Drive (under my name)

• Select MGT 360

© 2011 Lew Hofmann

Using Excel Solver cont.

• Select Excel Solver Models

• Select the Break-Even Analysis model.

© 2011 Lew Hofmann

Enabling the Macros

Mac

PC

© 2011 Lew Hofmann

Running The Model

• You will get this screen whether you enable the macros or not, but your answer won’t be correct if you don’t enable them.

© 2011 Lew Hofmann

Total Costs

Total Revenue

Using the Excel Solver, enter the data requested in the yellow blocks, and the answer will appear in the green block, along with the chart.

© 2011 Lew HofmannPatients (Patients (QQ))

Do

llar

sD

oll

ars

|| || || ||

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 Example(solved using graphical method)(solved using graphical method)

40,000 –40,000 –

30,000 –30,000 –

20,000 –20,000 –

10,000 –10,000 –

0 –0 –

© 2011 Lew Hofmann

40,000 –40,000 –

30,000 –30,000 –

20,000 –20,000 –

10,000 –10,000 –

0 –0 –

Patients (Patients (QQ))

DO

LL

AR

SD

OL

LA

RS

|| || || ||

500500 10001000 15001500 20002000

(2000, 40,000)(2000, 40,000)

Total annual revenuesTotal annual revenues


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

0 100,000 02000 300,000 400,000

© 2011 Lew Hofmann

Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($) (Q) (100,000 + 100Q) (200Q)

0 100,000 02000 300,000400,000

Total annual costsTotal annual costs


DO

LL

AR

SD

OL

LA

RS

|| || || ||

500500 10001000 15001500 20002000

Fixed costsFixed costs

(2000, 40,000)(2000, 40,000)

(2000, 30,000)(2000, 30,000)Total annual revenuesTotal annual revenues

40,000 –40,000 –

30,000 –30,000 –

20,000 –20,000 –

10,000 –10,000 –

0 –0 –

© 2011 Lew Hofmann




|| || || ||

500500 10001000 15001500 20002000


Break-even quantity is 1000 patientsBreak-even quantity is 1000 patients

(2000, 40,000)(2000, 40,000)

(2000, 30,000(2000, 30,000))

ProfitsProfits

LossLoss


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

0 100,000 02000 300,000 400,000

DO

LL

AR

SD

OL

LA

RS

40,000 –40,000 –

30,000 –30,000 –

20,000 –20,000 –

10,000 –10,000 –

0 –0 –

© 2011 Lew Hofmann

40,000 –40,000 –

30,000 –30,000 –

20,000 –20,000 –

10,000 –10,000 –

0 –0 –




|| || || ||

500500 10001000 15001500 20002000


ProfitsProfits

LossLoss

Sensitivity AnalysisSensitivity Analysis

Forecast (Q) = Forecast (Q) = 1,5001,500

pQ – (F + cQ)

200(1500) – [100,000 + 100(1500)]

= $5,000 profit

Per-patient cost of the procedure.

DO

LL

AR

SD

OL

LA

RS

© 2011 Lew Hofmann

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

• Breakeven analysis can be used to choose Breakeven analysis can be used to choose between two different processesbetween two different processes• Also can be used to decide between using an Also can be used to decide between using an

internal process or outsourcing that process internal process or outsourcing that process service.service.

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

• A forecast of sales (volume level) is then applied to see which alternative (process) has the lowest cost for that volume.

© 2011 Lew Hofmann

Two-Process Example

• Process #1 fixed costs for making widgets is $12,000, and the variable cost is $1.50 per unit.

• Process #2 fixed costs for making widgets is $2400 and the variable cost is $2.00 per unit.

• If expected demand is 25,000 widgets, which process is less expensive?

© 2011 Lew Hofmann

Breakeven forBreakeven forTwo ProcessesTwo Processes

For any volume above 19,200 units, Process #1 should be used.

© 2011 Lew Hofmann

Q =Fm – Fb

cb – cm

Q =12,000 – 2,400

2.0 – 1.5Breakeven forBreakeven forTwo ProcessesTwo Processes

Q = 19,200

© 2011 Lew Hofmann

• An analysis that allows you to rate alternatives by quantifying tangible and/or intangible criteria.

• Criteria are ranked and weighted for each alternative being evaluated.

• Each score is weighted according to its perceived importance to you, with the total weights typically equaling 100.• Thus it measures your preference.

• Alternative with highest sum of the weighted scores is the one you most prefer.

Preference MatrixPreference Matrix

© 2011 Lew Hofmann

Using the Preference Matrix

(A hypothetical example)

• Problem: Where to go to dinner.

• Possible Criteria:• Price• Quality• Distance• Atmosphere• Type of food

© 2011 Lew Hofmann

Weighting the Criteria

CriteriaPrice

Quality

Distance

Atmosphere

Type of food

Weight 4

1

3

1

1

These are the criteria I selected, and the weights are how important each criteria is relative to the other criteria.

I used a scale of 1-10 (1 being 10% of the weight), but any scale can be used.

© 2011 Lew Hofmann

Evaluating McDonalds

Criteria Weight (w)

Eval. (e)

Score (w)(e)

Price 4 10 40

Quality 1 2 2

Distance 3 8 24

Atmosphere 1 2 2

Type of food 1 5 5 73

For simplicity, the valuation scale should be the same as the one for the weights. Evaluations are subjective, and can be individual preference or group-consensus.

The score of 73 is used to compare with the scores from other options.

© 2011 Lew Hofmann

PerformancePerformance WeightsWeights ScoresScores Weighted ScoresWeighted ScoresCriterionCriterion ((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 Matrix(New product evaluation)(New product evaluation)

Management decides that a product evaluation must have a total score of at least 800 to be acceptable.

© 2011 Lew Hofmann


Preference MatrixPreference MatrixEstablishing the criteria weightsEstablishing the criteria weights

PerformancePerformance WeightsWeights ScoresScores Weighted ScoresWeighted Scores CriterionCriterion ((AA)) ((BB)) ((AA x x BB))

Market potentialMarket potential 30

Unit profit marginUnit profit margin 20

Operations compatibilityOperations compatibility 20

Competitive advantageCompetitive advantage 15

Investment requirementInvestment requirement 10

Project riskProject risk 5

In this example, the most weight is given to a product’s market potential.

© 2011 Lew Hofmann


Preference MatrixPreference MatrixRating a productRating a product

PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted Score CriterionCriterion ((AA)) ((BB)) ((AA x x BB))

Market potentialMarket potential 30 8

Unit profit marginUnit profit margin 20 10

Operations compatibilityOperations compatibility 20 6

Competitive advantageCompetitive advantage 15 10

Investment requirementInvestment requirement 10 2

Project riskProject risk 5 4

These are the ratings for one of the products being considered.

© 2011 Lew Hofmann



PerformancePerformance Weight Weight Score Score Weighted Score Weighted Score CriterionCriterion ((AA)) ((BB)) ((AA x x BB))

Total weighted score = 750Total weighted score = 750

Market potentialMarket potential 30 8 240

Unit profit marginUnit profit margin 20 10 200

Operations compatibilityOperations compatibility 20 6 120

Competitive advantageCompetitive advantage 15 10 150

Investment requirementInvestment requirement 10 2 20

Project riskProject risk 5 4 20

© 2011 Lew Hofmann



PerformancePerformance Weight Weight Score Score Weighted ScoreWeighted Score CriterionCriterion ((AA)) ((BB)) ((AA x x BB))

Weighted score =Weighted score = 750750

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

Market potentialMarket potential 30 8 240

Unit profit marginUnit profit margin 20 10 200

Operations compatibilityOperations compatibility 20 6 120

Competitive advantageCompetitive advantage 15 10 150

Investment requirementInvestment requirement 10 2 20

Project riskProject risk 5 4 20

© 2011 Lew Hofmann

© 2011 Lew Hofmann

Decision-Making Terminology

• Alternatives• Possible solutions or alternatives to a problem.

• States of Nature (Chance Events)

• Events effecting the outcome, but which the decision-maker cannot control.

• EG: What the stock market is going to do.

• Payoffs• Profits, losses, costs, etc. that result from

implementing an alternative.

© 2011 Lew Hofmann

Decision-Making Contexts

• Certainty• Only one state of nature can occur.• You have complete knowledge about the outcome.

(Break-even analysis is decision making under certainty.)

• Risk• Two or more states of nature• You know the probabilities of their occurrence

(Expected-value analysis is decision making under risk.)

• Uncertainty• The number of states of nature may be unknown.• Probabilities of occurrence are unknown.

(Payoff tables are a good example.)

© 2011 Lew Hofmann

A Continuum of Awareness

Decreasing Knowledge about the problem situation

Certainty Risk Uncertainty

Only 1 state of nature

More than one state of nature with known probabilities

States of nature may be unknown, or a least their probabilities are unknown.

© 2011 Lew Hofmann

Payoff Tables Under Uncertainty

Bear Market

Level Market

Bull Market

Stock A 400 500 600

Stock B 200 400 1100

Stock C 100 500 900

With uncertainty, you don’t know the probabilities for the states of nature.

States of Nature

Alternatives

© 2011 Lew Hofmann

Payoff Tables Under Uncertainty

• Maximax• The optimist’s approach

• Maximin• The pessimist’s approach

• Minimax Regret• Another pessimistic approach

© 2011 Lew Hofmann

Maximax ApproachPick the best of the best payoffs

Bear Market

Level Market

Bull Market

Stock A 400 500 600

Stock B 200 400 1100

Stock C 100 500 900

© 2011 Lew Hofmann

Maximin ApproachPick the Best of the Worst payoffs

Bear Market

Level Market

Bull Market

Stock A 400 500 600

Stock B 200 400 1100

Stock C 100 500 900

© 2011 Lew Hofmann

Minimax Regret ApproachMinimizes the regret you would have from making the wrong choice.

Bear Market

Level Market

Bull Market

Stock A 400 500 600

Stock B 200 400 1100

Stock C 100 500 900

Determine the maximum regret, if any, you could have for each payoff.

0 0

0

0

500

200 100

300 200

© 2011 Lew Hofmann

Regret MatrixCompute total regrets for each alternative

and select the one with the smallest total regret.

Bear Market

Level Market

Bull Market

Stock A 0 0 500

Stock B 200 100 0

Stock C 300 0 200

500

300

500Add across each row to get the total regret for each alternative.Pick the alternative that has the LEAST regret.

© 2011 Lew Hofmann

Expected Value AnalysisDecision Making Under Risk!

Bear Market

Level Market

Bull Market

Probabilities .2 .6 .2

Stock A 400 500 600

Stock B 200 400 1100

Stock C 100 500 900

© 2011 Lew Hofmann

Expected Value AnalysisComputing Expected Values

Bear Market

Level Market

Bull Market

EV

Probabilities .2 .6 .2 Stock A 400x.2 500x.6 600x.2

=80 =300 =120 500

Stock B 200x.2 400x.6 1100x.2

=40 =240 =220 500

Stock C 100x.2 500x.6 900x.2

=20 =300 =180 500

© 2011 Lew Hofmann

Expected Value Analysisusing the Excel Solver

Why does the solver model pick stock A? (All three have the same expected value!)

© 2011 Lew Hofmann

Probability Distributions as a measure of risk.

Probabilities

Expected Payoffs100 200 300 400 500 600 700 800 900 1000 1100

.1

.2

.3

.4

.5

.6

CB

A

Probability distributions for the alternatives

C CB

B

BAA

C A

© 2011 Lew Hofmann

Standard Deviation as a measure of risk

Alternative

Stock A

Stock B

Stock C

Standard Deviation

63.25

316.93

252.98

The lower the standard deviation, the less likely it is that payoffs will deviate from the mean.

© 2011 Lew Hofmann

Coefficient of Variation

• Standard Deviation only works as a measure of risk when the expected values you obtain are relatively similar.

• Coefficient of Variation must be used to measure risk when the expected values are widely different.

© 2011 Lew Hofmann

Using Coefficient of Variation

Std. Dev.

Expected Value

Coeff. Of Variation

Stock A 63.25 500 0.1265

Stock B 316.93 500 0.63386

Stock C 252.98 500 0.50596

Coefficient of Variation =Standard Deviation

Expected Value

Since the expected values are the same in this example, there is no need to use Coefficient of Variation.

© 2011 Lew Hofmann

Using Coefficient of Variation

Expected Value R.O.I

Standard Deviation

Coefficient of Variation

X 100 15% 23.5 .235

Y 100,000 15% 12,600 .126

Smaller coefficient of variation indicates less risk!

In this example the Expected Values of the alternatives are widely different, so we need to use Coefficient of Variation to make our comparison.

© 2011 Lew Hofmann

AlternativesAlternatives LowLow HighHigh

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

EventsEvents(Uncertain Demand)(Uncertain Demand)

MaxiMin Decision(another example)

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)

© 2011 Lew Hofmann


MaxiMax Decision

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)



© 2011 Lew Hofmann

MiniMax Regret


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 the best choice you could have made with a different and the best choice you could have made with a different alternative, given the same state of nature (event).alternative, given the same state of nature (event).



© 2011 Lew Hofmann

MiniMax Regret


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. You could not regret. You could not have done better with have done better with a different alternative.a different alternative.

If you chose a large facility and If you chose a large facility and demand is low, you regret you didn’t demand is low, you regret you didn’t build a small facility. Your regret is build a small facility. Your regret is 40, which is the difference between 40, which is the difference between the 160 you got and the 200 you the 160 you got and the 200 you could have gotten. could have gotten.



© 2011 Lew Hofmann

MiniMax Regret


Alternatives LowAlternatives Low HighHigh

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

EventsEvents

TotalTotalRegrets Regrets 530 530 40 4010001000

Regret MatrixRegret Matrix

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



If you chose a small If you chose a small facility and demand is facility and demand is high, you forgo the high, you forgo the higher payoff of 800, higher payoff of 800, and thus have a and thus have a regret of 530. regret of 530.

© 2011 Lew Hofmann

Expected ValueDecision Making under Risk

EventsEvents

200*200*0.40.4 + 270* + 270*0.60.6 = 242 = 242160*160*0.40.4 + 800* + 800*0.60.6 = 544 = 544

Multiply each payoff times the probability of Multiply each payoff times the probability of occurrence its associated event.occurrence its associated event.

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

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


© 2011 Lew Hofmann

• Decision Trees Decision 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 (states of nature) are Event points (states of nature) are represented by circles.represented by circles.

Decision TreesDecision Trees

© 2011 Lew Hofmann

= 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





EE 11& P

robab

ility

& Pro

babili

ty

Altern

ativ

e 1

Altern

ativ

e 1

Alternative 2

Alternative 2

Payoff 1Payoff 1

Payoff 2Payoff 2

1 2


© 2011 Lew Hofmann

Buy stock A

Buy stock B

Buy stock C

Bear Market

Bear Market

Bear Market

Level Market

Level Market

Level Market

Bull Market

Bull Market

Bull Market

$400 x .2 = $80

$500 x .6 = $300

$600 x .2 = $120

$200 x .2 = $40

$400 x .6 = $240

$1100 x .2 = $220

$100 x .2 = $20

$500 x .6 = $300

$900 x .2 = $180

.2

.6

.2

.2

.6

.2

.2

.6

.2

$500

$500

$500

© 2011 Lew Hofmann


•After drawing a decision tree, we solve it by working from right to left, starting with decisions furthest 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.

© 2011 Lew Hofmann

Sample ProblemSample Problem

A retailer must decide whether to build a small or a large facility at a new location. Demand can either be low or high, with the probabilities estimated to be 0.4 and 0.6 respectively.

If a small facility is built and demand is high, the manager may choose not to expand (payoff = $223,000) or expand (payoff = $270,000) However, if demand is low, there is no reason to expand. (payoff = $200,000)

If a large facility is built and demand is low, the retailer can do nothing ($40,000) or stimulate demand by advertising. Advertising is estimated to have a 0.3 chance of a modest response ($20,000) and a 0.7 chance of a large response ($220,000).

If a large facility is built and demand is high, the payoff is $800,000.

© 2011 Lew Hofmann

Smal

l fac

ility

Smal

l fac

ility

Large facility

Large facility

1

Drawing the TreeDrawing the Tree

There are two choices: Build a small facility or build a large facility.

A retailer must decide whether to build a small or a large facility at a new location.

© 2011 Lew Hofmann

Smal

l fac

ility

Smal

l fac

ility

Large facility

Large facility

Low demand [Low demand [0.40.4]]

Don’t expandDon’t expand

ExpandExpand

$200$200

$223$223

$270$270

High demand

High demand

[[0.60.6]]

1

2

Drawing the TreeDrawing the TreeThe “event” (state of nature) in this example is demand. It can be either high or low.

Demand can either be small or large, with the probabilities estimated to be 0.4 and 0.6 respectively. If a small facility is built and demand is high, the manager may choose not to expand (payoff = $223,000) or expand (payoff = $270,000) However, if demand is low, there is no reason to expand. (payoff = $200,000)

© 2011 Lew Hofmann

Smal

l fac

ility

Smal

l fac

ility

Large facility

Large facility

1

Low dem

and

Low dem

and

[[0.40.4]]



ExpandExpand

Do nothingDo nothing

AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800

Modest response [Modest response [0.30.3]]

Sizable response [Sizable response [0.70.7]]

$20$20

$220$220

High demand

High demand

[[0.60.6]]

High demand [High demand [0.60.6]]

2

3

Completed DrawingCompleted DrawingThis is the completed tree. Now we start pruning it from the right. We will begin with decision #3.

The state of nature for the 3rd decision is the possible response to the advertising

If a large facility is built and demand is high, the payoff is $800,000.

If a large facility is built and demand is low, the retailer can do nothing ($40,000) or stimulate demand by advertising. Advertising is estimated to have a 0.3 chance of a modest response ($20,000) and a 0.7 chance of a large response ($220,000).

© 2011 Lew Hofmann

Solving Decision Solving Decision #3#3

Low dem

and

Low dem

and

[0.4]

[0.4]

Smal

l fac

ility

Smal

l fac

ility

Large facility

Large facility

Low demand [0.4]Low demand [0.4]


ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800

Modest response [Modest response [0.30.3]]

Sizable response [Sizable response [0.70.7]]

$20$20

$220$220

High demand

High demand

[0.6][0.6]

High demand [0.6]High demand [0.6]

1

2

3

0.30.3 x $20 = x $20 = $6$6

0.70.7 x $220 = x $220 = $154$154$6 + $154 = $6 + $154 = $160$160

The 40% probability of low demand is not yet considered since it is the same for both advertising states of nature.

© 2011 Lew Hofmann


ExpandExpand


AdvertiseAdvertise

$200$200

$223$223

$270$270

$40$40

$800$800

$160$160Low d

emand

Low dem

and

[0.4]

[0.4]

Smal

l fac

ility

Smal

l fac

ility

Large facility

Large facility


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]


1

2

3


$160$160

We eliminate the “do nothing” option since it has a lower payoff than does advertising.

© 2011 Lew Hofmann

$160$160



$20$20

$220$220


Low dem

and

Low dem

and

[0.4]

[0.4]

$160$160

Smal

l fac

ility

Smal

l fac

ility

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

Here there is no state of nature involved with expanding or not expanding. They are simply choices if we end up with high demand.

Expanding has a Expanding has a higher expected higher expected value than not value than not expanding.expanding.

© 2011 Lew Hofmann

$242$242

x x 0.40.4 = $80 = $80

x x 0.60.6 = $162 = $162

$242$242

$160$160Low d

emand

Low dem

and

[0.4]

[0.4]

$270$270

$160$160

Smal

l fac

ility

Smal

l fac

ility

Large facility

Large facility



ExpandExpand


AdvertiseAdvertise

$200 $200

$223$223

$270$270

$40$40

$800$800



$20$20

$220$220

High demand

High demand

[[0.60.6]]


1

2

3

Solving Decision Solving Decision #1#1Low demand expected value of Low demand expected value of $80 is added to the high $80 is added to the high demand expected value of $162demand expected value of $162

© 2011 Lew Hofmann

Solving Decision #1Solving Decision #1

$242$242

$160$160Low d

emand

Low dem

and

[[0.40.4]]

$270$270

$160$160

Smal

l fac

ility

Smal

l fac

ility

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]

High demand [High demand [0.60.6]]

1

2

3

x x 0.60.6 = $480 = $480

0.40.4 x x $160$160 = $64= $64

$544$544

The expected value of high demand for the large facility ($480) is added to the expected value of low demand for the large facility ($64).

© 2011 Lew Hofmann

$160$160Low d

emand

Low dem

and

[0.4]

[0.4]

$270$270

$160$160

Smal

l fac

ility

Smal

l fac

ility

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

Solving Decision #1Solving Decision #1

$544$544

The expected value of building a small facility can now be compared to the expected value of building a large facility.

© 2011 Lew Hofmann

Advantages of Decision Trees

• Gives structure to a problem situation• Visual representation of the options• Forces management to consider each

alternative and compare them• Optimum courses of action are apparent.• The only technique for dealing with multiple

(sequential) decisions.

© 2011 Lew Hofmann

Disadvantages of Decision Trees

• Many problems are too complex for visual display• Complex trees are only computational

• Subject to estimation errors (As with any probabilistic decision tool)

• Only as good as the data used.(True with any model.)

© 2011 Lew Hofmann

Homework Assignment #1Six problems: Due in class next week this time.

1. Breakeven

2. Two ProcessesRecommend using the Excel Solver for the above problems.

3. Preference Matrix

4. Payoff Table

5. Decision-Tree problem #1 (a,b)

6. Decision-Tree problem #2 (a,b)Do these manually. On the exam you will not have the use of the computer program for analyzing preference matrices, payoff tables or decision trees. Doing these problems on the computer may NOT adequately prepare you for doing the problems on the exams.

© 2011 Lew Hofmann

1. Break Even Analysis

Mary Williams, owner of Williams Products, is evaluating whether to introduce a new product line. After thinking through the production process and the costs of raw materials and equipment, she estimates the variable costs of each unit produced and sold to be $6 and the fixed costs per year at $60,000. (Solver won’t provide answers to b, c, or d.)

a.If the selling price is set at $18 each, how many units must be produced and sold for Williams to break even?

b.Williams forecasts sales of 10,000 units for the first year if the selling price is $14 each. What would be the total contribution to profits from this new product during the first year?

c.If the selling price is set at $12.50, forecast sales is 15,000 units. Which pricing strategy ($14 or $12.50) would result in the greater total contribution to profits?

d.What other considerations would be crucial to the final decision about making and marketing the new product?

© 2011 Lew Hofmann

2. Two ProcessesUse Excel Solver

Gabriel Manufacturing must implement a manufacturing process that reduces the amount of toxic by-products. Two processes have been identified that provide the same level of toxic by-product reduction. The first process would incur $300,000 of fixed costs and $600 per unit of variable costs. The second process has fixed costs of $120,000 and variable costs of $900 per unit.

a.What is the break-even quantity beyond which the first process is more attractive?

b.What is the difference in total cost if the quantity produced is 800 units? (You can either estimate this from the solver solution graph, or use the formula given in slide #21.)

© 2011 Lew Hofmann

3. Preference MatrixYou can use the Solver software or do it on a spreadsheet.

Axel Express, Inc. collected the following information on two possible locations for a new warehouse (1 = poor, 10 = excellent).

a. Which location, A or B, should be chosen on the basis of the total weighted score?

b. If the factors were weighted equally, would the choice change?

© 2011 Lew Hofmann

4. Payoff TableYou can use the Solver software or do it on a spreadsheet, but you

will need to know how to solve it manually on the test.

Build-Rite Construction has received favorable publicity from guest appearances on a public TV home improvement program. Public TV programming decisions seem to be unpredictable, so Build-Rite cannot estimate the probability of continued benefits from its relationship with the show. Demand for home improvements next year may be either low or high. But they must decide now whether to hire more employees, do nothing, or develop subcontracts with other home improvement contractors. Build-Rite has developed the following payoff table.

Alternative Low Moderate High

Hire ($250,000) $100,000 $625,000

Subcontract $100,000 $150,000 $415,000

Do Nothing $ 50,000 $ 80,000 $300,000

Which alternative is best, according to each of the following criteria?a. Maximin b. Maximax c. Minimax regret

© 2011 Lew Hofmann

5. Decision Tree #1

A manager is trying to decide whether to buy one machine or two. If only one is purchased, and demand proves to be excessive, the second machine can be purchased later. Some sales will be lost, however, because the lead time for producing this type of machine is six months. In addition, the cost per machine will be lower if both are purchased at the same time. The probability of low demand is estimated to be 0.20. The after-tax net present value of the benefits from purchasing the two machines together is $90,000 if demand is low, and $180,000 if demand is high.

If one machine is purchased and demand is low, the net present value is $120,000. If demand is high, the manager has three options. Doing nothing has a net present value of $120,000; subcontracting, $160,000; and buying the second machine, $140,000.

a.Draw a decision tree for this problem.

b.How many machines should the company buy initially, and what is the expected payoff for this alternative?

Do this manually (no computer).

© 2011 Lew Hofmann

6. Decision Tree Problem #2Do this manually (no computer).

A manager is trying to decide whether to build a small, medium, or large facility. Demand can be low, average, or high, with the estimated probabilities being 0.25, 0.40, and 0.35 respectively.

A small facility is expected to earn an after-tax, net-present value of $18,000 if demand is low, and $75,000 if demand is medium or high. Expanding a small facility to medium size after demand is established as medium or high will only yield an after-tax net profit of $60,000. Expanding it to a large facility if demand is high, nets $125,000.

Initially building a medium-sized facility and not expanding it would result in a $25,000 loss if demand is low, but net $140,000 in medium demand and $150,000 in high demand. Expanding to a large facility at that point would only net $145,000.

Building a large facility will net $220,000 if demand is high; $125,000 if Building a large facility will net $220,000 if demand is high; $125,000 if demand is medium, and is expected to lose $60,000 if demand is low.demand is medium, and is expected to lose $60,000 if demand is low.

a.a.Draw an analyze a decision tree for this problem.Draw an analyze a decision tree for this problem.

b.b.What should management do to achieve the highest expected payoff?What should management do to achieve the highest expected payoff?

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