United StatesDepartment ofAgriculture

Forest Service

NortheasternResearch Station

General TechnicalReport NE-307

Multi-Criteria Decision Modelsfor Forestry and NaturalResources Management:An Annotated Bibliography

J. E. de SteiguerLeslie LibertiAlbert SchulerBruce Hansen

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Abstract

Foresters and natural resource managers must balance conflicting objectives whendeveloping land-management plans. Conflicts may encompass economic,environmental, social, cultural, technical, and aesthetic objectives. Selecting thebest combination of management uses from numerous objectives is difficult andchallenging. Multi-Criteria Decision Models (MCDM) provide a systematic means forcomparing tradeoffs and selecting alternatives that best satisfy the decisionmaker’sobjectives. First developed during World War II by the U.S. military for strategicdecisionmaking, MCDM have since been applied to such diverse fields as energyand financial planning, manufacturing, real estate investment, reservoir control,solid waste management, and water distribution. In recent years, the use of MCDMin forestry and natural resources management has generated a substantial body ofliterature. This annotated bibliography includes 124 important references rangingfrom theoretical studies to real-world applications of MCDM.

The Authors

J. E. DE STEIGUER is professor of natural resource economics, policy, andmanagement in the School of Renewable Natural Resources at the University ofArizona. Previously, he was a researcher with the USDA Forest Service. He holds aPh.D. degree in forestry economics and policy from Texas A&M University.

LESLIE LIBERTI is a Ph.D. candidate in the School of Renewable NaturalResources at the University of Arizona.

ALBERT SCHULER is a research economist with the USDA Forest Service’sNortheastern Research Station at Princeton, West Virginia. He received aB.S.degree in forest management from the New York State College of Forestry atSyracuse University in 1966 and a Ph.D. degree in forest economics and marketingfrom Iowa State University in 1975. He is currently analyzing markets forengineered wood products and assessing the competitive position of the domesticfurniture industry.

BRUCE HANSEN is an economist and Project Leader with the NortheasternResearch Station at Princeton, West Virgina. He received a B.S. degree ineconomics from Concord College, Athens, West Virginia, and M.B.A. and Ph.D.degrees in wood science and forest products marketing from Virginia PolytechnicInstitute and State University at Blacksburg, Virginia. He joined the Forest Servicein 1968.

Manuscript received for publication 12 November 2002

Contents

Introduction ................................................................................................................ 1Overview of MCDM in Forestry ................................................................................. 1

MODM Applications in ForestryGeneral ................................................................................................................... 3Linear Programming ............................................................................................... 3Goal Programming ................................................................................................. 4Interactive Mathematical Programming .................................................................. 6

Dynamic Programming ............................................................................................... 6Modeling to Generate Alternatives .......................................................................... 6Hierarchical Planning ............................................................................................. 8Improving Spatial Capabilities ................................................................................ 8Heuristic Methods ................................................................................................ 13

MADM Applications in Forestry and Land Management .......................................... 16Combined MODM/MADM Applications ................................................................ 18MCDM Applications to Water Resources .................................................................. 19MCDM Applications to Fisheries .............................................................................. 22Other Environmental Applications ............................................................................ 22Decision-Support Systems ......................................................................................... 23Author Index ............................................................................................................. 26Glossary ..................................................................................................................... 29

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IntroductionForesters and natural resource managers must balance conflicting objectives when developingland-management plans. Conflicts may encompass economic, environmental, social, cultural,technical and aesthetic objectives.1 Selecting the best combination of management uses fromnumerous objectives is difficult and challenging. Fortunately, Multi-Criteria Decision Models(MCDM) provide a systematic means for comparing tradeoffs and selecting alternatives thatbest satisfy the decisionmaker’s objectives.

First developed during World War II by the U.S. military for strategic decisionmaking,MCDM have since been applied to such diverse fields as energy and financial planning,manufacturing, real estate investment, reservoir control, solid waste management and waterdistribution. In recent years, the use of MCDM in forestry and natural resources managementhas generated a substantial body of literature. This annotated bibliography includes 124important references ranging from theoretical studies to real-world applications of MCDM.

Overview of MCDM in ForestryMCDM refers to quantitative techniques used to facilitate decisions that encompass competingmanagement objectives. Because they comprise numerous analytical methods, MCDM oftenare classified for convenience as Multi-Objective Decision Models (MODM) or Multi-Attribute Decision Models (MADM). MODM support the design of a range of separatedecision alternative1 techniques such as linear, goal, and integer programming. MADM supportthe “best” decision from among several alternatives using the Analytic Hierarchy Process andMulti-Attribute Utility Theory.

Forestry applications of MODM are concerned primarily with mathematical optimizationtechniques. The literature on the use of MODM for forest management can be divided intofour developmental phases. Early studies, or Phase I, of MODM use in forestry explored“modeling to generate alternatives.” Those who supported this approach believed thatmathematical programming could be used to construct a range of possible decision solutions.These alternatives would be presented to decisionmakers, who would then select the alternativethat best met the established criteria. Research on generating alternatives was especially popularduring the 1980’s, a period that coincided with the introduction of the linear programmingmodel FORPLAN by the USDA Forest Service. FORPLAN was designed to meet the long-term requirements of the National Forest Management Act of 1976.

Phase II began in the early 1990’s and focused on the connection between strategic and tacticalforest management planning. Tactical- or stand-level planning requires significantly more detailand data than strategic forest-level planning. Analysts found that FORPLAN could notaccommodate both stand- and forest-level plans because it generated excessively large models.As a result, stand-level planning was left to individual national forest districts to develop. Arelated branch of research attempted to find effective ways to bridge tactical and strategicplanning.

Phase III was characterized by efforts to incorporate spatial constraints into MODM. Thesestudies, which accounted for the major portion of MODM research during the 1990’s, resultedfrom FORPLAN’s earlier ineffectiveness with respect to spatial concerns, particularly thoserelating to wildlife habitat. This research addressed the need for more complex spatialconsiderations, for example, requirements for the regrowth of vegetation prior to subsequentreharvesting, i.e., “green-up constraint,” edge effects, and habitat fragmentation.

1De Montis, Andrea; De Toro, Pasquale; Droste-Franke, Bert; Ines, Omann; Stagl, Sigrid. 2000. Criteriafor quality assessment of MCDA—methods. In: 3rd biennial conference of the European Society forEcological Research; 2000 May 3-6; Vienna, Austria. Vienna, Austria: International Institute forEcological Economics. [http://www.kfunigraz.ac.at]

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The fourth and current phase of research concerns heuristic methods, that is, techniques forproblem solving through experimentation and trial and error. Interest in heuristics wasdeveloped after analysts realized that spatial programming formulations for real-worldmanagement situations were difficult if not impossible to apply with conventional linearprogramming algorithms, i.e., they typically required enormous computing capability.Supporters of heuristic methods contend that they can solve large, complex problems efficientlywhile approximating optimal solutions.

Proponents generally believe that MODM have been useful for natural resource planning andmanagement. Their research has focused on ways to modify MODM to improve realism andefficiency. Unfortunately, these researchers failed to consider the response to these models.Indeed, a major failure of FORPLAN was its lack of acceptance by public interest groups (andperhaps by many Forest Service employees). To many of these groups, models such asFORPLAN were difficult to comprehend and were associated with an enigmatic “black box”approach to planning.

MADM constitute a newer and perhaps more acceptable method for quantifying andevaluating public preferences. These models already have been used extensively in military,corporate, and medical applications. However, few studies have applied MADM to forestry orother natural resource situations. The Analytical Hierarchy Process within MADM is receivingspecial attention for natural resource applications. It is not known whether such techniques canimprove public involvement, collaboration, and acceptance of land management plans—or theplanning process itself. To capture the benefits of both MADM and MODM, some researchershave tried to combine them. Another recent trend has been to combine MADM and/orMODM methods with Decision-Support Systems.

Despite many years of effort, there is still much to do. Only about half of the citations in thisbibliography refer to empirical tests of the utility or feasibility of the MODM approach.Further, in most of the studies, researchers used hypothetical data or, at best, simplified decisionsituations; relatively few applied MODM to actual working forests. In fact, few studies weredesigned to implement a MCDM-generated management strategy.

The section on MODM applications in forestry that follows is divided into nine subsections.These are followed by sections on MADM applications in forestry and land planning,applications of combined MODM/MADM models, applications of MCDM to waterresources, fisheries, and other environmental entities, and to decision-support systems. Thebibliography includes an author index and a glossary.

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MODM Applications in Forestry

General

1. Bare, B. Bruce; Briggs, David G.; Roise, Joseph P.;Schreuder, Gerard F. 1984. A survey of systemsanalysis models in forestry and the forest productsindustries. European Journal of OperationalResearch. 18(1): 1-18.

A comprehensive survey of the range of problems relatedto forestry and the forest products industry that havebeen addressed using decision models such as linear,dynamic, goal, mixed-integer, and nonlinearprogramming. Applications are divided into forestmanagement (timber production), forest products,product yield, and process applications. Linearprogramming models have been used to facilitate nurseryoperations and seedling allocation for individual forest;optimize the cutting of trees to maximize productoutput and match that output with demand; integrateforest management, transportation layout, and productallocation for private wood-products companies; allocatefire control or harvesting equipment; and minimize theloss of material in paper-trimming processes. Citationsfor more than 70 systems analysis and forestry referencesare included.

2. Bell, Enoch F. 1977. Mathematical programming inforestry. Journal of Forestry. 75(6): 317-319.

Describes linear programming (LP) that is illustratedusing straightforward terminology. Each of theassumptions required by LP are reviewed, andlimitations that result from these assumptions arediscussed. The author suggests that LP often is used insituations where the assumptions of the model are notmet

3. Buongiorno, J. 2001. Quantifying the implicationsof transformation from even to uneven-aged foreststands. Forest Ecology and Management. 151: 121-132.

Discusses the role of optimization and simulation toachieve multiple economic and ecological objectives inchoosing a target stand, and in converting an initialstand to this target.

4. Buongiorno, J.; Gilless, J. K. 2003. Decisionmethods for forest resource management. SanDiego, CA: Academic Press. 439 p.

Introduces multi-criteria decision models for forestryand natural resource management, including linearprogramming models with economic and environmental

objectives in even-aged forests. Also discusses theeconomic and environmental management of uneven-aged forests, introducing a MAXMIN criterion ofdiversity, multiple-objective management with goalprogramming, and simulation models of even oruneven-aged forests, to include ecological and economiccriteria. Reviews the use of Markov models to addressuncertainty in managing for landscape diversity,biodiversity, and financial returns.

5. Garcia, Oscar. 1990. Linear programming andrelated approaches in forest planning. NewZealand Journal of Forestry Science. 20(3): 307-331.

Single-use forest planning (managing for timber) entailsdecisions regarding what management treatments andwhich spatial and temporal patterns of harvesting willbest achieve output objectives. Presents severalalternative formulations for the forest planning model,which is divided into the forestry model and theutilization model. The first is related to the physicalimpacts of various management treatments and theresponse of the forest to these actions. Three methods forformulating this model are discussed: a state spaceapproach and the traditional Model I and Model IIclassifications.

6. Nieuwenhuis, Maarten. 1989. Operations researchin forestry. Irish Forestry. 46(1): 51-58.

Discusses the general characteristics of the six mostcommonly used formulations in forest applications.These include linear, integer, goal, and dynamicprogramming, network analysis, and simulation. Themajor uses of each method are included, as are referencesfor each method in forestry/forest-industry applications.

Linear Programming

7. Boscolo, M.; Buongiorno, J. 1997. Managing atropical rainforest for timber, carbon storage andtree diversity. Commonwealth Forestry Review.76(4): 246-254.

Discusses the use of linear programming and MAXMINmethods to analyze tradeoffs among various objectives inmanaging a rain forest for timber, carbon storage, andtree diversity.

8. Buongiorno, J.; Dahir, S.; Lu, H. C.; Lin. C. R. 1994.Tree size diversity and economic returns inuneven-aged forest stands. Forest Science. 40(1): 83-103.

Discussions of linear and nonlinear programmingmodels illustrate tradeoffs related to

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diversity of stand structure (tree size), and economicreturns in managing northern hardwoods.

9. Ingram, D.; Buongiorno, J. 1996. Income anddiversity tradeoffs from management of mixedlowland dipterocarps in Malaysia. Journal ofTropical Forest Science. 9(2): 242-270.

Linear programming with MAXMIN criteria wasapplied to determine the short- and long-term effects ofcurrent management regimes on economic returns anddiversity of tree species and size. Criteria included theShannon-Wiener index of diversity, minimum numberof trees by species and size, soil rent, forest value,internal rate of return, and annual yield. Regimes werecompared in the steady state (long term) and duringconvergence (short term) of stands with different initialconditions.

10. Jamnick, Mark S. 1990. A comparison ofFORMAN and linear programming approaches totimber harvest scheduling. Canadian Journal ofForest Research. 20: 1351-1360.

Timber harvest scheduling in the United States isaccomplished primarily with linear programming (LP)or binary search. In Canada, simulation often is used tocreate harvest schedules. Harvest schedules producedusing a Model I LP approach were compared with thosegenerated by simulation (the FORMAN model). Themodels were applied to two hypothetical forests, eachabout 130,000 ha in size, over sixteen 5-year planningperiods. The only harvesting activity allowed wassoftwood clearcutting and harvest could be followed bynatural regeneration or one of three replanting options.

11. Johnson, K. Norman; Tedder, Philip L. 1983. Linearprogramming vs. binary search in period harvestlevel calculation. Forest Science. 29(3): 569-581.

Compares two general categories of procedures that canbe used to determine periodic harvest levels: binarysearch and linear programming, highlighting theadvantages of each approach. The search for a method tocombine the best features of each procedure is discussed.

12. Lu, H. C.; Buongiorno, J. 1993. Long- and short-term effects of alternative cutting regimes andeconomic returns and ecological diversity inmixed-species forests. Forest Ecology andManagement. 58: 173-192.

Six cutting regimes were compared by linearprogramming with respect to soil rent and ecologicaldiversity obtained in the short and long term in uneven-aged northern hardwood forests.

13. Omi, Philip N.; Murphy, James L.; Wensel, Lee C.1981. A linear programming model for wildlandfuel management planning. Forest Science. 27(1):81-94.

Linear programming (LP) was applied to optimize thetimestream of fuel management investments in forestwatersheds in southern California. Historical approachesfor evaluating fire management planning are outlined,limitations of these approaches are discussed, and theimportance of minimizing costs through optimization isstressed. An LP formulation also is presented thatmaximizes reduction in a “wildfire damage-potential”index. LP provided general guidelines for fuelmanagement planning but was inappropriate for tactical-level, site-specific evaluations.

14. Roise, Joseph; Chung, Joosang; Lancia, Richard;Lennartz, Mike. 1990. Red cockaded woodpeckerhabitat and timber management: productionpossibilities. Southern Journal of Applied Forestry.14(1): 6-12.

Examines alternative management strategies usingmultiple-objective linear programming to mitigate thenegative effects of financial timber rotations on red-cockaded woodpeckers. The financial consequences ofproviding cavity trees and protected areas also areexamined.

15. Rowse, John; Center, Calum J. 1998. Forestharvesting to optimize timber production andwater runoff. Socio-Economic Planning Sciences.32(4): 277-293.

Linear programming (LP) was used to assess the optimalsize and shape of harvest blocks to maximize net presentvalue from timber production and watershed runoff.Model parameters, decision variables, objective function,and constraints are detailed. The application of LP to asection of the Canadian Crow-Bow Forest over twenty-five 10-year planning periods is discussed. Eightdifferent scenarios are described.

Goal Programming

16. Buongiorno, J.; Peyron, J. L.; Houllier, F.;Bruciamacchie, M. 1995. Growth and managementof mixed-species, uneven-aged forests in theFrench Jura: implications for economic returnsand tree diversity. Forest Science. 41(3): 397-429.

Linear and goal programming were used to findmanagement regimes to achieve various objectives ofdiversity and economic efficiency. Criteria wereShannon’s index of tree diversity by species and size,

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minimum number of trees by species-size class, basalarea, present value of harvests, and rate of return oncapital.

17. Chang, S. J.; Buongiorno, J. 1981. A programmingmodel for multiple use forestry. Journal ofEnvironmental Management. 13: 45-58.

Goal programming and input-output analysis formultiple-use planning on public forests were combinedto specify goal levels, allow experimentation withmanagement intensity and management priorities, anddetermine tradeoffs between management activities.

18. de Steiguer, J. E. 2000. Applying EXCEL Solver toa watershed management goal-programmingproblem. In: Ffolliott, Peter F.; Baker, Malchus B.,Jr.; Edminster, Carleton B.; Dillon, Madelyn C.;Mora, Karen L.; tech-coords. Land stewardship in the21st century: the contributions of watershedmanagement; 2000 March 13-16; Tucson, AZ. Proc.RMRS-P-13. Fort Collins, CO: U.S. Department ofAgriculture, Forest Service, Rocky Mountain ResearchStation: 325-329.

Demonstrates the application of EXCEL® spreadsheetlinear programming (LP) solver to a watershedmanagement multiple-use goal programming (GP)problem. Data used to demonstrate the application arefrom a watershed study in northern Colorado. One ofthe desirable features of LP/GP problems formulated onspreadsheets is the highly visible display of the problem,which seems to invite inquiry and experimentation.Also, with the spreadsheet method, problems can bestructured and solved in different ways.

19. Hotvedt, James E. 1982. Application of linear goalprogramming to forest harvest scheduling.Southern Journal of Agricultural Economics. 15(1):103-108.

An early application of goal programming (GP) totimber harvest scheduling on an 84,000-acremanagement area in the Southeast. The model wasdesigned to minimize deviations from desired totalharvest volume, discounted and undiscounted cashflows, and discounted cost. Target levels for each of thefour goals were determined by solving four linearprogramming models to determine the optimum level ofachievement for each goal. The model developed aschedule that within 50 years would convert an“irregular forest structure” into a highly regulated one. Inaddition, managers were made aware of possibletradeoffs with respect to harvest volume and financialgoals.

20. Julio, Berbel; Zamora, Ricardo. 1995. Anapplication of MOP and GP to wildlifemanagement (deer). Journal of EnvironmentalManagement. 44: 29-38.

In forest modeling, wildlife decisions often aredisconnected from management criteria and consideredindirectly as constraints on a financial objectivefunction. An alternative approach, that makes wildlifeconcerns the primary goal of a management model is alinear formulation that includes both economic andecological goals as objective functions. The model wasapplied to hunting reserve management in Spain,specifically, to maximize the value of roe deer huntingwhile ensuring the sustainability of the population.Because these two goals are incompatible, amultiobjective generating technique was used to identifythe non-inferior solutions and determine the tradeoffsfor each alternative. To demonstrate the usefulness ofthis approach, the problem was reformulated as alexicographic goal program (GP) and solved. Using theGP method rather than maximizing the number of roedeer in each period stabilized the number of deer acrossall periods and improved the political acceptability of thesolution.

21. Nhantumbo, I.; Dent, J. B.; Kowero, G. 2001. Goalprogramming: application in the management ofthe miombo woodland in Mozambique. EuropeanJournal of Operational Research. 133: 310-322.

Goal programming (GP) was applied to a regional landplanning problem in Mozambique in which publicparticipation was a significant component. The goalsmodeled included protection of natural parks andreserves, timber harvesting, tourism, firewood collection,anddemand for animal, plant, and nonwood forestoutputs. The model also included constraints on landarea, labor, and capital and constraints relating to thediversity and adequacy of local diets. Both lexicographicGP and weighted GP are discussed and the rationale forusing the weighted approach is presented. Thelexicographic GP model was run using four different setsof goal weights. The model was an effective andappropriate alternative.

22. van Kooten, G. C. 1995. Modeling public forestland use tradeoffs on Vancouver Island. Journal ofForest Economics. 1(2): 191-217.

Discusses the use of goal programming to determinewhether and to what extent the level of outputs, i.e.benefits to residents of Vancouver Island, can beimproved over the currently proposed forestmanagement plan. The model formulation and fourscenarios for which the model was run are discussed.

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The plan proposed for the area will result in a loss tosociety of approximately $440 million per year over thescenarios that were evaluated in this study.

Interactive Mathematical Programming

23. Steuer, Ralph E.; Schuler, Albert T. 1978. Aninteractive multiple-objective linear programmingapproach to a problem in forest management.Operations Research. 26(2): 254-269.

A linear programming (LP) and vector maximizationmodel was applied to unit-level management planpreparation at the Swan Creek subunit of the MarkTwain National Forest. Five management objectives wereidentified and rank-ordered. Desired attainment goalswere determined for each. There were three constrainttypes related to acreage, budget, and sustained yield.Goal programming achieved limited success due to alack of clarity between decisionmakers’ criteriapreference weights and “tradeoff weights in the region ofoptimality.” A fuzzy LP approach with interval weightsalso was rejected. The procedure that was chosen is amodification of the interactive LP model. This model ismore flexible and easier to use than previous models.

24. Tecle, Aregai; Duckstein, Lucien; Korhonen, Pekka.1994. Interactive, multiobjective programming forforest resources management. Applied Mathematicsand Computation. 63: 75-93.

An interactive and a fuzzy approach to forestmanagement was applied to the 1.65 million-acre BeaverCreek watershed in Arizona. Five potential treatmentsand a “no action” alternative were considered. A standardlinear programming formulation was used for five of thesix objective functions and one constraint; fuzzy settheory was used to address the remaining functions andconstraints. PARETO RACE software was used tofacilitate a “free search” procedure that does not requireassumptions about the decisionmaker’s utility function.The sensitivity of the gross economic benefit achievedfrom each alternative to changes in the fuzzy variablevalues also was assessed. The model was easier to usethan more structured methods and allowed for imprecisedata. The authors note that this type of approach cannot guarantee “convergence toward a ‘satisfaction’.”

Dynamic Programming25. Anderson, David J.; Bare, B. Bruce. 1994. A

dynamic programming algorithm for optimizationof uneven-aged forest stands. Canadian Journal ofForest Research. 24: 1758-1765.

Dynamic programming (DP) was used for uneven-agedstand management despite demanding computationalrequirements. The method presented is formulated as aforward recursion, discrete, two-state DP. State variableswere trees and basal area per acre. The “neighborhoodstorage concept” was used to reduce the number ofpossible states that must be considered at each stage.There were four harvest parameters that differed in theharvesting method applied and the width ofneighborhood classes. Detailed results are examined withrespect to solution times and objective function values,i.e., present net value. The objective function of one runexceeded a previous “best solution” generation.

26. Lin, C. R.; Buongiorno, J. 1998. Tree diversity,landscape diversity, and economics of maple-birchforests: implications ofMarkovian models.Management Science. 44(10): 1351-1366.

Markov decision-process models solved by dynamicprogramming were used to choose managements withmultiple objectives. Criteria included landscape diversity(variety of stands in the forest), diversity of tree speciesand tree size, annual income, and present value.

27. Puumalainen, Janna. 1998. Optimal cross-cuttingand sensitivity analysis for various log dimensionconstraints by using dynamic programmingapproach. Scandinavian Journal of Forest Research.13: 74-82.

A forward recursive dynamic programming (DP) modelwas applied to tree bucking. DP can accommodate bothnonlinear and linear relationships and computation isbetter with DP than with linear programming. Themodel was applied to the bucking of 3,282 stems ofScots pine in three sawtimber grades and a pulpwoodclass. Four sets of constraints for minimum diameter andlog length were used for each quality category. The DPmodel was useful for bucking optimization and thesolution time was satisfactory.

Modeling to Generate Alternatives

28. Allen, Julia C. 1986. Multiobjective regional forestplanning using the noninferior set estimation(NISE) method in Tanzania and the United States.Forest Science. 32(2): 517-533.

The noninferior set estimation method (NISE) was usedto generate several feasible and nondominated solutionsto a multiobjective forest planning problem that wasformulated as a linear programming model with twoobjectives: minimize wood production andtransportation costs. Constraints included area, treegrowth, and wood volume. In Tanzania, NISE generated

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14 feasible solutions using three sets of modelassumptions. Because NISE does not rely on a priorelicitation of decisionmaker preferences, it is effective forreal-world situations. Potential problems include atendency for this technique to be computationallydemanding and represent less than the full range ofpossible solutions.

29. Bare, B. Bruce; Mendoza, Guillermo. 1988.Multiple objective forest land managementplanning: an illustration. European Journal ofOperational Research. 343: 44-55.

An alternative generating technique known as the stepmethod (STEM) is examined, and the rationale forgenerating multiple feasible solutions versus a singleoptimal solution is discussed. Applied to a mixed firforest in western Washington, the model generatedalternatives that represent levels of achievement for sevenobjective functions, including maximization of harvestvolume and populations of “indicator species” andminimization of populations of pest species. Outputs ofthe generated alternatives are compared using payofftables; the range of difference between each solution isdiscussed. STEM is a powerful tool for forest planningin situations in which the complexity of the systemprevents the capture of effective elements byoptimization techniques.

30. Boscolo, M.; Buongiorno, J. 1997. Simulatingoptions for carbon sequestration throughimproved management of lowland tropicalrainforest. Environmental and DevelopmentEconomics. 2: 241-243.

Simulates a tropical forest stand in Malaysia in its role asa source of income and as a carbon store, and quantifiesthe potential for and cost effectiveness of carbonsequestration by modifying current managementpractices.

31. Buongiorno, J.; Kolbe, A. 2000. Economic andecological effects of diameter-limit and BDqmanagement regimes: simulation results fornorthern hardwoods. Silva Fennica. 34(3): 223-235.

Long-term financial and ecological effects of diameter-limit and basal-area-diameter-q-ratios (BDq) in mixednorthern hardwood stands in the Lake States werecompared by using simulation.

32. Mendoza, Guillermo A.; Bare, B. Bruce; Campbell,Gene E. 1987. Multiobjective programming forgenerating alternatives: a multiple-use planningexample. Forest Science. 33(2): 458-468.

Presents modeling-to-generate-alternatives (MGA)approach to decisionmaking in forest planning. Thegeneral structure of this approach, known as a Hop,Skip, and Jump algorithm, was applied to multiple-useplanning. Five objective functions, includingmaximization of timber volume and forage productionand consideration of water production and recreationopportunities were considered. The technique generatedfour solutions related to output in a payoff matrix.Unlike optimization methods, MGA techniques areeffective in situations in which one or more objective isomitted from the analysis or where the model isformulated incorrectly.

33. Schulte, B.; Buongiorno, J. 1998. Effects ofuneven-aged silviculture on the stand structure,species composition, and economic returns ofloblolly pine stands. Forest Ecology andManagement. 111: 83-101.

The consequences of management regimes for economicand ecological criteria were predicted with the Southprosimulation program for mixed hardwoods and loblollypine stands in the Southern United States.

34. Volin, V. C.; Buongiorno, J. 1996. Effects ofalternative management regimes on forest standstructure, species composition, and income: amodel for the Italian Dolomites. Forest Ecologyand Management. 87:107-125.

Simulation methods were used to compare the effects ofextracting mortality only, applying Susmel’s guides,diameter-limit cuts, saving beech, and continuingcurrent harvest. Ecological criteria included forest coverand stand composition; economics were judged by netpresent value.

35. Willis, C. E.; Perlack, R. D. 1980. A comparison ofgenerating techniques and goal programming forpublic investment, multiple objective decisionmaking. American Journal of AgriculturalEconomics. February: 66-74.

Compares goal programming (GP) and two generatingtechniques—the weighting and constraint methods—interms of computational expense, explicit quantificationof tradeoffs, quantity of information generated, andvalidity of the interaction between decisionmaker andanalyst. GP was more efficient computationally butgenerating techniques provided explicit tradeoffsbetween objectives as well as much more information tothe decisionmaker than GP. Also, unlike GP, generatingtechniques determine feasible relationships but leave theevaluation process to the decisionmaker.

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Hierarchical Planning

36. Cea, Christian; Jofre, Alejandro. 2000. Linkingstrategic and tactical forestry planning decisions.Annals of Operations Research. 95: 131-158.

A multilevel model is proposed that links strategic-levelinvestment decisions with tactical-level planning inprivate forestry companies. The first step is thedevelopment of a general integer programming (IP)model that specifies the strategic planning problem. Theobjective function entails the maximization of presentnet value subject to constraints regarding harvestvolume, harvest area, and timber demand. Once thismodel has been solved, results for the macro-stands areused to set goals for individual stands in the tactical-levelproblem, also formulated as an IP problem. The tacticalmodel is decomposed into two submodels for road-building and transportation decisions. The road-decisionmodel is solved using simulated annealing and thetransportation problem is solved using LP, a secondaryalgorithm is used to improve the solution.

37. Church, Richard L.; Murray, Alan; Barber, Klaus.2000. Forest planning at the tactical level. Annalsof Operations Research. 95: 3-18.

Examines the decomposition of optimal strategic-levelsolutions to optimal tactical-level plans on forests. Thisis known as hierarchical planning. Three linearprogramming (LP) models are presented. The first, thecoordinated allocation of choice model, is an LPformulation that combines the use of a strata-basednoncontiguous planning structure and a zone-basedcontiguous planning structure. It maximizes the presentvalue of choices determined both on a zone basis and onthe basis of individual decisions made within analysisareas (strata). Also discussed are two Bridging AnalysisModels. In the first model, strategic-level goals areallocated proportionately to tactical planning unitssubject to implementation constraints. The goal is tomaintain the acreages of each prescribed treatment asclose as possible to the strategic levels. The second modelallocates tactical outputs based on strategic output goalsin two ways. The min-area formulation minimizes thenumber of constraints that are binding in the tacticalsolution, while the equiv-risk model attempts tomaximize the distance from the most constrainingconditions for each analysis area to preserve flexibility infuture planning.

38. Nelson, John; Brodie, J. Douglas; Sessions, John.1991. Integrating short-term, area-based loggingplans with long-term harvest schedules. ForestScience. 37(1): 101-122.

A three-stage model is proposed to link short-and long-term harvest planning in the development of optimalharvest schedules on a 4,000-ha, 62-unit forest withtimber as the sole output. In the first stage, a linearprogramming (LP) model is used to maximize thepresent net worth of all harvesting decisions across theforest. The solution provides volume and revenue targetsfor the second stage, the use of integer programming (IP)to determine harvest scheduling and transportation atthe stand level; the model is solved using the MonteCarlo heuristic procedure. After 200 feasible solutionswere generated, 5 were selected, each with a differentobjective for value, timber volume, and net revenue.These five alternatives were used to generate 15-decadeLP formulations that were entered into FORPLAN as acoordinated-choice allocation. By combining thestrategic solution from a strata-based LP and the spatialdistributions created using an area-based IP, one cancreate timber harvest plans that are spatially feasible overthe short term and acceptable over the long term.

39. Weintraub, Andres; Cholaky, Alejandro. 1991. Ahierarchical approach to forest planning. ForestScience. 37(2): 439-460.

Comprehensive forest planning has historically beenaccomplished through the use of “monolithic,” single-stage, linear or mixed integer programming models.Hierarchical planning is proposed that addresses theinability of traditional approaches to link strategic,operational, and tactical-level plans. In this study, theexplicit linkage of strategic and tactical models isillustrated. Neither adjacency constraints nor explicitrepresentation of roading variables are included. Theland-use allocation, per-period level of timberproduction, constraint targets, and road-building budgetderived from the model are used as direct inputs into thetactical model. Although the tactical model can be solvedonly with heuristic techniques, it is adequate for forestplanning in complex situations.

Improving Spatial Capabilities

40. Church, Richard L.; Murray, Alan T.; Weintraub,Andres. 1998. Locational issues in forestmanagement. Location Science. 6: 137-153.

Describes the most common “locational” forest issues.For each situation, a basic mathematical programmingmodel is formulated, illustrating the typical objectivefunction and constraint structure. Issues discussedinclude forest planning to maximize present net value,timber-harvest scheduling, transportation planning, anddesignating reserves to preserve biodiversity. The mostcommon solution methods are discussed for each

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situation, as are alternative means of formulation andsolution.

41. de Kluyver, C. A.; Daellenbach, H. G.; Whyte, G.D. 1980. A two-stag, multiple objectivemathematical programming approach to optimalthinning and harvesting. Forest Science. 26(4): 674-686.

Dynamic programming (DP) and linear programming(LP) are applied to create timber-harvesting plans forlarge forests. A DP approach selects from all potentialstand-management activities policies that are the mostefficient for each type of forest stand. This reduced set ofpolicies is then used in an LP model to schedule timberharvest across an entire forest. The decision variablesrepresent collections of activities applied across the entireplanning horizon rather than individual activities foreach period. The use of both management “policies” andDP to limit the set of activities considered significantlyreduces model size.

42. Epstein, R.; Nieto, E.; Weintraub, A.; Chevalier, P.;Gabarro, J. 1999. A system for the design of shortterm harvesting strategy. European Journal ofOperational Research. 119: 427-439.

Applies linear programming (LP) to short-term harvestdecisions by private forest companies, including whatbucking patterns to use, how much volume to cut on aweekly basis, types of machinery to use, and where toharvest, that are influenced by changing productdemand and the quality of previous harvests. An LPformulation is presented for maximizing present netvalue subject to volume, machine capacity,transportation capacity, and demand constraints. Dualvariables associated with the bucking constraints are usedto generate new bucking patterns to optimize productoutput. A flexible branch and bound algorithm is usedto determine the best pattern. Both the structure of thealgorithm and the rules that can be applied to controlthe selection process are described and selectionapproaches are compared with respect to product outputderived from the resulting patterns. This approach hasbeen used by Chilean companies to improve operationsand realize significant savings.

43. Guignard, Monique; Ryu, Choonho; Spielberg,Kurt. 1998. Model tightening for integrated timberharvest and transportation planning. EuropeanJournal of Operational Research. 111: 448-460.

A method is proposed to improve solution capabilities ofa mixed-integer programming (IP)model for integratingtransportation and timber planning. IP models such asthe IntegratedResource Planning Model cannot be

solved easily or quickly because of the size of mostforestmanagement problems and many 0-1 variablesrequired. Suggestions are included for improvingsolutiontime through the use of trigger constraints, constraintlifting, and the prioritization of branching for double-contraction variables. Four model structures, each usinga different combination of the three improvementtechniques, were tested on three small data sets. For thesecond data set, the original IP formulation was solvedto optimality only after 7 days had elapsed. Lifting thetrigger constraints did not significantly reducecomputation time but the addition of double-contraction priorities resulted in a solution time ofseveral minutes. Using all three improvements togetherresulted in computation times of less than 15 minutesfor all test cases.

44. Haight, Robert G.; Travis, Laurel E. 1997. Wildlifeconservation planning using stochasticoptimization and importance sampling. ForestScience. 43(1): 129-139.

Wildlife populations are particularly difficult to modelwith standard linear or integer programming approaches.A stochastic programming model is described thatminimizes the cost of habitat protection subject toconstraints related to species viability. The first half ofthe paper focuses on describing the formulation of theproblem and details the search algorithm used to solvethis model. To evaluate the approach, it is applied to ahypothetical problem related to the management of graywolf. Simulation models are used to generate the survivalprobabilities for the wolf under different managementplans. The model is run numerous times with differentpopulation targets to determine the tradeoff betweencost and risk. The sensitivity of the model to changes inpopulation growth and dispersal functions is assessed. Inaddition to its ability to incorporate uncertainty into theoptimization process, this approach offers a high degreeof flexibility in the types of wildlife functions that can beutilized. Although computation difficulty limits the sizeof problem that can be addressed, this model is a notedimprovement over traditional deterministic approaches.

45. Hof, John; Bevers, Michael. 2000. Direct spatialoptimization in natural resource management:four linear programming examples. Annals ofOperations Research. 95: 67-81.

Discusses how to optimize wildlife populations based ontheir spatial dynamics. Four species-specific and site-specific linear programming (LP) models thatincorporate wildlife issues intonatural resource planningare described. The objective function and all necessaryconstraints are outlined along with model assumptions

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and limitations. The first model attemptsto maximizethe population of a species that is being raised incaptivity and then released into thewild; the secondmaximizes a colonial species population given particularpopulation movement(dispersal) tendencies; the thirdminimizes pest populations, given particulardispersingbehavior and specific management activitiesfocused on reducing the population; the fourthis appliedto the survival of a species given strict spatial constraintson habitat.

46. Hof, John; Linda Joyce. 1993. A mixed integerlinear programming approach for spatiallyoptimizing wildlife and timber in managed forestecosystems. Forest Science. 39(4): 816-834.

A mixed-integer linear model is presented that addressesthe potential for a nonconvex decisionspace that couldprevent the identification of global optima; and theinability of nonlinearmodels to solve real-worldproblems or take into account the random nature offactors such ashabitat fragmentation. A grid-basedapproach is used that divides forest area into squaresubunits of equal size. The objective function includesthe weighted sum of timber output andpopulations ofboth edge-dependent and area-dependent species. Anonlinear edge-effect model is presented andreformulated as a mixed-integer linear model; the samemodification is used for habitat-fragmentation effects.Both of these model components and a linear habitat-size threshold constraint for area-dependent species areincorporated into the final formulation. Two scenariosare tested using sets of objective-function weights.Solution times ranged from 30 minutes to 2 hours.Although the model is designed primarily for relativelysmall problems, an optimal solution is guaranteed.

47. Hof, John G.; Joyce, Linda. 1992. Spatialoptimization for wildlife and timber in managedforest ecosystems. Forest Science. 38(3): 489-508.

Although there have been attempts to incorporatenonlinear relationships in linear programs, for example,through piecewise approximations, most have achievedlimited success due to significant increases in problemsize and computation. Three formulations that canconsider nonlinear functions related to wildlife habitatare presented. The first approach, which attempts toaccount for edge effects using a standard grid-basedallocation, uses integer nonlinear programming todetermine whether each cell will be harvested or left aswildlife habitat. However, real-world application of themodel is limited by lack of effective solution algorithms.The same basic procedure is repeated in the secondmodel but with a “geometric” allotment structure such

that land uses are allocated using circles of varyingdiameters. This approach does not require an integerformulation. In the third model, the geometric structureis used to model fragmentation effects.

48. Hof, John G.; Raphael, Martin G. 1993. Somemathematical programming approaches foroptimizing timber age-class distributions to meetmultispecies wildlife population objectives.Canadian Journal of Forest Research. 23: 828-834.

The typical forest-scheduling model considers wildlifeonly indirectly. Three alternative models that optimizewildlife factors directly are presented. The firstmaximizes the total number of viable species and isconsidered the “most efficiency oriented,” while theother two models maximize a specific measure ofpopulation viability. All three models are run using bothlinear and nonlinear viability functions. When nonlinearviability functions are used, the models must be solvedwith nonlinear programming. With linear functions,only the standard linear programming formulation isrequired. An exception is the second “viability” model,which has a nonlinear objective. The models, which weretested using data from a 1.1 million-ha forest inCalifornia, produced different optimal age-classdistributions. Using the logistic (nonlinear) viabilityfunction was the most realistic approach, though the twoviability models were more effective in spreading the riskof extinction equitably across all species. The “totalspecies maximization” approach yielded the highest totalnumber of viable species.

49. Hoganson, Howard M.; Borges, Jose G. 1998.Using dynamic programming and overlappingsubproblems to address adjacency in large harvestscheduling problems. Forest Science. 44(4): 526-538.

Dynamic programming (DP) was used to solve a mixed-integer harvest-scheduling problem in three scenariosconsisting of 40- by 25-unit “forests.” The planningproblem was decomposed into subproblems and thusincrease the problem size to which DP can be applied.The objective of this specific formulation was tomaximize net returns subject to adjacency constraints.The problems were solved using forward recursion. Theapplication entailed planning over five 10-year periodswith seven possible management alternatives. Forcomparison, each of the four problems also was solvedusing a simulation approach and an unconstrained(relaxed) DP. Solution times were satisfactorily short andthis method provided better solutions than thesimulation approach.

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50. Jones, J. Greg; Meneghin, Bruce J.; Kirby, MalcomW. 1991. Formulating adjacency constraints inlinear optimization models for scheduling projectsin tactical planning. Forest Science. 37(5): 1283-1297.

Several approaches are presented for minimizing thecomputational requirements of mathematical programsby reducing the number of constraints needed to handleadjacency considerations. The formulations are based onthe assumption that the forest management area isdivided into polygons rather than structured as a grid,and are presented as constraints in an integerprogramming model. The constraints are firstformulated for only one decision variable and oneplanning period. Type 1 formulation uses a group ratherthan pairs of polygons to restrict timber harvesting. Type2 combines several Type I constraints. The formulationsare applied to three planning areas consisting of 27, 112,and 279 polygons. Using Type 2 constraints couldreduce the number of constraints by nearly 75 percent. Iftrigger inequalities are used, Type 2 formulations wouldreduce the number of constraints by 27 percent.

51. Murray, Alan T. 1999. Spatial restrictions inharvest scheduling. Forest Science. 45(1): 45-52.

Discusses two common approaches to modelingadjacency constraints in harvest scheduling that are usedwhen irregularly delineated units represent the forestmanagement areas. Both approaches are presented asbinary integer programming models. The UnitRestriction Model is applied when management units areso large that the harvest of two adjacent units wouldnecessarily violate adjacency constraints. If managementunits are significantly smaller than the area limit of theadjacency constraint, harvesting of adjacent units doesnot necessarily violate the constraints and the AreaRestriction Model is used. Both exact and heuristicsolution methods for solving these models are discussed,and the issue of spatial unit definition in minimizingmodeling and computation requirements is addressed.

52. Murray, Alan T.; Church, Richard L. 1995.Measuring the efficacy of adjacency constraintstructure in forest planning models. CanadianJournal of Forest Research. 25: 1416-1424.

Reviews the traditional approach to adjacency constraintstructure (pairwise comparison), suggests eight improvedformulations, and compares computational efficiency ofthese new approaches using six harvest-schedulingscenarios that are based on the planning horizonconsidered (single or multiple period), number ofharvest units included in the analysis, and whether roadbuilding is considered in the problem. The different

approaches are compared according to the number ofconstraints required, optimal solution generated,number of branches, and iterations, and solution timerequired. The most significant findings are that: (1) thetraditional pairwise comparison method does notnecessarily result in the tightest constraint structure, (2)methods that most significantly reduce the number ofconstraints may have longer solution times, and (3)methods that rely on constraint tightening areparticularly efficient.

53. Murray, Alan T.; Church, Richard L. 1996.Analyzing cliques for imposing adjacencyrestrictions in forest models. Forest Science. 42(2):166-175.

A network theory-based technique known as the Type Iconstraint approach was first used in conjunction withquadruplet cliques, i.e., one constraint constructed foreach group of four cells. A modification to Type Iconstraints that allow this formulation to be used withcliques with more than four cells is discussed. Twoadditional constraint-reduction techniques are presented.The first focuses on the elimination of dominated cliqueconstraints and the second reduces the constraints to a“minimal subset.” All three approaches were applied tonine forest planning problems. For eight problems, theminimal clique constraint set resulted in the fewestadjacency constraints. All three methods resulted in thesame number of constraints in the ninth example,though the nondominated approach requiredsignificantly shorter computation times. This reductiontechnique is recommended where the number ofconstraints generated is sufficiently small that it is notbinding; otherwise, the minimal set approach is aneffective alterative.

54. Roise, Joseph P. 1990. Multicriteria nonlinearprogramming for optimal spatial allocation ofstands. Forest Science. 36(3): 487-501.

Draws on the “four color theorem” to develop anonlinear programming model for timber-harvestscheduling. For problems that require adjacent units tobe harvested no less than a specified number of yearsapart (the exclusion period), the theorem suggests afeasible solution is possible so long as the project periodlength divided by the exclusion period length is less thanor equal to four. Where a feasible solution is notpossible, the adjacency constraint can be used as theobjective function, thus maximizing the length of timebetween harvesting of adjacent units. The basicnonlinear model is presented and the objective functionand constraints are applied to four increasingly complexproblems. As the number of stands included increases,

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the solution time for the models grows exponentially.This technique is applicable only to forests with fewerthan 200 stands, but allows optimization of harvestdecisions at both the forest and stand level.

55. Snyder, S.; ReVelle, C. 1997. Multiobjective gridpacking model: an application in forestmanagement. Location Science. 5(3): 165-180.

Presents a method of integrating timber harvesting andwildlife habitat goals subject to spatial constraints. Abinary integer programming (IP) model was applied to ahypothetical and static data set comprised of a 25- by25-cell forest grid. The objective is to develop a harvestschedule that maximizes both harvest volume andwildlife habitat acreage. Adjacency constraints areevaluated by 2 by 2 grid-blocks rather than by individualpairs of cells. The study’s two objectives were combinedusing the weighting method. Three of the possibleweight combinations were used to solve the IP, and theimpact of various weights on the spatial distribution ofmanagement activities is discussed. The model wasreformulated with additional constraints and the processrepeated. This approach was successful in obtainingexact, optimal solutions in a minimal amount of time.

56. Snyder, Stephanie; ReVelle, Charles. 1996. Temporaland spatial harvesting of irregular systems ofparcels. Canadian Journal of Forest Research. 26:1079-1088.

A binary integer programming (IP) model was applied toa forest with irregular harvest-unit systems. Unlikeregular (grid) systems, irregular systems require morethan one type of constraint structure. The method forformulating constraints for irregular systems isdemonstrated and the effect of such a set of constraintson the computational efficiency of the IP model isassessed. With the maximization of timber volume as theobjective, the model is then applied to five hypotheticaland five real scenarios. Data sets representing irregularparcel systems of varying sizes and configurations areevaluated using both static and multiple-period models.Adjacency constraint formulations for the two modelsare presented separately, and the multiple-period modelis run for various planning horizon lengths. For thestatic model, the IP model performed well, requiringlittle, if any, branching and bounding. In some cases,considerable branching and bounding was required forthe multiple-period model.

57. Snyder, Stephanie; ReVelle, Charles. 1997. Dynamicselection of harvests with adjacency restrictions:the SHARe model. Forest Science. 43(2): 213-222.

Discusses the need to develop models that allow harvestplans to be subject to spatial constraints and temporalmanagement considerations to be integrated. A binaryinteger programming (IP) formulation is presented thatis the “shortest path network flow” model, which is ameans of structuring “relaxed” models that can be solvedto exact integer solutions. Several general formulations ofadjacency constraints that can be used in this approachare discussed, and a binary IP model is introduced thatincludes both spatial constraints over multiple periodsand the shortest-path-network structure. The model isformulated for an area represented by a grid of cells ofequal size. A set of hypothetical data is used to evaluatethe approach, with multiple runs conducted usingdifferent grid sizes, time-horizon lengths, initial forest-age structures, and adjacency restrictions. The results ofeach run along with solutions times are reported.

58. Weintraub, Andres; Barahona, Francisco; Epstein,Rafael. 1994. A column generation algorithm forsolving general forest planning problems withadjacency constraints. Forest Science. 40(1): 142-161.

Describes a method for solving forest-planning problemswith multiple periods and a significant set of constraints,representing a large forest area that is realistic. A two-stage approach is applied to both simplified andexpanded problems. The first entails scheduling unitswithin a single, homogenous harvest area; the expandedproblem entails unit scheduling across multiple areas.The first stage of the approach is the formulation of aninteger-programming (IP) model, which is solvedwithout the integer constraint (relaxed form) and thenby heuristic procedure to improve the relaxedcontinuous solution. This simplex-based procedureidentifies a “stable set” of subproblem alternatives thatsatisfy adjacency constraints; a three-step process is usedto solve the stable set problem. First, a greedy heuristicmethod is used to identify a near optimal solution. If itis not successful, a linear programming (LP) technique isused to find an integer solution. If the LP isunsuccessful, the problem is solved by the branch andbound method. The latter approach was applied to twoproblems, each with three forest configurations, over a10-year planning horizon. On average, the solutionswere within 3 percent of the optimal solution for therelaxed IP.

59. Weintraub, Andres P.; Epstein, Rafael; Murphy,Glen; Manley, Bruce. 2000. The impact ofenvironmental constraints on short termharvesting: use of planning tools andmathematical models. Annals of OperationsResearch. 95: 41-66.

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Seven planning models currently being applied to realsituations in New Zealand and Chile are described,including the typical planning horizon used and types ofinformation required by each model. Also discussed ishow forest management is facilitated by these modelswhich range from short-term and small-scale operationalapplications to long-range planning formulations usedfor harvest scheduling, wood-processing investmentdecisions, and forest-management planning. The impactof modification to better include environmentalprotection measures in the planning process is illustratedfor five of the models using these case studies. Impactsare assessed in terms of changes in net values and harvestvolumes resulting from the mitigation measures.

Heuristic Methods

60. Bettinger, Pete; Boston, Kevin; Sessions, John. 1999.Intensifying a heuristic forest harvest schedulingsearch procedure with 2-opt decision choices.Canadian Journal of Forest Research. 29: 1784-1792.

Describes a method for improving the performance oftabu search for solving a harvest-scheduling problem.Tabu search operates by making iterative changes, ormoves, to a selected solution based on specified searchrules. The relative benefits of using 1-opt versus 2-optmoves in this search process is evaluated. In 1-opt moves,only one attribute of one decision choice is altered, i.e., aunit is removed from the harvesting schedule. In 2-optmoves, that attribute is changed for two decision choicessimultaneously, i.e., one unit is added to the harvestschedule while another is removed. The objective of thisapplication is to maximize of harvest volume subject toadjacency and even-flow constraints. Hypothetical 5 by8 and 28 by 25 forest grids are generated. The problemis solved as a relaxed linear programming (LP) modeland as an integer program (IP). Two versions of tabusearch, one that allows only 1-opt moves and one thatallows both 1-opt and 2-opt moves, are used. Thesolution time for tabu search was significantly less thanfor the IP model; the combined (1- and 2-opt) tabumodel had a slightly longer solution time than the 1-optmodel. The tabu models had objective function valueswithin 3 percent (1-opt) and 1 percent (both) of therelaxed LP solution.

61. Bettinger, Pete; Johnson, K. Norman; Sessions, John.1996. Forest planning in an Oregon case study:defining the problem and attempting to meetgoals with a spatial-analysis technique.Environmental Management. 20(4): 565-577.

Spatial allocation is an important consideration innatural resource management, but it is difficult tooptimize activities in a spatial context. An operational-

level harvest-scheduling program called SNAP II+ usesthe more common integer programming formulationand a heuristic solution algorithm approach. The modelwas evaluated based on whether it could modelmanagement goals well and was flexible in evaluatingalternatives when applied to a small watershed in theupper Grand Ronde River Basin in Oregon. The modelwas formulated to maximize net present value over four10-year planning periods. SNAP II+ generated feasiblemanagement plans and was effective in addressing spatialallocation.

62. Bettinger, Pete; Sessions, John; Boston, Kevin. 1997.Using tabu search to schedule timber harvestssubject to spatial wildlife goals for big game.Ecological Modelling. 94: 111-123.

A tabu search heuristic is used to solve a large harvest-scheduling model that includes both temporal andspatial constraints for wildlife habitat. No othertechnique can directly incorporate habitat-qualityconsiderations while developing feasible harvestschedules. The objective function in this modelminimizes the sum of the squared differences betweenthe target level of harvest and the actual level of harvestfor each period, and contains penalty functions thatprevent: (1) adjacent units from being harvested in thesame period (adjacency constraint); and (2) blocks ofunits assigned as wildlife cover from being reducedbelow a minimum aggregate size (wildlife habitatconstraint). The data used were based on a hypotheticallandscape of 1-ha units (20 by 20 grid). Two scenarioswere run that represented differences in forage agelimitations and minimum harvest age. The algorithmwas run for 1,000 iterations for the first scenario andabout 400 iterations for the second. In both scenarios, atemporally and spatially feasible solution was obtained.

63. Bettinger, Pete; Sessions, John; Johnson, K. Norman.1998. Ensuring compatibility of aquatic habitatand commodity production goals in easternOregon with a tabu search procedure. ForestScience. 44(1): 96-112.

Describes the use of tabu search to simultaneouslyoptimize land-management plans and assess their impacton aquatic habitat. A basic linear-programmingformulation with an objective function that optimizesnet present value was applied to a 6,000-ha watershed ineastern Oregon. This method was able to optimizetimber and aquatic habitat goals simultaneously, thoughit may not generate a global optimal solution.

64. Bos, Jan. 1993. Zoning in forest management: aquadratic assignment problem solved by simulated

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annealing. Journal of Environmental Management.37: 127- 145.

Zoning-based management is based on the assumptionthat conflict can best be reduced by separation of landuses. Traditional planning models do not explicitlyinclude zoning decisions partly because they requireinteger variables that make the models difficult to solve.A forest zoning problem in the Netherlands is addressedusing a quadratic assignment formulation in which theobjective function comprises two elements. The firstelement is a function of both the suitability of a forestunit for each alternative use and the relative preferencefor those uses. The second considers the use of adjacentforest units and maximizes the grouping of uses thatcomplement each other. The model also considers actualor potential land uses that border the forest whenmaking zoning decisions. A heuristic algorithm(simulated annealing) is used to generate solutions. Datawere obtained for 84 units within the WaterbloemNational Forest and 80 “environmental” units thatadjoin the forest. The model effectively considered thespatial relationships of various land uses and the solutionalgorithm provided acceptable results.

65. Bullard, Steven H.; Sherali, Hanif D.; Klemperer, W.David. 1985. Estimating optimal thinning androtation for mixed-species timber stands using arandom search algorithm. Forest Science. 31(2):303-315.

Describes a method for generating “good” thinningregimes in even-aged, mixed-species stands, specifically, agrowth model consisting of up-growth and mortalityfunctions that generates data on stand structure andvolume. Growth information is used in a nonlinearinteger-programming model that addresses the thinningproblem. The model was formulated to maximizepresent net value of both current and future income. Acomparison of simple and multistage random searchheuristics is given for two hypothetical samples. Bothyielded nearly optimal solutions in several seconds toseveral minutes. In both cases, the multistage algorithmoutperformed the simple algorithm.

66. Kangas, Jyrki; Pukkala, Timo. 1996.Operationalization of biological diversity as adecision objective in tactical forest planning.Canadian Journal of Forest Research. 26: 103-111.

Describes HERO, a utility-based heuristic methoddesigned to address harvest-scheduling problems thatconsider biodiversity. The major premise of this method,which entails estimating an additive utility function andoptimizing that function, is that all constraints and

objectives can be formulated as preference and utilityfunctions. The method was applied to a 43-ha, 37-unitforest in eastern Finland with two 10-year planningperiods and 129 treatment schedules. Four scenarioswith varying degrees of biodiversity importance weretested. The strengths of this approach are its flexibilityand ability to consider nonlinear relationships, and makebiodiversity commensurable with other objectives.

67. Lockwood, Carey; Moore, Tom. 1992. Harvestscheduling with spatial constraints: a simulatedannealing approach. Canadian Journal of ForestResearch. 23: 468-478.

The use of simulated annealing (SA) to solve largeharvest-scheduling is proposed and the basic procedurefor this heuristic technique is described. A uniquecharacteristic of this formulation is that the objectivefunction is designed to minimize deviation from theharvest-volume target as well as penalty costs associatedwith constraint violations. Procedures for developing thefour penalty cost functions are presented and the processof applying SA to this specific formulation is described.Data were from a 240,000-ha subsection of a privateforest six harvest levels and three harvest block sizes usedin trial runs. This method generated feasible solutionsfor every run.

68. Murray, Alan T.; Church, Richard R. 1995.Heuristic solution approaches to operational forestplanning problems. OR Spektrum. 17: 193-203.

Explores the ability of three heuristic methods-interchange, tabu search, and simulated annealing togenerate near optimal plans for problems withconsiderable detail. These methods representimprovements on a Monte Carlo approach and wereapplied to two moderate-size forests in BritishColumbia. The first problem was a mixed-integerformulation with 300 decision variables (291 integer)and 740 constraints. In a previous study, this problemwas solved analytically in about 60 hours. For eachheuristic, the process began with the best Monte Carlosolution, which generate 1,300 additional solutions. Thebest objective-function value using the interchangemethod was within 2 percent of the optimal solution.The best solutions generated by tabu search andsimulated annealing were within 1 percent of theoptimal solution. For all three methods, objectivefunction values were significantly better than thesolution generated using Monte Carlo alone. Solutiontimes were 30 hours for tabu search, 11 hours forsimulated annealing, and 3 hours for interchange. Tabusearch solutions were the most consistent and closest tooptimal.

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69. Nelson, John; Bodie, J. Douglas. 1990. Comparisonof a random search algorithm and mixed integerprogramming for solving area-based forest plans.Canadian Journal of Forest Research. 20: 934-942.

Compares a Monte Carlo integer-programming heuristicand a mixed-integer programming (IP) model for solvingharvest-scheduling problems at the tactical level. TheMonte Carlo technique was applied to a 1,700-ha forestin British Columbia. The harvest problem was firstformulated as a mixed IP model with the objective ofmaximizing discounted net revenue. The problem wassolved using linear programming (LP) to determine theoptimal solution, and then reformulated as a MonteCarlo IP model. This heuristic model was solved usingthree search techniques: all-period, first selective, andsecond selective. Of the 1,300 Monte Carlo solutionsgenerated, 175 were within 10 percent of the optimalvalue, 12 were within 5 percent, and the highest valuedwas within 3 percent. The all-period search was the mosteffective of the search routines and Monte Carlo waseffective in creating harvest schedules for forest problemsthat are medium to large.

70. O’Hara, Anthony J.; Faaland, Bruce H.; Bare, B.Bruce. 1989. Spatially constrained timber harvestscheduling. Canadian Journal of Forest Research. 19:715-724.

The model SCRAM is the first algorithm that cangenerate feasible and “good” solutions to integerprogramming (IP) problems that include many units,multiple planning periods, and spatial constraints. Thebasic IP formulation that is to be solved and the biasedsampling search algorithm developed to solve it aredescribed. This heuristic is a modified version of theMonte Carlo IP that both randomly selects harvest unitsand allows the selection process to be biased towardthose units more likely to result in good solutions. Threedifferent pre-biasing techniques were used on data froma previous study of a 242-unit forest with a planninghorizon of five 10-year periods. This model is animportant innovation because it requires no special databeyond what is available for the average schedulingproblem, produces feasible/good integer solutions, anddoes not lose accuracy as the problem size increases.

71. van Deusen, Paul C. 1999. Multiple solutionharvest scheduling. Silva Fennica. 33(3): 207-216.

One of the most common heuristic methods is thesimulated annealing algorithm. The core of this solutiontechnique is a procedure known as the metropolisalgorithm (MA). Also related to the Monte Carlotechnique, MA focuses primarily on generating a largelist of feasible solutions, with less emphasis on economic

optimality. All problem constraints are incorporateddirectly into the objective function. This allowsconsistent treatment of problem criteria and locallyoptimal solutions can be identified by increasing theweight of a particular element in the objective function.This has been suggested as more appropriate type ofapproach for government agencies that wish to identifymore than the most economically efficient alternatives.As applied to a forest data set of 419 stands, MA proveda flexible approach to forest planning.

72. Wientraub, Andres; Church, Richard L.; Murray,Alan T.; Guinard, Monique. 2000. Forestmanagement models and combinatorialalgorithms: analysis of state of the art. Annals ofOperations Research. 96: 271-285.

The types of algorithms available to solve mixed-integerprogramming problems are reviewed and methods usedto solve harvest-scheduling problems with adjacencyconstraints are discussed. Also discussed are algorithmsthat have been applied to the simultaneous planning ofharvesting and road building. Although mostapplications have included the use of heuristicalgorithms, the basic integer formulation can bestrengthened to provide a good solution.

73. Weinttaub, Andres; Jones, Greg; Meacham, Mary;Magendzo, Adrian; Magendzo, Ariel; Malchuk,Daniel. 1995. Heuristic procedures for solvingmixed-integer harvest scheduling-transportationplanning models. Canadian Journal of ForestResearch. 25: 1618-1626.

Discusses the use of heuristic techniques to addressspatial constraints in harvest scheduling. The basicformulation, based on the Integrated Resources PlanningModel, is given as an linear programming (LP)optimization of present net value, and the heuristicprocedure for problems in which only road-decisionvariables are in 0-1 integer form is discussed. Thisiterative algorithm works with an LP solver to convertoptimal LP solutions to integer solutions. This approachwas applied using several small data sets and results wereevaluated on the basis of the best solution using a mixed-integer programming (IP) model. An extension of theoriginal formulation that considers both 0-1 road and 0-1 land-management variables is presented. Objectivefunction values were about 40 percent higher withheuristic solutions than with the IP solution.

74. Yoshimoto, Atushi; Brodie, J. Douglas. 1993.Comparative analysis of algorithms to generateadjacency constraints. Canadian Journal of ForestResearch. 24: 1277-1288.

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The need to incorporate environmental concerns intoharvest scheduling has led to the use of large number ofspatial constraints in MODM problems. Theconventional branch and bound algorithm has been solimited in use that efforts have been made to developheuristic methods that can reduce the set of constraintsthat must be included in a standard integerprogramming model. Conventional solution algorithmand two heuristic algorithms that are used to reduce thenumber of constraints are reviewed and a simpleanalytical algorithm to reduce the constraint set isproposed. Three original algorithms and four versions ofthe proposed heuristic are evaluated for computationaleffort and number of constraints needed. Although thetwo original heuristic methods resulted in fewerconstraints, computation time for each was greater thanthat for any version of the proposed heuristic. The lattermethod is preferred over conventional branch boundand other heuristic algorithms.

75. Yoshimoto, Atsushi; Brodie, J. Douglas; Sessions,John. 1994. A new heuristic to solve spatiallyconstrained long-term harvest schedulingproblems. Forest Science. 40(3): 365-396.

Describes a heuristic algorithm to solve integerprogramming (IP) harvest-scheduling problems. Thistwo-stage algorithm eliminates scheduling alternativesthat are infeasible over the entire planning period, andbreaks down the scheduling problem into subproblems:only two successive planning periods are considered atany one time so that a selected schedule will be feasibleboth in the current period and in the next period. Datawere from a forest containing 109 stands in 62 analysisareas and a second forest with 45 units. The objectivewas to maximize total present net worth for planningperiods. The solution was compared with that from abranch and bound solution for the original integerformulation and a relaxed linear programming (LP)solution. Exception for the one-period schedule, theheuristic algorithm had significantly shorter solutiontimes than the branch and bound method. Thedifference in objective function between the branch andbound and the heuristic solutions were less than 1percent for all problems. The heuristic solution wassignificantly less than the relaxed LP solution in the 1-and 2-year planning problems, and was within 2 and 3percent of the relaxed LP objective function value forlonger planning problems.

76. Zanakis, Stelios H.; Evans, James R. 1981. Heuristic“optimization”: why, when, and how to use it.Interfaces. 11(5): 84-93.

MADM Applicationsin Forestry and Land ManagementHeuristic methods are particularly applicable insituations where data are uncertain or limited orreasonable computation is not possible, or where there isan attempt to improve solutions through optimization.Ten features of the “ideal” heuristic method and eightguidelines for applying these features are presented.

77. Choo, Eng U.; Schoner, Bertram; Wedley, William.1999. Interpretation of criteria weights inmulticriteria decision making. Computers &Industrial Engineering. 37: 527- 541.

A comprehensive assessment of the use of criteriaweights in MADM models examining 13 interpretationsthat have been applied to these weights. Also examinedare aggregation rules, measurement units, othercomparative features of each interpretation, and themore common methods that use them.

78. Easley, Robert F.; Valacich, Joseph S.;Venkataramanan, M. A. 2000. Capturing grouppreferences in a multicriteria decision. EuropeanJournal of Operational Research. 125: 73-83.

Multi-attribute decision models are effective inquantifying the preferences of an individualdecisionmaker, though natural resource decisionsgenerally involve multiple stakeholders. As a result, thepreferences of a wide range of groups must beconsidered. The effectiveness of the analytic hierarchyprocess (AHP), a variation of the standard AHP(FNAHP), and two pairwise voting techniques areevaluated for their ability to capture the preferences ofmultiple decisionmakers and supporting groupdecisionmaking. Three approaches are applied to theallocation of sales territory between two representatives.The resulting alternative rankings and decisionmakerperceptions were compared across the four decisionmethods. The hierarchical model was the most effectivetechnique for capturing group preferences.

79. Gershon, Mark. 1984. The role of weights andscales in the application of multiobjective decisionmaking. European Journal of Operational Research.15: 244-250.

A major criticism of MCDM is that the results can beinfluenced, and any desired solution obtained, bymanipulating the weights used in the analysis.Algorithms that do not require subjective weights havebeen developed, though subjective input still is requiredwith these methods. Four MCDM compromiseprogramming, cooperative game theory, multiattribute

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utility theory, and ELECTRE—were studied todetermine the role played by their weighting schemes inthe evaluation of alternatives. A general classification ofthe “proper” way in which weights can be determined isproposed. Differences among three types of weightingapproaches are illustrated and the type of weightingscheme used, process of weight selection, and scalingsand other subjective parameters for each MCDM areidentified. Although these methods use the same input,each defines the concept of a “best” solution differently.

80. Hajkowicz, Stefan A.; McDonald, Geoff T.; Smith,Phil N. 2000. An evaluation of multiple objectivedecision support weighting techniques in naturalresource management. Journal of EnvironmentalPlanning and Management. 43(4): 505-518.

Explores the use of five weighting techniques to betterunderstand the implications of choosing a multi-attribute method choice for a particular natural resourceproblem. The weighting methods—fixed-point scoring,rating, ordinal ranking, graphical weighting, and pairedcomparisons—are described and then applied toprioritizing Australian National Heritage Trust projectsfor funding. The selection of decisionmakers, decisionalternatives, and evaluation criteria for this problem arediscussed, and weights obtained from each approachesare compared. Except for the paired comparison, alltechniques resulted in the same ranking of criteria,though actual weights varied significantly. For ease ofuse, the ranking method is the most preferred and thefixed-point approach is the least preferred. The rankingtechnique clarified the decision situation the most andthe graphical method the least. Decisionmakers shouldnot rely on a single weighting approach as differentmethods may have an unknown bias.

81. Howard, Andrew F. 1991. A critical look atmultiple criteria decision making techniques withreference to forestry applications. Canadian Journalof Forest Research. 21: 1649-1659.

Describes various MADM to include the componentsrelated to “procedural and mathematical formalities.”These include scale transformations, criterion weighting,choice of criteria, and specification of alternatives. Howeach of these steps is approached affects the outcome ofthe MADM process, that is, the ranking order of thealternatives and the number of criteria that are used toassess the achievement of an objective, influence theweight of that objective in the analysis. Crucial issuesthat should be recognized and addressed before MADMare applied are described.

82. Lahdelma, Risto; Salminen, Pekka; Hokkanen,Joonas. 2000. Using multicriteria methods in

environmental planning and management.Environmental Management. 26(6): 595 605.

MADM are appropriate and effective in environmentalplanning and management because of their ease of useand transparency to stakeholders. The three typical usesof MADM are the choice of a “best” alternative, rankingof several alternatives relative to each other, and analysisof the degree of acceptability of alternatives. The basicprocedure for implementing MADM-drivendecisionmaking is reviewed. The importance of early andconsistent stakeholder involvement choice of evaluationcriteria and selection of the most appropriate MADMtechnique are emphasized.

83. Martin, W. E.; Bender, H. Wise; Shields, D. J. 2000.Stakeholder objectives for public lands: rankingsof forest management alternative. Journal ofEnvironmental Management. 58: 21-32.

In response to the National Forest Management Act andthe National Environmental Policy Act, publicparticipation has become an important component inForest Service planning and decisionmaking. Inquantifying public preferences, additive utilitymethodology identifies the decision context,stakeholders, and alternatives; elicits preferences fromstakeholders regarding the alternatives and theirattributes; and develops value functions for eachstakeholder to rank alternatives. Additive utilityfunctions were applied in the evaluation of alternativemultiple-use management alternatives on the San JuanNational Forest in Colorado. Alternatives were ranked byeach stakeholder identifying the order of preference(ordinal ranking) and by cardinal value functions(cardinal ranking). Both methods produced inconsistentrankings, but the cardinal value functions generated themore useful evaluations.

84. Prato, T. 2000. Multiple attribute evaluation oflandscape management. Journal of EnvironmentalManagement. 60: 325-337.

The use of multi-attribute models in landscape-levelplanning is proposed, and the multi-attribute decisionprocedure is described and applied to the followingscenarios: a publicly owned watershed that isadministered by a land agency, and a basin that isprivately owned by multiple individuals. The mostefficient alternatives are identified and decisionmakerpreferences are then elicited to determine the mostfavored nondominated alternative. The multi-attributemodel is useful for landscape-scale planning but mightbe difficult to implement as substantial input by thedecisionmaker is required.

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85. Pukkala, Timo; Kangas, Jyrki. 1996. A method forintegrating risk and attitude into forest planning.Forest Science. 42(2): 198-204.

Demonstrates a method for incorporatingintergenerational perspectives into forest planning. Aheuristic method is proposed that integrates risk analysisand attitudes toward risk. The procedure incorporatesstochastic simulation of stand development underdifferent treatments and across various scenarios of treegrowth and timber prices; pairwise comparison ofobjectives using the analytic hierarchy process technique;and an estimation of the decisionmaker’s attitude towardrisk. The method is applied to a case study thatrepresents a typical planning situation facing a privateforest owner. A solution is determined for three levels ofrisk (low, normal, and high) and across three riskperspectives (risk avoider, risk seeker, and risk neutral).The method can be applied to both tactical and strategicforest planning.

86. Tecle, Aregai; Fogel, Martin M.; Duckstein, Lucien.1988. Multicriterion analysis of forest watershedmanagement alternatives.m Water ResourcesBulletin. 24(6): 1169-1179.

Two multi-attribute decision models, the outranking-based ELECTRE and the distance-based compromiseprogramming method, are compared on the basis of howthey select a preferred management alternative. Both areapplied to a portion of the Beaver Creek watershed inArizona. Compromise programming was preferred overthe ELECTRE-based model for consistency and ease ofuse. Neither approach was overly sensitive to changes incriteria weights, and the most and least preferredalternatives were the same for both methods.

87. Teeter, Lawrence D.; Dyer, A. Allen. 1986. Amultiattribute utility model for incorporating riskin fire management planning. Forest Science. 43(4):1032-1048.

The use for multiattribute utility theory (MAUT) isimportant when uncertain information is incorporatedinto planning analysis. A method for evaluating ForestService fire management strategies in terms of botheconomic efficiency and risk is proposed. Economicefficiency is represented by the direct costs ofimplementing a particular strategy plus any change invalue of the forest that might result, and the riskassociated with that strategy. Risk is considered not asvariability in net returns but as potential loss or injury.The process of constructing utility functions and thetechnical aspects of their application are reviewed andseven alternative strategies, including the historicalForest Service fire management approach, are evaluated.

These strategies consisted of combinations of particularactivities, such as firebreak construction or surveillance,and their required resources. Utility models such asMAUT are valuable for incorporating risk/uncertaintyinto complex planning processes and are useful whenoutcomes are deterministic (known) and stochastic(unknown).

Combined MODM/MADM Applications

88. Malczewski, J.; Moreno-Sanchez, R.; Bojorquez-Tapia, L. A.; Ongay-Delhumeau, E. 1997.Multicriteria group decision-making model forenvironmental conflict analysis in the CapeRegion, Mexico. Journal of Environmental Planningand Management. 40(3): 349-374.

The analytic hierarchy process (AHP) and integerprogramming (IP) are integrated into a model forconducting land-suitability planning. The AHPprocedure incorporates the preferences of interest groupsinto the suitability analysis, and each geographic unit isweighted according to its suitability for various land-management activities. The weights can be used in theobjective function of a binary IP model that maximizesthe total weighted value of each land use for each unit.This approach is applied to a 19,000-km2 area in Baja,Mexico with the goal of reducing conflicts amongvarious interest groups over land use. Emphasis wasplaced on the “political” nature of actual interactionswith these groups. The difficulties encountered inapplying this approach in a real-world situation arediscussed.

89. Mendoza, Guillermo A.; Sprouse, William. 1989.Forest planning and decision making under fuzzyenvironments: an overview and illustration. ForestScience. 35(2): 481 502.

Describes the use of fuzzy modeling-to-generate-alternatives (MGA) techniques and the analytichierarchy (AHP) as a two-stage process for evaluatingforest plans. The theory behind fuzzy decisionmakingand the procedure for converting a standard linearprogramming (LP) formulation a fuzzy LP are explained,and four alternative fuzzy MGA models—regular,selective, and weighted MAXMIN models and anadditive model—are described. The second stage of thisapproach entails the use of AHP to evaluate andprioritize the alternatives generated with the MGAmodels. The basic AHP procedure of making pairwisecomparisons and then synthesizing these priorities isexamined. The method is applied to data from a realforest. Objectives were to maximize net revenue as wellas areas suitable as wildlife habitat and for recreation; theplanning horizon was ten 10-year periods. This approach

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is flexible and a more realistic alternative tooptimization.

MCDM Applications to Water Resources

90. Belaineh, Getachew; Peralta, Richard C.; Hughes,Trevor C. 1999. Simulation/optimization modelingfor water resources management. Journal of WaterResources Planning and Management. May/June:154-161.

A combined simulation and optimization model is usedas a hypothesis-testing devise to demonstrate whether anenhanced representation of surface water-aquiferinteractions improves overall water-use management.This two-stage approach optimizes the water supplybased on groundwater withdrawal and stream diversionfactors, and then selects the optimal use strategy for thisincreased flow regime. The model was tested using fivesystem scenarios. The improved surface water-aquiferinteractions representation resulted in optimal solutionswith 13 percent more surface-aquifer interflow, a 52percent reduction in flow leaving the basin due to betteruse strategies, and an 80 percent increase in ground-water pumping. This technique is an effective alternativeto optimization methods.

91. Bella, Aimee; Duckstein, Lucien; Szidarovsky,Ferenc. 1996. A multicriterion analysis of the waterallocation conflict in the upper Rio Grande basin.Applied Mathematics and Computation. 77: 245-265.

Compromise programming (CP) and ELECTRE III areused to rank management alternatives for the Upper RioGrande River Basin. Thirty alternative managementactions and 18 criteria by which these actions could beevaluated were identified. Results for the two MADMapproaches are compared with both equal and unequalweightings on the criteria. The CP method was runseveral times with varying “p” values to determine howattribute deviations from the “ideal” are treated in theanalysis. Total rankings for all 30 alternatives arepresented for both methods. Each producedapproximately the same ranking order.

92. Chang, Ni-Bin; Wen, C. G.; Wu, S. L. 1995.Optimal management of environmental and landresources in a reservoir watershed bymultiobjective programming. Journal ofEnvironmental Management. 44: 145-161.

Presents a framework for incorporating economic, socialwelfare, and environmental quality factors into amultiobjective program for watershed planning inTaiwan. The processes of data acquisition, model

building, and model solution are described and 6objective functions, 10 constraints, and 15 alternativemanagement techniques are identified. Compromiseprogramming is applied to solve the resulting model,assuming equal weights on the objectives. This modelwas run twice, first assuming no pollution controlmeasures and then considering the impact of thesestrategies. Sensitivity analysis was conducted to assesseven planning scenarios.

93. da Conceicao, Cunha; Sousa, Maria; Sousa,Joaquim. 1999. Water distribution network designoptimization: simulated annealing approach.Journal of Water Resources Planning andManagement. July/August: 215-221.

Due to limitations with other MODM techniques, asimulated annealing (SA) algorithm is proposed indesigning a minimum-cost water-distribution network.The SA process is described and tested using simplifiednetworks. Two test problems were chosen that had beenevaluated by a variety of decision models. Results werecompared with those from previous evaluations. In thefirst test case consisting of six studies, the SA approachtied for third place in terms of the objective functionvalue (i.e., lowest cost) of eight evaluations. In thesecond test case, SA ranked fourth. This method is easyto use, can handle large, nonlinear, mixed-integerprogramming problems, and generates good results.

94. Das, Pransanta; Haimes, Yacov Y. 1979.Multiobjective optimization in water quality andland management. Water Resources Research. 15(6):1313-1322.

The surrogate worth tradeoff (SWT) method is appliedto a water-quality and land-management planningproblem to demonstrate the ability of a MODM tointegrate both nonpoint-source and point-sourcepollution into a single model. The two pollutionsubmodels with a cost minimization objective and athird model with a water quality objective wereintegrated into a single optimization problem that wassolved as a SWT problem using a generalized reducedgradient algorithm. Data, both actual and hypothetical,were generated for a basin in the Midwest that wasnearly 9,000 square mile s. Four (noninferior) alternativeplans were identified, and the level of attainment of eachobjective and tradeoffs among objectives were calculatedfor each alternative. The preferences of thedecisionmaker are used to develop surrogate worthfunctions that are used to determine the preferredsolution. This method can address large and complexproblems and is easier to use than other MODMmethods.

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95. David, Laszlo; Duckstein, Lucien. 1976. Multi-criterion ranking of alternative long range waterresources systems. Water Resources Bulletin. 12(4):731-754.

An existing water resource system is compared toalternative systems to identify a scheme that meetseconomic and social requirements for a watershed inHungary. A cost-effectiveness framework is used to guidethe planning process, with alternative evaluationcompleted using ELECTRE techniques. The study siteplanning objectives, evaluation criteria, and alternativesystem plans are described and displayed in a “systemversus criteria” matrix, and an incomplete ranking ofalternatives is presented. This is a simple method forranking alternative water-resource systems.

96. Duckstein, Lucien; Opricovic, Serafim. 1980.Multiobjective optimization in river basindevelopment. Water Resources Research. 16(1): 14-20.

A combined cost-effectiveness and compromiseprogramming (CP) approach was applied to the designof a water-resources system in Hungary. Cost-effectiveness methodology was used as the guidelines forevaluating and ranking alternatives; the CP method wasincorporated to allow multiobjective evaluation of thealternatives. Results were compared with those usingELECTRE techniques and multi-attribute utility theory.Five alternatives were ranked on the basis of 12 criteria.For all three methods, two of the five alternatives tendedto be ranked first or second; the exact order differedbetween approaches.

97. Flug, Marshall; Seitz, Heather L. H.; Scott, John F.2000. Multicriteria decision analysis applied toGlen Canyon Dam. Journal of Water ResourcesPlanning and Management. September/October: 270-276.

Presents a generic MADM method for evaluating flowalternatives for the Glen Canyon Dam in Arizona. Thismethod was used to evaluate nine alternatives withinseveral scenarios, each with a different weighting scheme.The analysis recommended that a new flow regime beadopted.

98. Gershon, Mark; Duckstein, Lucien; McAniff,Richard. 1982. Multiobjective river basin planningwith qualitative criteria. Water Resources Research.18(2): 193-202.

A combination of ELECTRE I and ELECTRE II is usedto select a management solution for the Santa Cruz Riverin Arizona. The models were used to evaluate 25 discrete

alternatives based on 13 evaluation criteria. ELECTRE Iwas used as a “screening” method to reduce the set ofalternatives under consideration; ELECTRE II rankedthe remaining alternatives. Sensitivity analysis wasconducted by varying the scale intervals and the criteriaweight. The impact of these changes on the finalrankings is reported.

99. Gershon, Mark; Duckstein, Lucien. 1983.Multiobjective approaches to river basin planning.Journal of Water Resources Planning andManagement. 109(1): 13-28.

Four MODM were applied to a 50-year planningproblem affecting the Santa Cruz River in Arizona.Objectives were water supply, flood protection,“environmental,” utilization of resources, and recreation,and five water-supply and five flood-protection optionswere identified and combined (total of 25 alternativemanagement schemes). The problem was evaluated byELECTRE, multi-attribute utility theory (MAUT),compromise programming (CP), and game theory.Results are presented as a set of rankings, one for eachtechnique; sensitivity analysis was used to examine theimpact on ranking order. Only MAUT and game theoryhad the same first-ranked alternative. Results showedthat each method evaluated is appropriate to this type ofdecision situation and that results were reasonablysimilar.

100. Haimes, Yacov Y.; Hall, Warren A. 1974.Multiobjectives in water resource systems analysis:the surrogate worth trade off method. WaterResources Research. 10(4): 615-623.

Discusses the surrogate worth tradeoff (SWT) method asa decision tool for multiobjective water-resourceplanning. The rationale for the use of SWT inmultiobjective planning, as well as the theory and basicformulation of the modes, are discussed. The model isrecommended because it addresses noncommensurableobjectives in a quantitative fashion and iscomputationally feasible.

101. Hipel, Keith W. 1992. Multiple objective decisionmaking in water resources. Water ResourcesBulletin. 28(1): 3-12.

Discusses the role of multiobjective decisionmaking inall phases of water-resources planning, includinggroundwater contamination management, water-qualitymonitoring, water allocation, and reservoir-systemoperation. MCDM techniques are divided into fourgroups depending on whether they are applied tosituations with one or multiple objectives and whetherthey can be used with one or multiple decisionmakers

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(DM). In this classification scheme, most operation-research methods are applicable in single-objective,single-DM situations. MADM can be used when there isa single DM and multiple objectives. Multiple DMsituations are restricted to analysis using team theory andgame theory.

102. Hobbs, Benjamin F.; Chankong, Vira; Hamadeh,Wael; Stakhiv, Eugene Z. 1992. Does choice ofmulticriteria method matter? An experiment inwater resources planning. Water ResourcesResearch. 28(7): 1767-1779.

Four multi-attribute models are applied to hypotheticalwater-supply projects and their appropriateness, ease ofuse, validity, and sensitivity of results are compared. Themethods evaluated are ELECTRE, goal programming(GP), multi-attribute utility (MAUT) functions, andadditive value functions. The latter method was assessedusing three weighting approaches; eight hypotheses weretested. The first three hypotheses concerned theperceptions of users toward the usefulness of the modelsand how easy or difficult they were to use. The fourthpertained to the perceived appropriateness of theapproach; the fifth and sixth addressed both the abilityof the models to predict unaided choices amongalternatives by the users, and the construct validity of therating weights; and the eighth concerned the degree ofsensitivity in the final rankings to differences in whoapplies a particular model and which model is used. GAwas the most understandable method and the one withwhich users were most comfortable, though all fourapproaches were trusted by fewer than half of the users.Generally, users were unconvinced of the utility ofMAUT; none of the four approaches was consistentlypreferred.

103. Kenney, Ralph L.; Wood, Eric F. 1977. Anillustrative example of the use of multiattributetheory for water resource planning. WaterResources Research. 13(4): 705-712.

Proposes the use of multi-attribute utility theory(MAUT) as an alternative to linear programming inwater resources planning, specifically, five alternativeplans for water-resource development in a river basin inHungary. A previous evaluation using ELECTRE didinclude uncertainty in the analysis and specifiedtradeoffs among attributes only implicitly. The fivealternative plans and objectives are described and aprocedure for utility function assessment is given alongwith methods for assessing component utility functionsand scaling factors. A utility value is associated with eachalternative, with the highest value indicating the mostpreferred option. This method of assessing utility

functions also provides a measure of how much better(more preferred) an alternative is relative to others.

104. Needham, Jason T.; Watkins, David W., Jr.; Lund,Jay R. 2000. Linear programming for flood controlin the Iowa and Des Moines rivers. Journal ofWater Resources Planning and Management. May/June: 118-127.

A mixed-integer programming model was used toevaluate the Iowa/Des Moines River Reservoir System’sflood-control operation. The goal was to determinewhether optimizing the operation of the entire reservoirsystem would be an improvement over the optimizationof reservoir subsystems independently. The model usedwas intended to minimize penalties associated withexcessive or inadequate storage, flow, or release from andbetween reservoirs. Formulation of the objectivefunction, the three penalty functions, and the constraintsare discussed and the 10 years with the largest floodevents from 70 years of flow data were chosen as the dataset for analysis. Results indicated that the optimaloperation procedure is controlling each reservoirindependently. Optimization models are particularlyuseful in this context but are “only as good as theirpenalty functions and constraints.”

105. Neely, Walter P.; North, Ronald M.; Fortson, JamesC. 1977. An operational approach to multipleobjective decision making for public waterresources projects using integer goalprogramming. American Journal of AgriculturalEconomics. February: 198-203.

Integer goal programming (GP) was applied to theselection of Tennessee Valley Authority (TVA) waterresources projects. Benefit-cost data for TVA waterprojects from 1965 to 1973 were used to illustrate theusefulness of integer GP as an alternativedecisionmaking tool. Two objectives—economicdevelopment and environmental quality—goal levels,and goal weights for the study are discussed. Several runswere conducted using different weights and levels, withthe original run giving equal weighting to bothobjectives. Comparisons were made between: (1) a runin which the economic objective has a higher goal leveland one in which environmental quality is the highergoal, and (2) a run in which both goal weights and levelsfavor economic development and one where both favorenvironmental quality. The resulting schedules, netpresent value (NPV), and output levels were comparedfor actual TVA project selections, an integer-programming model that maximizes NPV, and theinteger GP model with equal weights and goal levels thatfavor economic development.

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106. Pouwels, H. M.; Wind, H. G.; Witter, V. J. 1995.Multiobjective decision making in integratedwater management. Physics and Chemistry of theEarth. 20(3-4): 221-227.

Examines the usefulness of a general MADM techniquein evaluating alternatives for water management in theNetherlands. Problem formulation, criteria, measures,and the MADM algorithm used in the study aredescribed, and the significant effect of uncertainties onthe ranking of alternatives is discussed.

107. Yoon, Jae-Heung; Shoemaker, Christine A. 1999.Comparison of optimization methods for ground-water bioremediation. Journal of Water ResourcesPlanning and Management. January/February: 54-63.

Compares the computational performance of threeclasses of algorithms in the selection of a cost-effectivepolicy for ground-water bioremediation. Algorithmclasses evaluated include: (1) evolutionary algorithms,specifically, real-coded genetic algorithms (RGA),binary-coded genetic algorithms (BIG), andderandomized evolutionary strategy (DES); (2) directsearch methods, specifically, modified simplex (MSLX),Nelder-Mead simplex (NSLX), and parallel directivesearch (PDS); and (3) derivative-based optimizationmethods, specifically implicit filtering for constrainedoptimization (IFFCO) and a version of SALQR. The useof simulation to generate the impacts of alternativeground-water pumping policies on system characteristicsof interest is described. This simulation model is linkedto the optimization methods to determine optimalbioremediation policy. SALQR consistently performedthe fastest, though no algorithm produced the bestsolution in all cases. The BIGA method was considered apoor choice for use in ground-water bioremediation.

108. Zsuffa, I.; Bogardi, J. J. 1995. Floodplainrestoration by means of water regime control.Physics and Chemistry of the Earth. 20(3-4): 237-243.

ELECTRE II was used to evaluate several restorationtechniques for a flood plain in Hungary. Results of thecase study showed that ELECTRE II and MADM ingeneral are effective in helping decisionmakers choosethe “best compromise” alternative based on specificpreferences.

MCDM Applications to Fisheries109. Mardle, Simon; Pascoe, Sean. 1999. A review of

applications of multiple criteria decision-makingtechniques to fisheries. Marine ResourceEconomics. 14: 41-63.

A comprehensive survey of MCDM that have beenapplied to issues related to fishery management casestudies are categorized by multiple objectiveprogramming (MOP, MADM, and other MODM).MOP includes goal programming, generating methods,and nonlinear MOP. MADM include multiattributeutility theory and the analytic hierarchy process;multilevel programming is included as an “other”MODM. The basic formulation of each model and itsapplication and limitations are discussed. MCDM havegreat potential for improving fisheries managementpolicy because of their flexibility.

110. Önal, Hayri. 1996. Optimum management of ahierarchically exploited access resource: amultilevel optimization approach. AmericanJournal of Agricultural Economics. 78: 448-459.

Presents a multilevel optimization method for choosingthe best policy options for open-access resources that aresubject to hierarchical decision processes. The method isapplied to fisheries management planning, specifically,the perspectives of management authority and individualusers (or user groups) in making decisions concerningshrimp harvests in Texas. A single-level mathematicalprogram formulated to maximize total net revenue fromall fishing activities and a multilevel formulation andpotential solution methods are discussed. The model isapplied to scenarios for both regulated and unregulatedmanagement.

Other Environmental Applications111. Bonano, E. J.; Apostolakis, G. E.; Salter, P. F.;

Ghassemi, A.; Jennings, S. 2000. Application of riskassessment and decision analysis to the evaluation,ranking and selection of environmentalremediation alternatives. Journal of HazardousMaterials. 71: 35-57.

Presents a framework for combining risk assessment anda MADM for the selection of remediation alternatives ata hazardous waste site, and how it would be used toassess the impacts of alternatives, incorporate publicparticipation, educate stakeholders regarding risks, andgenerate good, defensible solutions. Four frameworkcomponents preliminary analysis, decision-analysisimpact assessment and integration, and deliberation ofintegration results are described. Decision analysisentails: 1) structuring the problem as a decisionhierarchy, specifically impact categories, objectives, andperformance measures, and 2) the use of the analytichierarchy process (AHP) and fuzzy theory to determinethe relative importance of each element at each level ofthe hierarchy. Simple pairwise comparisons are used torate impact categories and the objectives within each of

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those categories. Performance measures were evaluatedby AHP and fuzzy logic to define utility functions thatdescribed the level of “goodness” for the range ofpossible performance for each measure. Impactassessment was used to evaluate the performance of eachalternative on each performance measure. Riskassessment was used to convert these values into utilityfunctions so that uncertainties could be captured. Theresult was a ranking of all remediation alternatives foreach stakeholder and a mean ranking for each alternativefrom the group as a whole. The deliberation process wasused to determine how consensus was reached among allstakeholders on a “best” solution.

112. Cooper, W. W.; Hemphill, H.; Huang, Z.; Li, S.;Lelas, V.; Sullivan, D. W. 1996. Survey ofmathematical programming models in airpollution management. European Journal ofOperational Research. 96: 1-35.

Describes current MODM research in air pollutionmanagement to include institutions involved, regulatoryactivity, risk management, and selection of managementgoals and attributes. Basic mathematical programmingapproaches that are surveyed include deterministicprogramming, which is illustrated using linearprogramming and goal programming, and stochasticprogramming, which is illustrated with a chance-constrained programming model. The application ofthese and two additional approaches to problems relatedto management are discussed.

113. Hokkanen, Joonas; Salminen, Pekka. 1997.Choosing a solid waste management system usingmulticriteria decision analysis. European Journal ofOperational Research. 98: 19 36.

ELECTRE III was applied to the selection of amunicipal solid waste-management system in northernFinland. This method was chosen because it is fast andeasy to use, data were imprecise, and numerousdecisionmakers were involved who provided littleinformation on preferences. Results are presented as aranking of the alternatives; the impact of sensitivityanalysis on those rankings is discussed. This technique isuseful for situations in which keeping decisionmakersinformed is a requirement.

114. Tecle, Aregai; Fogel, Martin. 1986. Multiobjectivewastewater management planning in a semiaridregion. Hydrology and Water Resources in Arizonaand the Southwest. 16: 43-61.

ELECTRE and compromise programming were used inthe selection of the “best” design for a wastewater

treatment facility in Nogales, Arizona. The samealternative was selected with both models.

Decision-Support Systems

115. Brack, Christopher L.; Marshall, Peter L. 1996. Atest of knowledge-based forest operationsscheduling procedures. Canadian Journal of ForestResearch. 26: 1193-1202.

Solution outputs were compared for three knowledge-based search routines, two expert systems, linearprogramming (LP), mixed integer programming (IP),and simulation methods that were applied to two forestplantations in Australia. A set of operations scheduleswere compared for each site. An algorithm rated eachalternative on the basis of timber-yield flows, scenicbeauty, stand health, and water quality. The expertsystems and search routines performed well relative tothe IP and simulation techniques. The LP modelgenerated higher timber flows than most of the othermethods; one expert system produced an even higherflow using nonstandard management regimes.Knowledge-based approaches and expert systems do notattempt to create optimal plans, but their flexibility cangenerate good solutions.

116. Gurocak, Elizabeth Reilly; Whittlesey, Norman K.1998. Multiple criteria decisionmaking: a casestudy of the Columbia River salmon recovery plan.Environmental and Resource Economics. 12(4): 479-495.

A salmon recovery plan for the Columbia River was usedas a case study to compare the performance of twoMCDM—simple additive weighting and the interactivemethod—with a fuzzy expert system. Each methodranked alternatives on the basis of five attributes. Themethods are compared on the outputs obtained by thehighest ranked alternatives. Unlike the MCDM solutions,alternatives selected by the fuzzy expert system alwayswere appropriate, that is, decision rules were satisfied.

117. Hong, Hyoo B.; Vogel, Doug R. 1991. Data andmodel management in a generalized MCDM-DSS.Decision Sciences. 22: 1-25.

Describes a method for designing a decision-supportsystem (DSS) that supports an organization informulating and solving multi-criteria problems. Thetypical multi-attribute method of representingalternatives is reviewed. Multi-criteria models arecategorized, and various choice methods are described.Whether compensatory or noncompensatory, the modelsare categorized according to the cognitive demands ondecisionmakers. Choice rules discussed include the

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additive, additive-difference, dominance, conjunctive,disjunctive, lexicographic, and elimination by aspectsmodels. A set of principles for guiding the selection of anappropriate choice rule is suggested, and the process ofexecuting the chosen model is described. The basic DSSarchitecture and prototype model (ISBIS) are described,and two examples of the applicability of the approachare provided.

118. Malczewski, Jacek; Jackson, Marlene. 2000.Multicriteria spatial allocation of educationalresources: an overview. Socio-Economic PlanningSciences. 34: 219-235.

In response to criticism of optimization (MODM)techniques, decision-support systems are being used tofacilitate the allocation of education resources. Typicalallocational issues related to educational resources arereviewed, and basic multiobjective formulation andseveral models that have been applied to allocation issuesare presented. Typical planning attempts use dataenvelope analysis (which is based on a mathematicalprogramming model), parametric programming, andgoal programming. As an alternative approach toeducational resource planning, it is proposed that multi-criteria decision techniques and a geographicinformation system be combined into an interactiveSpatial Decision-Support System (SDSS) to takeadvantage of the visualization capabilities of aninteractive SDSS.

119. Naesset, Erik. 1997. A spatial decision supportsystem for long-term forest management planningby means of linear programming and ageographical information system. ScandinavianJournal of Forest Research. 12: 77-88.

Describes SGIS, a decision-support system thatintegrates a geographic information system and linearprogramming into a strategic planning system. Althoughlimited to areas with no more than 2,000 stands, SGISsimulates the effects of treatment schedules, selects theoptimal schedule, and generates maps and tables. SGISwas applied to a 719-ha, 872-unit forest in southeastNorway to determine the impact of establishingrestricted-use buffers around water bodies with respect tonet present value (NPV) and timber volume. The bufferareas resulted in a reduction in NPV of nearly 7 percentand reduction in timber volume of about 10 percent.Although SGIS is a valuable planning tool, it is notapplicable to large areas nor can it incorporate spatialconstraints into the optimization process.

120. Olson, Craig M.; Orr, Bruce. 1999. Combiningtree growth, fish and wildlife habitat, masswasting, sedimentation, and hydrologic models in

decision analysis and long term forest landplanning. Forest Ecology and Management. 114:339-348.

Discusses the trend toward using MCDM inconjunction with other processes and models to developa more diverse and comprehensive approach to forestmanagement planning. The methodology outlined isintended for landscape-scale management situations andhas been applied to areas ranging in size from 50,000 to230,000 acres. Models that were incorporated into thisplanning process include digital terrain models, site-quality information, vegetation-class data, timber growthand yield models, and a watershed risk index. Linearprogramming was used to maximize the present netvalue of management activities subject to numerousconstraints.

121. Purao, Sandeep; Jain, Hemant K.; Nazareth, DerekL. 1999. Supporting decision making incombinatorially explosive multicriteria situations.Decision Support Systems. 26: 225-247.

Presents a decision support system based on multi-objective and multi-attribute decision theory as aneffective method for addressing problems characterizedby a “combinatorially explosive” number of solutionsand many conflicting criteria. A weakness of threecategories of solution procedures, analytical, geneticalgorithm-based, and heuristic approaches, is theirinability to support decisionmaker learning. The firststep in the proposed decision support system entails a“broad exploration of the search space.” Informationgathered on search space limits and behavior is given tothe decisionmaker to facilitate educated preference inputin later stages. The second step consists of deep probesinto promising search space regions. The decisionmakeris guided in an iterative and systematic process ofexploring alternatives, steering the direction of the searchby the specification of his or her preferences. The modelprovides information about unexplored regions of thedecision space to the decisionmaker by assessing thelikelihood of improving on the current solution’s levelsof attainment for each criterion. When applied to aclient/server architecture problem, this method placesonly moderate demands on the decisionmaker andquantifies the risk of stopping the search process at anypoint.

122. Rauscher, H. Michael. 1999. Ecosystemmanagement decision support for federal forests inthe United States: a review. Forest Ecology andManagement. 114: 173 197.

Presents a generic decision-support system (DDS) forecosystem management on federal forests. The typical

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adaptive management process as it is applied toecosystem management is discussed and 33 ecosystemmanagement DSS are compared. Decision methods(MODM) are discussed as a single component in amuch larger planning process.

123. Tecle, Aregai; Shrestha, Bijaya P.; Duckstein,Lucien. 1998. A multiobjective decision supportsystem for multiresource forest management.Group Decision and Negotiation. 7: 23-40.

Describes FORMDSS, an interactive, multiobjectivedecision support system that incorporates bothcompromise programming and cooperative game theoryinto a single tool for resource management. Data arefrom a pine forest in north-central Arizona managed formultiple objectives. Five objectives, each of which isbased on a single variable—square feet of tree basal areaper acre—are intended to represent the views of adifferent interest group or decisionmaker. For eachobjective, a graph specifies the relationship between basalarea and a particular resource goal, and indicates thelevel of utility that would be achieved by a groupadvocating the maximization of that resource. Thisrelationship is described mathematically as a time-invariant continuous function. Tradeoffs that occuracross different basal-area densities are demonstrated for

both MCDM. The objectives were given equal weightsto identify a narrow range of basal-area densities that all(hypothetical) decisionmakers found satisfactory.FORMDSS can handle any number of objectivefunctions, allows for easy modification of preferencestructures and other model parameters, and facilitatesunderstanding through graphical representation ofmodel inputs and outputs.

124. Varma, Vive K.; Ferguson, Ian; Wild, Ian. 2000.Decision support system for the sustainable forestmanagement. Forest Ecology and Management. 128:49-55.

Describes a decision support system for forestmanagement that combines geographic informationsystems (GIS), a heuristic, and linear programming (LP)in a flexible model that addresses uncertainty andmaximizes the utility derived from the productsgenerated through alternative management plans. LPgenerates the optimal land allocation solution and thenthe spatial distribution of these uses is solved with aheuristic algorithm. Although this heuristic does notguarantee that the optimal utility level generated in theLP model will be attained, this approach should beeffective when sustainability in forest management is anissue.

26

Allen, Julia28

Anderson, David J.25

Apostolakis, G. E.111

Barahona, Francisco58

Barber, Klaus37

Bare, B. Bruce1, 25, 29, 32, 70

Belaineh, Getachew90

Bell, Enoch F. 2

Bella, Aimee91

Bender, H. Wise83

Bettinger, Pete60, 61, 62, 63

Bevers, Michael45

Bodie, J. Douglas69

Bogardi, J. J.108

Bojorquez-Tapia, L. A.88

Bonano, E. J.111

Borges, Jose G.49

Bos, Jan64

Boscolo, M.7, 30

Boston, Kevin60, 62

Brack, Christopher L.115

Briggs, David G.1

Brodie, J. Douglas38, 69, 74, 75

Bruciamacchie, M.16

Bullard, Steven H.65

Buongiorno, J.3, 4, 7, 8, 9, 12, 16, 17, 26,30, 31, 33, 34

Campbell, Gene E.32

Cea, Christian36

Center, Calum J.15

Chang, Ni-Bin92

Chang, S. J.17

Chankong, Vira102

Chevalier, P.42

Cholaky, Alejandro39

Choo, Eng U.77

Chung, Joosang14

Church, Richard L.37, 40, 52, 53, 72

Cooper, W. W.112

da Conceicao, Cunha93

Daellenbach, H. G.41

Dahir, S.8

Das, Pransanta94

de Kluyver, C. A.41

de Steiguer, J.E.18

Dent, J. B.21

Duckstein, Lucien24, 86, 91, 95, 96, 98, 99, 123

Dyer, A. Allen87

Easley, Robert F.78

Epstein, R.42

Epstein, Rafael58, 59

Evans, James R.76

Faaland, Bruce H.70

Ferguson, Ian124

Flug, Marshall97

Fogel, Martin M.86, 114

Fortson, James C.105

Gabarro, J.42

Garcia, Oscar5

Gershon, Mark79, 98, 99

Ghassemi, A.111

Gilless, J. K.4

Guinard, Monique43, 72

Gurocak, E. R.116

Haight, Robert G.44

Haimes, Yacov Y.94, 100

Hajkowicz, Stefan A.80

Hall, Warren A.100

Hamadeh, Wael102

Author Index

27

Hemphill, H.112

Hipel, Keith W.101

Hobbs, Benjamin F.102

Hof, John45, 46, 47, 48

Hoganson, Howard49

Hokkanen, Joonas82, 113

Hong, Hyoo B.117

Hotvedt, James E.19

Houllier, F.16

Howard, Andrew F.81

Huang, Z.112

Hughes, Trevor C.90

Ingram, D.9

Jackson, Marlene118

Jain, Hemant K.121

Jamnick, Mark S.10

Jennings, S.111

Jofre, Alejandro36

Johnson, Norman11, 61, 63

Jones, J. Greg50, 73

Joyce, Linda46, 47

Julio, Berbel20

Kangas, Jyrki66, 85

Keeney, Ralph L.103

Kirby, Malcom W.50

Klemperer, W. David65

Kolbe, A.31

Korhonen, Pekka24

Kowero, G.21

Lahdelma, Risto82

Lancia, Richard14

Laszlo, David95

Lelas, V.112

Lennartz, Mike14

Li, S.112

Lin, C.R.8, 26

Lockwood, Carey67

Lu, H.C.8, 12

Lund, Jay R.104

Magendzo, Adrian73

Magendzo, Ariel73

Malchuk, Daniel73

Malczewski, Jacek88, 118

Manley, Bruce59

Mardle, Simon109

Marshall, Peter L.115

Martin, W.E.83

McAniff, Richard98

McDonald, Geoff T.80

Meacham, Mary73

Mendoza, Guillermo A.29, 32, 89

Meneghin, Bruce J.50

Moore, Tom67

Moreno-Sanchez, R.88

Murphy, Glen59

Murphy, James L.13

Murray, Alan T.37, 40, 51, 52, 53, 68, 72

Naesset, Erik119

Nazareth, Derek L.121

Needham, Jason T.104

Neely, Walter P.105

Nelson, John38, 69

Nhantumbo, I.21

Nieto, E.42

Nieuwenhuis, Maarten6

North, Ronald M.105

O’Hara, Anthony70

Olson, Craig M.120

Omi, Philip N.13

28

Onal, Hayri110

Ongay-Delhumeau, E.88

Opricovic, Serafim96

Orr, Bruce120

Pascoe, Sean109

Peralta, Richard C.90

Perlack, R. D.35

Peyron, J. L.16

Pouwels, H. M.106

Prato, T.84

Pukkala, Timo66, 85

Purao, Sandeep121

Puumalainen, Janna27

Raphael, Martin G.48

Rauscher, H. Michael122

ReVelle, Charles55, 56, 57

Roise, Joseph P.1, 14, 54

Rowse, John15

Ryu, Choonho43

Salminen, Pekka82, 113

Salter, P. F.111

Schoner, Bertram77

Schreuder, Gerard F.1

Schuler, Albert T.23

Schulte, B.33

Scott, John F.97

Seitz, Heather L. H.97

Sessions, John38, 60, 61, 62, 63, 75

Sherali, Hanif D.65

Shields, D.J.83

Shoemaker, Christine A.107

Shrestha, Bijaya P.123

Smith, Phil N.80

Snyder, Stephanie55, 56, 57

Sousa, Joaquim93

Sousa, Maris93

Spielberg, Kurt43

Sprouse, William89

Stakhiv, Eugene Z.102

Steuer, Ralph E.23

Sullivan, D. W.112

Szidarovsky, Ferenc91

Tecle, Aregai24, 86, 114, 123

Tedder, Phillip L.11

Teeter, Lawrence D.87

Travis, Laurel E.44

Valacich, Joseph S.78

Van Deusen, Paul C.71

Van Kooten, G. C.22

Varma, Vive K.124

Venkataramanan, M. A.78

Vogel, Doug R.117

Volin, V.C.34

Watkins, David W., Jr.104

Wedley, William77

Weintraub, Andres P.39, 40, 42, 58, 59, 72, 73

Wen, C. G.92

Wensel, Lee C.13

Whittlesey, N. K.116

Whyte, G. D.41

Wild, Ian124

Willis, C. E.35

Wind, H.G.106

Witter, V. J.106

Wood, Eric F.103

Wu, S. L.92

Yoon, Jae-Heung107

Yoshimoto, Atsushi74, 75

Zamora, Richardo20

Zanakis, Stelios H.76

Zsuffa, I.108

29

Glossary0 — 1 Integer Programming (see Binary IntegerProgramming).

1 opt, 2 opt — concepts in heuristic timber harvestscheduling. With 1-opt moves, only one attribute of onedecision choice is altered, i.e., a unit is removed from theharvesting schedule. In 2-opt moves, that attribute ischanged for two decision choices simultaneously, i.e.,one unit is added to the harvest schedule while anotheris removed.

Adjacency Constraints — constraints in mathematicalprogramming that control the occurrence of spatiallyrelated activities, e.g., the harvesting of timber inadjacent forest plots.

Algorithm — in mathematics, any computationalprocedure (see Simplex Method as an example).

Analytic Hierarchical Process (AHP) — a decisionmethod in which a complex problem is structured as ahierarchy involving goals, criteria, objectives andalternatives; pair-wise comparisons of criteria andalternatives result in the specification of a preferredsolution.

Area-Restricted Model (ARM) — a concept in timberharvest modeling with adjacency constraints. Ifmanagement units are significantly smaller than the arealimit of the adjacency constraint, then harvest ofadjacent units does not necessarily violate the constraintsand the ARM is used (see URM).

Binary Coded Genetic Algorithm (BIGA). See GeneticAlgorithm and 0 - 1 Integer Programming.

Binary Integer Programming — a form of integerprogramming in which the values of the decisionvariables are restricted to 1 or 0.

Branch and Bound Algorithm — a technique that usesan efficient search algorithm for solving integerprogramming problems.

Bridging Analysis Models (BAM) — a method fordecomposing optimal strategic-level solutions intooptimal tactical-level plans on forests.

Compromise Programming (CP) — a solutiontechnique that uses distance metrics to weight variousobjectives to account for their different importance tothe decisionmaker. The alternative with the lowest

summed deviation from the objectives is designated asthe “best” solution.

Constraints — limits placed on and thus defining aproblem’s solution space, usually in the form ofequations stated as mathematical equalities orinequalities.

Cooperative Game Theory — a form of game theory inwhich the participants cooperate to find a solution asopposed to noncooperative solutions, i.e., participantscompete against each other.

Decision Support Systems (DSS) — a class ofinteractive computer-based systems and subsystems thathelp decisionmakers use data, documents, knowledge,and/or models to identify and solve problems and makedecisions.

Dominated Solutions (see Inferior Solutions).

Dynamic Programming (DP) — a problem-solvingapproach that allows a large problem to be broken into aseries of smaller problems or stages. The solution of allthe smaller individual problems results in an optimalsolution to the large problem.

Economically Inefficient (efficient) Solutions —solutions to economic cost-benefit analyses where costsare greater (less) than benefits.

ELECTRE, ELECTRE 1, 2, 3 — MADM techniquesthat facilitate decisionmaking by reducing the number offeasible alternatives to be considered.

Feasible Solution — A solution that satisfies all of thespecified constraints (see Infeasible Solution).

FORMDSS — an interactive, multiobjective decisionsupport system that incorporates both compromiseprogramming and cooperative game theory into a singletool for resource management.

FORPLAN — FORest PLANning model; a linearprogramming approach used by the USDA ForestService for land management planning.

Four Color Theorem — related to timber harvestscheduling with adjacency constraints. For problems thatrequire adjacent units to be harvested no less than aspecified number of years apart (the exclusion period),this theorem implies that a feasible solution is possible solong as the project period length divided by theexclusion period length is less than or equal to four. The

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theorem name is derived from the four colors used inmapmaking, for example, to distinguish differentpolitical states on a map.

Fuzzy Logic — an approach to computing based ondegrees of truth rather than the usual “true or false” (i.e.,1 or 0). Includes 0 and 1 as extreme cases of truth, butalso the various states of truth in between so that, forexample, the result of a comparison between two thingscould be not “tall” or “short” but “ .38 of tallness.”

Fuzzy Programming — mathematical programmingthat uses fuzzy logic (see Fuzzy Logic).

Generating Methods — Techniques for identifyingtradeoffs that are necessary among each of the decisionalternatives. This information is presented to thedecisionmaker who selects the most preferred option.

Genetic Algorithm (GA) — a heuristic solutionalgorithm in which the first step is generating a“population” of random solutions that are represented as“strings” composed of binary values for each decisionvariable. Each value corresponds to an “allele” on thestring, which represents DNA; hence the name.

Geographic Information System (GIS) — a computersystem for entering, processing, analyzing, anddisplaying spatial data and information, often a map-likeformat.

Goal Programming (GP) — a technique for solvingmultiobjective decision problems within the frameworkof linear programming. Target values are established for aset of separate goals and the programming objective is tominimize the collective deviation from these targets.

HERO — a utility-based heuristic method foraddressing harvest scheduling problems that explicitlyconsiders biodiversity.

Heuristic Techniques — methods for problem solvingthrough experimentation and especially trial and error.They are typically used for computationally hard-to-solve problems and seek a compromise between a quickfeasible solution and a feasible solution that is optimal.

Hierarchy — a structure for a decision problem usingvarious levels consisting of goals, criteria, objectives, anddecision alternatives (see AHP).

Infeasible Solution — occurs when two or moreconstraints have been specified that cannot be satisfied

simultaneously, for example, simultaneous satisfaction ofx> 100 and x< 75 is infeasible.

Inferior Solutions — solutions that are not Paretooptimal; also known as locally efficient solutions ordominated solutions.

Integer Programming (IP) — a problem-solvingapproach like linear programming except that decisionvariables are integers rather than continuous values.

Integrated Resource Planning Model (IRPM) — aninteger programming planning model used by theUSDA Forest Service.

Lagrangian Relaxation — a mathematicalprogramming technique for performing constrainedoptimization through the introduction of Lagrangianmultipliers—which are arbitrary non-zero constraints—to the constraints.

Lexicographic Goal Programming — a technique thatassigns absolute priorities to the goals. Also calledpreemptive GP, this approach satisfies the multipleobjectives sequentially in the order established by thepriorities.

Linear Programming (LP) — a mathematical problem-solving approach that entails maximization orminimization of a single linear objective function subjectto multiple linear constraints.

MAXMIN Model — attempts to maximize theminimum payoff; generally said to be a bettingpessimist’s strategy. Some argue that MAXMIN finds asocially “just” solution in the sense that it identifies thebest possible outcome for members of society who aremost needy.

Metropolis Algorithm (MA) — a timber-harvestscheduling algorithm related to the Monte Carloheuristic technique.

Mixed Integer Program — a mathematical programthat uses both integer and continuous decision variable.

Model I Formulation, Model II Formulation — twomethods for defining decision variables in a timberharvest scheduling problem. With Model I, decisionvariables are the same for both original and regeneratedstands. With Model II, different decision variables aredefined for the original and the regenerated stands.

31

Modeling to Generate Alternatives (MGA) — the useof mathematical programming models to generate aseries of possible alternative decision choices from whichthe decisionmaker chooses the preferred alternative.

Monte Carlo Heuristic Techniques — heuristicsolution methods using simulations analogous to theprobabilistic outcomes of roulette played in the casinosof Monte Carlo.

Monte Carlo Integer Programming — a heuristicsolution method for integer programs involving the useof probabilistic inputs generated by a Monte Carloprocess.

Multi-Attribute Decision Models (MADM) — asubdivision of MCDM, MADM support the selectionof the “best” decision alternative from among severalpossibilities. Examples of MADM methods include theAnalytic Hierarchy Process and Multi-Attribute UtilityTheory.

Multi-Attribute Utility Theory (MAUT) — assumesthat an individual can select among obtainablealternatives in a way that maximizes the amount ofsatisfaction he/she derives from that choice. This theoryassumes that individuals are aware of the alternativesavailable to them and are capable of evaluating thosealternatives.

Multi-Criteria Decision Models (MCDM) — refers toa variety of quantitative techniques used to facilitatedecisions involving multiple, competing objectives orgoals. MCDM were first developed for military strategicdecisionmaking but have been expanded to include suchdiverse fields as financial planning, real estateinvestment, reservoir control, water distribution, solidwaste management, energy planning, manufacturing,and forest management. Often subdivided into MODM(Multi-Objective Decision Models) and MADM (Multi-Attribute Decision Models).

Multi-Objective Decision Model (MODM) — asubdivision of MCDM, MODM support the design ofsuperior decision alternatives; methods include linear,goal, and integer programming.

Multi-Objective Programming (MOP) — programsthat require the simultaneous optimization of more thanone objective function. This method optimizes eachseparate objective function followed by an interactivesearch for a compromise solution that is Pareto optimal;also called Multi-Objective Linear Programming.

Network Analysis — a graphical description of adecision problem in terms of nodes and interconnectedarcs enabling solutions to problems related totransportation, information systems, and projectscheduling.

Non-Inferior Set Estimation (NISE) — a multi-objective programming solution algorithm that usesrepeated linear programming solutions to generate anestimate of a non-inferior set.

Non-convex Decision Space — a decision space orchoice not involving a decreasing rate of technicalsubstitution, i.e., not bowed toward the origin.

Non-Dominated Solutions (see Non-InferiorSolutions).

Non-Inferior Solutions — solutions that are Paretooptimal; also known as globally efficient or non-dominated solutions.

Non-linear Programming — an alternative to linearprogramming that uses a non-linear objective function.

Objective Function — an equation that expressesmathematically the goal of a decision problem/ usuallystated as a maximization of minimization problem.

Optimal Solution — a best solution, i.e., theattainment of a maximum or minimum value subject tospecified constraints.

Pareto Optimal — a feasible solution such that no otherpossible solution is superior to it.

PARETO RACE — a type of decision support systemthat enables a decisionmaker to freely search the efficientfrontier of a multiple objective quadratic-linearprogramming problem by controlling the speed anddirection of motion.

Programming — a general term applied to a host ofmathematical planning techniques, including linear,goal, integer, and non-linear programming.

Recursive Dynamic Programming — a solutionmethod by which a large problem is divided into smallerproblems or stages; each of the smaller problems issolved in sequence, feeding into the next higher stage.

SGIS — a decision support system that integrates ageographic information system and linear programminginto a single planning system.

32

SHARe Model — a harvest planning model that usesspatial constraints but also allows temporal managementconsiderations.

Shortest Path Network Flow Model — a networkmodel by which the optimal problem solution is foundby the shortest path between any pair of nodes in thenetwork.

Simple Additive Weighting (SAW) — an MCDMmethod.

Simplex Method — an algebraic procedure for solvinglinear programming problems.

Simulated Annealing (SA) — a heuristic solutionmethod based on simulation of the material temperingprocess know as annealing.

Simulation Modeling — a technique in whichcomputers typically are used to model the operation of acomplex system by abstracting, simplifying, and hencesimulating the true system.

SNAP 11+ — a harvest scheduling program that uses aninteger programming formulation and a heuristicsolution algorithm.

STEM — a Modeling to Generate Alternativestechnique for forest planning applications.

Stochastic Programming — a form of mathematicalprogramming in which the inputs are uncertain andsubject to variation; this contrasts with deterministic

models in which the inputs are certain and not subject tovariation.

Successive Approximation Linear QuadraticRegulator (SALQR) — a software program that hasbeen used for optimization problems in which non-linear simulation equations are made linear in theoptimization step.

Surrogate Worth Trade-Off (SWT) — a utility-basedalgorithm.

TABU search — a heuristic solution method that reliesupon near-neighbor solutions that can be reacheddirectly from an initial solution by a single move, i.e.,adding a unit, removing a unit, or exchanging two units.

Trigger Constraints — constraints of mathematicalprogramming problems invoked or “triggered” bypredetermined conditions.

Unit Restrictive Model (URM) — refers to timberharvesting with adjacency constraints. Applied whenmanagement units are so large that the harvest of twoadjacent units would necessarily violate adjacencyconstraints (see ARM).

Vector — in mathematics, a [1 x n] matrix.

Weighting Methods — used to indicate the relativeimportance of the evaluation criteria to thedecisionmaker. Examples of weighting methods are fixedpoint scoring, rating, ordinal ranking, graphicalweighting, and paired comparisons.

Printed on Recycled Paper

de Steiguer, J. E.; Liberti, Leslie; Schuler, Albert; Hansen, Bruce. 2003. Multi-criteria decision models for forestry and natural resources management:an annotated bibliography. Gen. Tech. Rep. NE-307. Newtown Square, PA:U.S. Department of Agriculture, Forest Service, Northeastern Research Station.32 p.

Foresters and natural resource managers must balance conflicting objectives whendeveloping land-management plans. Conflicts may encompass economic,environmental, social, cultural, technical, and aesthetic objectives. Selecting thebest combination of management uses from numerous objectives is difficult andchallenging. Multi-Criteria Decision Models (MCDM) provide a systematic means forcomparing tradeoffs and selecting alternatives that best satisfy the decisionmaker’sobjectives. In recent years, the use of MCDM in forestry and natural resourcesmanagement has generated a substantial body of literature. This annotatedbibliography includes 124 important references ranging from theoretical studies toreal-world applications of MCDM.

Keywords: linear programming, goal programming, mathematical programming,dynamic programming, hierarchical programming, heuristics

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