Measurable Multiattribute Value Functions for Portfolio Decision Analysis

Portfolio decision analysis models support selecting a portfolio of projects in view of multiple objectives and limited resources. These models often rely on the additive-linear portfolio value function, although empirical evidence suggests that the underlying preference assumptions do not always hold. In this paper we relax these assumptions and derive a more general class of portfolio value functions which deploy symmetric multilinear functions to capture non-linearities in the criterion specific portfolio values. These criterion specific portfolio values can be aggregated with an additive, a multiplicative or a multilinear function allowing a rich representation of preferences among the multiple objectives. We develop novel techniques for eliciting these value functions and also discuss the use of existing techniques that are often applied in practice. Furthermore, we demonstrate that the value functions can be maximized for problem sizes of practical relevance using an implicit enumeration algorithm or an approximate mixed integer linear programming model. Application of the results is illustrated with an example in ecological conservation site selection.