管理定量分析ch03-决策分析
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Chapter 3
Decision Analysis
Chapter Outline
3.1 Introduction 3.2 The Six Steps in Decision Making 3.3 Types of Decision-Making Environments 3.4 Decision Making under Uncertainty 3.5 Decision Making under Risk 3.6 Decision Trees 3.7 How Probability Values Are Estimated by Bayesian Analysis 3.8 Utility Theory
MAXIMUM IN A ROW ($) 200,000
Maximax
100,000 0
Maximin
Used to find the alternative that maximizes the minimum payoff.
Locate the minimum payoff for each alternative. Select the alternative with the maximum
3-14
Thompson’s Decision Tree
A State-of-Nature Node
Favorable Market
A Decision Node
1
Unfavorable Market
Favorable Market
Construct Small Plant
2
Unfavorable Market
Table 3.4
Realism
76,000 0
3-10
Equally Likely (Laplace)
Considers all the payoffs for each alternative
Find the average payoff for each alternative. Select the alternative with the highest average.
number.
STATE OF NATURE ALTERNATIVE Construct a large plant Construct a small plant Do nothing
Table 3.3
FAVORABLE MARKET ($) 200,000 100,000 0
UNFAVORABLE MARKET ($) –180,000 –20,000 0
MINIMUM IN A ROW ($) –180,000 –20,000 0
Maximin
3-9
Criterion of Realism (Hurwicz)
For the large plant alternative using
= 0.8:
(0.8)(200,000) + (1 – 0.8)(–180,000) = 124,000 For the small plant alternative using = 0.8: (0.8)(100,000) + (1 – 0.8)(–20,000) = 76,000
STATE OF NATURE ALTERNATIVE Construct a large plant Construct a small plant Do nothing
Table 3.5
3-11
FAVORABLE MARKET ($) 200,000 100,000 0
UNFAVORABLE MARKET ($) –180,000 –20,000 0
3-3
STARTING RIGHT CASE
What kind of the problem? decision-making-under-uncertainty Two events a favorable market (event 1) an unfavorable market (event 2) Four alternatives do nothing (alternative 1) invest in corporate bonds (alternative 2) invest in preferred stock (alternative 3) invest in common stock (alternative 4)
Decision Making Under Uncertainty
There are several criteria for making decisions under uncertainty: 1. Maximax (optimistic) 2. Maximin (pessimistic) 3. Criterion of realism (Hurwicz) 4. Equally likely (Laplace) 5. Minimax regret
3-7
Maximax
Used to find the alternative that maximizes the maximum payoff.
Locate the maximum payoff for each alternative. Select the alternative with the maximum number.
UNFAVORABLE MARKET ($) –180,000 –20,000 0 0.50
EMV ($) 10,000 40,000 0
Largest EMV
3-13
Structure of Decision Trees
Trees start from left to right. Trees represent decisions and outcomes
3-4
Payoff table
Laplace Event 1 Alternative 1 Alternative 2 Alternative 3 Alternative 4 120,000 240,000 0 Event 2 0 –10,000 –15,000 –30,000 Average Value 0.0 22,636.5 52,500.0 105,000.0 Minimum Maximum 0 –10,000 –15,000 –30,000 0 55,273 120,000 240,000 Hurwicz Value 0.00 –2,819.97 –150.00 –300.00
ROW AVERAGE ($) 10,000 40,000
Equally likely
0
Minimax Regret
Thompson’s Minimax Decision Using Opportunity Loss
STATE OF NATURE ALTERNATIVE Construct a large plant Construct a small plant Do nothing
Figure 3.2
3-15
Thompson’s Decision Tree
EMV for Node 1 = $10,000 Alternative with best EMV is selected
STATE OF NATURE FAVORABLE MARKET ($) 200,000 100,000 0 UNFAVORABLE MARKET ($) –180,000 –20,000 0 CRITERION OF REALISM ( = 0.8) $ 124,000
ALTERNATIVE Construct a large plant Construct a small plant Do nothing
Table 3.8
FAVORABLE MARKET ($) 0 100,000 200,000
UNFAVORABLE MARKET ($) 180,000 20,000 0
MAXIMUM IN A ROW ($) 180,000 100,000
Minimax
200,000
3-12
EMV for Thompson Lumber
in sequential order.
Squares represent decision nodes. Circles represent states of nபைடு நூலகம்ture nodes. Lines or branches connect the decisions
nodes and the states of nature.
[30000*(1+13%)*5]sum_{i=0,4}(1+0.045^i)
3-5
a. Sue Pansky is a risk avoider and should use the
maximin decision approach. She should do nothing and not make an investment in Starting Right. b. Ray Cahn should use a coefficient of realism of 0.11. The best decision is to do nothing. c. Lila Battle should eliminate alternative 1 of doing nothing and apply the maximin criterion. The result is to invest in the corporate bonds. d. George Yates should use the equally likely decision criterion. The best decision for George is to invest in common stock. e. Pete Metarko is a risk seeker. He should invest in common stock. f. Julia Day can eliminate the preferred stock alternative and still offer alternatives to risk seekers (common stock) and risk avoiders (doing nothing or investing in corporate 3-6 bonds).
3-2
The Six Steps in Decision Making
1. Clearly define the problem at hand. 2. List the possible alternatives. 3. Identify the possible outcomes or states of nature. 4. List the payoff (typically profit) of each combination of alternatives and outcomes. 5. Select one of the mathematical decision theory models. 6. Apply the model and make your decision.
STATE OF NATURE ALTERNATIVE Construct a large plant Construct a small plant Do nothing Probabilities
Table 3.9
FAVORABLE MARKET ($) 200,000 100,000 0 0.50
STATE OF NATURE ALTERNATIVE Construct a large plant Construct a small plant Do nothing
Table 3.2
3-8
FAVORABLE MARKET ($) 200,000 100,000 0
UNFAVORABLE MARKET ($) –180,000 –20,000 0
Decision Analysis
Chapter Outline
3.1 Introduction 3.2 The Six Steps in Decision Making 3.3 Types of Decision-Making Environments 3.4 Decision Making under Uncertainty 3.5 Decision Making under Risk 3.6 Decision Trees 3.7 How Probability Values Are Estimated by Bayesian Analysis 3.8 Utility Theory
MAXIMUM IN A ROW ($) 200,000
Maximax
100,000 0
Maximin
Used to find the alternative that maximizes the minimum payoff.
Locate the minimum payoff for each alternative. Select the alternative with the maximum
3-14
Thompson’s Decision Tree
A State-of-Nature Node
Favorable Market
A Decision Node
1
Unfavorable Market
Favorable Market
Construct Small Plant
2
Unfavorable Market
Table 3.4
Realism
76,000 0
3-10
Equally Likely (Laplace)
Considers all the payoffs for each alternative
Find the average payoff for each alternative. Select the alternative with the highest average.
number.
STATE OF NATURE ALTERNATIVE Construct a large plant Construct a small plant Do nothing
Table 3.3
FAVORABLE MARKET ($) 200,000 100,000 0
UNFAVORABLE MARKET ($) –180,000 –20,000 0
MINIMUM IN A ROW ($) –180,000 –20,000 0
Maximin
3-9
Criterion of Realism (Hurwicz)
For the large plant alternative using
= 0.8:
(0.8)(200,000) + (1 – 0.8)(–180,000) = 124,000 For the small plant alternative using = 0.8: (0.8)(100,000) + (1 – 0.8)(–20,000) = 76,000
STATE OF NATURE ALTERNATIVE Construct a large plant Construct a small plant Do nothing
Table 3.5
3-11
FAVORABLE MARKET ($) 200,000 100,000 0
UNFAVORABLE MARKET ($) –180,000 –20,000 0
3-3
STARTING RIGHT CASE
What kind of the problem? decision-making-under-uncertainty Two events a favorable market (event 1) an unfavorable market (event 2) Four alternatives do nothing (alternative 1) invest in corporate bonds (alternative 2) invest in preferred stock (alternative 3) invest in common stock (alternative 4)
Decision Making Under Uncertainty
There are several criteria for making decisions under uncertainty: 1. Maximax (optimistic) 2. Maximin (pessimistic) 3. Criterion of realism (Hurwicz) 4. Equally likely (Laplace) 5. Minimax regret
3-7
Maximax
Used to find the alternative that maximizes the maximum payoff.
Locate the maximum payoff for each alternative. Select the alternative with the maximum number.
UNFAVORABLE MARKET ($) –180,000 –20,000 0 0.50
EMV ($) 10,000 40,000 0
Largest EMV
3-13
Structure of Decision Trees
Trees start from left to right. Trees represent decisions and outcomes
3-4
Payoff table
Laplace Event 1 Alternative 1 Alternative 2 Alternative 3 Alternative 4 120,000 240,000 0 Event 2 0 –10,000 –15,000 –30,000 Average Value 0.0 22,636.5 52,500.0 105,000.0 Minimum Maximum 0 –10,000 –15,000 –30,000 0 55,273 120,000 240,000 Hurwicz Value 0.00 –2,819.97 –150.00 –300.00
ROW AVERAGE ($) 10,000 40,000
Equally likely
0
Minimax Regret
Thompson’s Minimax Decision Using Opportunity Loss
STATE OF NATURE ALTERNATIVE Construct a large plant Construct a small plant Do nothing
Figure 3.2
3-15
Thompson’s Decision Tree
EMV for Node 1 = $10,000 Alternative with best EMV is selected
STATE OF NATURE FAVORABLE MARKET ($) 200,000 100,000 0 UNFAVORABLE MARKET ($) –180,000 –20,000 0 CRITERION OF REALISM ( = 0.8) $ 124,000
ALTERNATIVE Construct a large plant Construct a small plant Do nothing
Table 3.8
FAVORABLE MARKET ($) 0 100,000 200,000
UNFAVORABLE MARKET ($) 180,000 20,000 0
MAXIMUM IN A ROW ($) 180,000 100,000
Minimax
200,000
3-12
EMV for Thompson Lumber
in sequential order.
Squares represent decision nodes. Circles represent states of nபைடு நூலகம்ture nodes. Lines or branches connect the decisions
nodes and the states of nature.
[30000*(1+13%)*5]sum_{i=0,4}(1+0.045^i)
3-5
a. Sue Pansky is a risk avoider and should use the
maximin decision approach. She should do nothing and not make an investment in Starting Right. b. Ray Cahn should use a coefficient of realism of 0.11. The best decision is to do nothing. c. Lila Battle should eliminate alternative 1 of doing nothing and apply the maximin criterion. The result is to invest in the corporate bonds. d. George Yates should use the equally likely decision criterion. The best decision for George is to invest in common stock. e. Pete Metarko is a risk seeker. He should invest in common stock. f. Julia Day can eliminate the preferred stock alternative and still offer alternatives to risk seekers (common stock) and risk avoiders (doing nothing or investing in corporate 3-6 bonds).
3-2
The Six Steps in Decision Making
1. Clearly define the problem at hand. 2. List the possible alternatives. 3. Identify the possible outcomes or states of nature. 4. List the payoff (typically profit) of each combination of alternatives and outcomes. 5. Select one of the mathematical decision theory models. 6. Apply the model and make your decision.
STATE OF NATURE ALTERNATIVE Construct a large plant Construct a small plant Do nothing Probabilities
Table 3.9
FAVORABLE MARKET ($) 200,000 100,000 0 0.50
STATE OF NATURE ALTERNATIVE Construct a large plant Construct a small plant Do nothing
Table 3.2
3-8
FAVORABLE MARKET ($) 200,000 100,000 0
UNFAVORABLE MARKET ($) –180,000 –20,000 0