Elements of GeNIe Diagrams: Multiple utility nodes
From DSL
Some outcomes of decision problems involve several, possibly conflicting attributes. For example, outcome of a business decision may optimize productions costs, product quality, company image, and employee satisfaction. While such complex utility structures can be modeled directly by one utility function, it is usually easier for a decision maker to elicit utility functions over each of the attributes and then combine them in a single multi-attribute utility function.
While we plan to support multi-attribute utility [MAU] functions of arbitrary form, at the moment GeNIe supports only linearly-additive multi-attribute utility functions. It is possible to have any number of value nodes structured hierarchically in such a way that nodes at the next level combine the utilities specified at the previous level by means of a linear function.
To create a MAU node create a normal Value node. [See Creating Influence Diagrams tutorial to learn how to create Value node].
Right click on the node, and choose Change Type, from the menu. From the Change Type dialog box, choose MAU - Multi Attribute Utility and click OK. See Change Type section in Node Menu for more information.
For user's convenience, GeNIe will automatically change the type of a utility node into MAU node if the user draws an arc into it from another utility node.
Consider the following simple model fragment containing four value nodes, three Utility nodes (Income, Growth, and Happiness) and one Multi-Attribute Utility Node (Total Satisfaction).
Each of the parent nodes is an ordinary Utility node. The node TotalSatisfaction is a MAU node that combines the parent utility nodes using the following linear function:
[ TotalSatisfaction = 0.8 * Happiness + 0.3 * Growth + 0.5 * Income ]
The weights are specified in the definition tab of the MAU node, which looks as follows:
There is one more functionality added to GeNIe for user's convenience. GeNIe allows several childless value nodes. In other words, it allows separate optimization over several attributes. In case of such several childless nodes, GeNIe computes the expected utility for each of them, indexed by the states of all decision nodes (i.e., the decision alternatives) and the predecessors of the decision nodes (i.e., nodes that will be observed before the decision is made). Expected utility displayed in the decision nodes, however, is a simple linearly-additive combination of the utilities of the childless nodes with the assumption that the weights are all equal to 1.0.
