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Decision trees and dealing with uncertainty

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The first decision node asks ‘launch early?’

The top branch is for ‘yes’ which has a cost of 3m. Next on that branch is a chance node called ‘beat rival?’. This splits into two branches. The top brach is for ‘yes’ and has a 0.8 probability. This leads to a chance node called ‘sales’ which has three branches for high , medium and low. The respective probabilities are 0.6, 0.25 and 0.15. Finally there are the three respective final values starting with high sales 9 million, medium, 5 million And low 1 million.

Returning to the ‘beat rival?’ chance node the second branch is for ‘no’ and has a 0.2 probability. This leads to a decision node ‘promotion?’ which has two branches. The top branch is for ‘yes’ and costs -1.5 million and leads to a ‘sales’ chance node. This node has three branches for levels of sale, high , probability 0.5 and value 9 million, medium 0.4 probability and value 5 million and low, 0.1 probability 1 million.

Returning to the promotion node, the second branch is for ‘no’ and leads to a chance node ‘sales’ with three branches high, probability 0.35 value 9 million, medium 0.45 value 5 million and low 0.2 and 1 million.

Returning to the ‘launch early? Node the bottom branch is for no. Next on that branch is a chance node called ‘beat rival?’. This splits into two branches. The top branch is for ‘yes’ and has a 0.2 probability. This leads to a chance node called ‘sales’ which has three branches for high , medium and low. The respective probabilities are 0.6, 0.25 and 0.15. Finally there are the three respective final values starting with high sales 9 million, medium, 5 million And low 1 million. Returning to the ‘beat rival?’ chance node the second branch is for ‘no’ and has a 0.8 probability. This leads to a decision node ‘promotion?’ which has two branches. The top branch is for ‘yes’ and costs 1.5 million and leads to a ‘sales’ chance node. This node has three branches for levels of sale, high , probability 0.5 and value 9 million, medium 0.4 probability and value 5 million and low, 0.1 probability 1 million.

Returning to the promotion node, the second branch is for ‘no’ and leads to a chance node ‘sales’ with three branches high, probability 0.35 value 9 million, medium 0.45 value 5 million and low 0.2 and 1 million.