Decisions in an Uncertain World

1
Decisions in an Uncertain World
2
Topics

• the chain of events
• structuring a decision as a tree
• decision tree analysis identifying the best
  course in an uncertain world
• reading
• Hannagan p.386-389
• Owen Jones p.227-230, 233-236, 251-261
• Thomas p.65-73

3
Tree diagrams an aircraft disaster?
success
engine OK
success
correct pilot action
control OK
auto- warn
engine fails
4
Tree diagrams an aircraft disaster?
success
control fails
disaster
engine OK
success
correct pilot action
control OK
auto- warn
engine fails
5
Tree diagrams an aircraft disaster?
success
control fails
disaster
engine OK
success
correct pilot action
control OK
disaster
wrong pilot action
auto- warn
engine fails
6
Tree diagrams an aircraft disaster?
success
0.99000
control fails
disaster
0.00036
engine OK
success
0.00684
correct pilot action
control OK
disaster
0.00180
wrong pilot action
auto- warn
control fails
disaster
0.00006
correct pilot action
engine fails
auto-warn fails
success
0.00054
control OK
wrong pilot action
disaster
0.00040
P(success) 0.990000.006840.00054 0.99738
P(disaster) 0.000360.001800.000060.00040
0.00262
7
Coping with an imperfect forecast

• completed the initial development of a new
  product
• considering whether to finance the final stage
  the product launch
• could result in high, medium or low sales
• or instead of launching product, could sell the
  concept

8
A decision tree
high sales
medium sales
launch product
-100K
low sales
abandon project and sell product concept
250K
9
Estimating the uncertainties
sales
p0.2
1000K
high sales
medium sales
500K
launch product
p0.4
-100K
low sales
200K
p0.4
abandon project and sell product concept
250K
10
Summarising the expected values
sales total prob. expected value value
p0.2
1000K
900 0.2 180
high sales
medium sales
500K
400 0.4 160
launch product
p0.4
-100K
low sales
200K
p0.4
100 0.4 40
abandon project and sell product concept
250K
11
An alternative layout
sales prob. expected sales
p0.2
1000K
0.2 200
high sales
medium sales
500K
0.4 200
launch product
p0.4
-100K
low sales
200K
p0.4
0.4 80
480
abandon project and sell product concept
250K
12
Extending the analysis

• 3 options
• launch product
• sell concept
• conduct more market research at a cost of 50,000
• market research buys information
• the future is better understood
• the probabilities change

13
Further options market research?
launch
-100K
positive
sell
250K
conduct market research
-50K
launch product
-100K
250K
sell product concept
14
But the market research may not be encouraging
launch
-100K
positive
sell
250K
launch
-100K
negative
conduct market research
sell
250K
-50K
launch product
-100K
250K
sell product concept
15
Incorporating the uncertainties
launch
-100K
positive
sell
250K
launch
-100K
negative
conduct market research
sell
250K
-50K
launch product
-100K
250K
sell product concept
16
Calculating the expected values
0.4
1000K
0.4 400
high
launch
medium
-100K
500K
0.4 200
640K
0.4
200K
0.2
low
0.2 40
positive
sell
p0.7
250K
640
0.1
launch
-100K
0.1
negative
conduct market research
p0.3
0.8
sell
250K
-50K
0.2
launch product
0.4
-100K
0.4
250K
sell product concept
17
Comparing the secondary options
0.4
launch
-100K
640K
0.4
0.2
positive
sell
p0.7
250K
0.1
launch
-100K
310K
0.1
negative
conduct market research
p0.3
0.8
sell
250K
-50K
0.2
launch product
480K
0.4
-100K
0.4
250K
sell product concept
18
Building up the expected values
0.4
launch
-100K
640K
540K
0.4
0.2
0.75400.3250
positive
sell
p0.7
250K
0.1
launch
453K
-100K
310K
250K
0.1
negative
conduct market research
p0.3
0.8
sell
250K
-50K
0.2
launch product
480K
0.4
-100K
0.4
250K
sell product concept
19
Building up the expected values
0.4
launch
-100K
640K
540K
0.4
0.2
positive
sell
p0.7
250K
0.1
launch
453K
-100K
310K
250K
0.1
negative
conduct market research
p0.3
0.8
sell
250K
-50K
0.2
launch product
480K
0.4
-100K
0.4
403K
250K
sell product concept
max(453-50, 480-100, 250)
20
The final decision
0.4
launch
-100K
640K
540K
0.4
0.2
positive
sell
p0.7
250K
0.1
launch
453K
-100K
310K
250K
0.1
negative
conduct market research
p0.3
0.8
sell
250K
-50K
0.2
launch product
480K
0.4
-100K
0.4
403K
250K
sell product concept
21
The value of information

• if the cost of market research increases, would
  it still be worthwhile?
• the two options (research or no research) would
  have equal expected values if the market research
  cost 73,000
• information/ research is often expensive
  managers have to live with uncertainty take
  educated gambles