Screening Discrete Alternatives with Imprecisely Assessed Additive Multi-Attribute Functions

The classical problem of ranking alternatives when there exists partial information on the scaling constants for additive multi-attribute utility functions (MAUFs) is reexamined. Most approaches assume that the unknown scaling constants can be precisely known. In this paper, we argue that this assumption may not be realistic, and we develop a new approach based on an assumption that is less restrictive and does not require that the Decision Maker be “consistent” over the given partial information regarding the unknown scaling constants. Definitions and computationally efficient procedures are developed to identify nondominated alternatives with respect to partial information on the scaling constants, which is called “utility nondominancy.” The concepts and procedures developed demonstrate, through two tests (solving two linear programming problems), whether or not the set of alternatives can be further screened. Finding the best alternative via an interactive method in which the proportion of alternatives screened may be changed is discussed. The approach is generalized and related to other MAUF structures such as multilinear, quasi-concave, and quasi-convex. It is demonstrated that linear programming is sufficient to solve all ensuing problems. Some examples are provided.