Decision Trees and Multi-attribute Utility Models
A decision tree uses two types of nodes: choice nodes, represented by a square and chance nodes, represented by a circle. An analyst constructs a decision tree. For the chance nodes the probabilities along outgoing branch must sum to one. One then calculates the expected payoffs for each branch in the tree. A decision tree has two major advantages. First, a decision tree shows graphically the relationships among the problem elements. Second, it can deal with more complex situations in a compact form.
One can use a generalized Decision Analysis program to model the following situation, based on Lee, Moore, and Taylor, 1985. Our company has two possible choices: Either we introduce our product (A1), or we don't (A2). If we introduce our product, we incur $100,000 in R&D costs. If we introduce the product our competitor may introduce a competing product. So Alternative 1 can have two outcomes: Our competitor introduces a competing product (O1), or does not (O2). Based on our knowledge of the marketplace, our competitor, and some marketing intelligence, we assess the probability of O1 to be 70%, and that of 02 to be 30%. O1 and O2 are outcome or chance nodes. The final outcomes of the Promotional Campaign can depend, among other things, on our actions, our competitor's actions, the size of our promotional campaign, and the size of our competitor's campaign. Thus, we can analyze the final outcomes in terms of three possible promotional campaigns: We launch a big campaign (N1), we launch a medium campaign (N2), or we launch a small campaign (N3). We need to estimate the profitability and probabilities associated with N1, N2 and N3. The "best" strategy depends on the criterion used. In a marketing analysis, the criterion is typically maximizing Expected Monetary Value (EMV). Figure 9.3 shows part of the decision tree for this decision situation.
Multi-attribute utility analysis (MAUA) is a popular decision analysis tool. When this tool is used the attributes are sometimes called decision factors or criteria. The attributes are then given importance weights. The decision-maker provides information about each alternative on each attribute. This step involves measuring the decision-maker's utility or perception of usefulness of an alternative in terms of the desired attributes. There is an extensive specialized literature on Multi-Attribute Utility Analysis (cf., Watson and Buede, 1987; Golub, 1997).
MAUA has traditionally been used in selection problems in which there is certainty regarding the attribute levels of the alternatives. Another operations research technique, subjective probability assessment, can be used to develop a distribution of attribute levels when there is uncertainty in these values. These probability distributions can be used in conjunction with MAUA to provide a consistent framework for making selection decisions.