# Decision Theory Models Decision Tree _ Utility Theory by malj

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```									  Decision Theory Models
Decision Tree & Utility Theory
Kusdhianto Setiawan
Introduction
• What is a good decision?
– Based on logic
– Is rational model applied by all people in making
logical decision?
– What is rational model?
• Types of Decision-Making Environment
– Under Certainty: tahu semua konsekuensinya
– Under Risk: tahu probabilitas dari outcomes
– Under Uncertainty: tidak tahu probabilitas dari
outcomes
Decision Making Under Risk
- Risky choice = Gamble that can yield
various outcomes with different
probabilities?

- Psychophysical Analysis relevant?

- Daniel Bernoully (1978):
- people are generally averse to risk and risk
aversion decreases with increasing wealth.
- People do not evaluate prospects by the
expectation of their monetary outcomes, but rather
by the expectation of subjective value of these
outcome
- Von Neumann & Morgenstein (1947) –
Concept of Rationality
- Preference of rational decision making should
follow:
- Transitivity, if A is preferred to B and B is preferred to C,
then A is preferred to C.
- Substitution, if A is preferred to B, then an even chance
to get A or C is preferred to an even chance to get B or
C).
- Dominance, if prospect A is at least as good as prospect
B in every respect and better than B in at least one
respect, then A should be preferred to B.
- Invariance, preference order between prospects should
not depend on the manner in which they are described.
Expected Monetary Value
• EMV is the weighted sum of possible
payoffs for each alternative (prospect)
• EMV (alternative i) =
(payoff of first state of nature) x (probability of first state of nature)
+ (payoff of 2nd state of nature) x (probability of 2nd state of nature)
+ ……… + (payoff of last state of nature) x (probability of last state
of nature).
• What does EMV means?
– Nilai moneter (uang) yang akan kita terima secara rata-rata jika
mengambil keputusan dalam kondisi tertentu (state of nature)
berulang kali.
EMV Continued
John Thompson Case
State of Nature
Alternative                                EMV
Fav. Mkt    Unf. Mkt
Construct a large plant   200.000     -180.000   10.000

Construct a small plant   100.000      -20.000   40.000
Do Nothing              0            0        0
Probabilities          0.5          0.5
Expected Value of Perfect
Information (EVPI)
• EVPI merupakan harga dari perfect information,
misal: jasa konsultan yang diharapkan akan
memberikan informasi paling benar (harga
tertinggi yang mungkin kita bayar).
• EVPI = expected value with perfect information
(EVwPI)– maximum EMV
• EVwPI = (best outcome for the 1st SoN) x (P(1st
SoN)) + …. + (best outcomes of last SoN) x
(P(last SoN)).
Opportunity Loss
•    maximizing EMV = minimizing expected opportunity loss (EOL)

State of Nature
Alternative                                         EOL
Fav. Mkt       Unf. Mkt
200.000 –
Construct a large plant                 0 – (-180.000)   90.000
200.000
200.000 –
Construct a small plant                 0 – (-20.000)    60.000
100.000
Do Nothing           200.000 – 0        0- 0        100.000
Probabilities            0.5            0.5
Sensitivity Analysis
• SA investigaes how our decision might
change with different input data.
• EMV(large p) = 200.000P – 180.000(1-P)
= 380.000P – 180.000
• EMV(small p) = 100.000P – 20.000(1-P)
= 120.000P – 20.000
• EMV(do nothing) = 0P + 0(1-P) = 0
Sensitivity Analysis
EMV Values

EMV Do Nothing
0.167       0.62
-20.000
Probability of Favourable Market

-180.000
Decision Making Under Uncertainty
•   Maximax (Optimistic Approach)
•   Maximin (Pessimistic Approach)
•   Equally Likely (Laplace)
•   Criterion of Realism (Hurwicz Criterion)
•   Minimax (based on opportunity loss)
Marginal Analysis: Discrete
Distribution
Example: Café’ du Donut
Buying price from the producer: \$4/cartoon
Selling price to customer: \$6/cartoon, then
Marginal Profit (MP) = 6 – 4 = \$2/cartoon
Marginal Loss (ML) = \$4, lets
P = probability that demand ≥ supply (or the
probability of selling at least one additional unit)
1 – P = probability that demand will be less than
supply.
• The Optimal Decision Rule
P(MP) ≥ (1 - P)(ML)
or P(MP) + P(ML) ≥ ML
or P(MP + ML) ≥ ML
or P ≥ ML/(MP+ML), meaning that:
as long as the probability of selling one
more unit (P) is greater than or equal to
ML/(MP + ML), we would stock additional
unit.
Café’ Du Donut Case
P that Sales
P that sales
will be at
Daily Sales   will be at
• P ≥ ML/(MP+ML) =                 this level
this level or
greater
4/(4+2) = 4/6
4            0.05          1 ≥ 0.66
• P ≥ 0.66
5            0.15        0.95 ≥ 0.66

6            0.15         0.8 ≥ 0.66

7            0.20            0.65

8            0.25            0.45

9             0.1            0.2

10            0.1            0.1
Marginal Analysis with Normal
Distribution
•    Data Requirement
–   The average or mean for the product, μ
–   The standard deviation of sales, σ
–   The Marginal Profit
–   The Marginal Loss
•    Steps
1. Determine P = ML/(MP+ML)
2. Locate P on the Normal Distribution, and find Z for a
given area under the curve, then find X*
Z = (X* - m)/s
Chicago Tribune Distributor Case
• Average Sales/day = 50 papers
• Standard Deviation = 10 papers
• Marginal Profit = 6 cents
• Marginal Loss = 4 cents
• Determine Stocking Policy!
Step 1
P = ML/(ML+MP)=4/(4+6)=0.4
Step 2
1 - 0.4 = 0.6 … look at the z table, and find for z
Z = 0.25 standard deviation from the mean
0.25 = (X*- 50)/10  X*=10(0.25) + 50 = 52.3 or 53 papers
Decision: The distributor should order 53 paper daily.

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