1. Decision Theory Models Decision Tree & Utility Theory
Kusdhianto Setiawan
Gadjah Mada University

2. 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

3. 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

4. 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.

5. 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.

6. EMV Continued John Thompson Case Alternative State of Nature EMV
Fav. Mkt
Unf. Mkt
Construct a large plant
10.000
Construct a small plant
40.000
Do Nothing
Probabilities
0.5

7. 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)).

8. Opportunity Loss
maximizing EMV = minimizing expected opportunity loss (EOL)
Alternative
State of Nature
EOL
Fav. Mkt
Unf. Mkt
Construct a large plant –
0 – ( )
90.000
Construct a small plant –
0 – ( )
60.000
Do Nothing
– 0
0- 0
Probabilities
0.5

9. Sensitivity Analysis
SA investigaes how our decision might change with different input data.
EMV(large p) = P – (1-P)
= P –
EMV(small p) = P – (1-P)
= P –
EMV(do nothing) = 0P + 0(1-P) = 0

10. Sensitivity Analysis EMV Values EMV Large Plant EMV Small Plant
EMV Do Nothing
0.167
0.62
Probability of Favourable Market

11. Decision Making Under Uncertainty
Maximax (Optimistic Approach)
Maximin (Pessimistic Approach)
Equally Likely (Laplace)
Criterion of Realism (Hurwicz Criterion)
Minimax (based on opportunity loss)

12. 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.

13. 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.

14. Café’ Du Donut Case P ≥ ML/(MP+ML) = 4/(4+2) = 4/6 P ≥ 0.66
Daily Sales
P that sales will be at this level
P that Sales will be at this level or greater 4
0.05
1 ≥ 0.66 5
0.15
0.95 ≥ 0.66 6
0.8 ≥ 0.66 7
0.20
0.65 8
0.25
0.45 9
0.1
0.2 10
P ≥ ML/(MP+ML) = 4/(4+2) = 4/6
P ≥ 0.66

15. 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
Determine P = ML/(MP+ML)
Locate P on the Normal Distribution, and find Z for a given area under the curve, then find X*
Z = (X* - m)/s

16. 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
= 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.