Incomplete Cost and Budget Information in Robust Portfolio Modelling (RPM)

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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_at_tkk.fi

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Contents

• Robust Portfolio Modelling (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

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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
• RD 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)

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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 i1,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

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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

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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

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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

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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

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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)

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Incomplete information on costs and budget (1/3)

• Incomplete information on costs and budget
• 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

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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?
• Portfolios 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

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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

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Illustrative example in product release planning

• Inspired by a case study for Nokia Networks
• http//www.sal.tkk.fi/Opinnot/Mat-2.177/projektit2
  006/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)

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Features (1/2)

• Follow-up projects
• Synergies

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Features (2/2)
Follow-up
Benefit synergy
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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
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Portfolio value as a function of resources
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Follow-up
CI 1
Cost synergy
Follow-up
Benefit synergy
Follow-up
CI 0
Benefit synergy
Budget level R
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Final selection (1/2)

• Budget fixed for 650
• 15 non-dominated portfolios in
• ND-portfolio 14 maximises minimum value

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Final selection (2/2)
core

• Budget fixed for 650
• Projects included in the Maximin-portfolio 14
  marked with red bars

border
exterior
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Conclusions

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

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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 RD 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