1. 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, TKK, Finland

2. 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

3. 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)

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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)

10. 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

11. 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

12. 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

13. Illustrative example in product release planning
Inspired by a case study for Nokia Networks
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)

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

15. Features (2/2)
Follow-up
Benefit synergy

16. 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

17. Portfolio value as a function of resources

18. 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

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

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

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

22. 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
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
Kleinmuntz, C.E, Kleinmuntz, D.N., (1999). Strategic approach to allocating capital in healthcare organizations, Healthcare Financial Management, Vol. 53, pp
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
Salo, A. and R. P. Hämäläinen, (1992). Preference Assessment by Imprecise Ratio Statements, Operations Research, Vol. 40, pp
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