Decision networks are a particular type of Bayesian network that include
Decision and
Utility nodes. A decision node is used to represent alternative decisions while utility nodes are used to store benefits or costs. Decision networks are very useful for doing cost-benefit analysis because they allow you to determine the expected net benefit of alternative decisions. Lets look at an example.
The decision tree in
Figure 1 represents alternative decisions that a manufacturer may be faced with. The manufacturer can either develop a new product by undertaking a
thorough development or a
rapid development. Alternatively, the manufacturer can
consolidate existing products by
strengthening the existing products or
selling them as is (reap products). In total there are four decision pathways, each of which may result in a
good,
moderate or
poor market reaction (see
Figure 1).
Figure 1
The type of market reaction obtained will determine the amount of
income the manufacturer can generate. There is a
40% chance (
0.4 probability) that a
good market reaction will be achieved if the manufacturer undertakes a
thorough development of a new product. If a good market reaction is achieved then the expected income is
$1,000,000. Notice that the probabilities for each decision path sum to
1 or
100%.
Figure 2
Besides the possible market reaction, the manufacturer also has to take into account the
cost of each decision. For instance, while selling products as is (
reap products) is expected to generate the least income, it will also have the least cost.
Figure 3 shows the expected cost of each decision in the decision tree.
Figure 3
Now lets look at how this decision tree can be put into a decision network to identify the decision with the highest expected net benefit.
Click
here to open the
Product Development Example network in DBL Interactive (see
Figure 4). This network has a blue decision node called
Decisions that lists the four alternative manufacturer decisions. This influences the market reaction, hence there is a link from the decision node to the
Market Reaction node, which has the states
Good,
Moderate and
Poor. The
Market Reaction node stores the probability that each decision will achieve a
good,
moderate or
poor market reaction (see
Figure 5). The decision node (
Decisions and the
Market Reaction node are linked to a utility node called
Income because both the decision and the market reaction influence the expected income. The
Benefit utility node stores the expected income for each market reaction under each decision (see
Figure 6). Finally, the decision node is also linked to another utility node called
Cost, which stores the cost of each decision (see
Figure 7).
Figure 4: Product Development Example Network
Figure 5: Probability Table For The Market Reaction Node
To open the probability table for the
Market Reaction Node node, select the drop down arrow in the right hand corner then select the
Probabilities option.
Figure 6: Utility Table For Benefit Node
Figure 7: Utility Table For Cost Node (Note that the costs are stored as negative utilities)
The number beside each decision in the decision node is the
expected net benefit of each decision. Hence the best decision would be for the manufacturer to undertake a
thorough development of a new product since this is the decision that has the
highest expected net benefit (
$270,400) according to our decision network.
Lets look at how the expected net benefit is calculated for the New Thorough product development decision. First, the expected income from each market reaction is multiplied by the probability of achieving each market reaction:
Good Market Reaction = $1,000,000 x 0.4 = $400,000
Moderate Market Reaction = $50,000 x 0.4 = $20,000
Poor Market Reaction = $2,000 x 0.2 = $400
Then the probability adjusted incomes are added together to give an expected income:
$400,000 + $20,000 + $400 = $420,400
Finally, the cost of the decision is taken away from the expected income:
$420,400 - $150,000 = $270,400