Colaco Soda Problem with Application of WinQSB for
Decision Tree: Problem Statement and Solution
Source of the problem: page 758, W. L. Winston, "Operations Research, Application and
Algorithms", 4th Edition, Thomson Learning, 2004, ISBN: 0-534-38058-1
By: Parisay
Problem statement:
Colaco currently has assets of $150,000 and wants to decide whether to market a new
chocolate-flavored soda, Chocola. Cocola has three alternatives:
Alternative 1- Test market Cocola locally, then utilize the results of the market study to
determine whether or not to market Cocola nationally.
Alternative 2- Immediately (without test marketing) market Cocola nationally.
Alternative 3- Immediately (without test marketing) decide not to market Cocola
nationally.
In the absence of a market study, Colaco believes that Cocola has a 55% chance of being
a national success and a 45% chance of being a national failure. If Cocola is a national
success, Colaco’s asset position will increase by $300,000, and if Cocola is a national
failure, Colaco’s asset position will decrease by $100,000.
If Colaco performs a market study (at a cost of $30,000), there is a 60% chance that the
study will yield favorable results (referred to as a local success) and a 40% chance that
the study will yield unfavorable results (referred to a local failure). If a local success is
observed, there an 85% chance that Cocola will be a national success. If a local failure is
observed, there is only a 10% chance that Cocola will be a national success. If Colaco is
risk-neutral (wants to maximize its expected final asset position), what strategy should
the company follow?
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Summary of problem:
Input data to WinQSB:
Node Number Node Name
1 testYN
2 localSF
3 marketYN1
4 marketYN2
5 marketYN3
6 nationalSF1
7 nationalSF2
8 nationalSF3
9 terminal1
10 terminal2
11 terminal3
12 terminal4
13 terminal5
14 terminal6
15 terminal7
16 terminal8
17 terminal9
Node Type
D
C
D
D
D
C
C
C
Immediate Following
Node
2,3
4,5
6,17
9,7
12,8
15,16
10,11
13,14
Node Payoff Probability
0.6
0.4
12000
420000
20000
120000
420000
20000
450000
50000
150000
0.85
0.15
0.1
0.9
0.55
0.45
2
3
Decision Tree:
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Output result, solution from WinQSB:
1/19/2003 Node/Event
1 testYN
2 localSF
3 marketYN1
4 marketYN2
5 marketYN3
6 nationalSF1
7 nationalSF2
8 nationalSF3
9 terminal1
10 terminal2
11 terminal3
12 terminal4
13 terminal5
14 terminal6
15 terminal7
16 terminal8
17 terminal9
Overall
Expected
Type
Decision node
Chance node
Decision node
Decision node
Decision node
Chance node
Chance node
Chance node
End node
End node
End node
End node
End node
End node
End node
End node
End node
Value =
Expected value Decision
$270,000 marketYN1
$264,000.03
$270,000 nationalSF1
$360,000 nationalSF2
$120,000 terminal4
$270,000
$360,000
$60,000
$12,000
$420,000
$20,000
$120,000
$420,000
$20,000
$450,000
$50,000
$150,000
$270,000
Prepared: 1-21-03
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