Modeling project preferences in multiattribute portfolio decision analysis

When choosing a portfolio of projects with a multi-attribute weighting model, it is necessary to elicit trade-off statements about how important these attributes are relative to each other. Such statements correspond to weight constraints, and thus impact on which project portfolios are potentially optimal or non-dominated in view of the resulting set of feasible attribute weights. In this paper, we extend earlier preference elicitation approaches by allowing the decision maker to make direct statements about the selection and rejection of individual projects. We convert such project preference statements to weight information by determining the weights for which (i) the selected project is included in all potentially optimal or non-dominated portfolios, or (ii) the rejected project is not included in any potentially optimal or non-dominated portfolio. We prove that the two complementary selection rules will exclude exactly the same set of weights. However, analyses that apply the dominance structure often lead to multiple, mutually exclusive feasible weight sets, and therefore the approach based on potential optimality is more relevant for practical decision analysis. We also propose ex ante value of information measures to guide the elicitation of project preference statements, and illustrate our results by analyzing a real case on the selection of infrastructure maintenance projects.