Mini-course 1 Decision Analysis (Dr. Mariya Sodenkamp) / Class 3 / ITB_L3_ 2015_04_20
.pdf
Equal Likely Strategy (Laplace criterion)
Laplace criterion works good if the decision maker cannot prefer any of the viewed hypotheses.
p1 = p2 = ... = pH =1/ H , |
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ph − probabilities of the |
states of nature. |
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e( A*) = max{ |
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∑eih} |
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H h=1 |
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Political situation (P) |
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stable, |
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unstable, p |
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unstable, |
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Alternative |
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Competition grade (Q) |
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weak, |
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strong, |
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weak, |
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Hypothesis (Z) |
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Z1 |
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Z2 |
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Z3 |
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Z4 pq |
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A1 |
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240 |
460 |
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530 |
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220 |
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A2 |
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300 |
390 |
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490 |
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270 |
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A3 |
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260 |
420 |
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575 |
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190 |
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J = 4
362.5
362.5
361.25
Max, e( A*) 362.5
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A1 and A2 are the best alternatives !
Case: John’s investment decision
John Torres inherited money and wants to make investment of this capital next year. He is considering 3 alterna+ves: bonds, stocks and deposit. It is known that the market economy can face with growth, infla+on or don’t change.
In case of growth interest on bonds will be 12%, on stocks 15% and on deposit 6.5%. If market economy will not undergo any changes the interest on bounds will be 6%, on stocks 3%, on deposit 5.5%. In case of infla+on interest on bonds will be 3%, on stocks (-2)% and on deposit 6.5%.
Construct payo /loss matrix. Make choices using five di erent rules for decision making under uncertainty. Explain and compare results.
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Case: Choice of so.ware architecture
Company ABC develops a new software package. The project manager must make a decision about choice of architecture of this software.
He finally comes up with two alternatives:
1. Client-server architecture. In this case expected costs of the software development will be 5 thousand $.
2. Three-tier model. This product would give more opportunities, but expenses would be higher as well – 15 thousand $.
Profit sufficiently depends on the number of sold copies. As previous experience shows, sales can be poor (in average 10 copies per month), medium (about 15 copies per month) or good (nearly 25 copies per month). Politics of the company is as follows:
• If sales are poor than price for one copy of either a product with client-server or threetier architecture are 1.500 $.
• If sales are medium than the price for the first type of product is 2.000$, and the second type of product – 3.000$.
• If sales are good than the price for the first type of product must be fixed on the level of 2.000$, for the second – 4.000$.
Construct payoff/loss matrix. Make choices using Max-Min and Max-Max rules, Hurwitz and Laplace methods. Compare and explain your results.
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Decision making under risk
Outline
• Equal likely strategy
• Expected Payo (Bayes principle)
• Expected Opportunity Loss
• Cases
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Payo matrix with probabili+es
Alternatives, |
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Hypotheses Zh , |
h=1,…,H |
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Ai, i=1,…,I |
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Z1 |
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ZH |
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A1 |
e11 |
e12 |
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e1H |
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A2 |
e21 |
e22 |
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e2H |
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eij |
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AI |
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eI2 |
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eIH |
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Probabilities, |
p1 |
p2 |
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pH |
ph |
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eih – expected payo s for the alterna3ve i and occured hypothesis Zj . ph – probabili*es of the states of environment.
H
∑ ph = 1
h=1 |
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Bayes principle
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e( A*) = max{ei } |
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ei = ∑eih ph |
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h=1 |
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Political situation (PS) |
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stable, |
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unstable, |
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unstable, p |
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Alternative |
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Competition grade (Q) |
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Markets |
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weak, |
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strong, |
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strong, |
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weak, q |
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Hypothesis (Z) |
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Z1 |
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Z2 |
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Z3 |
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Z4 pq |
A1 |
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240 |
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460 |
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530 |
220 |
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A2 |
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300 |
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390 |
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490 |
270 |
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A3 |
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260 |
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420 |
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575 |
190 |
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Probabilities, ph |
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0.28 |
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0.30 |
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0.19 |
0.23 |
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e1= e(A1) = 240*0.28 + 460*0.30 + 530*0.19 + 220*0.23 = 356.5
e2= e(A2) = 300*0.28 + 390*0.30 + 490*0.19 + 270*0.23 - MAX e3= e(A3) = 260*0.28 + 420*0.30 + 575*0.19 + 190*0.23 = 351.75
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A1 is the best alternative ! 56 |
Expected opportunity loss
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H |
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wi |
= ∑ wih ph , |
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w(A*) = min{wi }. |
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h=1 |
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Alternative |
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Hypotheses (Z) |
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markets |
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Z1 |
pq |
Z2 |
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Z3 |
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Z4 |
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A1 |
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60 |
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45 |
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A2 |
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70 |
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A3 |
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80 |
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Probabilities, |
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0.28 |
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0.30 |
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0.23 |
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w1= w(A1) = 60*0.28 + 45*0.19 + 50*0.23 |
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w2= w(A2) = 70*0.30 + 85*0.19 = 37.15 |
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w3= w(A3) = 40*0.28 + 40*0.30 + 80*0.23 = 41.6 |
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A1 is the best alternative ! |
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Case: Choice of soxware architecture
Solve the problem of so.ware architecture choice using the decision methods under risk (Bayes principle & Expected opportunity loss).
Assume that the marke3ng department gave probabili3es for the market states:
• Poor sales – 0.4;
• Medium sales – 0.4;
• Good sales – 0.2.
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Case: John’s investment decision (cont’d)
Assume that John knows that probability of economy growth is 0.5, of infla3on 0.2 and of stable state 0.3. What would be the best investment for John?
Compare results of two di erent methods.
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Case: Welth & Duke
see „Welth and Duke.pdf“
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