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Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Antti Punkka Name of the doctoral dissertation Rank-based information in multi-attribute decision and efficiency analysis Publisher School of Science Unit Department of Mathematics and Systems Analysis Series Aalto University publication series DOCTORAL DISSERTATIONS 160/2012 Field of research Systems and Operations Research Manuscript submitted 11 September 2012 Date of the defence 11 January 2013 Permission to publish granted (date) 18 October 2012 Language English Monograph Article dissertation (summary + original articles) Abstract Additive multi-attribute value models are widely employed in decision and efficiency analysis. Difficulties in specifying preferences for these models have motivated the development of methods that admit incomplete preference information, identify nondominated alternatives and provide recommendations with heuristic decision rules. These methods accommodate many types of preference statements. Yet, several studies suggest that decision makers prefer to provide rank-based information rather than numerical statements.Additive multi-attribute value models are widely employed in decision and efficiency analysis. Difficulties in specifying preferences for these models have motivated the development of methods that admit incomplete preference information, identify nondominated alternatives and provide recommendations with heuristic decision rules. These methods accommodate many types of preference statements. Yet, several studies suggest that decision makers prefer to provide rank-based information rather than numerical statements. First, this thesis defines the notion of incomplete ordinal information, which can capture statements about the relative importance of the attributes and about the achievement levels of alternatives. The thesis then develops an optimization model for identifying non-dominated alternatives when alternatives and preferences are characterized by incomplete ordinal information and possibly by other types of incomplete information. These forms of information can, for example, help stakeholders to arrive at a joint preference characterization. Second, the thesis shows that the recommendations of many decision rules depend on the selected normalization of value functions. Motivated partly by this, the thesis develops optimization models to determine all the rankings the alternatives attain with the model parameters that are consistent with the stated incomplete information. The resulting ranking intervals help, for example, analyze how sensitive the alternatives' rankings are to the model parameters. Third, the thesis introduces dominance relations and ranking intervals for the efficiency analysis of decision making units when efficiency is measured through ratios of multi-attribute output and input values, as in the original data envelopment analysis method. These relations and intervals, which can be computed with the optimization models developed in the thesis, make it possible to compare any two decision making units independent of what other units are included in the analysis and to analyze how sensitive the efficiency of a unit is to the output and input attribute weights.