RPM

1
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_at_tkk.fi

2
Problem framework

• Choose a portfolio of projects from a large set
  of proposals
• Projects evaluated on multiple criteria
• Resource and other portfolio constraints
• 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)
• Software tools, e.g.
• Catalyze Ltd (UK) / Hiview Equity
• Strata Decision Technology LLC / StrataCap
• Expert Choice / EC Resource AlignerTM

3
Additive representation of portfolio value

• Projects with costs
• Scores and weights
• Feasible portfolios
• Project value weighted sum of scores
• Portfolio value sum of projects values
• Maximize portfolio value

4
Incomplete information in portfolio problems

• Elicitation of complete information (point
  estimates) on weights and scores may be costly or
  even impossible
• 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
• Provide guidance for focusing the elicitation
  efforts
• Liesiö, Mild, Salo, (2005). Preference
  Programming for Robust Portfolio Modeling and
  Project Selection, conditionally accepted

5
Modeling of incomplete information

• 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)
• Interval scores
• Lower and upper bounds on criterion-specific
  scores of each project
• Information set
• Feasible values for and

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Non-dominated portfolios

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

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Project-oriented analysis

• 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

8
Sequential specification of information

• Dominance relations depend on S
• Loose statements often lead to a large number of
  ND portfolios
• Complete information typically leads to a unique
  portfolio
• Additional information to reduce
• Modeled through a smaller weight set (
  ) and/or narrower scoreintervals (
  )
• No new portfolio can become non-dominated
• 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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RPM for project portfolio selection
Selected
Core projects ? choose
Large set of projects Multiple
criteria Resource and portfolio constraints
Add. core
Preceding core proj.
Additional information
Decision rules, heuristics
Loose statements on weights and scores
Borderline projects? focus on
Borderline
Not selected
Add. exter.
Compute non-dom. portfolios
Negotiation, iteration
Update ND portfolios
Exterior proj. ? discard
Preceding exterior
10
Application to road pavement projects (1/4)

• Real data from Finnish Road Administration
• Selection of the annual pavement program in one
  major road district
• 223 project proposals
• Generated by a specific road condition follow-up
  system
• Coherent road segments ? proposals are
  independent
• Three technical measurement criteria on each
  project
• Damage coverage in the proposed site
• Annual cost savings attained by road users (if
  repaired)
• Durability life of the repair
• Budget of 16.3 M, sufficient for funding some
  160 projects

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Application to road pavement projects (2/4)

• Illustrative ex post data analysis with RPM tools
• Sequential weight information
• Start with no information
• Rank-ordering stated by FINNRA experts
• Complete score information (point estimates)
• Computations by PRO-OPTIMAL software
• http//www.rpm.tkk.fi

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Application to road pavement projects (3/4)

• No information,
• 542 portfolios
• 103 core projects
• 16 exterior projects
• 104 borderline proj., from which some 60 can be
  funded with remaining resources

13
Application to road pavement projects (4/4)

• Rank-ordering,
• 109 portfolios
• 127 core projects
• 32 exterior projects
• 64 borderline proj., from which some 30 can be
  funded with remaining resources

14
Conclusions

• Key features
• Admits incomplete information about weights and
  projects
• Accounts for competing projects, scarce resources
  and portfolio constraints
• Determines all non-dominated portfolios
• Robust decision recommendations
• Core Index values for individual projects derived
  from portfolio level analyses
• Decision rules for portfolios (e.g., maximin,
  minimax regret)
• 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

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 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. 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