Chapter 1
Decision Analysis
决策分析
1.1 A Decision Tree Model and its Analysis
1.2 Another Decision Tree Model and it
Analysis
1.3 The Need for a Systematic Theory of
Probability
1.4 Exercises
1.1 A Decision Tree Model and its Analysis
Decision analysis is a logical and systematic
way to address a wide variety of problems involving
decision-making in an uncertain environment.
决策分析是在不确定环境下进行决策时对面临的众多问题描述处理的一种逻辑和系统的方法。
Bill Sampras’ Summer Job Decision
Bill Sampras is in the third week of his first
semester at the Sloan School of Management at the
Massachusetts Institute of Technology(MIT),In addition
to spending time preparing for classes,Bill has begun to
think seriously about summer employment in the next
summer,and in particular about a decision he must make
in the next several weeks.
Bill Sampras在第一学期第三周考虑明年夏天的暑假打工计划，在以后几个星期中要做出决策。
Salaries
1.Offer from John $12,000
2.Table 1.1 on Page7
3.Offer from Vanessa $14,000
the probabilities
scenario Offer No offer
Probability 60% 40%
Decision Tree
Accept Vanessa’s Offer
Reject Vanessa’s Offer
$12,000
A
C
B
D
E
Accept John’s Offer
Reject John’s Offer
Offer from Vanessa
No Offer from Vanessa
$16,800
$6,000
0.05
0.25
0.40
0.25
0.05
$21,600
$12,000
$0
0.6
0.4
0.05
0.25
0.40
0.25
0.05
$21,600
$12,000
$0
$6,000
$16,800
$14,000
Figure 1.6,The completed decision tree
The expected monetary value(EMV)
The EMV of an uncertain event is the weighted
average of all possible numerical outcomes,with the
probabilities of each of the possible outcomes used as
the weights.
EMV是所有可能结果的加权平均值,其中权重是各个可能结果的发生概率 。
EMV=0.05× $21,600+0.25× $16,800+
0.40× $12,000+0.25× $6,000+0.05× $0
=$11,580
1.2 Another Decision Tree Model
and its Analysis
Continue to illustrate the methodology of
decision analysis by considering a strategic
development decision problem encountered by a new
company called Bio-imagine,Incorporated.
通过思考 Bio-imaging公司在战略发展决策中所遇到的一个问题继续阐述决策分析方法。
Bio-imaging Development Strategies
现状
● The software program has not been tested fully.
该软件尚未通过完整的性能测试
● The software program is more advanced and much
more accurate than other methods in diagnosing lesions.
比现有的其他诊断机能障碍的方法更先进、更准确
Table of estimated revenues of Bio-imaging
under different situation
Scenario Probability Total Revenues
High Profit 20% $3,000,000
Medium Profit 40% $500,000
Low Profit 40% $0
Table 1.2,Estimated revenues of Bio-Imaging,if three-dimensional prototype
is operational,and if Bio-Imaging is awarded SBIR grant.
Scenario Probability Total Revenues
High Profit 20% $10,000,000
Medium Profit 40% $3,000,000
Low Profit 40% $0
Table 1.2,Estimated revenues of Bio-Imaging,if three-dimensional prototype
is operational,under financing from Nugrowth development.
A
Continue Development
Accept Medtech
Table 1.12,Representation of the first decision faced by Bio-Imaging.
A
Continue Development
Accept Medtech
B
C
3D Successful
3D Not Successful
0.6
0.4
Apply for SBIR
Accept Nugrowth
D
Apply for SBIR
Abandon
-$200
High Project
E
Win SBIR
Lose SBIR
$150
0.70
0.20 $2,800
$300
-$200
G 0.40
0.40
Medium Project
Low Project
0.20 $1,800
$400
-$200
H 0.40
0.40
Medium Project
Low Project
High Project
0.30
F
Win SBIR
Lose SBIR
0.25 $1,200
-$300
I
0.75
Low Project
High Project
-$300
0.20
0.80
-$200
Table 1.17,the complete decision tree for Bio-Imaging.
EMV of the nodes
EMV(H)=0.20× $1,800,000+0.40× $400,000+
0.40× (-$200,000)
=$440,000
EMV(G)=0.20× $2,800,000+0.40× $300,000+
0.40× (-$200,000)
=$600,000
EMV(E)=0.70× $600,000+0.30× (-$200,000)
=$ 440,000
(continued)
EMV(I)=0.25× $1,200,000+0.75× (-$300,000)
=$ 75,000
EMV(F)=0.2× $75,000+0.8× (-$300,000)
=$ 225,000
EMV(B)=0.6× $440,000+0.40× (-$200,000)
=$184,000
(end)
1.3 The Need for a Systematic Theory of
Probability
The probability numbers presented in the problem
were exactly in the form needed in order to construct
and solve the decision tree.
要建立决策树并进行解答，必须给出各事件发生的概率。
Development of a New Consumer Product
Scenario Probability Total Profits
Strong market 30% $18,000,000
Weak market 70% -$8,000,000
两种选择
● Not to produce Suds-Away,to conduct the market
survey test prior to deciding whether or not to produce.
先进行市场调查再决定是否生产该产品 。
● or to go ahead with production without conducting
such a market survey test.
不进行市场调查直接投产。
Result of $2,400,000 market survey
Position Negative
Strong market 80% 20%
Weak market 10% 90%
A
Do not producer
Positive survey
results
No survey,produce
D
Produce
Do not produce
$18 million
- $8 million
B
0.70
Strong
0.30
C E
Strong
Week
Week
$15.6 million
- $10.4 million
- $2.4 million
F
Produce
Do not produce
G
Strong
Week
$15.6 million
- $10.4 million
- $2.4 million
Conduct market survey test
Negative survey results
P3=?
P4=?P1=?
P2=?
P5=?
P6=?
$0
Decision Analysis
决策分析
1.1 A Decision Tree Model and its Analysis
1.2 Another Decision Tree Model and it
Analysis
1.3 The Need for a Systematic Theory of
Probability
1.4 Exercises
1.1 A Decision Tree Model and its Analysis
Decision analysis is a logical and systematic
way to address a wide variety of problems involving
decision-making in an uncertain environment.
决策分析是在不确定环境下进行决策时对面临的众多问题描述处理的一种逻辑和系统的方法。
Bill Sampras’ Summer Job Decision
Bill Sampras is in the third week of his first
semester at the Sloan School of Management at the
Massachusetts Institute of Technology(MIT),In addition
to spending time preparing for classes,Bill has begun to
think seriously about summer employment in the next
summer,and in particular about a decision he must make
in the next several weeks.
Bill Sampras在第一学期第三周考虑明年夏天的暑假打工计划，在以后几个星期中要做出决策。
Salaries
1.Offer from John $12,000
2.Table 1.1 on Page7
3.Offer from Vanessa $14,000
the probabilities
scenario Offer No offer
Probability 60% 40%
Decision Tree
Accept Vanessa’s Offer
Reject Vanessa’s Offer
$12,000
A
C
B
D
E
Accept John’s Offer
Reject John’s Offer
Offer from Vanessa
No Offer from Vanessa
$16,800
$6,000
0.05
0.25
0.40
0.25
0.05
$21,600
$12,000
$0
0.6
0.4
0.05
0.25
0.40
0.25
0.05
$21,600
$12,000
$0
$6,000
$16,800
$14,000
Figure 1.6,The completed decision tree
The expected monetary value(EMV)
The EMV of an uncertain event is the weighted
average of all possible numerical outcomes,with the
probabilities of each of the possible outcomes used as
the weights.
EMV是所有可能结果的加权平均值,其中权重是各个可能结果的发生概率 。
EMV=0.05× $21,600+0.25× $16,800+
0.40× $12,000+0.25× $6,000+0.05× $0
=$11,580
1.2 Another Decision Tree Model
and its Analysis
Continue to illustrate the methodology of
decision analysis by considering a strategic
development decision problem encountered by a new
company called Bio-imagine,Incorporated.
通过思考 Bio-imaging公司在战略发展决策中所遇到的一个问题继续阐述决策分析方法。
Bio-imaging Development Strategies
现状
● The software program has not been tested fully.
该软件尚未通过完整的性能测试
● The software program is more advanced and much
more accurate than other methods in diagnosing lesions.
比现有的其他诊断机能障碍的方法更先进、更准确
Table of estimated revenues of Bio-imaging
under different situation
Scenario Probability Total Revenues
High Profit 20% $3,000,000
Medium Profit 40% $500,000
Low Profit 40% $0
Table 1.2,Estimated revenues of Bio-Imaging,if three-dimensional prototype
is operational,and if Bio-Imaging is awarded SBIR grant.
Scenario Probability Total Revenues
High Profit 20% $10,000,000
Medium Profit 40% $3,000,000
Low Profit 40% $0
Table 1.2,Estimated revenues of Bio-Imaging,if three-dimensional prototype
is operational,under financing from Nugrowth development.
A
Continue Development
Accept Medtech
Table 1.12,Representation of the first decision faced by Bio-Imaging.
A
Continue Development
Accept Medtech
B
C
3D Successful
3D Not Successful
0.6
0.4
Apply for SBIR
Accept Nugrowth
D
Apply for SBIR
Abandon
-$200
High Project
E
Win SBIR
Lose SBIR
$150
0.70
0.20 $2,800
$300
-$200
G 0.40
0.40
Medium Project
Low Project
0.20 $1,800
$400
-$200
H 0.40
0.40
Medium Project
Low Project
High Project
0.30
F
Win SBIR
Lose SBIR
0.25 $1,200
-$300
I
0.75
Low Project
High Project
-$300
0.20
0.80
-$200
Table 1.17,the complete decision tree for Bio-Imaging.
EMV of the nodes
EMV(H)=0.20× $1,800,000+0.40× $400,000+
0.40× (-$200,000)
=$440,000
EMV(G)=0.20× $2,800,000+0.40× $300,000+
0.40× (-$200,000)
=$600,000
EMV(E)=0.70× $600,000+0.30× (-$200,000)
=$ 440,000
(continued)
EMV(I)=0.25× $1,200,000+0.75× (-$300,000)
=$ 75,000
EMV(F)=0.2× $75,000+0.8× (-$300,000)
=$ 225,000
EMV(B)=0.6× $440,000+0.40× (-$200,000)
=$184,000
(end)
1.3 The Need for a Systematic Theory of
Probability
The probability numbers presented in the problem
were exactly in the form needed in order to construct
and solve the decision tree.
要建立决策树并进行解答，必须给出各事件发生的概率。
Development of a New Consumer Product
Scenario Probability Total Profits
Strong market 30% $18,000,000
Weak market 70% -$8,000,000
两种选择
● Not to produce Suds-Away,to conduct the market
survey test prior to deciding whether or not to produce.
先进行市场调查再决定是否生产该产品 。
● or to go ahead with production without conducting
such a market survey test.
不进行市场调查直接投产。
Result of $2,400,000 market survey
Position Negative
Strong market 80% 20%
Weak market 10% 90%
A
Do not producer
Positive survey
results
No survey,produce
D
Produce
Do not produce
$18 million
- $8 million
B
0.70
Strong
0.30
C E
Strong
Week
Week
$15.6 million
- $10.4 million
- $2.4 million
F
Produce
Do not produce
G
Strong
Week
$15.6 million
- $10.4 million
- $2.4 million
Conduct market survey test
Negative survey results
P3=?
P4=?P1=?
P2=?
P5=?
P6=?
$0
