Identifying nondominated alternatives with partial information for multiple-objective discrete and linear programming problems

The problem addressed is that of reducing the set of finite (discrete) multiple-criteria alternatives to a subset of alternatives based on three assumptions: that the (multiattribute) utility function is additive over attributes; that single-attribute functions are known; and that scaling constants are not known exactly but are specified by a set of linear equalities through interactions with the decision-maker (DM). Definitions, theories, and computationally efficient procedures are developed to determine whether an alternate is worthy of further consideration, should be eliminated, or is the most preferred alternative for the given partial information. The concepts of convex and tradeoff nondominancy are defined. All ensuing problems can be solved by linear programming. A computationally efficient algorithm is discussed. Other uses for the concepts developed are presented. It is shown that multiattribute discrete problems can be formulated as multiple-objective linear programming (MOLP) problems