1 helsinki university of technology systems analysis laboratory selecting forest sites for voluntary...

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Helsinki University of Technology Systems Analysis Laboratory

Selecting Forest Sites for Voluntary Selecting Forest Sites for Voluntary

Conservation with Robust Portfolio Conservation with Robust Portfolio

ModelingModeling

Antti Punkka, Juuso Liesiö and Ahti SaloSystems Analysis Laboratory

Helsinki University of TechnologyP.O. Box 1100, 02150 TKK, Finland

http://www.sal.tkk.fi/[email protected]


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METSO ProgramMETSO Program

Objective is to protect biodiversity in forests of Finland– Southern Finland, Lapland, Province of Oulu

Lead by Ministry of Agriculture and Forestry in cooperation

with the Ministry of the Environment

Subprograms include testing of voluntary conservation

methods


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Pilot Projects for Voluntary Conservation (1/4)Pilot Projects for Voluntary Conservation (1/4)

Five pilots– Forest owners offer their sites for conservation against monetary compensation

– In Satakunta pilot, 400000 euros have been spent annually since 2003 to

preserve a total of some 2400 ha for 10 years

Usual process1. The forest owners are informed about voluntary conservation methods

2. Owners express their interest

3. Preliminary assessment of the site together with the owner

4. The owner makes an offer (help provided)

5. Negotiations and selection


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Multi-criteria methods used to1. Form compensation estimates for forest owners

2. Evaluate sites

– Additive scoring models for conservation values

Value tree analysis– Value of a site is the sum of its criterion-specific values

» or a weighted average of normalized criterion-specific values (’scores’)

– Weights wi represent trade-offs between criteria

n

i

jNi

j xvwxVi

1

)()(

n

i

ji

j xvxV1

)()(


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Example: site’s value is the sum of its values of area, dead

wood, distance to other conservation sites and burned wood

)()(

)()()(

.... .. bN

woodburneddN

siteconstodist

deadN

wooddeadareaN

areaha

xvwxvw

xvwxvwxV

woodburnedsiteconstodist

wooddeadarea

Vha(x) denotes the value of site x per hectare


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Limitations of pilot projects’ models– Lack of sensitivity analysis

» use of point estimates for scores and weights leads to a single overall value for a site

– Piecewise constant criterion-specific value functions» e.g., landscape values are subjective evaluations, where especially discontinuous

value functions may cause big differences among experts’ evaluations» e.g., 4.6 m3/ha of conifer snags is 150% more valuable than 4.4 m3/ha, which is as

valuable as 2.0 m3/ha

– One-by-one selection of sites» aim of choosing a good portfolio may be missed» possible inefficient use of budget

– Structural requirements not explicitly accounted for» e.g., the total area of sites selected must be at least 250 ha


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Preference ProgrammingPreference Programming

Some limitations can be addressed with the use of incomplete

information– The relative importance of criteria can be set as intervals or as a rank-

ordering of the importance of criteria» e.g., increase of 1 m3/ha in dead wood is at least as important as increase of 1 m3/ha

in burned wood» e.g., dead wood is the most important criterion

– Sites can be evaluated with incomplete information about their

characteristics» e.g., the site’s landscape values are between 5 and 10 on scale 0-20

Set of feasible parameter values (weights, scores)– The overall values become intervals


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Site Selection ProblemSite Selection Problem

Which of the m independently evaluated sites should be selected, given budget B?

Subset of sites is a portfolio

– Select a feasible site portfolio p to maximize overall value – Portfolio preferred to another if it has greater overall value

BcztsxVz jm

jj

m

jj

z

j

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}1,0{..)(max

1},,...,{ 1 jjm zpxxxp


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RPM - Robust Portfolio Modeling (1/4)RPM - Robust Portfolio Modeling (1/4) Combines Preference Programming with portfolio selection Use of incomplete information: no precise overall values...

– Portfolios compared through dominance relations» portfolio p is dominated, if there exists another portfolio p’ that has a higher overall

value for all feasible scores and weights

– Dominated portfolio should not be selected, since there is another portfolio that

is better for every feasible parameter combination

…and thus no unique optimal portfolio

– Non-dominated portfolios are of interest

– For a non-dominated portfolio, there is not another feasible portfolio with a

greater overall value across the feasible weights and scores


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RPM - Robust Portfolio Modeling (2/4)RPM - Robust Portfolio Modeling (2/4)

Portfolio-oriented selection– Consider non-dominated site portfolios as decision alternatives– Decision rules: Maximax, Maximin, Central values, Minimax regret– Methods based on exploring the set of non-dominated portfolios

» e.g., adjustment of aspiration levels

Site-oriented selection– Portfolio is a set of site-specific yes/no decisions– Site compositions of non-dominated portfolios typically overlap– Which sites are incontestably included in a non-dominated portfolio?– Robust decisions on individual sites in the light of incomplete information


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Core index of site– Share of non-dominated portfolios in which a site is included (CI=0%-100%)

– Site-specific performance measure in the portfolio context» accounts for competing sites and scarce resources

– Core sites are included in all non-dominated portfolios (CI=100%),

– Exterior sites are not included in any of the nd-portfolios (CI=0%),

– Border line sites are included in some of the nd-portfolios (0%<CI<100%),


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Approach to promote robustness through incomplete information (integrated sensitivity analysis).Account for group statements


Decision rules, e.g. minimax regret

•Narrower intervals•Stricter weights

•Wide intervals•Loose weight

statements

Large number

of sites.

Evaluated w.r.t.

multiple criteria.

Border line sites

“uncertain zone” Focus

Exterior sites

“Robust zone” Discard

Core sites“Robust zone”

Choose

Core

Border

Exterior

Negotiation.Manual iteration.Heuristic rules.

Se

lecte

dN

ot se

lecte

d

Gradual selection: Transparency w.r.t. individual sitesTentative conclusions at any stage of the process


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Illustrative Example (1/5)Illustrative Example (1/5)

Real data in form of criterion-specific values – 27 sites that were selected in Satakunta in 2003

» 227 = over 134 million possible portfolios

– Evaluated with regard to 17 criteria» criteria related to wood value excluded» irrelevant criteria (= all sites have the same value) excluded» some criteria united (e.g. logs and snags are ’dead wood’)

– Here 9 evaluation criteria» area, dead wood, landscape values, etc.

– Point estimate weights and scores derived from the criterion-specific values

– Sum of offers some 300,000 euros» offers between 130 and 300 euros / ha / year

Budget 25, 50 or 75 % of sum of offers


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Data / values


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Illustrative example (3/5)Illustrative example (3/5)

Perturbation of weight estimates Five levels of weight accuracy

– Point estimates (no perturbation)

– 5, 10, 20 % relative interval on the point estimates» e.g. with 10 % the weight of ’old aspens’ is allowed to vary within

[0.9 x 0.120, 1.1 x 0.120] = [0.108, 0.132]

– Incomplete ordinal information (the RICH method, Salo and Punkka 2005)» 6 groups of criteria» importance-order of the groups known» no stance is taken on the order of

importance within the groups» criteria with same point estimate

weights form a group


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Core indexes (budget 50%)

point estimatesa unique solution

5% interval2 non-d. portfolios



incomplete ordinal information904 non-d. portfolios

Site #


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Variation in budget (incomplete rank-ordering)

25%

Site #

50%

75%

432 non-d. portfolios




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Conclusions & Future DirectionsConclusions & Future Directions

Robust Portfolio Modeling– Sensitivity analysis with regard to criterion weights and sites’ characteristics

explicitly included in the model» means for subjective evaluation of qualitative criteria

– Selection of a full portfolio instead of one-by-one selection of sites» synergies and minimum requirements can be explicitly included in the model

Future task: to develop a unified framework for selecting site

portfolio– Dedicated decision support system required


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References References

» Liesiö, J., Mild, P., Salo, A., (2005). Preference Programming for Robust Portfolio Modeling and Project Selection, submitted manuscript available at http://www.sal.hut.fi/Publications/pdf-files/mlie05.pdf

» Memtsas, D., (2003). Multiobjective Programming Methods in the Reserve Selection Problem, European Journal of Operational Research, Vol. 150, pp. 640-652.

» Salo, A., Punkka, A., (2005). Rank Inclusion in Criteria Hierarchies, European Journal of Operational Research, Vol. 163, pp. 338-356.

» Stoneham, G., Chaudhri, V., Ha, A., Strappazzon, A., (2003). Auctions for Conservation Contracts: An Empirical Examination of Victoria's BushTender Trial, The Australian Journal of Agricultural and Resource Economics, Vol. 47, pp. 477-500.

» Robust Portfolio Modeling site: http://www.rpm.tkk.fi

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