Incomplete Cost and Budget Information in Robust Portfolio Modelling (RPM) Juuso Liesiö, Pekka Mild and Ahti Salo Systems Analysis Laboratory Helsinki University of Technology P.O. Box 1100, 02015 TKK, Finland http://www.sal.tkk.fi firstname.lastname@tkk.fi

Contents Robust Portfolio Modelling (RPM) Project interactions in RPM A framework for multi-criteria project portfolio selection under incomplete preference information Project interactions in RPM Synergies, logical requirements etc. Incomplete cost and budget information in RPM Interval costs, efficient portfolios Illustrative example

Multi-criteria project portfolio selection Choose a portfolio of projects from a large set of proposals Projects evaluated on multiple criteria Resource and other portfolio constraints Not all projects can be selected Applications R&D Portfolio selection (Golabi, Kirkwood and Sicherman, 1981; Stummer and Heidenberger 2003) Capital budgeting (Kleinmuntz and Kleinmuntz, 1999) Strategic product portfolio selection (Lindstedt, Liesiö and Salo, 2006) Innovation management (Salo, Mild, Pentikäinen, 2006) Selecting forest sites for conservation (later in this session) Road asset management (later in this session)

Robust Portfolio Modeling (RPM) Liesiö, Mild, Salo, (2006). Preference Programming for Robust Portfolio Modeling and Project Selection, forthcoming in EJOR Projects Projects evaluated on multiple criteria Criteria i=1,…n, score of project with regard to criterion i: Importance of criteria captured through weights Additive value representation Project value: weighted sum of criterion score

Project Portfolios Portfolio p is a subset of projects Value of p is sum of projects’ value included in p (Golabi et al. 1981) Feasible portfolios satisfy a set of linear feasibility constraints Maximize portfolio value Standard Zero-One Linear Programming problem if weights and score precise

Modeling incomplete information Elicitation of complete information (point estimates) on weights and scores may be costly or even impossible Feasible weight set Several kinds of preference statements impose linear constraints on weights (Incomplete) rank-orderings on criteria (cf., Salo and Punkka, 2005) Interval SMART/SWING (Mustajoki et al., 2005) Interval scores Lower and upper bounds on criterion-specific scores of each project Information set

Which portfolios can be recommended? Definition. Portfolio p dominates p’ on S, denoted by , if Do not choose p’ since p certainly yields higher overall value! Non-dominated portfolios Computed by a dedicated dynamic programming algorithm Multi-Objective Zero-One LP (MOZOLP) problem with interval-valued objective function coefficients

Which projects can be recommended? Core Index of a project, Share of non-dominated portfolios on S in which a project is included Core projects, i.e. , can be surely recommended Would belong to all ND portfolios even with additional information Exterior projects, i.e. , can be safely rejected Cannot enter any ND portfolio even with additional information Borderline projects, i.e. , need further analysis Negotiation / iteration zone for augmenting the set of core projects Narrow score intervals needed

Project Interactions Different versions of the same project Follow-up projects: project 2 can be selected only if project 1 is selected Portfolio balance: minimum number of projects have to be started from each subgroup etc. Resource synergies: two projects are less expensive if both are selected Value synergies: selection of all projects in a group yield a higher value that the sum of projects’ values Modeled with additional feasibility constraints and dummy projects Interval valued synergy effects The problem remains linear Results on dominance, additional information, core indexes still apply New algorithm for computation for ND-portfolios needed (Liesiö et al. 2006b)

Incomplete information on costs and budget (1/3) Project costs uncertain Often budget is not tight nor should poor projects be selected even if they can be afforded Benefit-to-cost analysis Modeling Interval project costs Portfolio cost Focus on non-dominated portfolios no longer justified Which portfolios are efficient in sense of both value and cost

Incomplete Costs and Budget (2/3) Portfolio p is efficient if exists no feasible portfolio p’ s.t. with at least one inequality strict for some How to compute efficient portfolios? Portfolio’s cost added as a as a criterion to be minimized Cost intervals as negative score intervals Extended information set is equal to the set of efficient portfolios The same interval-MOZOLP algorithm can be used to compute all efficient portfolios

Incomplete costs and budget (3/3) The set of efficient portfolios includes non-dominated portfolios for every budget level R and cost information pair-wise dominance checks can be used to identified ND-portfolios in with any budget level R and Results can be visualized as a function of budget level Budget dependent Core index Share of non-dominated portfolios certainly attainable with budget R that include the project Overall value per budget min/max overall value of non-dominated portfolios certainly attainable with budget R that

Illustrative example in product release planning Inspired by a case study for Nokia Networks http://www.sal.tkk.fi/Opinnot/Mat-2.177/projektit2006/FinalReportNET.pdf Select which of the 40 features to include in a product release in order to maximize benefits of three customers Customer importance Interval costs for features, maximum budget 800 (about 25% of sum of all costs) Positioning constraints; at least three features from each of three technological areas (A,B and C)

Features (1/2) Follow-up projects Synergies Follow-up Cost synergy Benefit synergy Follow-up projects Synergies

Features (2/2) Follow-up Benefit synergy

Efficient portfolios Total of 767 efficient portfolios 20 borderline projects, for which narrower cost intervals should be estimated Feature A7 included in all efficient portfolios Feature C4 not included in any efficient portfolios Feature C17 included in 50% of efficient portfolios

Portfolio value as a function of resources

CI = 1 CI= 0 Budget level R Follow-up Cost synergy Follow-up Features A8 and A9 are certain choices and thus synergy 1 is utilised Follow-up CI = 1 Cost synergy Follow-up Benefit synergy Positioning constraint forces selection of 3 features in are C, which are not necessarily optimal with higher budget levels Features B14 is included in some non-dominated portfolios when R>480. Then , synergy 2 occurs Follow-up CI= 0 Benefit synergy Budget level R

Final selection (1/2) Budget fixed for 650 15 non-dominated portfolios in ND-portfolio #14 maximises minimum value

Final selection (2/2) Budget fixed for 650 core border exterior Projects included in the Maximin-portfolio #14 marked with red bars border exterior

Conclusions Robust project portfolio selection under incomplete cost and preference information Advanced benefit to cost analysis Modelling of interval synergies

References 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. Liesiö, J., Mild, P., Salo, A. (2006) Preference Programming for Robust Portfolio Modelling and Project Selection, European Journal of Operational Research, forthcoming Liesiö, J., Mild, P., Salo, A. (2006b) Robust Portfolio Modelling with Incomplete Cost and Budget Information, manuscript. Lindstedt, M., Liesiö, J., Salo, A., (2006). Participatory Development of a Strategic Product Portfolio in a Telecommunication Company, International Journal of Technology Management, (to appear). 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., Mild, P., Pentikäinen, T., (2006). Exploring Causal Relationships in an Innovation Program with Robust Portfolio Modeling, Technological Forecasting and Social Change, special issue on 'Tech Mining' (to appear). Salo, A. and Punkka, A., (2005). Rank Inclusion in Criteria Hierarchies, European Journal of Operations Research, Vol. 163, pp. 338 - 356