The document discusses various decision making techniques including break-even analysis, preference matrices, and payoff tables. Break-even analysis is used to determine the sales volume needed for total revenue to equal total costs. Preference matrices allow alternatives to be evaluated based on weighted criteria. Payoff tables can be used under uncertainty when the probabilities of different outcomes are unknown. Maximizing the highest potential payoff is one approach, known as maximax.

1. Decision Making
© 2011 Lew Hofmann

2. Overview
• Break-Even Analysis
• Preference Matrices
• Payoff Tables (Decision Tables)
• Decision Trees
© 2011 Lew Hofmann

3. Break-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

4. 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

5. Break-Even Graph
Total Revenues fi ts
Pro
Total Costs
Dollars
Break-Even Point
s s
Lo Fixed Costs
Volume of Output (Q)
© 2011 Lew Hofmann

6. 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

7. The Complications of
Non-linearity
Dollars
Variable Costs
Fixed Costs
Volume of Output (Q)
© 2011 Lew Hofmann

8. Break-Even Analysis
(You don’t need the formula for exams.)
• 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
© 2011 Lew Hofmann

9. 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

10. Hospital 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 patients
Where Q = total # of patients; F = fixed costs; p = revenue per unit;
c = variable costs per patient
© 2011 Lew Hofmann

11. Using Excel Solver
• Select the Break-Even solver model on the L-Drive
(under my name)
• Select MGT 360
© 2011 Lew Hofmann

12. Using Excel Solver cont.
• Select Excel Solver Models
• Select the Break-Even
Analysis model.
© 2011 Lew Hofmann

13. Enabling the Macros
Mac
PC
© 2011 Lew Hofmann

14. 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

15. 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.
Total Revenue
Total Costs
© 2011 Lew Hofmann

16. Hospital Example
(solved using graphical method)
40,000 –
Quantity Total Annual Total Annual
30,000 –
(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
Dollars
20,000 – 0 100,000 0
2000 300,000 400,000
10,000 –
0–
| | | |
500 1000 1500 2000
Patients (Q)
© 2011 Lew Hofmann

17. Quantity Total Annual Total Annual
(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 0
2000 300,000 400,000
40,000 – (2000, 40,000)
30,000 – Total annual revenues
20,000 –
DOLLARS
10,000 –
0–
| | | |
500 1000 1500 2000
Patients (Q)
© 2011 Lew Hofmann

18. Quantity Total Annual Total Annual
(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 0
2000 300,000
400,000
40,000 – (2000, 40,000)
30,000 –
Total annual revenues
(2000, 30,000)
20,000 – Total annual costs
DOLLARS
10,000 –
0– Fixed costs
| | | |
500 1000 1500 2000
Patients (Q)
© 2011 Lew Hofmann

19. Quantity Total Annual Total Annual
(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 0
2000 300,000 400,000
40,000 – (2000, 40,000)
Profits
30,000 –
Total annual revenues
(2000, 30,000)
20,000 – Total annual costs
DOLLARS
Break-even quantity is 1000 patients
10,000 –
0– Loss Fixed costs
| | | |
500 1000 1500 2000
Patients (Q)
© 2011 Lew Hofmann

20. Per-patient cost of the
procedure.
Sensitivity Analysis
pQ – (F + cQ)
Total annual revenues
200(1500) ––[100,000 + 100(1500)]
40,000
= $5,000 profit Profits
30,000 –
Total annual costs
20,000 –
DOLLARS
Forecast (Q) = 1,500
10,000 –
0– Loss Fixed costs
| | | |
500 1000 1500 2000
Patients (Q)
© 2011 Lew Hofmann

21. Two Processes and
Make-or-Buy Decisions
• Breakeven analysis can be used to choose
between two different processes
• Also can be used to decide between using an
internal process or outsourcing that process
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

22. 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

23. Breakeven for
Two Processes
For any volume above 19,200
units, Process #1 should be
used.
© 2011 Lew Hofmann

24. Fm – Fb
Q=
cb – cm
Breakeven for 12,000 – 2,400
Q=
Two Processes 2.0 – 1.5
Q = 19,200
© 2011 Lew Hofmann

25. Preference Matrix
• 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.
© 2011 Lew Hofmann

26. 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

27. Weighting the Criteria
Criteria Weight
Price 4
Quality 1
Distance 3
Atmosphere 1
Type of food 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

28. Evaluating
McDonalds
Criteria Weight Eval. Score
(w) (e) (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

29. Preference Matrix
(New product evaluation)
Management decides that a product
Threshold score = 800 evaluation must have a total score of at
least 800 to be acceptable.
Performance Weights Scores Weighted Scores
Criterion (A ) (B ) (A x B )
Market potential
Unit profit margin
Operations compatibility
Competitive advantage
Investment requirement
Project risk
© 2011 Lew Hofmann

30. Preference Matrix
Establishing the criteria weights
Threshold score = 800
Performance Weights Scores Weighted Scores
Criterion (A ) (B ) (A x B )
Market potential 30
In this example,
Unit profit margin 20
the most weight
Operations compatibility 20
is given to a
Competitive advantage 15 product’s market
Investment requirement 10 potential.
Project risk 5
© 2011 Lew Hofmann

31. Preference Matrix
Rating a product
These are the ratings for one of
Threshold score = 800 the products being considered.
Performance Weight Score Weighted Score
Criterion (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
© 2011 Lew Hofmann

32. Preference Matrix
Threshold score = 800
Performance Weight Score Weighted Score
Criterion (A ) (B ) (A x B )
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
© 2011 Lew Hofmann Total weighted score = 750

33. Preference Matrix
Score does not meet the
Threshold score = 800 threshold and is rejected.
Performance Weight Score Weighted Score
Criterion (A ) (B ) ( A x B)
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
© 2011 Lew Hofmann Weighted score = 750

34. © 2011 Lew Hofmann

35. 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

36. 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

37. A Continuum of
Awareness
Decreasing Knowledge about the problem situation
Certainty Risk Uncertainty
Only 1 state More than one States of nature
of nature state of nature may be unknown,
with known or a least their
probabilities probabilities are
unknown.
© 2011 Lew Hofmann

38. Payoff Tables
Under Uncertainty
States of Nature
Bear Level Bull
Market Market Market
Alternatives
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.
© 2011 Lew Hofmann

39. Payoff Tables
Under Uncertainty
• Maximax
• The optimist’s approach
• Maximin
• The pessimist’s approach
• Minimax Regret
• Another pessimistic approach
© 2011 Lew Hofmann

40. Maximax Approach
Pick the best of the best payoffs
Bear Level Bull
Market Market Market
Stock A 400 500 600
Stock B 200 400 1100
Stock C 100 500 900
© 2011 Lew Hofmann

41. Maximin Approach
Pick the Best of the Worst payoffs
Bear Level Bull
Market Market Market
Stock A 400 500 600
Stock B 200 400 1100
Stock C 100 500 900
© 2011 Lew Hofmann

42. Minimax Regret Approach
Minimizes the regret you would have from making the wrong choice.
Bear Level Bull
Market Market Market
Stock A 400 500 600
0 0 500
Stock B 200 400 1100
200 100 0
Stock C 100 500 900
300 0 200
Determine the maximum regret, if any, you could have for each payoff.
© 2011 Lew Hofmann

43. Regret Matrix
Compute total regrets for each alternative
and select the one with the smallest total regret.
Bear Level Bull
Market Market Market
Stock A 0 0 500 500
Stock B 200 100 0 300
Stock C 300 0 200 500
Add across each row to get the total regret for each alternative.
Pick the alternative that has the LEAST regret.
© 2011 Lew Hofmann

44. Expected Value Analysis
Decision Making Under Risk!
Bear Level Bull
Market Market Market
Probabilities
.2 .6 .2
Stock A 400 500 600
Stock B 200 400 1100
Stock C 100 500 900
© 2011 Lew Hofmann

45. Expected Value Analysis
Computing Expected Values
Bear Level Bull EV
Market Market Market
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

46. Expected Value Analysis
using the Excel Solver
Why does the solver model pick stock A?
(All three have the same expected value!)
© 2011 Lew Hofmann

47. Probability Distributions
as a measure of risk.
Probabilities B CA
.6
.5 Probability
distributions for
.4 the alternatives
.3
C B A A C B
.2
.1
100 200 300 400 500 600 700 800 900 1000 1100 Expected Payoffs
A
B
C
© 2011 Lew Hofmann

48. Standard Deviation
as a measure of risk
The lower the standard deviation,
the less likely it is that payoffs will deviate from the mean.
Alternative Standard Deviation
Stock A 63.25
Stock B 316.93
Stock C 252.98
© 2011 Lew Hofmann

49. 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

50. Using Coefficient of Variation
Standard Deviation
Coefficient of Variation =
Expected Value
Expected Coeff. Of
Std. Dev.
Value Variation
Stock A 63.25 500 0.1265
Stock B 316.93 500 0.63386
Stock C 252.98 500 0.50596
Since the expected values are the same in this example, there is no need to use Coefficient of Variation.
© 2011 Lew Hofmann

51. Using Coefficient of Variation
Expected Standard Coefficient
R.O.I
Value Deviation 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

52. MaxiMin Decision
(another example)
Events
(Uncertain Demand)
Alternatives Low High
Small facility 200 270
Large facility 160 800
Do nothing 0 0
1. Look at the payoffs for each alternative and identify the
lowest payoff for each.
2. Choose the alternative that has the highest of these.
(the maximum of the minimums)
© 2011 Lew Hofmann

53. MaxiMax Decision
Events
(Uncertain Demand)
Alternatives Low High
Small facility 200 270
Large facility 160 800
Do nothing 0 0
1. Look at the payoffs for each alternative and identify the
“highest” payoff for each.
2. Choose the alternative that has the highest of these.
(the maximum of the maximums)
© 2011 Lew Hofmann

54. MiniMax Regret
Events
(Uncertain Demand)
Alternatives Low High
Small facility 200 270
Large facility 160 800
Do nothing 0 0
Look at each payoff and ask yourself, “If I end up here, do
I have any regrets?”
Your regret, if any, is the difference between that payoff
and the best choice you could have made with a different
alternative, given the same state of nature (event).
© 2011 Lew Hofmann

55. MiniMax Regret
Events
(Uncertain Demand)
Alternatives Low High
Small facility 200 270
Large facility 160 800
Do nothing 0 0
If you chose a small If you chose a large facility and
facility and demand is demand is low, you regret you didn’t
low, you have zero build a small facility. Your regret is
regret. You could not 40, which is the difference between
have done better with the 160 you got and the 200 you
a different alternative. could have gotten.
© 2011 Lew Hofmann

56. MiniMax Regret
Events If you chose a small
(Uncertain Demand) facility and demand is
high, you forgo the
Alternatives Low High higher payoff of 800,
and thus have a
Small facility 200 270 regret of 530.
Large facility 160 800
Do nothing 0 0
Regret Matrix Events
Building a large Alternatives Low High Total
Regrets
facility offers the Small facility 0 530 530
least regret. Large facility 40 0 40
Do nothing 200 800 1000
© 2011 Lew Hofmann

57. Expected Value
Decision Making under Risk
Multiply each payoff times the probability of
occurrence its associated event.
Events
Alternatives Low High
(0.4) (0.6)
Small facility 200 270 200*0.4 + 270*0.6 = 242
Large facility 160 800 160*0.4 + 800*0.6 = 544
Do nothing 0 0
Select the alternative with the highest weighted payoff.
© 2011 Lew Hofmann

58. Decision Trees
• Decision Trees are schematic models
of alternatives available along with
their possible consequences.
• They are used in sequential decision
situations.
• Decision points are represented by
squares.
• Event points (states of nature) are
represented by circles.
© 2011 Lew Hofmann

59. Decision Trees
E1& Probability
Payoff 1
E2& Probability Payoff 2
1
e
ativ E3& Probability Payoff 3
rn
Alte Alternative 3
Payoff 1
Alternative 4
1 2 Payoff 2
ty
1st Al bi li Alternative 5
decision
te
rn ba Possible Payoff 3
at Pro 2nd decision
iv &
e E1
2
E2& Probability
= Event node Payoff 1
E3& Probability Payoff 2
= Decision node
© 2011 Lew Hofmann

60. .2 $400 x .2 = $80
Bear Market
Level Market .6 $500
$500 x .6 = $300
Buy stock A .2
Bull Market $600 x .2 = $120
Bear Market .2 $200 x .2 = $40
Buy stock B Level Market .6 $500
$400 x .6 = $240
Bull Market .2
$1100 x .2 = $220
Bear Market .2 $100 x .2 = $20
Buy stock C
Level Market .6 $500 x .6 = $300 $500
Bull Market .2
$900 x .2 = $180
© 2011 Lew Hofmann

61. Decision Trees
•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

62. Sample 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

63. Drawing the Tree
A retailer must decide whether to build
a small or a large facility at a new
ty
ci li location.
l fa
al
Sm
There are two choices:
1 Build a small facility or
La build a large facility.
rg
e
fa
ci
lit
y
© 2011 Lew Hofmann

64. The “event” (state of
nature) in this example
Drawing the Tree
is demand. It can be
either high or low.
Low demand [0.4]
$200
Hi
gh
ty d
i li [0 em
c .6 an Don’t expand
l fa ] d
al $223
Sm 2 Expand
$270
1
La
rg Demand can either be small or large, with the
e
fa probabilities estimated to be 0.4 and 0.6 respectively.
ci
lit
y 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

65. 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
Completed Drawing
0.3 chance of a modest response
This is the completed tree.
($20,000) and a 0.7 chance of a
Low demand [0.4] Now we start pruning it
large response ($220,000). $200 from the right. We will
begin with decision #3.
Hi
gh
ty d
i li [0 em
fa
c .6 an
]
Don’t expand The state of nature for
l d
al $223 the 3rd decision is the
Sm 2 possible response to the
Expand
advertising
$270
Do nothing
1
La $40
rg Advertise
e d Modest response [0.3]
fa an 3 $20
ci m
lit
y de 4]
w 0.
Lo [ Sizable response [0.7]
$220
If a large facility is built
and demand is high, the
High demand [0.6]
$800 payoff is $800,000.
© 2011 Lew Hofmann

66. Solving Decision #3
Low demand [0.4]
$200
Hi
gh
ty d
i li [0 em
c .6 an Don’t expand
l fa ] d
al $223
Sm 2 Expand
$270
Do nothing
1 0.3 x $20 = $6
La $40
rg Advertise
e d Modest response [0.3]
fa an 3 $20
ci m
lit
y de 4]
w 0.
The 40% probability Lo [ Sizable response [0.7]
of low demand is $6 + $154 = $160 $220
not yet considered 0.7 x $220 = $154
since it is the same
for both advertising High demand [0.6]
© 2011of nature.
states Lew Hofmann $800

67. Solving Decision #3
Low demand [0.4]
$200
Hi
gh We eliminate the “do
ty d
ili [0 em nothing” option since it has a
ac .6 an
]
Don’t expand
lf d lower payoff than does
al $223
Sm advertising.
2 Expand
$270
Do nothing
1
La $40
rg Advertise
e d Modest response [0.3]
fa an 3 $20
ci m
lit
y de 4]
w 0. $160
Lo [ Sizable response [0.7]
$160 $220
High demand [0.6]
© 2011 Lew Hofmann $800

68. Here there is no state of
nature involved with
expanding or not expanding.
Solving Decision #2
They are simply choices if we
end up with high demand.
Low demand [0.4]
$200
Hi
gh
ty d
i li [0 em Expanding has a
c .6 an Don’t expand
l fa ] d higher expected
al $223
Sm value than not
2 Expand expanding.
$270 Do nothing
$270
1
La $40
rg Advertise
e d Modest response [0.3]
fa an 3 $20
ci m
lit
y de 4]
w 0. $160
Lo [ Sizable response [0.7]
$160 $220
High demand [0.6]
© 2011 Lew Hofmann $800

69. Low demand expected value of
$80 is added to the high
demand expected value of $162 Solving Decision #1
Low demand [0.4]
$200 x 0.4 = $80
$242
Hi
gh
ci li
ty d
[0 em
.6 an Don’t expand
$242
l fa ] d
al $223
Sm 2 Expand
$270 $270 x 0.6 = $162
Do nothing
1
La $40
rg Advertise
e d Modest response [0.3]
fa an 3 $20
ci m
lit
y de 4]
. $160
Low [0
Sizable response [0.7]
$160 $220
High demand [0.6]
© 2011 Lew Hofmann $800

70. Solving Decision #1
Low demand [0.4]
$200 The expected value of
$242 high demand for the large
Hi
facility ($480) is added to
gh the expected value of low
ty d
i li [0 em demand for the large
c .6 an Don’t expand
l fa ] d facility ($64).
al $223
Sm 2 Expand
$270 Do nothing
$270
1
La $40
rg Advertise
e d Modest response [0.3]
fa an 3 $20
ci m
lit
y de 4]
. $160
Lo w [0
Sizable response [0.7]
0.4 x $160 = $64 $160 $220
$544 High demand [0.6]
© 2011 Lew Hofmann $800 x 0.6 = $480

71. Solving Decision #1
Low demand [0.4]
$200
The expected value of
Hi building a small facility
gh
ty d can now be compared to
ili $242 [0 em
c .6 an Don’t expand the expected value of
l fa ] d
al $223 building a large facility.
Sm 2 Expand
$270 Do nothing
$270
1
La $40
rg Advertise
e d Modest response [0.3]
fa an 3 $20
$544 ci
lit
y
m
de 4]
.
ow [0 $160
L Sizable response [0.7]
$160 $220
$544 High demand [0.6]
$800
© 2011 Lew Hofmann

72. 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

73. 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

74. Homework Assignment #1
Six problems: Due in class next week this time.
1. Breakeven
2. Two Processes
Recommend 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

75. 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

76. 2. Two Processes
Use 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

77. 3. Preference Matrix
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 total
weighted score?
b. If the factors were weighted equally, would the choice change?
© 2011 Lew Hofmann

78. 4. Payoff Table
You 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
© 2011 Lew Hofmann
b. Maximax c. Minimax regret

79. 5. Decision Tree #1
Do this manually (no computer).
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?
© 2011 Lew Hofmann

80. 6. Decision Tree Problem #2
Do 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
demand is medium, and is expected to lose $60,000 if demand is low.
a.Draw an analyze a decision tree for this problem.
b.What should management do to achieve the highest expected payoff?
© 2011 Lew Hofmann