SCREENING DISCRETE ALTERNATIVES WITH IMPRECISELY ASSESSED ADDITIVE MULTIATTRIBUTE FUNCTIONS

The classical problem of ranking alternatives when there exists partia l information on the scaling constants for additive multi-attribute ut ility functions (MAUFs) is reexamined. Most approaches assume that the unknown scaling constants can be precisely known. In this paper, we a rgue that this assumption may not be realistic, and we develop a new a pproach based on an assumption that is less restrictive and does not r equire that the Decision Maker be ''consistent'' over the given partia l information regarding the unknown scaling constants. Definitions and computationally efficient procedures are developed to identify nondom inated 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 line ar programming problems), whether or not the set of alternatives can b e further screened. Finding the best alternative via an interactive me thod in which the proportion of alternatives screened may be changed i s discussed. The approach is generalized and related to other MAUF str uctures such as multilinear, quasi-concave, and quasi-convex. It is de monstrated that linear programming is sufficient to solve all ensuing problems. Some examples are provided.