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?

Summary of problem:

Input data to WinQSB:

Node Number / Node Name / Node Type / Immediate Following Node / Node Payoff / Probability
1 / testYN / D / 2,3
2 / localSF / C / 4,5
3 / marketYN1 / D / 6,17
4 / marketYN2 / D / 9,7 / 0.6
5 / marketYN3 / D / 12,8 / 0.4
6 / nationalSF1 / C / 15,16
7 / nationalSF2 / C / 10,11
8 / nationalSF3 / C / 13,14
9 / terminal1 / 12000
10 / terminal2 / 420000 / 0.85
11 / terminal3 / 20000 / 0.15
12 / terminal4 / 120000
13 / terminal5 / 420000 / 0.1
14 / terminal6 / 20000 / 0.9
15 / terminal7 / 450000 / 0.55
16 / terminal8 / 50000 / 0.45
17 / terminal9 / 150000


Decision Tree:


Output result, solution from WinQSB:

1/19/2003 / Node/Event / Type / Expected value / Decision
1 / testYN / Decision node / $270,000 / marketYN1
2 / localSF / Chance node / $264,000.03
3 / marketYN1 / Decision node / $270,000 / nationalSF1
4 / marketYN2 / Decision node / $360,000 / nationalSF2
5 / marketYN3 / Decision node / $120,000 / terminal4
6 / nationalSF1 / Chance node / $270,000
7 / nationalSF2 / Chance node / $360,000
8 / nationalSF3 / Chance node / $60,000
9 / terminal1 / End node / $12,000
10 / terminal2 / End node / $420,000
11 / terminal3 / End node / $20,000
12 / terminal4 / End node / $120,000
13 / terminal5 / End node / $420,000
14 / terminal6 / End node / $20,000
15 / terminal7 / End node / $450,000
16 / terminal8 / End node / $50,000
17 / terminal9 / End node / $150,000
Overall / Expected / Value = / $270,000

Prepared: 1-21-03

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