Decision Aiding Rank inclusion in criteria hierarchies Ahti Salo * , Antti Punkka Systems Analysis Laboratory, Helsinki University of Technology, P.O. Box 1100, HUT 02015, Finland Received 21 June 2002; accepted 14 October 2003 Available online 19 December 2003 Abstract This paper presents a method called Rank Inclusion in Criteria Hierarchies (RICH) for the analysis of incomplete preference information in hierarchical weighting models. In RICH, the decision maker is allowed to specify subsets of attributes which contain the most important attribute or, more generally, to associate a set of rankings with a given set of attributes. Such preference statements lead to possibly non-convex sets of feasible attribute weights, allowing decision recommendations to be obtained through the computation of dominance relations and decision rules. An illustrative example on the selection of a subcontractor is presented, and the computational properties of RICH are considered. Ó 2003 Elsevier B.V. All rights reserved. Keywords: Multiple criteria analysis; Decision analysis; Hierarchical weighting models; Incomplete preference information 1. Introduction Methods of multiple criteria decision making (MCDM) are widely employed in problems char- acterized by incommensurate objectives. Numer- ous successful MCDM applications have been developed in fields such as energy policy, envi- ronmental decision making and comparison of industrial investment opportunities (see, e.g., Corner and Kirkwood, 1991; H€ am€ al€ ainen, 2004; Keefer et al., 2004). In MCDM applications, the decision problem is structured by associating measurable attributes with the objectives that are relevant to the decision maker (DM). In most methods––such as the Analytic Hierarchy Process (AHP; Saaty, 1980) and value tree analysis (Kee- ney and Raiffa, 1976)––the DM is also requested to supply weights as a measure for the relative importance of attributes. In practice, the elicitation of precisely specified attribute weights may be difficult. This may be due to the urgency of the decision, lack of resources for completing the elicitation process, or conceptual difficulties in the interpretation of intangible objectives (see, e.g., Weber, 1987). In group set- tings, difficulties in determining attribute weights for the groupÕs joint preference model may arise from differences in the group membersÕ level of knowledge or their interpretation of what the relevant objectives mean (H€ am€ al€ ainen et al., 1992). * Corresponding author. Tel.: +358-9-4519055; fax: +358-9- 4519096. E-mail addresses: ahti.salo@hut.fi (A. Salo), antti.pun- kka@hut.fi (A. Punkka). 0377-2217/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2003.10.014 European Journal of Operational Research 163 (2005) 338–356 www.elsevier.com/locate/dsw