Decision Theory
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Transcript Decision Theory
Supplement A
Decision
Making
Objectives
Apply break-even analysis, using both the graphic
and algebraic approaches, to evaluate new products
and services and different process methods.
evaluate decision alternatives with a preference
matrix for multiple criteria.
Construct a payoff table and then select the best
alternative by using a decision rule such as maximin,
maximax, Laplace, minimax regret, or expected
value.
Calculate the value of perfect information.
Draw and analyze a decision tree.
Break-Even Analysis
Quantity
(patients)
(Q)
0
2000
Total Cost
Total Revenue
Revenue = Cost
Break Even Point
Total Annual
Cost ($)
(100,000 + 100Q)
100,000
300,000
Total Annual
Revenue ($)
(200Q)
0
400,000
= Fixed Cost + Variable Cost * Volume sold
= Revenue per unit * Volume Sold
= pQ = F + cQ
= Fixed Cost / (revenue – variable cost)
Break-Even Analysis
(2000, 400)
Dollars (in thousands)
400 –
300 –
Total annual revenues
200 –
100 –
0–
|
500
|
Quantity
(patients)
(Q)
Total Annual
Cost ($)
(100,000 + 100Q)
0
2000
100,000
300,000
|
1000
1500
Patients (Q)
|
2000
Total Annual
Revenue ($)
(200Q)
0
400,000
Break-Even Analysis
(2000, 400)
Dollars (in thousands)
400 –
300 –
(2000, 300)
Total annual revenues
Total annual costs
200 –
100 –
(0, 100)
Fixed costs
0–
(0, 0)|
500
|
|
1000
1500
Patients (Q)
|
2000
Break-Even Analysis
(2000, 400)
Dollars (in thousands)
400 –
Profits
300 –
(2000, 300)
Total annual revenues
Total annual costs
200 –
Break-even quantity
100 –
Fixed costs
Loss
0–
|
500
|
|
1000
1500
Patients (Q)
|
2000
Sensitivity Analysis
Dollars (in thousands)
400 –
Profits
300 –
Total annual revenues
Total annual costs
200 –
Forecast = 1,500
100 –
Fixed costs
Loss
0–
|
500
Example A.2
|
|
1000
1500
Patients (Q)
|
2000
Sensitivity Analysis
Dollars (in thousands)
400 –
Profits
300 –
Total annual revenues
Total annual costs
200 –
Forecast = 1,500
100 –
pQ – (F + cQ)
Fixed costs
Loss
0–
200(1500) – [100,000 + 100(1500)] =
|
500
|
|
1000
1500
Patients (Q)
|
2000
$50,000
Preference Matrix
Threshold score = 800
Performance
Criterion
Weight
(A)
Score
(B)
Weighted Score
(A x B)
Market potential
Unit profit margin
Operations compatibility
Competitive advantage
Investment requirement
Project risk
30
20
20
15
10
5
8
10
6
10
2
4
240
200
120
150
20
20
Weighted score = 750
Example A.4
Preference Matrix
Threshold score = 800
Performance
Criterion
Weight
(A)
Score
(B)
Weighted Score
(A x B)
Market potential
Unit profit margin
Operations compatibility
Competitive advantage
Investment requirement
Project risk
30
20
20
15
10
5
8
10
6
10
2
4
240
200
120
150
20
20
Weighted score = 750
Example A.4
Decision Theory: Under Certainty
Alternative
Small facility
Large facility
Do nothing
Possible
Future Demand
Low
High
200
160
0
270
800
0
If future demand will be low—Choose the small facility.
Example A.5
Under Uncertainty
Alternative
Small facility
Large facility
Do nothing
Example A.6
Possible
Future Demand
Low
High
200
160
0
270
800
0
Under Uncertainty
Alternative
Small facility
Large facility
Do nothing
Example A.6
Possible
Future Demand
Low
High
200
160
0
270 Maximin—Small
800
0 Best of the worst
Under Uncertainty
Alternative
Small facility
Large facility
Do nothing
Possible
Future Demand
Low
High
200
160
0
270
800
0
Maximin—Small
Maximax—Large
Best of the best
Example A.6
Under Uncertainty
Alternative
Small facility
Large facility
Do nothing
Small facility
Large facility
Example A.6
Possible
Future Demand
Low
High
200
160
0
270
800
0
Maximin—Small
Maximax—Large
Laplace—Large
0.5(200) + 0.5(270) = 235
0.5(160) + 0.5(800) = 480
Best
weighted
payoff
Under Uncertainty
Possible
Future Demand
Low
High
Alternative
Small facility
Large facility
Do nothing
Small facility
Large facility
Example A.6
200
160
0
270
800
0
Maximin—Small
Maximax—Large
Laplace—Large
Minimax Regret—Large
Regret
Low Demand
High Demand
200 – 200 = 0
800 – 270 = 530
200 – 160 = 40 800 – 800 = 0
Best
worst
regret
Under Uncertainty
Alternative
Small facility
Large facility
Do nothing
Example A.6
Possible
Future Demand
Low
High
200
160
0
270
800
0
Maximin—Small
Maximax—Large
Laplace—Large
Minimax Regret—Large
Under Risk
Alternative
Small facility
Large facility
Do nothing
Possible
Future Demand
Low
High
200
160
0
270
800
0
Alternative
Expected Value
Small facility
Large facility
0.4(200) + 0.6(270) = 242
0.4(160) + 0.6(800) = 544
Example A.7
Psmall = 0.4
Plarge = 0.6
Under Risk
Alternative
Small facility
Large facility
Do nothing
Possible
Future Demand
Low
High
200
160
0
270
800
0
Alternative
Expected Value
Small facility
Large facility
0.4(200) + 0.6(270) = 242
0.4(160) + 0.6(800) = 544
Example A.7
Psmall = 0.4
Plarge = 0.6
Highest
Expected
Value
Under Risk
Figure A.4
Perfect Information
Alternative
Small facility
Large facility
Do nothing
Possible
Future Demand
Low
High
200
160
0
Event
Best Payoff
Low demand
High demand
200
800
Example A.8
270
800
0
Psmall = 0.4
Plarge = 0.6
Perfect Information
Alternative
Small facility
Large facility
Do nothing
Possible
Future Demand
Low
High
200
160
0
Event
Best Payoff
Low demand
High demand
200
800
Example A.8
270
800
0
Psmall = 0.4
Plarge = 0.6
EVperfect = 200(0.4) + 800(0.6) = 560
EVimperfect = 160(0.4) + 800(0.6) = 544
Perfect Information
Alternative
Small facility
Large facility
Do nothing
Possible
Future Demand
Low
High
200
160
0
Event
Best Payoff
Low demand
High demand
200
800
Example A.8
270
800
0
Psmall = 0.4
Plarge = 0.6
EVperfect = 200(0.4) + 800(0.6) = 560
EVimperfect = 160(0.4) + 800(0.6) = 544
Value of perfect information = $560,000 - $544,000
Decision Trees
E1 [P(E1)]
Payoff 1
E2 [P(E2)]
E3 [P(E3)]
Payoff 2
Payoff 3
Alternative 3
1
1st
decision
= Event node
2
Payoff 2
Alternative 5
Payoff 3
Possible
2nd decision
E2 [P(E2)]
E3 [P(E3)]
= Decision node
Alternative 4
Payoff 1
Payoff 1
Payoff 2
Ei = Event i
P(Ei) = Probability of event i
Figure A.5
Decision Trees
Low demand [0.4]
$200
Don’t expand
$223
2
Expand
$270
1
Do nothing
$40
3
Modest response [0.3]
Advertise
Sizable response [0.7]
High demand [0.6]
$800
$20
$220
Example A.9
Decision Trees
Low demand [0.4]
$200
Don’t expand
$223
2
Expand
$270
1
0.3(20) + 0.7(220)
Do nothing
$40
3
Modest response [0.3]
Advertise
Sizable response [0.7]
High demand [0.6]
$800
$20
$220
Example A.9
Decision Trees
Low demand [0.4]
$200
Don’t expand
$223
2
Expand
$270
1
0.3(20) + 0.7(220)
Do nothing
$40
3
Modest response [0.3]
Advertise
Sizable response [0.7]
$160
High demand [0.6]
$800
$20
$220
Example A.9
Decision Trees
Low demand [0.4]
$200
Don’t expand
$223
2
Expand
$270
$270
1
Do nothing
$40
3
Modest response [0.3]
Advertise
$160
Sizable response [0.7]
$160
High demand [0.6]
$800
$20
$220
Example A.9
Decision Trees
Low demand [0.4]
$200
0.4(200) + 0.6(270)
Don’t expand
$223
2
Expand
$270
$270
1
Do nothing
$40
3
Modest response [0.3]
Advertise
$160
Sizable response [0.7]
0.4(160)($160)
+ 0.6(800)
High demand [0.6]
$800
$20
$220
Example A.9
Decision Trees
Low demand [0.4]
$200
0.4(200) + 0.6(270)
Don’t expand
$242
$223
2
Expand
$270
$270
1
Do nothing
$40
3
Modest response [0.3]
Advertise
$160
Sizable response [0.7]
0.4(160)($160)
+ 0.6(800)
$544
High demand [0.6]
$800
$20
$220
Example A.9
Decision Trees
Low demand [0.4]
$200
Don’t expand
$242
$223
2
Expand
$270
$270
1
Do nothing
$40
$544
3
Advertise
$160
Sizable response [0.7]
$160
$544
Modest response [0.3]
High demand [0.6]
$800
$20
$220
Example A.9
Solved Problem 1
250 –
F
Q
pc
56,000
Q
25 7
Q 3,111unit s
Dollars (in thousands)
200 –
Total revenues
150 –
100 –
Break-even
quantity
$77.7
Total costs
50 –
0– |
1
3.1
|
|
|
|
|
|
|
2
3
4
5
6
7
8
Units (in thousands)
BE Revenue = pQ
Revenue = 25*3111
Revenue = $77,775
Solved Problem 3
To determine the
payoff amounts:
Buy roses for $15 dozen
Sell roses for $40 dozen
Sell 25, Order 25, =
pQ – cQ = 40(25) – 15(25) =625
Payoff Scenarios
Probabilities--->
2:
3:
Event 1
Event 2
Event 3
Low
Medium
High
Order 25 dozen
625
625
625
Order 60 dozen
100
1500
1500
Order 130dozen
-950
450
3250
0
0
0
Do nothing
Sell 60, Order 130 =
pQ – cQ = 40(60) – 15(130) = 450
1:
Solved Problem 3
Maximin – best of the worst. If demand is Low,
the best alternative is to order 25 dozen.
Maximax – best of the best. If demand is high,
the best alternative is to order 130 dozen.
Laplace – Best weighted payoff.
25 dozen: 625(.33) + 625(.33) +625(.33) = 625
60 dozen: 100(.33) + 1500(.33) + 1500(.33) = 1023
130 dozen: -950(.33) + 450(.33) + 3250(.33) = 907
Solved Problem 3
Payoffs
Event 1
Probabilities--->
Low
Event 2
Regret
Medium
Event 3
High
Regret
Regret
Max Regret
Order 25 dozen
625
0
625
875
625
2625
2625
Order 60 dozen
100
525
1500
0
1500
1750
1750
Order 130dozen
-950
1575
450
1050
3250
0
1575
0
625
0
1500
0
3250
3250
Do nothing
Best Payoff:
625
1500
3250
Solved Problem
Minimax Regret –best “worst regret”
Maximum regret of 25 dozen occurs if demand is
high: $3250 – $625 = $2625
Maximum regret of 60 dozen occurs if demand is
high: $3250 - $1500 = $1750
Maximum regret of 130 dozen occurs if demand is
low: $625 - -$950 = $1575
The minimum of regrets is ordering 130 dozen!
Solved Problem 4
Bad times [0.3]
Normal times [0.5]
$191
$240
One lift
$225.3
$256.0
Bad times [0.3]
Two lifts
Normal times [0.5]
$256.0
Figure A.8
Good times [0.2]
Good times [0.2]
$240
$151
$245
$441