Title: Preference Programming with Incomplete Ordinal Information

Authors: Antti Punkka and Ahti Salo

Date: December 21, 2004

Status: Manuscript

Keywords: Decision analysis, multiple criteria; Programming, linear, algorithms; Utility/preference, estimation.

In this paper, we develop the RICHER method (Rank Inclusion in Criteria Hierarchies with Extended Rankings) which extends uses of incomplete preference information in value trees by allowing the decision maker (DM) to provide incomplete ordinal preference statements about (i) the relative importance of attributes and (ii) the relative performance of alternatives with regard to a set of attributes. Such statements can be elicited by asking the DM to associate a set of rankings to a set of alternatives (e.g., `alternatives x1 and x2 are among the three best ones with regard to costs´) or attributes (e.g., `the most important attribute is either a1, a2 or a3´). Because statements of this kind may lead to non-convex sets of feasible parameters, we develop equivalent mixed integer linear programming (MILP) formulations which allow such statements to be combined with any preference programming methods that correspond to linear inequalities. The potential of RICHER is illustrated with an example on the siting of an office facility.