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Dec is ion Making
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Overview
Break-Even Analysis
Preference Matrices
Payoff Tables (Decision Tables)
Decision Trees
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Break-Even Analys is
Break-even analysisis used to compare processesby finding the volume at which two differentprocesses have equal total costs.
Break-even pointis the volume at which totalrevenues equal total costs.
Variable costs (c)are costs that vary directly withthe volume of output. (EG: material costs, labor, etc.)
Fixed costs (F)are those costs that remain constantwith changes in output level. (EG: Insurance, rent,property taxes, etc.)
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Break-Even Analys is
Gives you a comparison of Revenues andTotal Costs over a range of operations/output.
Assumes all changes are linear
Fixed Costs(F) are assumed to be level andconstant as output changes.
Variable Costs(c) are assumed to change linearlywith output.
Revenuesare assumed to change linearly withoutput.
In reality, no changes are linear, but thetechnique can still be helpful.
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Break-Even Graph
Dollars
Volume of Output (Q)
Fixed Costs
Total Costs
Total Revenues
Break-Even Point
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Break-Even Analys is
in the real world .
Fixed costsincrease incrementally as outputcapacity increases.
As capacity increases, periodic expansion of plantand equipment is required, insurance cost andtaxes increase
Variable Costincrease is curvilinear asoutput production increases.
As you purchase greater quantities of materials,you usually get quantity discounts.
Revenueincrease is curvilinear as outputincreases. Quantity discounts are given to larger sales.
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The Compl icat ions o f
Non-l ineari ty
Dollars
Volume of Output (Q)
Fixed Costs
Variable Costs
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Qis the volume in units
cis the variable cost per unit
Fis the total fixed costs
pis the revenue per unit
cQis 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 = Totalcosts: pQ = F+ cQ
Break-Even Analys is(You dont need the formula for exams.)
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Break-Even Analys is
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 tobreak 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.
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Hosp ital 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 $100 per patient.
How many patients do they need to cover their costs?(I.E. what is the break-even level for this service?)
Q= F/ (p- c) = 100,000/ (200-100) = 1,000 patien ts
Where Q= total # of patients; F= fixed costs; p= revenue per unit;
c= variable costs per patient
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Using Excel Solver
Select the Break-Even solver model on the L-Drive(under my name)
Select MGT 360
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Using Excel Solver cont.
Select Excel Solver Models
Select the Break-Even
Analysis model.
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Enabling the Macros
Mac
PC
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Running The Model
You will get this screen whether you enable themacros or not, but your answer wont be correct if
you dont enable them.
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Total Costs
Total Revenue
Using the Excel Solver,enter the data requestedin the yellow blocks, andthe answer will appear inthe green block, alongwith the chart.
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Patients (Q)
Dollars
| | | |
500 1000 1500 2000
Quantity Total Annual Total Annual
(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
Hosp i tal Examp le(solved using graphical method)
40,000
30,000
20,000
10,000
0
Q tit T t l A l T t l A l
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40,000
30,000
20,000
10,000
0
Patients (Q)
DOLLARS
| | | |
500 1000 1500 2000
(2000, 40,000)
Total annual revenues
Quantity Total Annual Total Annual
(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
Q tit T t l A l T t l A l
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Quantity Total Annual Total Annual
(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000
400,000
Total annual costs
Patients (Q)
DOLLARS
| | | |
500 1000 1500 2000
Fixed costs
(2000, 40,000)
(2000, 30,000)Total annual revenues
40,000
30,000
20,000
10,000
0
Q tit T t l A l T t l A l
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Total annual revenues
Total annual costs
Patients (Q)
| | | |
500 1000 1500 2000
Fixed costs
Break-even quantity is 1000 patients
(2000, 40,000)
(2000, 30,000)
Profits
Loss
Quantity Total Annual Total Annual
(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
DOLLARS
40,000
30,000
20,000
10,000
0
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40,000
30,000
20,000
10,000
0
Total annual revenues
Total annual costs
Patients (Q)
| | | |
500 1000 1500 2000
Fixed costs
Profits
Loss
Sens i tiv i ty Analys is
Forecast (Q) = 1,500
pQ(F+ cQ)
200(1500)[100,000 + 100(1500)]
= $5,000 profit
Per-patient cost of theprocedure.
DOLLARS
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Two Processes and
Make-o r-Buy Dec is ions
Breakeven analysis can be used to choosebetween two different processes
Also can be used to decide between using an
internal process or outsourcing that processservice.
The solution finds the point at which the totalcosts of each of the two processes are equal.
A forecast of sales (volume level) is thenapplied to see which alternative (process)has the lowest cost for that volume.
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Two-Process Example
Process #1 fixed costs for makingwidgets is $12,000, and the variablecost is $1.50 per unit.
Process #2 fixed costs for makingwidgets is $2400 and the variable costis $2.00 per unit.
If expected demand is 25,000 widgets,which process is less expensive?
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Breakeven for
Two Processes
For any volume above 19,200units, Process #1 should beused.
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Q=FmFb
cbcm
Q=12,0002,400
2.01.5
Breakeven for
Two Processes
Q = 19,200
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An analysis that allows you to rate alternatives byquantifying tangible and/or intangible criteria.
Criteria are ranked and weighted for eachalternative being evaluated.
Each score is weighted according to its perceivedimportance to you, with the total weights typicallyequaling 100.
Thus it measures your preference.
Alternative with highest sum of the weightedscores is the one you most prefer.
Preference Matr ix
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Using the
Preference Matrix(A hyp othet ical example)
Problem: Where to go to dinner.
Possible Criteria:
Price
Quality
Distance
Atmosphere
Type of food
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Weigh t ing the Cri ter ia
Criteria
Price
QualityDistance
Atmosphere
Type of food
Weight
4
13
1
1
These are the criteria I selected, and the weights are howimportant each criteria is relative to the other criteria.
I used a scale of 1-10 (1 being 10% of the weight), but anyscale can be used.
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Evaluat ingMcDonalds
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 theweights. Evaluations are subjective, and can be individual preference orgroup-consensus.
The score of 73 is used to compare with the scores from other options.
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Performance Weights Scores Weighted Scores
Criterion (A ) (B) (A x B)Market potentialUnit profit marginOperations compatibilityCompetitive advantage
Investment requirementProject risk
Thresho ld sco re = 800
Preference Matr ix(New product evaluation)
Management decides that a productevaluation must have a total score of atleast 800 to be acceptable.
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Thresho ld score = 800
Preference Matr ixEstablishing the criteria weights
Performance Weights Scores Weighted ScoresCriterion (A ) (B) (A x B)
Market potential 30
Unit profit margin 20
Operations compatibility 20
Competitive advantage 15
Investment requirement 10
Project risk 5
In this example,the most weight
is given to aproducts marketpotential.
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Thresho ld sco re = 800
Preference Matr ixRating a produ ct
Performance Weight Score Weighted ScoreCriterion (A ) (B) (A x B)
Market potential 30 8
Unit profit margin 20 10
Operations compatibility 20 6
Competitive advantage 15 10
Investment requirement 10 2
Project risk 5 4
These are the ratings for one ofthe products being considered.
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Thresho ld score = 800
Preference Matr ix
Performance Weight Score Weighted ScoreCriterion (A ) (B) (A x B)
Total weighted score = 750
Market potential 30 8 240
Unit profit margin 20 10 200
Operations compatibility 20 6 120
Competitive advantage 15 10 150
Investment requirement 10 2 20
Project risk 5 4 20
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Thresho ld score = 800
Preference Matr ix
Performance Weight Score Weighted ScoreCriterion (A ) (B) (A x B)
Weighted score = 750
Score does no t meet the
threshold and is rejected.
Market potential 30 8 240
Unit profit margin 20 10 200
Operations compatibility 20 6 120
Competitive advantage 15 10 150
Investment requirement 10 2 20
Project risk 5 4 20
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Decision-Making
Terminology
Alternatives
Possible solutions or alternatives to a problem.
States of Nature(Chance Events) Events effecting the outcome, but which thedecision-maker cannot control.
EG: What the stock market is going to do.
Payoffs Profits, losses, costs, etc. that result from
implementing an alternative.
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Decis ion-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.)
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A Cont inuum of
Awareness
Decreasing Knowledge about the problem situation
Certainty Risk Uncertainty
Only 1 state
of nature
More than one
state of naturewith knownprobabilities
States of nature
may be unknown,or a least theirprobabilities areunknown.
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Payo ff Tab les
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 dont know the probabilities for the states of nature.
States of Nature
Alternatives
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Payo ff Tab les
Under Uncertainty
Maximax
The optimists approach Maximin
The pessimists approach
Minimax Regret Another pessimistic approach
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MaximaxApproachPick the best of the best payoffs
BearMarket
LevelMarket
BullMarket
Stock A 400 500 600
Stock B 200 400 1100
Stock C 100 500 900
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MaximinApproachPick the Best of the Worst payoffs
BearMarket
LevelMarket
BullMarket
Stock A 400 500 600
Stock B 200 400 1100
Stock C 100 500 900
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Minimax RegretApproachMinimizes the regret you would have from making the wrong choice.
BearMarket
LevelMarket
BullMarket
Stock A 400 500 600
Stock B 200 400 1100
Stock C100 500 900
Determine the maximum regret, if any, you could have for each payoff.
0 0
0
0
500
200 100
300 200
R t M t i
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Regret MatrixCompute total regrets for each alternative
and select the one with the smallest total regret.
BearMarket
LevelMarket
BullMarket
Stock A 0 0 500
Stock B 200 100 0
Stock C 300 0 200
500
300
500
Add across each row to get the total regret for each alternative.Pick the alternative that has the LEASTregret.
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Expected Value Analys isDecision Making Under Risk!
BearMarket
LevelMarket
BullMarket
Probabilities .2 .6 .2
Stock A 400 500 600
Stock B 200 400 1100
Stock C 100 500 900
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Expected Value Analys isComputing 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
E t d V l A l i
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Expected Value Analysisusing the Excel Solver
Why does the solver model pick stock A?(All three have the same expected value!)
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Probabi l i ty Distr ibut ions
as a measu re of r isk.
Probabilities
Expected Payoffs100 200 300 400 500 600 700 800 900 1000 1100
.1
.2
.3
.4
.5
.6
C
BA
Probabilitydistributions for
the alternatives
C CB
B
BAA
C A
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Standard Deviat ion
as a measu re of r isk
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.
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Coeff ic ien t o f Variat ion
Standard Deviationonly works as a measureof risk when the expected values you obtain
are relatively similar.
Coefficient of Variationmust be used tomeasure risk when the expected values arewidely different.
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Using Coeff ic ient of Variat ion
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.
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Using Coeffic ien t o f Variat ion
ExpectedValue
R.O.IStandardDeviation
Coefficientof 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.
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Alternatives Low High
Small facility 200 270Large facility 160 800Do nothing 0 0
Events(Uncertain Demand)
MaxiMin Decis ion(another examp le)
1. Look at the payoffs for each alternative and identify thelowest payoff for each.
2. Choose the alternative that has the highest of these.(the maximum of the minimums)
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Events(Uncertain Demand)
MaxiMaxDecis ion
1. Look at the payoffs for each alternative and identify thehighest payoff for each.
2. Choose the alternative that has the highest of these.(the maximum of the maximums)
Alternatives Low High
Small facility 200 270Large facility 160 800Do nothing 0 0
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MiniMax Regret
Events(Uncertain Demand)
Look at eachpayoff and ask yourself, If I end up here, doI have any regrets?
Your regret, if any, is the difference between that payoffand the best choice you could have made with a differentalternative, given the same state of nature (event).
Alternatives Low High
Small facility 200 270Large facility 160 800Do nothing 0 0
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MiniMax Regret
Events(Uncertain Demand)
If you chose a small
facility and demand islow, you have zeroregret. You could nothave done better witha different alternative.
If you chose a large facility and
demand is low, you regret you didntbuild a small facility. Your regret is40, which is the difference betweenthe 160 you got and the 200 youcould have gotten.
Alternatives Low High
Small facility 200 270Large facility 160 800Do nothing 0 0
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MiniMax Regret
Events(Uncertain Demand)
Alternatives Low High
Small facility 0 530Large facility 40 0Do nothing 200 800
EventsTotalRegrets530401000
Regret MatrixBuilding a large
facility offers the
least regret.
Alternatives Low High
Small facility 200 270Large facility 160 800Do nothing 0 0
If you chose a smallfacility and demand ishigh, you forgo thehigher payoff of 800,and thus have a
regret of 530.
Expec ted Value
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Expec ted ValueDecision Making under Risk
Events
200*0.4+ 270*0.6= 242
160*0.4+ 800*0.6= 544
Multiply each payoff times the probability ofoccurrence its associated event.
Select the alternative with the highest weighted payoff.
Alternatives Low High(0.4) (0.6)
Small facility 200 270Large facility 160 800
Do nothing 0 0
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Decis ion Trees are schematic modelsof alternatives available along with their
possible consequences. They are used in sequential decisionsituations.
Decision points are represented bysquares.
Event points (states of nature) arerepresented by circles.
Dec ision Trees
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= Event node
= Decision node
1stdecision
Possible2nd decision
Payoff 1
Payoff 2
Payoff 3
Alternative 3
Alternative 4
Alternative 5
Payoff 1
Payoff 2
Payoff 3
E1& Probabi l i ty
E2& Probabi l i ty
E3& Prob abi l ity
E2& Probabi l i ty
E3& Probabi l i ty
Payoff 1
Payoff 2
1 2
Dec ision Trees
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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
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Dec ision Trees
After drawing a decision tree, we solve it by workingfrom right to left, starting with decisions furthest to theright, and calculating the expected payoff for each of
its possible paths.
We pick the alternative for that decision that has thebest expected payoff.
We saw off, or prune, the branches not chosen bymarking two short lines through them.
The decision nodes expected payoff is the one
associated with the single remaining branch.
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Sample Prob lem
A retailer must decide whether to build a small or a large facility at a newlocation. Demand can either be low or high, with the probabilitiesestimated to be 0.4and 0.6respectively.
If a small facility is built and demand is high, the manager may choosenot 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 alarge response ($220,000).
If a large facility is built and demand is high, the payoff is $800,000.
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1
Draw ing the Tree
There are two choices:Build a small facility orbuild a large facility.
A retailer must decide whether to builda small or a large facility at a newlocation.
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Low demand [0.4]
Dont expand
Expand
$200
$223
$270
1
2
Draw ing the TreeThe event (state ofnature) in this exampleis demand. It can beeither high or low.
Demand can either be small or large, with the
probabilities estimated to be 0.4and 0.6respectively.If a small facility is built and demand is high, themanager may choose not to expand (payoff =$223,000) or expand (payoff = $270,000) However, ifdemand is low, there is no reason to expand. (payoff= $200,000)
If a large facility is built anddemand is low, the retailer can do
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1
Low demand [0.4]
Dont expand
Expand
Do nothing
Advertise
$200
$223
$270
$40
$800
Modest response [0.3]
Sizable response [0.7]
$20
$220
High demand [0.6]
2
3
Completed Draw ingThis is the completed tree.
Now we start pruning itfrom the right. We willbegin with decision #3.
The state of nature for
the 3rd
decision is thepossible response to theadvertising
If a large facility is builtand demand is high, thepayoff is $800,000.
nothing ($40,000) or stimulatedemand by advertising.
Advertising is estimated to have a0.3 chance of a modest response
($20,000) and a 0.7 chance of alarge response ($220,000).
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Solv ing Decis ion #3
Low demand [0.4]
Dont expand
Expand
Do nothing
Advertise
$200
$223
$270
$40
$800
Modest response [0.3]
Sizable response [0.7]
$20
$220
High demand [0.6]
1
2
3
0.3x $20 = $6
0.7x $220 = $154
$6 + $154 = $160The 40% probabilityof low demand is notyet considered sinceit is the same forboth advertisingstates of nature.
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Dont expand
Expand
Do nothing
Advertise
$200
$223
$270
$40
$800
$160
Low demand [0.4]
Modest response [0.3]
Sizable response [0.7]
$20
$220
High demand [0.6]
1
2
3
Solv ing Decis ion #3
$160
We eliminate the do
nothing option since it has a
lower payoff than doesadvertising.
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$160
Modest response [0.3]
Sizable response [0.7]
$20
$220
Solv ing Decis ion #2
$160
Low demand [0.4]
Dont expand
Expand
Do nothing
Advertise
$200
$223
$270
$40
$800
High demand [0.6]
1
2
3
$270
Here there is no state ofnature involved withexpanding or not expanding.They are simply choices if we
end up with high demand.
Expanding h as a
higher expected
value than n ot
expanding.
Low demand expected value of
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$242
x 0.4= $80
x 0.6= $162
$242
$160
$270
$160
Low demand [0.4]
Dont expand
Expand
Do nothing
Advertise
$200
$223
$270
$40
$800
Modest response [0.3]
Sizable response [0.7]
$20
$220
High demand [0.6]
1
2
3
Solv ing Decis ion #1p
$80 is added to the high
demand expected value of $162
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So lving Dec is ion #1
$242
$160
$270
$160
Low demand [0.4]
Dont expand
Expand
Do nothing
Advertise
$200
$223
$270
$40
$800
Modest response [0.3]
Sizable response [0.7]
$20
$220
High demand [0.6]
1
2
3
x 0.6= $480
0.4x $160= $64
$544
The expected value ofhigh demand for the largefacility ($480) is added tothe expected value of lowdemand for the largefacility ($64).
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$160
$270
$160
$242
$544
Low demand [0.4]
Dont expand
Expand
Do nothing
Advertise
$200
$223
$270
$40
$800
Modest response [0.3]
Sizable response [0.7]
$20
$220
High demand [0.6]
1
2
3
So lving Dec is ion #1
$544
The expected value ofbuilding a small facilitycan now be compared tothe expected value of
building a large facility.
Ad t f
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Advantages of
Decis ion Trees
Gives structure to a problem situation
Visual representation of the options
Forces management to consider eachalternative and compare them
Optimum courses of action are apparent.
The only technique for dealing with multiple(sequential) decisions.
Disadvantages o f
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Disadvantages o f
Dec ision Trees
Many problems are too complex forvisual 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.)
H k A i t #1
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Homework Assignment #1Six problems: Due in class next week this time.
1. Breakeven
2. Two Processes
Recommend using the Excel Solver for the above problems.
3. Preference Matrix4. Payoff Table
5. Decision-Tree problem #1 (a,b)
6. Decision-Tree problem #2 (a,b)Do these manually.On the exam you will nothave the use of thecomputer program for analyzing preference matrices, payoff tables ordecision trees. Doing these problems on the computer may NOT adequatelyprepare you for doing the problems on the exams.
1 Break Even Analysis
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1. Break Even Analysis
Mary Williams, owner of Williams Products, is evaluating whether tointroduce a new product line. After thinking through the productionprocess and the costs of raw materials and equipment, she estimates thevariable costs of each unit produced and sold to be $6 and the fixed costsper year at $60,000. (Solver wont 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 fromthis 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 totalcontribution to profits?
d. What other considerations would be crucial to the final decision aboutmaking and marketing the new product?
2 Two Processes
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2. Two ProcessesUse Excel Solver
Gabriel Manufacturing must implement a manufacturing processthat reduces the amount of toxic by-products. Two processeshave 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 secondprocess has fixed costs of $120,000 and variable costs of $900per 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 solversolution graph, or use the formula given in slide #21.)
3. Preference Matrix
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You 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 totalweighted score?
b. If the factors were weighted equally, would the choice change?
4. Payoff Table
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yYou 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 TVprogramming decisions seem to be unpredictable, so Build-Rite cannotestimate the probability of continued benefits from its relationship withthe show. Demand for home improvements next year may be either lowor high. But they must decide now whether to hire more employees, do
nothing, or develop subcontracts with other home improvementcontractors. 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
5 Decision Tree #1
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5. Decision Tree #1
A manager is trying to decide whether to buy one machine or two. Ifonly one is purchased, and demand proves to be excessive, the secondmachine can be purchased later. Some sales will be lost, however,because the lead time for producing this type of machine is six months. Inaddition, the cost per machine will be lower if both are purchased at thesame time. The probability of low demand is estimated to be 0.20. The
after-tax net present value of the benefits from purchasing the twomachines together is $90,000 if demand is low, and $180,000 if demand ishigh.
If one machine is purchased and demand is low, the net present valueis $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 isthe expected payoff for this alternative?
Do this manually (no computer).
6. Decision Tree Problem #2
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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 probabilitiesbeing 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 itto 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 wouldonly net $145,000.
Building a large facility will net $220,000 if demand is high; $125,000 ifdemand is medium, and is expected to lose $60,000 if demand is low.
a. Draw an analyze a decision tree for this problem.