1 Helsinki University of Technology Systems Analysis Laboratory Selecting Forest Sites for Voluntary Conservation with Robust Portfolio Modeling Antti Punkka, Juuso Liesiö and Ahti Salo Systems Analysis Laboratory Helsinki University of Technology P.O. Box 1100, TKK, Finland

Helsinki University of Technology Systems Analysis Laboratory 2 METSO Program n Objective is to protect biodiversity in forests of Finland –Southern Finland, Lapland, Province of Oulu n Lead by Ministry of Agriculture and Forestry in cooperation with the Ministry of the Environment n Subprograms include testing of voluntary conservation methods

Helsinki University of Technology Systems Analysis Laboratory 3 Pilot Projects for Voluntary Conservation (1/4) n Five pilots –Forest owners offer their sites for conservation against monetary compensation –In Satakunta pilot, euros have been spent annually since 2003 to preserve a total of some 2400 ha for 10 years n Usual process 1.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

Helsinki University of Technology Systems Analysis Laboratory 4 Pilot Projects for Voluntary Conservation (2/4) n Multi-criteria methods used to 1.Form compensation estimates for forest owners 2.Evaluate sites –Additive scoring models for conservation values n 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 w i represent trade-offs between criteria

Helsinki University of Technology Systems Analysis Laboratory 5 Pilot Projects for Voluntary Conservation (3/4) n Example: site’s value is the sum of its values of area, dead wood, distance to other conservation sites and burned wood V ha (x) denotes the value of site x per hectare

Helsinki University of Technology Systems Analysis Laboratory 6 Pilot Projects for Voluntary Conservation (4/4) n 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 m 3 /ha of conifer snags is 150% more valuable than 4.4 m 3 /ha, which is as valuable as 2.0 m 3 /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

Helsinki University of Technology Systems Analysis Laboratory 7 Preference Programming n 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 m 3 /ha in dead wood is at least as important as increase of 1 m 3 /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 n Set of feasible parameter values (weights, scores) –The overall values become intervals

Helsinki University of Technology Systems Analysis Laboratory 8 Site Selection Problem n Which of the m independently evaluated sites should be selected, given budget B? n 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

Helsinki University of Technology Systems Analysis Laboratory 9 RPM - Robust Portfolio Modeling (1/4) n Combines Preference Programming with portfolio selection n 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 n …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

Helsinki University of Technology Systems Analysis Laboratory 10 RPM - Robust Portfolio Modeling (2/4) n 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 n 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

Helsinki University of Technology Systems Analysis Laboratory 11 RPM - Robust Portfolio Modeling (3/4) n 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%),

Helsinki University of Technology Systems Analysis Laboratory 12 Approach to promote robustness through incomplete information (integrated sensitivity analysis). Account for group statements RPM - Robust Portfolio Modeling (4/4) 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. Selected Not selected Gradual selection: Transparency w.r.t. individual sites Tentative conclusions at any stage of the process

Helsinki University of Technology Systems Analysis Laboratory 13 Illustrative Example (1/5) n Real data in form of criterion-specific values –27 sites that were selected in Satakunta in 2003 »2 27 = 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 n Budget 25, 50 or 75 % of sum of offers

Helsinki University of Technology Systems Analysis Laboratory 14 Illustrative Example (2/5) n Data / values

Helsinki University of Technology Systems Analysis Laboratory 15 Illustrative example (3/5) n Perturbation of weight estimates n 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

Helsinki University of Technology Systems Analysis Laboratory 16 Illustrative Example (4/5) n Core indexes (budget 50%) point estimates a unique solution 5% interval 2 non-d. portfolios 10% interval 6 non-d. portfolios 20% interval 24 non-d. portfolios incomplete ordinal information 904 non-d. portfolios Site #

Helsinki University of Technology Systems Analysis Laboratory 17 Illustrative Example (5/5) n Variation in budget (incomplete rank-ordering) 25% Site # 50% 75% 432 non-d. portfolios 904 non-d. portfolios 303 non-d. portfolios

Helsinki University of Technology Systems Analysis Laboratory 18 Conclusions & Future Directions n 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 n Future task: to develop a unified framework for selecting site portfolio –Dedicated decision support system required

Helsinki University of Technology Systems Analysis Laboratory 19 References »Liesiö, J., Mild, P., Salo, A., (2005). Preference Programming for Robust Portfolio Modeling and Project Selection, submitted manuscript available at »Memtsas, D., (2003). Multiobjective Programming Methods in the Reserve Selection Problem, European Journal of Operational Research, Vol. 150, pp »Salo, A., Punkka, A., (2005). Rank Inclusion in Criteria Hierarchies, European Journal of Operational Research, Vol. 163, pp »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 »Robust Portfolio Modeling site: