a solved example of how to draw a decision tree

1. Decision tree in decision analysis
BY Dr.Ammara Omer Khakwani

2. Decision tree analysis
• A decision tree is a graphic device of decision
making process.
• It is a graphical presentation of the various
alternatives.
• It is also known as tree-diagram

3. Decision tree
 A decision tree is a decision support tool
that uses a tree-like graph or model of
decisions and their possible consequences,
including chance, event outcomes, resource
costs, and utility.
 It is one way to display an algorithm.
 Decision trees are commonly used in
Operations Research, specifically in Decision
Analysis, to help identify a strategy most
likely to reach a goal.

4. Types of nodes
A decision Tree consists of 3 types of nodes:-
1. Decision nodes - commonly represented by
squares.
2. Chance nodes - represented by circles.
3. End nodes - represented by triangles.
A decision tree has burst nodes (splitting paths)
no sink nodes (converging paths).

5. Example
Problem:-
A glass factory that specializes in crystal is
developing a substantial back-log and for this the
firm’s management is considering three courses of
action ; the correct choice depends largely upon
the future demand, which may be low , medium,
or high.
1. Show this decision situation in the form of a
decision tree.
2. Indicate the most preferred decision
3. Its corresponding expected value.

6. Demand
Course of action
Probabilities S1 S2 S3
Low 0.10 10 -20 -150
Medium 0.50 50 60 20
high 0.40 50 100 200
S1=Sub-contracting
S2=being-overtime
S3=construct new facility

7. Expected monetary value
• EMV(S1)= (0.10x10)+(0.50x50)+(0.40x50) =46
• EMV(S2)= (0.10x-20)+(0.50x60)+(0.40x100) =68
• EMVS3 = (0.10x-150)+(0.50x20)+(0.40x200) =75
Highest EMV will be selected
so, S3 will be selected.

8. Decision tree
As per decision tree analysis
S3 is selected=75
D 2
3
0.10x10=1
0.50x50=25
0.40x50=20
=46
0.10x20=-2
0.50x60=30
0.40x100=40
=40
0.10x-150=-15
0.50x20=10
0.40x200=80
=75
S2=being-overtime
1
node
Alternatives
EMV

9. To find out Most preferred
Alternative
•
• Always find out
• EMV

10. Expected value of Sample information
• way of measuring market information.
• Is increase in expected value resulting from the sample information.
• EVSI=(EV with SI + Cost ) – (EV without SI)
• = (75+200) – (46)
• = 229
• = $229 are need for market study
Where
– EVSI= Expected value of sample information
– EV with SI = expected value with sample information.
– EV without SI = expected value without sample information.

11. Efficiency of sample information
• Efficiency of sample information=
• if the sample information was perfect then the
efficiency would be 100%
%100
EVPI
EVSI
%100
EVPI
EVSI

12. Sensitivity analysis
• EMV (node 1)
• =(-150)P – (1-P)10
• =-150P+10P-10
• =-140P-10
• -140P=10
• P=10/-140=-0.0714