Making Decision using PREPARED BY: Decision Tree RAIHANA ZAINORDIN
EXAMPLE: Shahrul is planning to open a café. From his evaluation, he found that with a good market, he could get a return of RM30 thousands if he opens the café, but with a bad market, he could lose RM10 thousands. Certainly, if he does not open the café, he will not get any proft. Shahrul believes that there is a 50% chance that the market will be good. Shahrul has asked a marketing manager to conduct a marketing research to see how the market for the café looks like. He agreed to pay the manager RM1.4 thousands for the research. The research can either indicate positive result, that is, good market for the café, or negative result, that is, bad market for the café. There is a 60% chance that the research will
EXAMPLE (CONTINUED): For conducting the research, there is a 75% chance that the market for the café will be good given that the research result is positive and there is a 25% chance that the market will be bad given that the research result is positive. In addition, there is a 20% chance that the market for the café will be good given that the research result is negative and there is an 80% chance that the market will be bad given that the research result is negative. Determine the best decision for Shahrul by using decision tree.
SOLUTION: Identify alternatives and states of nature and build a payof table. Alternativ State of Nature e Good Bad Market Market Open a cafĂŠ
30 thousands
-10 thousands
Open no 0 Take out probability cafe information. P(Good market) = 0.50
P(Good market | Positive) = 0.75
P(Bad market) = 0.50
P(Bad market | Positive) = 0.25
P(Positive) = 0.60
P(Good market | Negative) = 0.20
Good
1. Draw tree
Positie
Open cafe
Bad
Do not open cafe Conduct research
Good Open cafe Negatie
Bad
Do not open cafe Good Do not conduct research
Open cafe
Do not open cafe
Bad
2. Write payof
Positie
Open cafe
Good
30
Bad
-10
Do not open cafe Conduct research Open cafe Negatie
0 Good
30
Bad
-10
Do not open cafe
Do not conduct research
Open cafe
Do not open cafe
0 Good
30
Bad
-10 0
Good
3. Write notatons of probability at all state of nature branches P(Positiee
Positie
Open cafe
P(Good|Positiee
Bad P(Bad|Positiee
Do not open cafe Conduct research
P(Good|Negatiee
Negatie
-10 0
Good Open cafe
30
Bad P(Bad|Negatiee
30 -10
P(Negatiee
Do not open cafe
Do not conduct research
Open cafe
0 Good
30
Bad
-10
P(Goode
P(Bade
Do not open cafe
0
Good
4. Assign probabilites P(Positiee =0.6
Positie
Open cafe
30
P(Good|Positiee =0.75
Bad
-10
P(Bad|Positiee =0.25
Do not open cafe Conduct research
0 Good
Open cafe
30
P(Good|Negatiee =0.20
Negatie
Bad
-10
P(Bad|Negatiee =0.80
P(Negatiee=0.40
Do not open cafe
Do not conduct research
Open cafe
0 Good
30
Bad
-10
P(Goode =0.50
P(Bade =0.50
Do not open cafe
0
5. Calculate EMV
(30 x 0.75e + (-10 x 0.25e = 20 Open P(Positiee =0.6 20 cafe Positie
Good
30
P(Good|Positiee =0.75
Bad
-10
P(Bad|Positiee =0.25
Do not open cafe Conduct research
(30 x 0.20e + (-10 x 0.80e = -2 Open cafe
0 Good
30
P(Good|Negatiee =0.20
-2 Bad
Negatie
-10
P(Bad|Negatiee =0.80
P(Negatiee=0.40
Do not open cafe (30 x 0.50e + (-10 x 0.50e = 10 Do not conduct research
Open cafe
0 Good
30
Bad
-10
P(Goode =0.50
10 P(Bade =0.50
Do not open cafe
0
5. Calculate EMV
(30 x 0.75e + (-10 x 0.25e = 20 Open P(Positiee =0.6 20 cafe Positie 20
Good
√
Bad
(30 x 0.20e + (-10 x 0.80e = -2 Open cafe
-10
P(Bad|Positiee =0.25
Do not open cafe Conduct research
30
P(Good|Positiee =0.75
0 Good
30
P(Good|Negatiee =0.20
-2 Bad
Negatie
-10
P(Bad|Negatiee =0.80
P(Negatiee=0.40
Do not open cafe (30 x 0.50e + (-10 x 0.50e = 10 Do not conduct research
Open cafe
0 Good
30
Bad
-10
P(Goode =0.50
10 P(Bade =0.50
Do not open cafe
0
5. Calculate EMV
(30 x 0.75e + (-10 x 0.25e = 20 Open P(Positiee =0.6 20 cafe Positie 20
Good
√
Bad
(30 x 0.20e + (-10 x 0.80e = -2
Negatie
0
Open cafe
-10
P(Bad|Positiee =0.25
Do not open cafe Conduct research
30
P(Good|Positiee =0.75
0 Good
30
P(Good|Negatiee =0.20
-2 Bad
-10
P(Bad|Negatiee =0.80
P(Negatiee=0.40
Do not open cafe (30 x 0.50e + (-10 x 0.50e = 10 Do not conduct research
Open cafe
0
√
Good
30
Bad
-10
P(Goode =0.50
10 P(Bade =0.50
Do not open cafe
0
5. Calculate EMV
(30 x 0.75e + (-10 x 0.25e = 20 Open P(Positiee =0.6 20 cafe Positie 20
Good
√
Bad
(30 x 0.20e + (-10 x 0.80e = -2
Negatie
0
Open cafe
-10
P(Bad|Positiee =0.25
Do not open cafe Conduct research
30
P(Good|Positiee =0.75
0 Good
30
P(Good|Negatiee =0.20
-2 Bad
-10
P(Bad|Negatiee =0.80
P(Negatiee=0.40
Do not open cafe (30 x 0.50e + (-10 x 0.50e = 10 Do not conduct research
10
Open cafe
0
30
Bad
-10
P(Goode =0.50
10
√
Do not open cafe
√
Good
P(Bade =0.50
0
5. Calculate EMV
(20 x 0.60e + (0 x 0.40e = 12 Conduct research 12
(30 x 0.75e + (-10 x 0.25e = 20 Open P(Positiee =0.6 20 cafe Positie 20
Good
√
Bad
(30 x 0.20e + (-10 x 0.80e = -2
Negatie
0
-10
P(Bad|Positiee =0.25
Do not open cafe
Open cafe
30
P(Good|Positiee =0.75
0 Good
30
P(Good|Negatiee =0.20
-2 Bad
-10
P(Bad|Negatiee =0.80
P(Negatiee=0.40
Do not open cafe (30 x 0.50e + (-10 x 0.50e = 10 Do not conduct research
10
Open cafe
0
30
Bad
-10
P(Goode =0.50
10
√
Do not open cafe
√
Good
P(Bade =0.50
0
5. Calculate EMV
(30 x 0.75e + (-10 x 0.25e = 20 Open P(Positiee =0.6 20 cafe Positie 20
Good
30
P(Good|Positiee =0.75
√
Bad
-10
P(Bad|Positiee =0.25
Do not open cafe (20 x 0.60e + (0 x 0.40e = 12 0 Conduct (30 x 0.20e + (-10 x 0.80e = -2 Good research 12 30 P(Good|Negatiee =0.20 Open Cost of research = 1.4 -2 cafe 12 – 1.4 = 10.6 Bad 0 -10 P(Bad|Negatiee =0.80 Negatie P(Negatiee=0.40
Do not open cafe (30 x 0.50e + (-10 x 0.50e = 10 Do not conduct research
10
Open cafe
0
30
Bad
-10
P(Goode =0.50
10
√
Do not open cafe
√
Good
P(Bade =0.50
0
5. Calculate EMV
(30 x 0.75e + (-10 x 0.25e = 20 Open P(Positiee =0.6 20 cafe Positie 20
Good
30
P(Good|Positiee =0.75
√
Bad
-10
P(Bad|Positiee =0.25
Do not open cafe (20 x 0.60e + (0 x 0.40e = 12 0 Conduct (30 x 0.20e + (-10 x 0.80e = -2 Good research 12 30 P(Good|Negatiee =0.20 Open Cost of research = 1.4 -2 cafe 12 – 1.4 = 10.6 Bad 0 -10 P(Bad|Negatiee =0.80 √ Negatie 10.6 P(Negatiee=0.40
Do not open cafe (30 x 0.50e + (-10 x 0.50e = 10 Do not conduct research
10
Open cafe
0
30
Bad
-10
P(Goode =0.50
10
√
Do not open cafe
√
Good
P(Bade =0.50
0
6. Make decision Conduct research. If the research indicates positie result, open café. If the research indicates negatie result, do not open café.
(30 x 0.75e + (-10 x 0.25e = 20 Open P(Positiee =0.6 20 cafe Positie 20
Good
30
P(Good|Positiee =0.75
√
Bad
-10
P(Bad|Positiee =0.25
Do not open cafe (20 x 0.60e + (0 x 0.40e = 12 0 Conduct (30 x 0.20e + (-10 x 0.80e = -2 Good research 12 30 P(Good|Negatiee =0.20 Open Cost of research = 1.4 -2 cafe 12 – 1.4 = 10.6 Bad 0 -10 P(Bad|Negatiee =0.80 √ Negatie 10.6 P(Negatiee=0.40
Do not open cafe (30 x 0.50e + (-10 x 0.50e = 10 Do not conduct research
10
Open cafe
0
30
Bad
-10
P(Goode =0.50
10
√
Do not open cafe
√
Good
P(Bade =0.50
0