HELSINKI UNIVERSITY OF TECHNOLOGY Department of Mathematics and Systems Analysis

of master's thesis Abstract: Methods of multi-criteria decision analysis (MCDA) provide normative support for decision making processes. Out of these methods, Robust Portfolio Modeling (RPM) helps decision makers (DMs) to select the best possible subset or portfolio of available projects in the presence of scarce resources. The RPM methods provide a computationally efficient way of generating non-dominated portfolios by accommodating incomplete preference information. This Thesis extends the RPM methods to group decision making context, where the different and possibly conflicting interests of multiple DMs need to be synthesized to obtain a satisfactory compromise. As in the single DM case, the information may be given with the preferred accuracy, and it is accommodated by set inclusion without the need for averaging or randomization. The methods also allow the group weight information describing the possible inequality in the DMs' influence to be incomplete. A distinction between individual and joint approaches is made. In the individual approach the group choice is based on the DMs' individually non-dominated sets. The joint approach seeks to aggregate the DMs' individual information into a single preference model. A few decision rules with method-specific variants are presented for generating decision recommendations. Based on an illustrative case study, the methods seem computationally efficient and provide robust decision recommendations. As in the single DM case, the group RPM methods are transparent and do not necessarily require mathematical expertise from the DMs. Owing to computational efficiency, multiple iterations may be carried out, whereby additional preference information can be elicited and utilized as the process evolves. While the main contribution of this Thesis is the development of efficient group methods for portfolio selection problems with incomplete information , also methods for generating group weight information sets based on the DMs' assessments are presented. arvioista. Acknowledgements The work was carried out in the Systems Analysis Laboratory at Helsinki University of Technology. I would like to thank the entire staff for creating a warm and motivational working environment. I would also like to thank Ville Brummer, Juuso Liesiö and Antti Punkka for their valuable advise and the interest they have shown towards my work. My gratitude goes especially to the supervisor of this Thesis, Professor Ahti Salo, for his devotion, guidance and genuine interest in my work and other aspirations. Finally, I would like to thank my family and friends for constant support during the many years of my studies.