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Helsinki University of Technology Systems Analysis Laboratory RPM – Robust Portfolio Modeling for Project Selection Pekka Mild, Juuso Liesiö and Ahti Salo Systems Analysis Laboratory Helsinki University of Technology P.O. Box 1100, 02150 TKK, Finland http://www.sal.tkk.fi firstname.lastname@tkk.fi

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Helsinki University of Technology Systems Analysis Laboratory 2 Problem framework n Choose a portfolio of projects from a large set of proposals n Projects evaluated on multiple criteria n Resource and other portfolio constraints n Reported applications in contexts such as –Corporate R & D (Stummer and Heidenberger, 2003) –Healthcare (Kleinmuntz and Kleinmuntz, 1999) –Infrastructure (Golabi et al., 1981; Golabi, 1987) n Software tools, e.g. –Catalyze Ltd (UK) / Hiview & Equity –Strata Decision Technology LLC / StrataCap ® –Expert Choice ® / EC Resource Aligner TM

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Helsinki University of Technology Systems Analysis Laboratory 3 Additive representation of portfolio value n Projects with costs n Scores and weights n Feasible portfolios n Project value: weighted sum of scores n Portfolio value: sum of projects’ values n Maximize portfolio value

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Helsinki University of Technology Systems Analysis Laboratory 4 Incomplete information in portfolio problems n Elicitation of complete information (point estimates) on weights and scores may be costly or even impossible n If we only have incomplete information, what portfolios and projects can be recommended? –We extend the solution concepts of Preference Programming methods (e.g., Salo and Hämäläinen, 1992; 2001) to portfolio problems n Provide guidance for focusing the elicitation efforts n Liesiö, Mild, Salo, (2005). Preference Programming for Robust Portfolio Modeling and Project Selection, conditionally accepted

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Helsinki University of Technology Systems Analysis Laboratory 5 Modeling of incomplete information n Feasible weight set –Several kinds of preference statements impose linear constraints on weights → Rank-orderings on criteria (cf., Salo and Punkka, 2005) → Interval SMART/SWING (Mustajoki et al., 2005) n Interval scores –Lower and upper bounds on criterion-specific scores of each project n Information set –Feasible values for and

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Helsinki University of Technology Systems Analysis Laboratory 6 Non-dominated portfolios n Incomplete information leads to value intervals on portfolios –Typically, no portfolio has the highest value for all feasible weights and scores n Portfolio dominates on S, denoted by, iff n Non-dominated portfolios n Computed by dedicated dynamic programming algorithm –Multi-Objective Zero-One LP (MOZOLP) problem with interval coefficients

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Helsinki University of Technology Systems Analysis Laboratory 7 Project-oriented analysis n Core Index of a project, –Share of non-dominated portfolios on S in which a project is included n Core projects, i.e., can be surely recommended –Would belong to all ND portfolios even with additional information n Exterior projects, i.e., can be safely rejected –Cannot enter any ND portfolio even with additional information n Borderline projects, i.e., need further analysis –Negotiation / iteration zone for augmenting the set of core projects

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Helsinki University of Technology Systems Analysis Laboratory 8 Sequential specification of information n Dominance relations depend on S –Loose statements often lead to a large number of ND portfolios –Complete information typically leads to a unique portfolio n Additional information to reduce –Modeled through a smaller weight set ( ) and/or narrower score intervals ( ) –No new portfolio can become non-dominated: n Elicitation efforts can be focused on borderline projects –Additional information can affect the status of borderline projects only –Narrower score intervals needed for borderline projects only

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Helsinki University of Technology Systems Analysis Laboratory 9 Add. exter. RPM for project portfolio selection Selected Not selected Decision rules, heuristics Additional information Large set of projects Multiple criteria Resource and portfolio constraints Borderline projects focus on Exterior proj. discard Core projects choose Borderline Negotiation, iteration Compute non-dom. portfolios Update ND portfolios Add. core Preceding core proj. Preceding exterior Loose statements on weights and scores

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Helsinki University of Technology Systems Analysis Laboratory 10 Application to road pavement projects (1/4) n Real data from Finnish Road Administration –Selection of the annual pavement program in one major road district n 223 project proposals –Generated by a specific road condition follow-up system –Coherent road segments proposals are independent n Three technical measurement criteria on each project 1.Damage coverage in the proposed site 2.Annual cost savings attained by road users (if repaired) 3.Durability life of the repair n Budget of 16.3 M€, sufficient for funding some 160 projects

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Helsinki University of Technology Systems Analysis Laboratory 11 Application to road pavement projects (2/4) n Illustrative ex post data analysis with RPM tools n Sequential weight information 1.Start with no information: 2.Rank-ordering stated by FINNRA experts: n Complete score information (point estimates) n Computations by PRO-OPTIMAL software –http://www.rpm.tkk.fi

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Helsinki University of Technology Systems Analysis Laboratory 12 Application to road pavement projects (3/4) n No information, n 542 portfolios n 103 core projects n 16 exterior projects n 104 borderline proj., from which some 60 can be funded with remaining resources

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Helsinki University of Technology Systems Analysis Laboratory 13 Application to road pavement projects (4/4) n Rank-ordering, n 109 portfolios n 127 core projects n 32 exterior projects n 64 borderline proj., from which some 30 can be funded with remaining resources

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Helsinki University of Technology Systems Analysis Laboratory 14 Conclusions n Key features –Admits incomplete information about weights and projects –Accounts for competing projects, scarce resources and portfolio constraints –Determines all non-dominated portfolios n Robust decision recommendations –Core Index values for individual projects derived from portfolio level analyses –Decision rules for portfolios (e.g., maximin, minimax regret) n Benefits –May lead to considerable savings in the costs of preference elicitation –Enables sequential decision support process with useful tentative results –Applications in project portfolio management and technology foresight

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Helsinki University of Technology Systems Analysis Laboratory 15 References »Golabi, K., (1987). Selecting a Group of Dissimilar Projects for Funding, IEEE Transactions on Engineering Management, Vol. 34, pp. 138 – 145. »Golabi, K., Kirkwood, C.W., Sicherman, A., (1981). Selecting a Portfolio of Solar Energy Projects Using Multiattribute Preference Theory, Management Science, Vol. 27, pp. 174-189. »Mustajoki, J., Hämäläinen, R.P., Salo, A., (2005). Decision Support by Interval SMART/SWING - Incorporating Imprecision in the SMART and SWING Methods, Decision Sciences, Vol. 36, pp. 317 - 339. »Kleinmuntz, C.E, Kleinmuntz, D.N., (1999). Strategic approach to allocating capital in healthcare organizations, Healthcare Financial Management, Vol. 53, pp. 52-58. »Stummer, C., Heidenberger, K., (2003). Interactive R&D Portfolio Analysis with Project Interdependencies and Time Profiles of Multiple Objectives, IEEE Trans. on Engineering Management, Vol. 50, pp. 175 - 183. »Salo, A. and R. P. Hämäläinen, (1992). Preference Assessment by Imprecise Ratio Statements, Operations Research, Vol. 40, pp. 1053-1061. »Salo, A. and Hämäläinen, R. P., (2001). Preference Ratios in Multiattribute Evaluation (PRIME) - Elicitation and Decision Procedures under Incomplete Information, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 3, pp. 533-545. »Salo, A. and Punkka, A., (2005). Rank Inclusion in Criteria Hierarchies, European Journal of Operations Research, Vol. 163, pp. 338 - 356

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