Helsinki University of Technology Systems Analysis Laboratory RPM – Robust Portfolio Modeling for...

Helsinki University of Technology Systems Analysis Laboratory

RPM – Robust Portfolio Modeling RPM – Robust Portfolio Modeling

for Project Selectionfor Project Selection

Pekka Mild, Juuso Liesiö and Ahti SaloSystems Analysis Laboratory

Helsinki University of Technology

P.O. Box 1100, 02150 TKK, Finland

http://www.sal.tkk.fi

[email protected]


2

Problem frameworkProblem 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


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Additive representation of portfolio valueAdditive 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

jx X

1

( )n

j ji i

i

V x wv

[ ]ji ijv v 1 1,...., , ,...,

T

nw w w i n

px

j

j

xVpV )()(

1( ), ,..., ,jC x j m

| ( )j

jF x pP p X C x B

max ( )Fp PV p


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Incomplete information in portfolio problemsIncomplete 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


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Modeling of incomplete informationModeling 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

+R | jn m j jiv i iS v v v v

; ( , )w vS S S w v S w [ ]ijv

0 | 0, 1w w i iS S w w w


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Non-dominated portfoliosNon-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

Fp P ' Fp P 'Sp p

( ) ( ') for all ( , )( ) ( ') for some ( , )V p V p w v SV p V p w v S

( ) | ' s.t. 'N F F SP S p P p P p p


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Project-oriented analysisProject-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

( , ) 1jCI x S

( , ) 0jCI x S

0 ( , ) 1jCI x S

( ) |( , )

( )

jNj

N

p P S x pCI x S

P S


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Sequential specification of informationSequential 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 score

intervals ( )

– 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

w wS S( )NP S

v vS S

( ) ( )N NP S P S


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Add. exter.

RPM for project portfolio selectionRPM for project portfolio selection

Se

lec

ted

No

t se

lec

ted

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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Application to road pavement projects (1/4)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 project1. Damage coverage in the proposed site

2. Annual cost savings attained by road users (if repaired)

3. 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)Application to road pavement projects (2/4)

Illustrative ex post data analysis with RPM tools

Sequential weight information

1. Start with no information:

2. Rank-ordering stated by FINNRA experts:

Complete score information (point estimates)

Computations by PRO-OPTIMAL software– http://www.rpm.tkk.fi

0 | 0, 1w i iS w w w 0

1 2 3|rankw wS w S w w w


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No information,

542 portfolios

103 core projects

16 exterior projects

104 borderline proj.,

from which some 60

can be funded with

remaining resources

0wS


13


Rank-ordering,

109 portfolios

127 core projects

32 exterior projects

64 borderline proj.,

from which some 30

can be funded with

remaining resources

rankwS


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ConclusionsConclusions

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


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References 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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