United States

Department of

Agriculture

Forest Service

Northeastern

Research Station

General Technical

Report NE-307

Multi-Criteria Decision Models

for Forestry and Natural

Resources Management:

An Annotated Bibliography

J. E. de Steiguer

Leslie Liberti

Albert Schuler

Bruce Hansen
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Abstract

Foresters and natural resource managers must balance conflicting objectives when

developing land-management plans. Conflicts may encompass economic,

environmental, social, cultural, technical, and aesthetic objectives. Selecting the

best combination of management uses from numerous objectives is difficult and

challenging. Multi-Criteria Decision Models (MCDM) provide a systematic means for

comparing tradeoffs and selecting alternatives that best 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 water distribution. In recent years, the use of MCDM

in forestry and natural resources management has generated a substantial body of

literature. This annotated bibliography includes 124 important references ranging

from theoretical studies to real-world applications of MCDM.

The Authors

J. E. DE STEIGUER is professor of natural resource economics, policy, and

management in the School of Renewable Natural Resources at the University of

Arizona. Previously, he was a researcher with the USDA Forest Service. He holds a

Ph.D. degree in forestry economics and policy from Texas A&M University.

LESLIE LIBERTI is a Ph.D. candidate in the School of Renewable Natural

Resources at the University of Arizona.

ALBERT SCHULER is a research economist with the USDA Forest Service’s

Northeastern Research Station at Princeton, West Virginia. He received a

B.S.degree in forest management from the New York State College of Forestry at

Syracuse University in 1966 and a Ph.D. degree in forest economics and marketing

from Iowa State University in 1975. He is currently analyzing markets for

engineered wood products and assessing the competitive position of the domestic

furniture industry.

BRUCE HANSEN is an economist and Project Leader with the Northeastern

Research Station at Princeton, West Virgina. He received a B.S. degree in

economics from Concord College, Athens, West Virginia, and M.B.A. and Ph.D.

degrees in wood science and forest products marketing from Virginia Polytechnic

Institute and State University at Blacksburg, Virginia. He joined the Forest Service

in 1968.

Manuscript received for publication 12 November 2002
Contents

Introduction ................................................................................................................ 1

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

MODM Applications in Forestry

General ................................................................................................................... 3

Linear Programming ............................................................................................... 3

Goal Programming ................................................................................................. 4

Interactive Mathematical Programming .................................................................. 6

Dynamic Programming ............................................................................................... 6

Modeling to Generate Alternatives.......................................................................... 6

Hierarchical Planning ............................................................................................. 8

Improving Spatial Capabilities ................................................................................ 8

Heuristic Methods ................................................................................................ 13

MADM Applications in Forestry and Land Management .......................................... 16

Combined MODM/MADM Applications ................................................................ 18

MCDM Applications to Water Resources .................................................................. 19

MCDM Applications to Fisheries .............................................................................. 22

Other Environmental Applications ............................................................................ 22

Decision-Support Systems ......................................................................................... 23

Author Index ............................................................................................................. 26

Glossary ..................................................................................................................... 29
1

Introduction

Foresters and natural resource managers must balance conflicting objectives when developing

land-management plans. Conflicts may encompass economic, environmental, social, cultural,

technical and aesthetic objectives.1

 Selecting the best combination of management uses from

numerous objectives is difficult and challenging. Fortunately, Multi-Criteria Decision Models

(MCDM) provide a systematic means for comparing tradeoffs and selecting alternatives that

best 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 water

distribution. In recent years, the use of MCDM in forestry and natural resources management

has generated a substantial body of literature. This annotated bibliography includes 124

important references ranging from theoretical studies to real-world applications of MCDM.

Overview of MCDM in Forestry

MCDM refers to quantitative techniques used to facilitate decisions that encompass competing

management objectives. Because they comprise numerous analytical methods, MCDM often

are classified for convenience as Multi-Objective Decision Models (MODM) or MultiAttribute Decision Models (MADM). MODM support the design of a range of separate

decision alternative1

 techniques such as linear, goal, and integer programming. MADM support

the “best” decision from among several alternatives using the Analytic Hierarchy Process and

Multi-Attribute Utility Theory.

Forestry applications of MODM are concerned primarily with mathematical optimization

techniques. The literature on the use of MODM for forest management can be divided into

four developmental phases. Early studies, or Phase I, of MODM use in forestry explored

“modeling to generate alternatives.” Those who supported this approach believed that

mathematical programming could be used to construct a range of possible decision solutions.

These alternatives would be presented to decisionmakers, who would then select the alternative

that best met the established criteria. Research on generating alternatives was especially popular

during the 1980’s, a period that coincided with the introduction of the linear programming

model FORPLAN by the USDA Forest Service. FORPLAN was designed to meet the longterm 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 tactical

forest management planning. Tactical- or stand-level planning requires significantly more detail

and data than strategic forest-level planning. Analysts found that FORPLAN could not

accommodate 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. A

related branch of research attempted to find effective ways to bridge tactical and strategic

planning.

Phase III was characterized by efforts to incorporate spatial constraints into MODM. These

studies, which accounted for the major portion of MODM research during the 1990’s, resulted

from FORPLAN’s earlier ineffectiveness with respect to spatial concerns, particularly those

relating to wildlife habitat. This research addressed the need for more complex spatial

considerations, for example, requirements for the regrowth of vegetation prior to subsequent

reharvesting, i.e., “green-up constraint,” edge effects, and habitat fragmentation.

1

De Montis, Andrea; De Toro, Pasquale; Droste-Franke, Bert; Ines, Omann; Stagl, Sigrid. 2000. Criteria

for quality assessment of MCDA—methods. In: 3rd biennial conference of the European Society for

Ecological Research; 2000 May 3-6; Vienna, Austria. Vienna, Austria: International Institute for

Ecological Economics. [http://www.kfunigraz.ac.at]
2

The fourth and current phase of research concerns heuristic methods, that is, techniques for

problem solving through experimentation and trial and error. Interest in heuristics was

developed after analysts realized that spatial programming formulations for real-world

management situations were difficult if not impossible to apply with conventional linear

programming algorithms, i.e., they typically required enormous computing capability.

Supporters of heuristic methods contend that they can solve large, complex problems efficiently

while approximating optimal solutions.

Proponents generally believe that MODM have been useful for natural resource planning and

management. Their research has focused on ways to modify MODM to improve realism and

efficiency. 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 (and

perhaps by many Forest Service employees). To many of these groups, models such as

FORPLAN 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 and

evaluating public preferences. These models already have been used extensively in military,

corporate, and medical applications. However, few studies have applied MADM to forestry or

other natural resource situations. The Analytical Hierarchy Process within MADM is receiving

special attention for natural resource applications. It is not known whether such techniques can

improve public involvement, collaboration, and acceptance of land management plans—or the

planning process itself. To capture the benefits of both MADM and MODM, some researchers

have tried to combine them. Another recent trend has been to combine MADM and/or

MODM methods with Decision-Support Systems.

Despite many years of effort, there is still much to do. Only about half of the citations in this

bibliography 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 decision

situations; relatively few applied MODM to actual working forests. In fact, few studies were

designed 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 water

resources, fisheries, and other environmental entities, and to decision-support systems. The

bibliography includes an author index and a glossary.
3

MODM Applications in Forestry

General

1. Bare, B. Bruce; Briggs, David G.; Roise, Joseph P.;

Schreuder, Gerard F. 1984. A survey of systems

analysis models in forestry and the forest products

industries. European Journal of Operational

Research. 18(1): 1-18.

A comprehensive survey of the range of problems related

to forestry and the forest products industry that have

been addressed using decision models such as linear,

dynamic, goal, mixed-integer, and nonlinear

programming. Applications are divided into forest

management (timber production), forest products,

product yield, and process applications. Linear

programming models have been used to facilitate nursery

operations and seedling allocation for individual forest;

optimize the cutting of trees to maximize product

output and match that output with demand; integrate

forest management, transportation layout, and product

allocation for private wood-products companies; allocate

fire control or harvesting equipment; and minimize the

loss of material in paper-trimming processes. Citations

for more than 70 systems analysis and forestry references

are included.

2. Bell, Enoch F. 1977. Mathematical programming in

forestry. Journal of Forestry. 75(6): 317-319.

Describes linear programming (LP) that is illustrated

using straightforward terminology. Each of the

assumptions required by LP are reviewed, and

limitations that result from these assumptions are

discussed. The author suggests that LP often is used in

situations where the assumptions of the model are not

met

3. Buongiorno, J. 2001. Quantifying the implications

of transformation from even to uneven-aged forest

stands. Forest Ecology and Management. 151: 121-

132.

Discusses the role of optimization and simulation to

achieve multiple economic and ecological objectives in

choosing a target stand, and in converting an initial

stand to this target.

4. Buongiorno, J.; Gilless, J. K. 2003. Decision

methods for forest resource management. San

Diego, CA: Academic Press. 439 p.

Introduces multi-criteria decision models for forestry

and natural resource management, including linear

programming models with economic and environmental

objectives in even-aged forests. Also discusses the

economic and environmental management of unevenaged forests, introducing a MAXMIN criterion of

diversity, multiple-objective management with goal

programming, and simulation models of even or

uneven-aged forests, to include ecological and economic

criteria. Reviews the use of Markov models to address

uncertainty in managing for landscape diversity,

biodiversity, and financial returns.

5. Garcia, Oscar. 1990. Linear programming and

related approaches in forest planning. New

Zealand Journal of Forestry Science. 20(3): 307-331.

Single-use forest planning (managing for timber) entails

decisions regarding what management treatments and

which spatial and temporal patterns of harvesting will

best achieve output objectives. Presents several

alternative formulations for the forest planning model,

which is divided into the forestry model and the

utilization model. The first is related to the physical

impacts of various management treatments and the

response of the forest to these actions. Three methods for

formulating this model are discussed: a state space

approach and the traditional Model I and Model II

classifications.

6. Nieuwenhuis, Maarten. 1989. Operations research

in forestry. Irish Forestry. 46(1): 51-58.

Discusses the general characteristics of the six most

commonly used formulations in forest applications.

These include linear, integer, goal, and dynamic

programming, network analysis, and simulation. The

major uses of each method are included, as are references

for each method in forestry/forest-industry applications.

Linear Programming

7. Boscolo, M.; Buongiorno, J. 1997. Managing a

tropical rainforest for timber, carbon storage and

tree diversity. Commonwealth Forestry Review.

76(4): 246-254.

Discusses the use of linear programming and MAXMIN

methods to analyze tradeoffs among various objectives in

managing a rain forest for timber, carbon storage, and

tree diversity.

8. Buongiorno, J.; Dahir, S.; Lu, H. C.; Lin. C. R. 1994.

Tree size diversity and economic returns in

uneven-aged forest stands. Forest Science. 40(1): 83-

103.

Discussions of linear and nonlinear programming

models illustrate tradeoffs related to
4

diversity of stand structure (tree size), and economic

returns in managing northern hardwoods.

9. Ingram, D.; Buongiorno, J. 1996. Income and

diversity tradeoffs from management of mixed

lowland dipterocarps in Malaysia. Journal of

Tropical Forest Science. 9(2): 242-270.

Linear programming with MAXMIN criteria was

applied to determine the short- and long-term effects of

current management regimes on economic returns and

diversity of tree species and size. Criteria included the

Shannon-Wiener index of diversity, minimum number

of trees by species and size, soil rent, forest value,

internal rate of return, and annual yield. Regimes were

compared in the steady state (long term) and during

convergence (short term) of stands with different initial

conditions.

10. Jamnick, Mark S. 1990. A comparison of

FORMAN and linear programming approaches to

timber harvest scheduling. Canadian Journal of

Forest Research. 20: 1351-1360.

Timber harvest scheduling in the United States is

accomplished primarily with linear programming (LP)

or binary search. In Canada, simulation often is used to

create harvest schedules. Harvest schedules produced

using a Model I LP approach were compared with those

generated by simulation (the FORMAN model). The

models were applied to two hypothetical forests, each

about 130,000 ha in size, over sixteen 5-year planning

periods. The only harvesting activity allowed was

softwood clearcutting and harvest could be followed by

natural regeneration or one of three replanting options.

11. Johnson, K. Norman; Tedder, Philip L. 1983. Linear

programming vs. binary search in period harvest

level calculation. Forest Science. 29(3): 569-581.

Compares two general categories of procedures that can

be used to determine periodic harvest levels: binary

search and linear programming, highlighting the

advantages of each approach. The search for a method to

combine the best features of each procedure is discussed.

12. Lu, H. C.; Buongiorno, J. 1993. Long- and shortterm effects of alternative cutting regimes and

economic returns and ecological diversity in

mixed-species forests. Forest Ecology and

Management. 58: 173-192.

Six cutting regimes were compared by linear

programming with respect to soil rent and ecological

diversity obtained in the short and long term in unevenaged northern hardwood forests.

13. Omi, Philip N.; Murphy, James L.; Wensel, Lee C.

1981. A linear programming model for wildland

fuel management planning. Forest Science. 27(1):

81-94.

Linear programming (LP) was applied to optimize the

timestream of fuel management investments in forest

watersheds in southern California. Historical approaches

for evaluating fire management planning are outlined,

limitations of these approaches are discussed, and the

importance of minimizing costs through optimization is

stressed. An LP formulation also is presented that

maximizes reduction in a “wildfire damage-potential”

index. LP provided general guidelines for fuel

management planning but was inappropriate for tacticallevel, site-specific evaluations.

14. Roise, Joseph; Chung, Joosang; Lancia, Richard;

Lennartz, Mike. 1990. Red cockaded woodpecker

habitat and timber management: production

possibilities. Southern Journal of Applied Forestry.

14(1): 6-12.

Examines alternative management strategies using

multiple-objective linear programming to mitigate the

negative effects of financial timber rotations on redcockaded woodpeckers. The financial consequences of

providing cavity trees and protected areas also are

examined.

15. Rowse, John; Center, Calum J. 1998. Forest

harvesting to optimize timber production and

water runoff. Socio-Economic Planning Sciences.

32(4): 277-293.

Linear programming (LP) was used to assess the optimal

size and shape of harvest blocks to maximize net present

value from timber production and watershed runoff.

Model parameters, decision variables, objective function,

and constraints are detailed. The application of LP to a

section of the Canadian Crow-Bow Forest over twentyfive 10-year planning periods is discussed. Eight

different scenarios are described.

Goal Programming

16. Buongiorno, J.; Peyron, J. L.; Houllier, F.;

Bruciamacchie, M. 1995. Growth and management

of mixed-species, uneven-aged forests in the

French Jura: implications for economic returns

and tree diversity. Forest Science. 41(3): 397-429.

Linear and goal programming were used to find

management regimes to achieve various objectives of

diversity and economic efficiency. Criteria were

Shannon’s index of tree diversity by species and size,
5

minimum number of trees by species-size class, basal

area, present value of harvests, and rate of return on

capital.

17. Chang, S. J.; Buongiorno, J. 1981. A programming

model for multiple use forestry. Journal of

Environmental Management. 13: 45-58.

Goal programming and input-output analysis for

multiple-use planning on public forests were combined

to specify goal levels, allow experimentation with

management intensity and management priorities, and

determine tradeoffs between management activities.

18. de Steiguer, J. E. 2000. Applying EXCEL Solver to

a watershed management goal-programming

problem. In: Ffolliott, Peter F.; Baker, Malchus B.,

Jr.; Edminster, Carleton B.; Dillon, Madelyn C.;

Mora, Karen L.; tech-coords. Land stewardship in the

21st century: the contributions of watershed

management; 2000 March 13-16; Tucson, AZ. Proc.

RMRS-P-13. Fort Collins, CO: U.S. Department of

Agriculture, Forest Service, Rocky Mountain Research

Station: 325-329.

Demonstrates the application of EXCEL® spreadsheet

linear programming (LP) solver to a watershed

management multiple-use goal programming (GP)

problem. Data used to demonstrate the application are

from a watershed study in northern Colorado. One of

the desirable features of LP/GP problems formulated on

spreadsheets is the highly visible display of the problem,

which seems to invite inquiry and experimentation.

Also, with the spreadsheet method, problems can be

structured and solved in different ways.

19. Hotvedt, James E. 1982. Application of linear goal

programming to forest harvest scheduling.

Southern Journal of Agricultural Economics. 15(1):

103-108.

An early application of goal programming (GP) to

timber harvest scheduling on an 84,000-acre

management area in the Southeast. The model was

designed to minimize deviations from desired total

harvest volume, discounted and undiscounted cash

flows, and discounted cost. Target levels for each of the

four goals were determined by solving four linear

programming models to determine the optimum level of

achievement for each goal. The model developed a

schedule that within 50 years would convert an

“irregular forest structure” into a highly regulated one. In

addition, managers were made aware of possible

tradeoffs with respect to harvest volume and financial

goals.

20. Julio, Berbel; Zamora, Ricardo. 1995. An

application of MOP and GP to wildlife

management (deer). Journal of Environmental

Management. 44: 29-38.

In forest modeling, wildlife decisions often are

disconnected from management criteria and considered

indirectly as constraints on a financial objective

function. An alternative approach, that makes wildlife

concerns the primary goal of a management model is a

linear formulation that includes both economic and

ecological goals as objective functions. The model was

applied to hunting reserve management in Spain,

specifically, to maximize the value of roe deer hunting

while ensuring the sustainability of the population.

Because these two goals are incompatible, a

multiobjective generating technique was used to identify

the non-inferior solutions and determine the tradeoffs

for each alternative. To demonstrate the usefulness of

this approach, the problem was reformulated as a

lexicographic goal program (GP) and solved. Using the

GP method rather than maximizing the number of roe

deer in each period stabilized the number of deer across

all periods and improved the political acceptability of the

solution.

21. Nhantumbo, I.; Dent, J. B.; Kowero, G. 2001. Goal

programming: application in the management of

the miombo woodland in Mozambique. European

Journal of Operational Research. 133: 310-322.

Goal programming (GP) was applied to a regional land

planning problem in Mozambique in which public

participation was a significant component. The goals

modeled included protection of natural parks and

reserves, timber harvesting, tourism, firewood collection,

anddemand for animal, plant, and nonwood forest

outputs. The model also included constraints on land

area, labor, and capital and constraints relating to the

diversity and adequacy of local diets. Both lexicographic

GP and weighted GP are discussed and the rationale for

using the weighted approach is presented. The

lexicographic GP model was run using four different sets

of goal weights. The model was an effective and

appropriate alternative.

22. van Kooten, G. C. 1995. Modeling public forest

land use tradeoffs on Vancouver Island. Journal of

Forest Economics. 1(2): 191-217.

Discusses the use of goal programming to determine

whether and to what extent the level of outputs, i.e.

benefits to residents of Vancouver Island, can be

improved over the currently proposed forest

management plan. The model formulation and four

scenarios for which the model was run are discussed.
6

The plan proposed for the area will result in a loss to

society of approximately $440 million per year over the

scenarios that were evaluated in this study.

Interactive Mathematical Programming

23. Steuer, Ralph E.; Schuler, Albert T. 1978. An

interactive multiple-objective linear programming

approach to a problem in forest management.

Operations Research. 26(2): 254-269.

A linear programming (LP) and vector maximization

model was applied to unit-level management plan

preparation at the Swan Creek subunit of the Mark

Twain National Forest. Five management objectives were

identified and rank-ordered. Desired attainment goals

were determined for each. There were three constraint

types related to acreage, budget, and sustained yield.

Goal programming achieved limited success due to a

lack of clarity between decisionmakers’ criteria

preference weights and “tradeoff weights in the region of

optimality.” A fuzzy LP approach with interval weights

also was rejected. The procedure that was chosen is a

modification of the interactive LP model. This model is

more flexible and easier to use than previous models.

24. Tecle, Aregai; Duckstein, Lucien; Korhonen, Pekka.

1994. Interactive, multiobjective programming for

forest resources management. Applied Mathematics

and Computation. 63: 75-93.

An interactive and a fuzzy approach to forest

management was applied to the 1.65 million-acre Beaver

Creek watershed in Arizona. Five potential treatments

and a “no action” alternative were considered. A standard

linear programming formulation was used for five of the

six objective functions and one constraint; fuzzy set

theory was used to address the remaining functions and

constraints. PARETO RACE software was used to

facilitate a “free search” procedure that does not require

assumptions about the decisionmaker’s utility function.

The sensitivity of the gross economic benefit achieved

from each alternative to changes in the fuzzy variable

values also was assessed. The model was easier to use

than more structured methods and allowed for imprecise

data. The authors note that this type of approach can

not guarantee “convergence toward a ‘satisfaction’.”

Dynamic Programming

25. Anderson, David J.; Bare, B. Bruce. 1994. A

dynamic programming algorithm for optimization

of uneven-aged forest stands. Canadian Journal of

Forest Research. 24: 1758-1765.

Dynamic programming (DP) was used for uneven-aged

stand management despite demanding computational

requirements. The method presented is formulated as a

forward recursion, discrete, two-state DP. State variables

were trees and basal area per acre. The “neighborhood

storage concept” was used to reduce the number of

possible states that must be considered at each stage.

There were four harvest parameters that differed in the

harvesting method applied and the width of

neighborhood classes. Detailed results are examined with

respect to solution times and objective function values,

i.e., present net value. The objective function of one run

exceeded a previous “best solution” generation.

26. Lin, C. R.; Buongiorno, J. 1998. Tree diversity,

landscape diversity, and economics of maple-birch

forests: implications ofMarkovian models.

Management Science. 44(10): 1351-1366.

Markov decision-process models solved by dynamic

programming were used to choose managements with

multiple objectives. Criteria included landscape diversity

(variety of stands in the forest), diversity of tree species

and tree size, annual income, and present value.

27. Puumalainen, Janna. 1998. Optimal cross-cutting

and sensitivity analysis for various log dimension

constraints by using dynamic programming

approach. Scandinavian Journal of Forest Research.

13: 74-82.

A forward recursive dynamic programming (DP) model

was applied to tree bucking. DP can accommodate both

nonlinear and linear relationships and computation is

better with DP than with linear programming. The

model was applied to the bucking of 3,282 stems of

Scots pine in three sawtimber grades and a pulpwood

class. Four sets of constraints for minimum diameter and

log length were used for each quality category. The DP

model was useful for bucking optimization and the

solution time was satisfactory.

Modeling to Generate Alternatives

28. Allen, Julia C. 1986. Multiobjective regional forest

planning 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 used

to generate several feasible and nondominated solutions

to a multiobjective forest planning problem that was

formulated as a linear programming model with two

objectives: minimize wood production and

transportation costs. Constraints included area, tree

growth, and wood volume. In Tanzania, NISE generated
7

14 feasible solutions using three sets of model

assumptions. Because NISE does not rely on a prior

elicitation of decisionmaker preferences, it is effective for

real-world situations. Potential problems include a

tendency for this technique to be computationally

demanding and represent less than the full range of

possible solutions.

29. Bare, B. Bruce; Mendoza, Guillermo. 1988.

Multiple objective forest land management

planning: an illustration. European Journal of

Operational Research. 343: 44-55.

An alternative generating technique known as the step

method (STEM) is examined, and the rationale for

generating multiple feasible solutions versus a single

optimal solution is discussed. Applied to a mixed fir

forest in western Washington, the model generated

alternatives that represent levels of achievement for seven

objective functions, including maximization of harvest

volume and populations of “indicator species” and

minimization of populations of pest species. Outputs of

the generated alternatives are compared using payoff

tables; the range of difference between each solution is

discussed. STEM is a powerful tool for forest planning

in situations in which the complexity of the system

prevents the capture of effective elements by

optimization techniques.

30. Boscolo, M.; Buongiorno, J. 1997. Simulating

options for carbon sequestration through

improved management of lowland tropical

rainforest. Environmental and Development

Economics. 2: 241-243.

Simulates a tropical forest stand in Malaysia in its role as

a source of income and as a carbon store, and quantifies

the potential for and cost effectiveness of carbon

sequestration by modifying current management

practices.

31. Buongiorno, J.; Kolbe, A. 2000. Economic and

ecological effects of diameter-limit and BDq

management regimes: simulation results for

northern hardwoods. Silva Fennica. 34(3): 223-235.

Long-term financial and ecological effects of diameterlimit and basal-area-diameter-q-ratios (BDq) in mixed

northern hardwood stands in the Lake States were

compared by using simulation.

32. Mendoza, Guillermo A.; Bare, B. Bruce; Campbell,

Gene E. 1987. Multiobjective programming for

generating alternatives: a multiple-use planning

example. Forest Science. 33(2): 458-468.

Presents modeling-to-generate-alternatives (MGA)

approach to decisionmaking in forest planning. The

general structure of this approach, known as a Hop,

Skip, and Jump algorithm, was applied to multiple-use

planning. Five objective functions, including

maximization of timber volume and forage production

and consideration of water production and recreation

opportunities were considered. The technique generated

four solutions related to output in a payoff matrix.

Unlike optimization methods, MGA techniques are

effective in situations in which one or more objective is

omitted from the analysis or where the model is

formulated incorrectly.

33. Schulte, B.; Buongiorno, J. 1998. Effects of

uneven-aged silviculture on the stand structure,

species composition, and economic returns of

loblolly pine stands. Forest Ecology and

Management. 111: 83-101.

The consequences of management regimes for economic

and ecological criteria were predicted with the Southpro

simulation program for mixed hardwoods and loblolly

pine stands in the Southern United States.

34. Volin, V. C.; Buongiorno, J. 1996. Effects of

alternative management regimes on forest stand

structure, species composition, and income: a

model for the Italian Dolomites. Forest Ecology

and Management. 87:107-125.

Simulation methods were used to compare the effects of

extracting mortality only, applying Susmel’s guides,

diameter-limit cuts, saving beech, and continuing

current harvest. Ecological criteria included forest cover

and stand composition; economics were judged by net

present value.

35. Willis, C. E.; Perlack, R. D. 1980. A comparison of

generating techniques and goal programming for

public investment, multiple objective decision

making. American Journal of Agricultural

Economics. February: 66-74.

Compares goal programming (GP) and two generating

techniques—the weighting and constraint methods—in

terms of computational expense, explicit quantification

of tradeoffs, quantity of information generated, and

validity of the interaction between decisionmaker and

analyst. GP was more efficient computationally but

generating techniques provided explicit tradeoffs

between objectives as well as much more information to

the decisionmaker than GP. Also, unlike GP, generating

techniques determine feasible relationships but leave the

evaluation process to the decisionmaker.
8

Hierarchical Planning

36. Cea, Christian; Jofre, Alejandro. 2000. Linking

strategic and tactical forestry planning decisions.

Annals of Operations Research. 95: 131-158.

A multilevel model is proposed that links strategic-level

investment decisions with tactical-level planning in

private forestry companies. The first step is the

development of a general integer programming (IP)

model that specifies the strategic planning problem. The

objective function entails the maximization of present

net value subject to constraints regarding harvest

volume, harvest area, and timber demand. Once this

model has been solved, results for the macro-stands are

used to set goals for individual stands in the tactical-level

problem, also formulated as an IP problem. The tactical

model is decomposed into two submodels for roadbuilding and transportation decisions. The road-decision

model is solved using simulated annealing and the

transportation problem is solved using LP, a secondary

algorithm is used to improve the solution.

37. Church, Richard L.; Murray, Alan; Barber, Klaus.

2000. Forest planning at the tactical level. Annals

of Operations Research. 95: 3-18.

Examines the decomposition of optimal strategic-level

solutions to optimal tactical-level plans on forests. This

is known as hierarchical planning. Three linear

programming (LP) models are presented. The first, the

coordinated allocation of choice model, is an LP

formulation that combines the use of a strata-based

noncontiguous planning structure and a zone-based

contiguous planning structure. It maximizes the present

value of choices determined both on a zone basis and on

the basis of individual decisions made within analysis

areas (strata). Also discussed are two Bridging Analysis

Models. In the first model, strategic-level goals are

allocated proportionately to tactical planning units

subject to implementation constraints. The goal is to

maintain the acreages of each prescribed treatment as

close as possible to the strategic levels. The second model

allocates tactical outputs based on strategic output goals

in two ways. The min-area formulation minimizes the

number of constraints that are binding in the tactical

solution, while the equiv-risk model attempts to

maximize the distance from the most constraining

conditions for each analysis area to preserve flexibility in

future planning.

38. Nelson, John; Brodie, J. Douglas; Sessions, John.

1991. Integrating short-term, area-based logging

plans with long-term harvest schedules. Forest

Science. 37(1): 101-122.

A three-stage model is proposed to link short-and longterm harvest planning in the development of optimal

harvest schedules on a 4,000-ha, 62-unit forest with

timber as the sole output. In the first stage, a linear

programming (LP) model is used to maximize the

present net worth of all harvesting decisions across the

forest. The solution provides volume and revenue targets

for the second stage, the use of integer programming (IP)

to determine harvest scheduling and transportation at

the stand level; the model is solved using the Monte

Carlo heuristic procedure. After 200 feasible solutions

were generated, 5 were selected, each with a different

objective for value, timber volume, and net revenue.

These five alternatives were used to generate 15-decade

LP formulations that were entered into FORPLAN as a

coordinated-choice allocation. By combining the

strategic solution from a strata-based LP and the spatial

distributions created using an area-based IP, one can

create timber harvest plans that are spatially feasible over

the short term and acceptable over the long term.

39. Weintraub, Andres; Cholaky, Alejandro. 1991. A

hierarchical approach to forest planning. Forest

Science. 37(2): 439-460.

Comprehensive forest planning has historically been

accomplished through the use of “monolithic,” singlestage, linear or mixed integer programming models.

Hierarchical planning is proposed that addresses the

inability of traditional approaches to link strategic,

operational, and tactical-level plans. In this study, the

explicit linkage of strategic and tactical models is

illustrated. Neither adjacency constraints nor explicit

representation of roading variables are included. The

land-use allocation, per-period level of timber

production, constraint targets, and road-building budget

derived from the model are used as direct inputs into the

tactical model. Although the tactical model can be solved

only with heuristic techniques, it is adequate for forest

planning in complex situations.

Improving Spatial Capabilities

40. Church, Richard L.; Murray, Alan T.; Weintraub,

Andres. 1998. Locational issues in forest

management. Location Science. 6: 137-153.

Describes the most common “locational” forest issues.

For each situation, a basic mathematical programming

model is formulated, illustrating the typical objective

function and constraint structure. Issues discussed

include forest planning to maximize present net value,

timber-harvest scheduling, transportation planning, and

designating reserves to preserve biodiversity. The most

common solution methods are discussed for each
9

situation, as are alternative means of formulation and

solution.

41. de Kluyver, C. A.; Daellenbach, H. G.; Whyte, G.

D. 1980. A two-stag, multiple objective

mathematical programming approach to optimal

thinning and harvesting. Forest Science. 26(4): 674-

686.

Dynamic programming (DP) and linear programming

(LP) are applied to create timber-harvesting plans for

large forests. A DP approach selects from all potential

stand-management activities policies that are the most

efficient for each type of forest stand. This reduced set of

policies is then used in an LP model to schedule timber

harvest across an entire forest. The decision variables

represent collections of activities applied across the entire

planning horizon rather than individual activities for

each period. The use of both management “policies” and

DP to limit the set of activities considered significantly

reduces model size.

42. Epstein, R.; Nieto, E.; Weintraub, A.; Chevalier, P.;

Gabarro, J. 1999. A system for the design of short

term harvesting strategy. European Journal of

Operational Research. 119: 427-439.

Applies linear programming (LP) to short-term harvest

decisions by private forest companies, including what

bucking patterns to use, how much volume to cut on a

weekly basis, types of machinery to use, and where to

harvest, that are influenced by changing product

demand and the quality of previous harvests. An LP

formulation is presented for maximizing present net

value subject to volume, machine capacity,

transportation capacity, and demand constraints. Dual

variables associated with the bucking constraints are used

to generate new bucking patterns to optimize product

output. A flexible branch and bound algorithm is used

to determine the best pattern. Both the structure of the

algorithm and the rules that can be applied to control

the selection process are described and selection

approaches are compared with respect to product output

derived from the resulting patterns. This approach has

been used by Chilean companies to improve operations

and realize significant savings.

43. Guignard, Monique; Ryu, Choonho; Spielberg,

Kurt. 1998. Model tightening for integrated timber

harvest and transportation planning. European

Journal of Operational Research. 111: 448-460.

A method is proposed to improve solution capabilities of

a mixed-integer programming (IP)model for integrating

transportation and timber planning. IP models such as

the IntegratedResource Planning Model cannot be

solved easily or quickly because of the size of most

forestmanagement problems and many 0-1 variables

required. Suggestions are included for improvingsolution

time through the use of trigger constraints, constraint

lifting, and the prioritization of branching for doublecontraction variables. Four model structures, each using

a different combination of the three improvement

techniques, were tested on three small data sets. For the

second data set, the original IP formulation was solved

to optimality only after 7 days had elapsed. Lifting the

trigger constraints did not significantly reduce

computation time but the addition of doublecontraction priorities resulted in a solution time of

several minutes. Using all three improvements together

resulted in computation times of less than 15 minutes

for all test cases.

44. Haight, Robert G.; Travis, Laurel E. 1997. Wildlife

conservation planning using stochastic

optimization and importance sampling. Forest

Science. 43(1): 129-139.

Wildlife populations are particularly difficult to model

with standard linear or integer programming approaches.

A stochastic programming model is described that

minimizes the cost of habitat protection subject to

constraints related to species viability. The first half of

the paper focuses on describing the formulation of the

problem and details the search algorithm used to solve

this model. To evaluate the approach, it is applied to a

hypothetical problem related to the management of gray

wolf. Simulation models are used to generate the survival

probabilities for the wolf under different management

plans. The model is run numerous times with different

population targets to determine the tradeoff between

cost and risk. The sensitivity of the model to changes in

population growth and dispersal functions is assessed. In

addition to its ability to incorporate uncertainty into the

optimization process, this approach offers a high degree

of flexibility in the types of wildlife functions that can be

utilized. Although computation difficulty limits the size

of problem that can be addressed, this model is a noted

improvement over traditional deterministic approaches.

45. Hof, John; Bevers, Michael. 2000. Direct spatial

optimization in natural resource management:

four linear programming examples. Annals of

Operations Research. 95: 67-81.

Discusses how to optimize wildlife populations based on

their spatial dynamics. Four species-specific and sitespecific linear programming (LP) models that

incorporate wildlife issues intonatural resource planning

are described. The objective function and all necessary

constraints are outlined along with model assumptions
10

and limitations. The first model attemptsto maximize

the population of a species that is being raised in

captivity and then released into thewild; the second

maximizes a colonial species population given particular

population movement(dispersal) tendencies; the third

minimizes pest populations, given particular

dispersingbehavior and specific management activities

focused on reducing the population; the fourthis applied

to the survival of a species given strict spatial constraints

on habitat.

46. Hof, John; Linda Joyce. 1993. A mixed integer

linear programming approach for spatially

optimizing wildlife and timber in managed forest

ecosystems. Forest Science. 39(4): 816-834.

A mixed-integer linear model is presented that addresses

the potential for a nonconvex decisionspace that could

prevent the identification of global optima; and the

inability of nonlinearmodels to solve real-world

problems or take into account the random nature of

factors such ashabitat fragmentation. A grid-based

approach is used that divides forest area into square

subunits of equal size. The objective function includes

the weighted sum of timber output andpopulations of

both edge-dependent and area-dependent species. A

nonlinear edge-effect model is presented and

reformulated as a mixed-integer linear model; the same

modification is used for habitat-fragmentation effects.

Both of these model components and a linear habitatsize threshold constraint for area-dependent species are

incorporated into the final formulation. Two scenarios

are tested using sets of objective-function weights.

Solution times ranged from 30 minutes to 2 hours.

Although the model is designed primarily for relatively

small problems, an optimal solution is guaranteed.

47. Hof, John G.; Joyce, Linda. 1992. Spatial

optimization for wildlife and timber in managed

forest ecosystems. Forest Science. 38(3): 489-508.

Although there have been attempts to incorporate

nonlinear relationships in linear programs, for example,

through piecewise approximations, most have achieved

limited success due to significant increases in problem

size and computation. Three formulations that can

consider nonlinear functions related to wildlife habitat

are presented. The first approach, which attempts to

account for edge effects using a standard grid-based

allocation, uses integer nonlinear programming to

determine whether each cell will be harvested or left as

wildlife habitat. However, real-world application of the

model is limited by lack of effective solution algorithms.

The same basic procedure is repeated in the second

model but with a “geometric” allotment structure such

that land uses are allocated using circles of varying

diameters. This approach does not require an integer

formulation. In the third model, the geometric structure

is used to model fragmentation effects.

48. Hof, John G.; Raphael, Martin G. 1993. Some

mathematical programming approaches for

optimizing timber age-class distributions to meet

multispecies wildlife population objectives.

Canadian Journal of Forest Research. 23: 828-834.

The typical forest-scheduling model considers wildlife

only indirectly. Three alternative models that optimize

wildlife factors directly are presented. The first

maximizes the total number of viable species and is

considered the “most efficiency oriented,” while the

other two models maximize a specific measure of

population viability. All three models are run using both

linear and nonlinear viability functions. When nonlinear

viability functions are used, the models must be solved

with nonlinear programming. With linear functions,

only the standard linear programming formulation is

required. An exception is the second “viability” model,

which has a nonlinear objective. The models, which were

tested using data from a 1.1 million-ha forest in

California, produced different optimal age-class

distributions. Using the logistic (nonlinear) viability

function was the most realistic approach, though the two

viability models were more effective in spreading the risk

of extinction equitably across all species. The “total

species maximization” approach yielded the highest total

number of viable species.

49. Hoganson, Howard M.; Borges, Jose G. 1998.

Using dynamic programming and overlapping

subproblems to address adjacency in large harvest

scheduling problems. Forest Science. 44(4): 526-

538.

Dynamic programming (DP) was used to solve a mixedinteger harvest-scheduling problem in three scenarios

consisting of 40- by 25-unit “forests.” The planning

problem was decomposed into subproblems and thus

increase the problem size to which DP can be applied.

The objective of this specific formulation was to

maximize net returns subject to adjacency constraints.

The problems were solved using forward recursion. The

application entailed planning over five 10-year periods

with seven possible management alternatives. For

comparison, each of the four problems also was solved

using a simulation approach and an unconstrained

(relaxed) DP. Solution times were satisfactorily short and

this method provided better solutions than the

simulation approach.
11

50. Jones, J. Greg; Meneghin, Bruce J.; Kirby, Malcom

W. 1991. Formulating adjacency constraints in

linear optimization models for scheduling projects

in tactical planning. Forest Science. 37(5): 1283-

1297.

Several approaches are presented for minimizing the

computational requirements of mathematical programs

by reducing the number of constraints needed to handle

adjacency considerations. The formulations are based on

the assumption that the forest management area is

divided into polygons rather than structured as a grid,

and are presented as constraints in an integer

programming model. The constraints are first

formulated for only one decision variable and one

planning period. Type 1 formulation uses a group rather

than pairs of polygons to restrict timber harvesting. Type

2 combines several Type I constraints. The formulations

are applied to three planning areas consisting of 27, 112,

and 279 polygons. Using Type 2 constraints could

reduce the number of constraints by nearly 75 percent. If

trigger inequalities are used, Type 2 formulations would

reduce the number of constraints by 27 percent.

51. Murray, Alan T. 1999. Spatial restrictions in

harvest scheduling. Forest Science. 45(1): 45-52.

Discusses two common approaches to modeling

adjacency constraints in harvest scheduling that are used

when irregularly delineated units represent the forest

management areas. Both approaches are presented as

binary integer programming models. The Unit

Restriction Model is applied when management units are

so large that the harvest of two adjacent units would

necessarily violate adjacency constraints. If management

units are significantly smaller than the area limit of the

adjacency constraint, harvesting of adjacent units does

not necessarily violate the constraints and the Area

Restriction Model is used. Both exact and heuristic

solution methods for solving these models are discussed,

and the issue of spatial unit definition in minimizing

modeling and computation requirements is addressed.

52. Murray, Alan T.; Church, Richard L. 1995.

Measuring the efficacy of adjacency constraint

structure in forest planning models. Canadian

Journal of Forest Research. 25: 1416-1424.

Reviews the traditional approach to adjacency constraint

structure (pairwise comparison), suggests eight improved

formulations, and compares computational efficiency of

these new approaches using six harvest-scheduling

scenarios that are based on the planning horizon

considered (single or multiple period), number of

harvest units included in the analysis, and whether road

building is considered in the problem. The different

approaches are compared according to the number of

constraints required, optimal solution generated,

number of branches, and iterations, and solution time

required. The most significant findings are that: (1) the

traditional pairwise comparison method does not

necessarily result in the tightest constraint structure, (2)

methods that most significantly reduce the number of

constraints may have longer solution times, and (3)

methods that rely on constraint tightening are

particularly efficient.

53. Murray, Alan T.; Church, Richard L. 1996.

Analyzing cliques for imposing adjacency

restrictions in forest models. Forest Science. 42(2):

166-175.

A network theory-based technique known as the Type I

constraint approach was first used in conjunction with

quadruplet cliques, i.e., one constraint constructed for

each group of four cells. A modification to Type I

constraints that allow this formulation to be used with

cliques with more than four cells is discussed. Two

additional constraint-reduction techniques are presented.

The first focuses on the elimination of dominated clique

constraints and the second reduces the constraints to a

“minimal subset.” All three approaches were applied to

nine forest planning problems. For eight problems, the

minimal clique constraint set resulted in the fewest

adjacency constraints. All three methods resulted in the

same number of constraints in the ninth example,

though the nondominated approach required

significantly shorter computation times. This reduction

technique is recommended where the number of

constraints generated is sufficiently small that it is not

binding; otherwise, the minimal set approach is an

effective alterative.

54. Roise, Joseph P. 1990. Multicriteria nonlinear

programming for optimal spatial allocation of

stands. Forest Science. 36(3): 487-501.

Draws on the “four color theorem” to develop a

nonlinear programming model for timber-harvest

scheduling. For problems that require adjacent units to

be harvested no less than a specified number of years

apart (the exclusion period), the theorem suggests a

feasible solution is possible so long as the project period

length divided by the exclusion period length is less than

or equal to four. Where a feasible solution is not

possible, the adjacency constraint can be used as the

objective function, thus maximizing the length of time

between harvesting of adjacent units. The basic

nonlinear model is presented and the objective function

and constraints are applied to four increasingly complex

problems. As the number of stands included increases,
12

the solution time for the models grows exponentially.

This technique is applicable only to forests with fewer

than 200 stands, but allows optimization of harvest

decisions at both the forest and stand level.

55. Snyder, S.; ReVelle, C. 1997. Multiobjective grid

packing model: an application in forest

management. Location Science. 5(3): 165-180.

Presents a method of integrating timber harvesting and

wildlife habitat goals subject to spatial constraints. A

binary integer programming (IP) model was applied to a

hypothetical and static data set comprised of a 25- by

25-cell forest grid. The objective is to develop a harvest

schedule that maximizes both harvest volume and

wildlife habitat acreage. Adjacency constraints are

evaluated by 2 by 2 grid-blocks rather than by individual

pairs of cells. The study’s two objectives were combined

using the weighting method. Three of the possible

weight combinations were used to solve the IP, and the

impact of various weights on the spatial distribution of

management activities is discussed. The model was

reformulated with additional constraints and the process

repeated. This approach was successful in obtaining

exact, optimal solutions in a minimal amount of time.

56. Snyder, Stephanie; ReVelle, Charles. 1996. Temporal

and spatial harvesting of irregular systems of

parcels. Canadian Journal of Forest Research. 26:

1079-1088.

A binary integer programming (IP) model was applied to

a forest with irregular harvest-unit systems. Unlike

regular (grid) systems, irregular systems require more

than one type of constraint structure. The method for

formulating constraints for irregular systems is

demonstrated and the effect of such a set of constraints

on the computational efficiency of the IP model is

assessed. With the maximization of timber volume as the

objective, the model is then applied to five hypothetical

and five real scenarios. Data sets representing irregular

parcel systems of varying sizes and configurations are

evaluated using both static and multiple-period models.

Adjacency constraint formulations for the two models

are presented separately, and the multiple-period model

is run for various planning horizon lengths. For the

static model, the IP model performed well, requiring

little, if any, branching and bounding. In some cases,

considerable branching and bounding was required for

the multiple-period model.

57. Snyder, Stephanie; ReVelle, Charles. 1997. Dynamic

selection of harvests with adjacency restrictions:

the SHARe model. Forest Science. 43(2): 213-222.

Discusses the need to develop models that allow harvest

plans to be subject to spatial constraints and temporal

management considerations to be integrated. A binary

integer programming (IP) formulation is presented that

is the “shortest path network flow” model, which is a

means of structuring “relaxed” models that can be solved

to exact integer solutions. Several general formulations of

adjacency constraints that can be used in this approach

are discussed, and a binary IP model is introduced that

includes both spatial constraints over multiple periods

and the shortest-path-network structure. The model is

formulated for an area represented by a grid of cells of

equal size. A set of hypothetical data is used to evaluate

the approach, with multiple runs conducted using

different grid sizes, time-horizon lengths, initial forestage structures, and adjacency restrictions. The results of

each run along with solutions times are reported.

58. Weintraub, Andres; Barahona, Francisco; Epstein,

Rafael. 1994. A column generation algorithm for

solving general forest planning problems with

adjacency constraints. Forest Science. 40(1): 142-

161.

Describes a method for solving forest-planning problems

with multiple periods and a significant set of constraints,

representing a large forest area that is realistic. A twostage approach is applied to both simplified and

expanded problems. The first entails scheduling units

within a single, homogenous harvest area; the expanded

problem entails unit scheduling across multiple areas.

The first stage of the approach is the formulation of an

integer-programming (IP) model, which is solved

without the integer constraint (relaxed form) and then

by heuristic procedure to improve the relaxed

continuous solution. This simplex-based procedure

identifies a “stable set” of subproblem alternatives that

satisfy adjacency constraints; a three-step process is used

to solve the stable set problem. First, a greedy heuristic

method is used to identify a near optimal solution. If it

is not successful, a linear programming (LP) technique is

used to find an integer solution. If the LP is

unsuccessful, the problem is solved by the branch and

bound method. The latter approach was applied to two

problems, each with three forest configurations, over a

10-year planning horizon. On average, the solutions

were within 3 percent of the optimal solution for the

relaxed IP.

59. Weintraub, Andres P.; Epstein, Rafael; Murphy,

Glen; Manley, Bruce. 2000. The impact of

environmental constraints on short term

harvesting: use of planning tools and

mathematical models. Annals of Operations

Research. 95: 41-66.
13

Seven planning models currently being applied to real

situations in New Zealand and Chile are described,

including the typical planning horizon used and types of

information required by each model. Also discussed is

how forest management is facilitated by these models

which range from short-term and small-scale operational

applications to long-range planning formulations used

for harvest scheduling, wood-processing investment

decisions, and forest-management planning. The impact

of modification to better include environmental

protection measures in the planning process is illustrated

for five of the models using these case studies. Impacts

are assessed in terms of changes in net values and harvest

volumes resulting from the mitigation measures.

Heuristic Methods

60. Bettinger, Pete; Boston, Kevin; Sessions, John. 1999.

Intensifying a heuristic forest harvest scheduling

search procedure with 2-opt decision choices.

Canadian Journal of Forest Research. 29: 1784-1792.

Describes a method for improving the performance of

tabu search for solving a harvest-scheduling problem.

Tabu search operates by making iterative changes, or

moves, to a selected solution based on specified search

rules. The relative benefits of using 1-opt versus 2-opt

moves in this search process is evaluated. In 1-opt moves,

only one attribute of one decision choice is altered, i.e., a

unit is removed from the harvesting schedule. In 2-opt

moves, that attribute is changed for two decision choices

simultaneously, i.e., one unit is added to the harvest

schedule while another is removed. The objective of this

application is to maximize of harvest volume subject to

adjacency and even-flow constraints. Hypothetical 5 by

8 and 28 by 25 forest grids are generated. The problem

is solved as a relaxed linear programming (LP) model

and as an integer program (IP). Two versions of tabu

search, one that allows only 1-opt moves and one that

allows both 1-opt and 2-opt moves, are used. The

solution time for tabu search was significantly less than

for the IP model; the combined (1- and 2-opt) tabu

model had a slightly longer solution time than the 1-opt

model. The tabu models had objective function values

within 3 percent (1-opt) and 1 percent (both) of the

relaxed LP solution.

61. Bettinger, Pete; Johnson, K. Norman; Sessions, John.

1996. Forest planning in an Oregon case study:

defining the problem and attempting to meet

goals with a spatial-analysis technique.

Environmental Management. 20(4): 565-577.

Spatial allocation is an important consideration in

natural resource management, but it is difficult to

optimize activities in a spatial context. An operationallevel harvest-scheduling program called SNAP II+ uses

the more common integer programming formulation

and a heuristic solution algorithm approach. The model

was evaluated based on whether it could model

management goals well and was flexible in evaluating

alternatives when applied to a small watershed in the

upper Grand Ronde River Basin in Oregon. The model

was formulated to maximize net present value over four

10-year planning periods. SNAP II+ generated feasible

management plans and was effective in addressing spatial

allocation.

62. Bettinger, Pete; Sessions, John; Boston, Kevin. 1997.

Using tabu search to schedule timber harvests

subject to spatial wildlife goals for big game.

Ecological Modelling. 94: 111-123.

A tabu search heuristic is used to solve a large harvestscheduling model that includes both temporal and

spatial constraints for wildlife habitat. No other

technique can directly incorporate habitat-quality

considerations while developing feasible harvest

schedules. The objective function in this model

minimizes the sum of the squared differences between

the target level of harvest and the actual level of harvest

for each period, and contains penalty functions that

prevent: (1) adjacent units from being harvested in the

same period (adjacency constraint); and (2) blocks of

units assigned as wildlife cover from being reduced

below a minimum aggregate size (wildlife habitat

constraint). The data used were based on a hypothetical

landscape of 1-ha units (20 by 20 grid). Two scenarios

were run that represented differences in forage age

limitations and minimum harvest age. The algorithm

was run for 1,000 iterations for the first scenario and

about 400 iterations for the second. In both scenarios, a

temporally and spatially feasible solution was obtained.

63. Bettinger, Pete; Sessions, John; Johnson, K. Norman.

1998. Ensuring compatibility of aquatic habitat

and commodity production goals in eastern

Oregon with a tabu search procedure. Forest

Science. 44(1): 96-112.

Describes the use of tabu search to simultaneously

optimize land-management plans and assess their impact

on aquatic habitat. A basic linear-programming

formulation with an objective function that optimizes

net present value was applied to a 6,000-ha watershed in

eastern Oregon. This method was able to optimize

timber and aquatic habitat goals simultaneously, though

it may not generate a global optimal solution.

64. Bos, Jan. 1993. Zoning in forest management: a

quadratic assignment problem solved by simulated
14

annealing. Journal of Environmental Management.

37: 127- 145.

Zoning-based management is based on the assumption

that conflict can best be reduced by separation of land

uses. Traditional planning models do not explicitly

include zoning decisions partly because they require

integer variables that make the models difficult to solve.

A forest zoning problem in the Netherlands is addressed

using a quadratic assignment formulation in which the

objective function comprises two elements. The first

element is a function of both the suitability of a forest

unit for each alternative use and the relative preference

for those uses. The second considers the use of adjacent

forest units and maximizes the grouping of uses that

complement each other. The model also considers actual

or potential land uses that border the forest when

making zoning decisions. A heuristic algorithm

(simulated annealing) is used to generate solutions. Data

were obtained for 84 units within the Waterbloem

National Forest and 80 “environmental” units that

adjoin the forest. The model effectively considered the

spatial relationships of various land uses and the solution

algorithm provided acceptable results.

65. Bullard, Steven H.; Sherali, Hanif D.; Klemperer, W.

David. 1985. Estimating optimal thinning and

rotation for mixed-species timber stands using a

random search algorithm. Forest Science. 31(2):

303-315.

Describes a method for generating “good” thinning

regimes in even-aged, mixed-species stands, specifically, a

growth model consisting of up-growth and mortality

functions that generates data on stand structure and

volume. Growth information is used in a nonlinear

integer-programming model that addresses the thinning

problem. The model was formulated to maximize

present net value of both current and future income. A

comparison of simple and multistage random search

heuristics is given for two hypothetical samples. Both

yielded nearly optimal solutions in several seconds to

several minutes. In both cases, the multistage algorithm

outperformed the simple algorithm.

66. Kangas, Jyrki; Pukkala, Timo. 1996.

Operationalization of biological diversity as a

decision objective in tactical forest planning.

Canadian Journal of Forest Research. 26: 103-111.

Describes HERO, a utility-based heuristic method

designed to address harvest-scheduling problems that

consider biodiversity. The major premise of this method,

which entails estimating an additive utility function and

optimizing that function, is that all constraints and

objectives can be formulated as preference and utility

functions. The method was applied to a 43-ha, 37-unit

forest in eastern Finland with two 10-year planning

periods and 129 treatment schedules. Four scenarios

with varying degrees of biodiversity importance were

tested. The strengths of this approach are its flexibility

and ability to consider nonlinear relationships, and make

biodiversity commensurable with other objectives.

67. Lockwood, Carey; Moore, Tom. 1992. Harvest

scheduling with spatial constraints: a simulated

annealing approach. Canadian Journal of Forest

Research. 23: 468-478.

The use of simulated annealing (SA) to solve large

harvest-scheduling is proposed and the basic procedure

for this heuristic technique is described. A unique

characteristic of this formulation is that the objective

function is designed to minimize deviation from the

harvest-volume target as well as penalty costs associated

with constraint violations. Procedures for developing the

four penalty cost functions are presented and the process

of applying SA to this specific formulation is described.

Data were from a 240,000-ha subsection of a private

forest six harvest levels and three harvest block sizes used

in trial runs. This method generated feasible solutions

for every run.

68. Murray, Alan T.; Church, Richard R. 1995.

Heuristic solution approaches to operational forest

planning problems. OR Spektrum. 17: 193-203.

Explores the ability of three heuristic methodsinterchange, tabu search, and simulated annealing to

generate near optimal plans for problems with

considerable detail. These methods represent

improvements on a Monte Carlo approach and were

applied to two moderate-size forests in British

Columbia. The first problem was a mixed-integer

formulation with 300 decision variables (291 integer)

and 740 constraints. In a previous study, this problem

was solved analytically in about 60 hours. For each

heuristic, the process began with the best Monte Carlo

solution, which generate 1,300 additional solutions. The

best objective-function value using the interchange

method was within 2 percent of the optimal solution.

The best solutions generated by tabu search and

simulated annealing were within 1 percent of the

optimal solution. For all three methods, objective

function values were significantly better than the

solution generated using Monte Carlo alone. Solution

times were 30 hours for tabu search, 11 hours for

simulated annealing, and 3 hours for interchange. Tabu

search solutions were the most consistent and closest to

optimal.
15

69. Nelson, John; Bodie, J. Douglas. 1990. Comparison

of a random search algorithm and mixed integer

programming for solving area-based forest plans.

Canadian Journal of Forest Research. 20: 934-942.

Compares a Monte Carlo integer-programming heuristic

and a mixed-integer programming (IP) model for solving

harvest-scheduling problems at the tactical level. The

Monte Carlo technique was applied to a 1,700-ha forest

in British Columbia. The harvest problem was first

formulated as a mixed IP model with the objective of

maximizing discounted net revenue. The problem was

solved using linear programming (LP) to determine the

optimal solution, and then reformulated as a Monte

Carlo IP model. This heuristic model was solved using

three search techniques: all-period, first selective, and

second selective. Of the 1,300 Monte Carlo solutions

generated, 175 were within 10 percent of the optimal

value, 12 were within 5 percent, and the highest valued

was within 3 percent. The all-period search was the most

effective of the search routines and Monte Carlo was

effective in creating harvest schedules for forest problems

that are medium to large.

70. O’Hara, Anthony J.; Faaland, Bruce H.; Bare, B.

Bruce. 1989. Spatially constrained timber harvest

scheduling. Canadian Journal of Forest Research. 19:

715-724.

The model SCRAM is the first algorithm that can

generate feasible and “good” solutions to integer

programming (IP) problems that include many units,

multiple planning periods, and spatial constraints. The

basic IP formulation that is to be solved and the biased

sampling search algorithm developed to solve it are

described. This heuristic is a modified version of the

Monte Carlo IP that both randomly selects harvest units

and allows the selection process to be biased toward

those units more likely to result in good solutions. Three

different pre-biasing techniques were used on data from

a previous study of a 242-unit forest with a planning

horizon of five 10-year periods. This model is an

important innovation because it requires no special data

beyond what is available for the average scheduling

problem, produces feasible/good integer solutions, and

does not lose accuracy as the problem size increases.

71. van Deusen, Paul C. 1999. Multiple solution

harvest scheduling. Silva Fennica. 33(3): 207-216.

One of the most common heuristic methods is the

simulated annealing algorithm. The core of this solution

technique is a procedure known as the metropolis

algorithm (MA). Also related to the Monte Carlo

technique, MA focuses primarily on generating a large

list of feasible solutions, with less emphasis on economic

optimality. All problem constraints are incorporated

directly into the objective function. This allows

consistent treatment of problem criteria and locally

optimal solutions can be identified by increasing the

weight of a particular element in the objective function.

This has been suggested as more appropriate type of

approach for government agencies that wish to identify

more than the most economically efficient alternatives.

As applied to a forest data set of 419 stands, MA proved

a flexible approach to forest planning.

72. Wientraub, Andres; Church, Richard L.; Murray,

Alan T.; Guinard, Monique. 2000. Forest

management models and combinatorial

algorithms: analysis of state of the art. Annals of

Operations Research. 96: 271-285.

The types of algorithms available to solve mixed-integer

programming problems are reviewed and methods used

to solve harvest-scheduling problems with adjacency

constraints are discussed. Also discussed are algorithms

that have been applied to the simultaneous planning of

harvesting and road building. Although most

applications have included the use of heuristic

algorithms, the basic integer formulation can be

strengthened to provide a good solution.

73. Weinttaub, Andres; Jones, Greg; Meacham, Mary;

Magendzo, Adrian; Magendzo, Ariel; Malchuk,

Daniel. 1995. Heuristic procedures for solving

mixed-integer harvest scheduling-transportation

planning models. Canadian Journal of Forest

Research. 25: 1618-1626.

Discusses the use of heuristic techniques to address

spatial constraints in harvest scheduling. The basic

formulation, based on the Integrated Resources Planning

Model, is given as an linear programming (LP)

optimization of present net value, and the heuristic

procedure for problems in which only road-decision

variables are in 0-1 integer form is discussed. This

iterative algorithm works with an LP solver to convert

optimal LP solutions to integer solutions. This approach

was applied using several small data sets and results were

evaluated on the basis of the best solution using a mixedinteger programming (IP) model. An extension of the

original formulation that considers both 0-1 road and 0-

1 land-management variables is presented. Objective

function values were about 40 percent higher with

heuristic solutions than with the IP solution.

74. Yoshimoto, Atushi; Brodie, J. Douglas. 1993.

Comparative analysis of algorithms to generate

adjacency constraints. Canadian Journal of Forest

Research. 24: 1277-1288.
16

The need to incorporate environmental concerns into

harvest scheduling has led to the use of large number of

spatial constraints in MODM problems. The

conventional branch and bound algorithm has been so

limited in use that efforts have been made to develop

heuristic methods that can reduce the set of constraints

that must be included in a standard integer

programming model. Conventional solution algorithm

and two heuristic algorithms that are used to reduce the

number of constraints are reviewed and a simple

analytical algorithm to reduce the constraint set is

proposed. Three original algorithms and four versions of

the proposed heuristic are evaluated for computational

effort and number of constraints needed. Although the

two original heuristic methods resulted in fewer

constraints, computation time for each was greater than

that for any version of the proposed heuristic. The latter

method is preferred over conventional branch bound

and other heuristic algorithms.

75. Yoshimoto, Atsushi; Brodie, J. Douglas; Sessions,

John. 1994. A new heuristic to solve spatially

constrained long-term harvest scheduling

problems. Forest Science. 40(3): 365-396.

Describes a heuristic algorithm to solve integer

programming (IP) harvest-scheduling problems. This

two-stage algorithm eliminates scheduling alternatives

that are infeasible over the entire planning period, and

breaks down the scheduling problem into subproblems:

only two successive planning periods are considered at

any one time so that a selected schedule will be feasible

both in the current period and in the next period. Data

were from a forest containing 109 stands in 62 analysis

areas and a second forest with 45 units. The objective

was to maximize total present net worth for planning

periods. The solution was compared with that from a

branch and bound solution for the original integer

formulation and a relaxed linear programming (LP)

solution. Exception for the one-period schedule, the

heuristic algorithm had significantly shorter solution

times than the branch and bound method. The

difference in objective function between the branch and

bound and the heuristic solutions were less than 1

percent for all problems. The heuristic solution was

significantly less than the relaxed LP solution in the 1-

and 2-year planning problems, and was within 2 and 3

percent of the relaxed LP objective function value for

longer 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 Applications

in Forestry and Land Management

Heuristic methods are particularly applicable in

situations where data are uncertain or limited or

reasonable computation is not possible, or where there is

an attempt to improve solutions through optimization.

Ten features of the “ideal” heuristic method and eight

guidelines for applying these features are presented.

77. Choo, Eng U.; Schoner, Bertram; Wedley, William.

1999. Interpretation of criteria weights in

multicriteria decision making. Computers &

Industrial Engineering. 37: 527- 541.

A comprehensive assessment of the use of criteria

weights in MADM models examining 13 interpretations

that have been applied to these weights. Also examined

are aggregation rules, measurement units, other

comparative features of each interpretation, and the

more common methods that use them.

78. Easley, Robert F.; Valacich, Joseph S.;

Venkataramanan, M. A. 2000. Capturing group

preferences in a multicriteria decision. European

Journal of Operational Research. 125: 73-83.

Multi-attribute decision models are effective in

quantifying the preferences of an individual

decisionmaker, though natural resource decisions

generally involve multiple stakeholders. As a result, the

preferences of a wide range of groups must be

considered. The effectiveness of the analytic hierarchy

process (AHP), a variation of the standard AHP

(FNAHP), and two pairwise voting techniques are

evaluated for their ability to capture the preferences of

multiple decisionmakers and supporting group

decisionmaking. Three approaches are applied to the

allocation of sales territory between two representatives.

The resulting alternative rankings and decisionmaker

perceptions were compared across the four decision

methods. The hierarchical model was the most effective

technique for capturing group preferences.

79. Gershon, Mark. 1984. The role of weights and

scales in the application of multiobjective decision

making. European Journal of Operational Research.

15: 244-250.

A major criticism of MCDM is that the results can be

influenced, and any desired solution obtained, by

manipulating the weights used in the analysis.

Algorithms that do not require subjective weights have

been developed, though subjective input still is required

with these methods. Four MCDM compromise

programming, cooperative game theory, multiattribute
17

utility theory, and ELECTRE—were studied to

determine the role played by their weighting schemes in

the evaluation of alternatives. A general classification of

the “proper” way in which weights can be determined is

proposed. Differences among three types of weighting

approaches are illustrated and the type of weighting

scheme used, process of weight selection, and scalings

and other subjective parameters for each MCDM are

identified. 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 objective

decision support weighting techniques in natural

resource management. Journal of Environmental

Planning and Management. 43(4): 505-518.

Explores the use of five weighting techniques to better

understand the implications of choosing a multiattribute method choice for a particular natural resource

problem. The weighting methods—fixed-point scoring,

rating, ordinal ranking, graphical weighting, and paired

comparisons—are described and then applied to

prioritizing Australian National Heritage Trust projects

for funding. The selection of decisionmakers, decision

alternatives, and evaluation criteria for this problem are

discussed, and weights obtained from each approaches

are compared. Except for the paired comparison, all

techniques resulted in the same ranking of criteria,

though actual weights varied significantly. For ease of

use, the ranking method is the most preferred and the

fixed-point approach is the least preferred. The ranking

technique clarified the decision situation the most and

the graphical method the least. Decisionmakers should

not rely on a single weighting approach as different

methods may have an unknown bias.

81. Howard, Andrew F. 1991. A critical look at

multiple criteria decision making techniques with

reference to forestry applications. Canadian Journal

of Forest Research. 21: 1649-1659.

Describes various MADM to include the components

related to “procedural and mathematical formalities.”

These include scale transformations, criterion weighting,

choice of criteria, and specification of alternatives. How

each of these steps is approached affects the outcome of

the MADM process, that is, the ranking order of the

alternatives and the number of criteria that are used to

assess the achievement of an objective, influence the

weight of that objective in the analysis. Crucial issues

that should be recognized and addressed before MADM

are 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 environmental

planning and management because of their ease of use

and transparency to stakeholders. The three typical uses

of MADM are the choice of a “best” alternative, ranking

of several alternatives relative to each other, and analysis

of the degree of acceptability of alternatives. The basic

procedure for implementing MADM-driven

decisionmaking is reviewed. The importance of early and

consistent stakeholder involvement choice of evaluation

criteria and selection of the most appropriate MADM

technique are emphasized.

83. Martin, W. E.; Bender, H. Wise; Shields, D. J. 2000.

Stakeholder objectives for public lands: rankings

of forest management alternative. Journal of

Environmental Management. 58: 21-32.

In response to the National Forest Management Act and

the National Environmental Policy Act, public

participation has become an important component in

Forest Service planning and decisionmaking. In

quantifying public preferences, additive utility

methodology identifies the decision context,

stakeholders, and alternatives; elicits preferences from

stakeholders regarding the alternatives and their

attributes; and develops value functions for each

stakeholder to rank alternatives. Additive utility

functions were applied in the evaluation of alternative

multiple-use management alternatives on the San Juan

National Forest in Colorado. Alternatives were ranked by

each stakeholder identifying the order of preference

(ordinal ranking) and by cardinal value functions

(cardinal ranking). Both methods produced inconsistent

rankings, but the cardinal value functions generated the

more useful evaluations.

84. Prato, T. 2000. Multiple attribute evaluation of

landscape management. Journal of Environmental

Management. 60: 325-337.

The use of multi-attribute models in landscape-level

planning is proposed, and the multi-attribute decision

procedure is described and applied to the following

scenarios: a publicly owned watershed that is

administered by a land agency, and a basin that is

privately owned by multiple individuals. The most

efficient alternatives are identified and decisionmaker

preferences are then elicited to determine the most

favored nondominated alternative. The multi-attribute

model is useful for landscape-scale planning but might

be difficult to implement as substantial input by the

decisionmaker is required.
18

85. Pukkala, Timo; Kangas, Jyrki. 1996. A method for

integrating risk and attitude into forest planning.

Forest Science. 42(2): 198-204.

Demonstrates a method for incorporating

intergenerational perspectives into forest planning. A

heuristic method is proposed that integrates risk analysis

and attitudes toward risk. The procedure incorporates

stochastic simulation of stand development under

different treatments and across various scenarios of tree

growth and timber prices; pairwise comparison of

objectives using the analytic hierarchy process technique;

and an estimation of the decisionmaker’s attitude toward

risk. The method is applied to a case study that

represents a typical planning situation facing a private

forest owner. A solution is determined for three levels of

risk (low, normal, and high) and across three risk

perspectives (risk avoider, risk seeker, and risk neutral).

The method can be applied to both tactical and strategic

forest planning.

86. Tecle, Aregai; Fogel, Martin M.; Duckstein, Lucien.

1988. Multicriterion analysis of forest watershed

management alternatives.m Water Resources

Bulletin. 24(6): 1169-1179.

Two multi-attribute decision models, the outrankingbased ELECTRE and the distance-based compromise

programming method, are compared on the basis of how

they select a preferred management alternative. Both are

applied to a portion of the Beaver Creek watershed in

Arizona. Compromise programming was preferred over

the ELECTRE-based model for consistency and ease of

use. Neither approach was overly sensitive to changes in

criteria weights, and the most and least preferred

alternatives were the same for both methods.

87. Teeter, Lawrence D.; Dyer, A. Allen. 1986. A

multiattribute utility model for incorporating risk

in fire management planning. Forest Science. 43(4):

1032-1048.

The use for multiattribute utility theory (MAUT) is

important when uncertain information is incorporated

into planning analysis. A method for evaluating Forest

Service fire management strategies in terms of both

economic efficiency and risk is proposed. Economic

efficiency is represented by the direct costs of

implementing a particular strategy plus any change in

value of the forest that might result, and the risk

associated with that strategy. Risk is considered not as

variability in net returns but as potential loss or injury.

The process of constructing utility functions and the

technical aspects of their application are reviewed and

seven alternative strategies, including the historical

Forest Service fire management approach, are evaluated.

These strategies consisted of combinations of particular

activities, such as firebreak construction or surveillance,

and their required resources. Utility models such as

MAUT are valuable for incorporating risk/uncertainty

into complex planning processes and are useful when

outcomes are deterministic (known) and stochastic

(unknown).

Combined MODM/MADM Applications

88. Malczewski, J.; Moreno-Sanchez, R.; BojorquezTapia, L. A.; Ongay-Delhumeau, E. 1997.

Multicriteria group decision-making model for

environmental conflict analysis in the Cape

Region, Mexico. Journal of Environmental Planning

and Management. 40(3): 349-374.

The analytic hierarchy process (AHP) and integer

programming (IP) are integrated into a model for

conducting land-suitability planning. The AHP

procedure incorporates the preferences of interest groups

into the suitability analysis, and each geographic unit is

weighted according to its suitability for various landmanagement activities. The weights can be used in the

objective function of a binary IP model that maximizes

the 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 among

various interest groups over land use. Emphasis was

placed on the “political” nature of actual interactions

with these groups. The difficulties encountered in

applying this approach in a real-world situation are

discussed.

89. Mendoza, Guillermo A.; Sprouse, William. 1989.

Forest planning and decision making under fuzzy

environments: an overview and illustration. Forest

Science. 35(2): 481 502.

Describes the use of fuzzy modeling-to-generatealternatives (MGA) techniques and the analytic

hierarchy (AHP) as a two-stage process for evaluating

forest plans. The theory behind fuzzy decisionmaking

and the procedure for converting a standard linear

programming (LP) formulation a fuzzy LP are explained,

and four alternative fuzzy MGA models—regular,

selective, and weighted MAXMIN models and an

additive model—are described. The second stage of this

approach entails the use of AHP to evaluate and

prioritize the alternatives generated with the MGA

models. The basic AHP procedure of making pairwise

comparisons and then synthesizing these priorities is

examined. The method is applied to data from a real

forest. Objectives were to maximize net revenue as well

as areas suitable as wildlife habitat and for recreation; the

planning horizon was ten 10-year periods. This approach
19

is flexible and a more realistic alternative to

optimization.

MCDM Applications to Water Resources

90. Belaineh, Getachew; Peralta, Richard C.; Hughes,

Trevor C. 1999. Simulation/optimization modeling

for water resources management. Journal of Water

Resources Planning and Management. May/June:

154-161.

A combined simulation and optimization model is used

as a hypothesis-testing devise to demonstrate whether an

enhanced representation of surface water-aquifer

interactions improves overall water-use management.

This two-stage approach optimizes the water supply

based on groundwater withdrawal and stream diversion

factors, and then selects the optimal use strategy for this

increased flow regime. The model was tested using five

system scenarios. The improved surface water-aquifer

interactions representation resulted in optimal solutions

with 13 percent more surface-aquifer interflow, a 52

percent reduction in flow leaving the basin due to better

use strategies, and an 80 percent increase in groundwater pumping. This technique is an effective alternative

to optimization methods.

91. Bella, Aimee; Duckstein, Lucien; Szidarovsky,

Ferenc. 1996. A multicriterion analysis of the water

allocation conflict in the upper Rio Grande basin.

Applied Mathematics and Computation. 77: 245-

265.

Compromise programming (CP) and ELECTRE III are

used to rank management alternatives for the Upper Rio

Grande River Basin. Thirty alternative management

actions and 18 criteria by which these actions could be

evaluated were identified. Results for the two MADM

approaches are compared with both equal and unequal

weightings on the criteria. The CP method was run

several times with varying “p” values to determine how

attribute deviations from the “ideal” are treated in the

analysis. Total rankings for all 30 alternatives are

presented for both methods. Each produced

approximately the same ranking order.

92. Chang, Ni-Bin; Wen, C. G.; Wu, S. L. 1995.

Optimal management of environmental and land

resources in a reservoir watershed by

multiobjective programming. Journal of

Environmental Management. 44: 145-161.

Presents a framework for incorporating economic, social

welfare, and environmental quality factors into a

multiobjective program for watershed planning in

Taiwan. The processes of data acquisition, model

building, and model solution are described and 6

objective functions, 10 constraints, and 15 alternative

management techniques are identified. Compromise

programming is applied to solve the resulting model,

assuming equal weights on the objectives. This model

was run twice, first assuming no pollution control

measures and then considering the impact of these

strategies. Sensitivity analysis was conducted to asses

seven planning scenarios.

93. da Conceicao, Cunha; Sousa, Maria; Sousa,

Joaquim. 1999. Water distribution network design

optimization: simulated annealing approach.

Journal of Water Resources Planning and

Management. July/August: 215-221.

Due to limitations with other MODM techniques, a

simulated annealing (SA) algorithm is proposed in

designing a minimum-cost water-distribution network.

The SA process is described and tested using simplified

networks. Two test problems were chosen that had been

evaluated by a variety of decision models. Results were

compared with those from previous evaluations. In the

first test case consisting of six studies, the SA approach

tied for third place in terms of the objective function

value (i.e., lowest cost) of eight evaluations. In the

second test case, SA ranked fourth. This method is easy

to use, can handle large, nonlinear, mixed-integer

programming problems, and generates good results.

94. Das, Pransanta; Haimes, Yacov Y. 1979.

Multiobjective optimization in water quality and

land management. Water Resources Research. 15(6):

1313-1322.

The surrogate worth tradeoff (SWT) method is applied

to a water-quality and land-management planning

problem to demonstrate the ability of a MODM to

integrate both nonpoint-source and point-source

pollution into a single model. The two pollution

submodels with a cost minimization objective and a

third model with a water quality objective were

integrated into a single optimization problem that was

solved as a SWT problem using a generalized reduced

gradient algorithm. Data, both actual and hypothetical,

were generated for a basin in the Midwest that was

nearly 9,000 square mile s. Four (noninferior) alternative

plans were identified, and the level of attainment of each

objective and tradeoffs among objectives were calculated

for each alternative. The preferences of the

decisionmaker are used to develop surrogate worth

functions that are used to determine the preferred

solution. This method can address large and complex

problems and is easier to use than other MODM

methods.
20

95. David, Laszlo; Duckstein, Lucien. 1976. Multicriterion ranking of alternative long range water

resources systems. Water Resources Bulletin. 12(4):

731-754.

An existing water resource system is compared to

alternative systems to identify a scheme that meets

economic and social requirements for a watershed in

Hungary. A cost-effectiveness framework is used to guide

the planning process, with alternative evaluation

completed using ELECTRE techniques. The study site

planning objectives, evaluation criteria, and alternative

system plans are described and displayed in a “system

versus criteria” matrix, and an incomplete ranking of

alternatives is presented. This is a simple method for

ranking alternative water-resource systems.

96. Duckstein, Lucien; Opricovic, Serafim. 1980.

Multiobjective optimization in river basin

development. Water Resources Research. 16(1): 14-

20.

A combined cost-effectiveness and compromise

programming (CP) approach was applied to the design

of a water-resources system in Hungary. Costeffectiveness methodology was used as the guidelines for

evaluating and ranking alternatives; the CP method was

incorporated to allow multiobjective evaluation of the

alternatives. Results were compared with those using

ELECTRE 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 tended

to be ranked first or second; the exact order differed

between approaches.

97. Flug, Marshall; Seitz, Heather L. H.; Scott, John F.

2000. Multicriteria decision analysis applied to

Glen Canyon Dam. Journal of Water Resources

Planning and Management. September/October: 270-

276.

Presents a generic MADM method for evaluating flow

alternatives for the Glen Canyon Dam in Arizona. This

method was used to evaluate nine alternatives within

several scenarios, each with a different weighting scheme.

The analysis recommended that a new flow regime be

adopted.

98. Gershon, Mark; Duckstein, Lucien; McAniff,

Richard. 1982. Multiobjective river basin planning

with qualitative criteria. Water Resources Research.

18(2): 193-202.

A combination of ELECTRE I and ELECTRE II is used

to select a management solution for the Santa Cruz River

in Arizona. The models were used to evaluate 25 discrete

alternatives based on 13 evaluation criteria. ELECTRE I

was used as a “screening” method to reduce the set of

alternatives under consideration; ELECTRE II ranked

the remaining alternatives. Sensitivity analysis was

conducted by varying the scale intervals and the criteria

weight. The impact of these changes on the final

rankings is reported.

99. Gershon, Mark; Duckstein, Lucien. 1983.

Multiobjective approaches to river basin planning.

Journal of Water Resources Planning and

Management. 109(1): 13-28.

Four MODM were applied to a 50-year planning

problem 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 options

were identified and combined (total of 25 alternative

management schemes). The problem was evaluated by

ELECTRE, multi-attribute utility theory (MAUT),

compromise programming (CP), and game theory.

Results are presented as a set of rankings, one for each

technique; sensitivity analysis was used to examine the

impact on ranking order. Only MAUT and game theory

had the same first-ranked alternative. Results showed

that each method evaluated is appropriate to this type of

decision situation and that results were reasonably

similar.

100. Haimes, Yacov Y.; Hall, Warren A. 1974.

Multiobjectives in water resource systems analysis:

the surrogate worth trade off method. Water

Resources Research. 10(4): 615-623.

Discusses the surrogate worth tradeoff (SWT) method as

a decision tool for multiobjective water-resource

planning. The rationale for the use of SWT in

multiobjective planning, as well as the theory and basic

formulation of the modes, are discussed. The model is

recommended because it addresses noncommensurable

objectives in a quantitative fashion and is

computationally feasible.

101. Hipel, Keith W. 1992. Multiple objective decision

making in water resources. Water Resources

Bulletin. 28(1): 3-12.

Discusses the role of multiobjective decisionmaking in

all phases of water-resources planning, including

groundwater contamination management, water-quality

monitoring, water allocation, and reservoir-system

operation. MCDM techniques are divided into four

groups depending on whether they are applied to

situations with one or multiple objectives and whether

they can be used with one or multiple decisionmakers
21

(DM). In this classification scheme, most operationresearch methods are applicable in single-objective,

single-DM situations. MADM can be used when there is

a single DM and multiple objectives. Multiple DM

situations are restricted to analysis using team theory and

game theory.

102. Hobbs, Benjamin F.; Chankong, Vira; Hamadeh,

Wael; Stakhiv, Eugene Z. 1992. Does choice of

multicriteria method matter? An experiment in

water resources planning. Water Resources

Research. 28(7): 1767-1779.

Four multi-attribute models are applied to hypothetical

water-supply projects and their appropriateness, ease of

use, validity, and sensitivity of results are compared. The

methods evaluated are ELECTRE, goal programming

(GP), multi-attribute utility (MAUT) functions, and

additive value functions. The latter method was assessed

using three weighting approaches; eight hypotheses were

tested. The first three hypotheses concerned the

perceptions of users toward the usefulness of the models

and how easy or difficult they were to use. The fourth

pertained to the perceived appropriateness of the

approach; the fifth and sixth addressed both the ability

of the models to predict unaided choices among

alternatives by the users, and the construct validity of the

rating weights; and the eighth concerned the degree of

sensitivity in the final rankings to differences in who

applies a particular model and which model is used. GA

was the most understandable method and the one with

which users were most comfortable, though all four

approaches were trusted by fewer than half of the users.

Generally, users were unconvinced of the utility of

MAUT; none of the four approaches was consistently

preferred.

103. Kenney, Ralph L.; Wood, Eric F. 1977. An

illustrative example of the use of multiattribute

theory for water resource planning. Water

Resources Research. 13(4): 705-712.

Proposes the use of multi-attribute utility theory

(MAUT) as an alternative to linear programming in

water resources planning, specifically, five alternative

plans for water-resource development in a river basin in

Hungary. A previous evaluation using ELECTRE did

include uncertainty in the analysis and specified

tradeoffs among attributes only implicitly. The five

alternative plans and objectives are described and a

procedure for utility function assessment is given along

with methods for assessing component utility functions

and scaling factors. A utility value is associated with each

alternative, with the highest value indicating the most

preferred 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 control

in the Iowa and Des Moines rivers. Journal of

Water Resources Planning and Management. May/

June: 118-127.

A mixed-integer programming model was used to

evaluate the Iowa/Des Moines River Reservoir System’s

flood-control operation. The goal was to determine

whether optimizing the operation of the entire reservoir

system would be an improvement over the optimization

of reservoir subsystems independently. The model used

was intended to minimize penalties associated with

excessive or inadequate storage, flow, or release from and

between reservoirs. Formulation of the objective

function, the three penalty functions, and the constraints

are discussed and the 10 years with the largest flood

events from 70 years of flow data were chosen as the data

set for analysis. Results indicated that the optimal

operation procedure is controlling each reservoir

independently. Optimization models are particularly

useful in this context but are “only as good as their

penalty functions and constraints.”

105. Neely, Walter P.; North, Ronald M.; Fortson, James

C. 1977. An operational approach to multiple

objective decision making for public water

resources projects using integer goal

programming. American Journal of Agricultural

Economics. February: 198-203.

Integer goal programming (GP) was applied to the

selection of Tennessee Valley Authority (TVA) water

resources projects. Benefit-cost data for TVA water

projects from 1965 to 1973 were used to illustrate the

usefulness of integer GP as an alternative

decisionmaking tool. Two objectives—economic

development and environmental quality—goal levels,

and goal weights for the study are discussed. Several runs

were conducted using different weights and levels, with

the original run giving equal weighting to both

objectives. Comparisons were made between: (1) a run

in which the economic objective has a higher goal level

and one in which environmental quality is the higher

goal, and (2) a run in which both goal weights and levels

favor economic development and one where both favor

environmental quality. The resulting schedules, net

present value (NPV), and output levels were compared

for actual TVA project selections, an integerprogramming model that maximizes NPV, and the

integer GP model with equal weights and goal levels that

favor economic development.
22

106. Pouwels, H. M.; Wind, H. G.; Witter, V. J. 1995.

Multiobjective decision making in integrated

water management. Physics and Chemistry of the

Earth. 20(3-4): 221-227.

Examines the usefulness of a general MADM technique

in evaluating alternatives for water management in the

Netherlands. Problem formulation, criteria, measures,

and the MADM algorithm used in the study are

described, and the significant effect of uncertainties on

the ranking of alternatives is discussed.

107. Yoon, Jae-Heung; Shoemaker, Christine A. 1999.

Comparison of optimization methods for groundwater bioremediation. Journal of Water Resources

Planning and Management. January/February: 54-63.

Compares the computational performance of three

classes of algorithms in the selection of a cost-effective

policy for ground-water bioremediation. Algorithm

classes evaluated include: (1) evolutionary algorithms,

specifically, real-coded genetic algorithms (RGA),

binary-coded genetic algorithms (BIG), and

derandomized evolutionary strategy (DES); (2) direct

search methods, specifically, modified simplex (MSLX),

Nelder-Mead simplex (NSLX), and parallel directive

search (PDS); and (3) derivative-based optimization

methods, specifically implicit filtering for constrained

optimization (IFFCO) and a version of SALQR. The use

of simulation to generate the impacts of alternative

ground-water pumping policies on system characteristics

of interest is described. This simulation model is linked

to the optimization methods to determine optimal

bioremediation policy. SALQR consistently performed

the fastest, though no algorithm produced the best

solution in all cases. The BIGA method was considered a

poor choice for use in ground-water bioremediation.

108. Zsuffa, I.; Bogardi, J. J. 1995. Floodplain

restoration by means of water regime control.

Physics and Chemistry of the Earth. 20(3-4): 237-

243.

ELECTRE II was used to evaluate several restoration

techniques for a flood plain in Hungary. Results of the

case study showed that ELECTRE II and MADM in

general are effective in helping decisionmakers choose

the “best compromise” alternative based on specific

preferences.

MCDM Applications to Fisheries

109. Mardle, Simon; Pascoe, Sean. 1999. A review of

applications of multiple criteria decision-making

techniques to fisheries. Marine Resource

Economics. 14: 41-63.

A comprehensive survey of MCDM that have been

applied to issues related to fishery management case

studies are categorized by multiple objective

programming (MOP, MADM, and other MODM).

MOP includes goal programming, generating methods,

and nonlinear MOP. MADM include multiattribute

utility theory and the analytic hierarchy process;

multilevel programming is included as an “other”

MODM. The basic formulation of each model and its

application and limitations are discussed. MCDM have

great potential for improving fisheries management

policy because of their flexibility.

110. Önal, Hayri. 1996. Optimum management of a

hierarchically exploited access resource: a

multilevel optimization approach. American

Journal of Agricultural Economics. 78: 448-459.

Presents a multilevel optimization method for choosing

the best policy options for open-access resources that are

subject to hierarchical decision processes. The method is

applied to fisheries management planning, specifically,

the perspectives of management authority and individual

users (or user groups) in making decisions concerning

shrimp harvests in Texas. A single-level mathematical

program formulated to maximize total net revenue from

all fishing activities and a multilevel formulation and

potential solution methods are discussed. The model is

applied to scenarios for both regulated and unregulated

management.

Other Environmental Applications

111. Bonano, E. J.; Apostolakis, G. E.; Salter, P. F.;

Ghassemi, A.; Jennings, S. 2000. Application of risk

assessment and decision analysis to the evaluation,

ranking and selection of environmental

remediation alternatives. Journal of Hazardous

Materials. 71: 35-57.

Presents a framework for combining risk assessment and

a MADM for the selection of remediation alternatives at

a hazardous waste site, and how it would be used to

assess the impacts of alternatives, incorporate public

participation, educate stakeholders regarding risks, and

generate good, defensible solutions. Four framework

components preliminary analysis, decision-analysis

impact assessment and integration, and deliberation of

integration results are described. Decision analysis

entails: 1) structuring the problem as a decision

hierarchy, specifically impact categories, objectives, and

performance measures, and 2) the use of the analytic

hierarchy process (AHP) and fuzzy theory to determine

the relative importance of each element at each level of

the hierarchy. Simple pairwise comparisons are used to

rate impact categories and the objectives within each of
23

those categories. Performance measures were evaluated

by AHP and fuzzy logic to define utility functions that

described the level of “goodness” for the range of

possible performance for each measure. Impact

assessment was used to evaluate the performance of each

alternative on each performance measure. Risk

assessment was used to convert these values into utility

functions so that uncertainties could be captured. The

result was a ranking of all remediation alternatives for

each stakeholder and a mean ranking for each alternative

from the group as a whole. The deliberation process was

used to determine how consensus was reached among all

stakeholders on a “best” solution.

112. Cooper, W. W.; Hemphill, H.; Huang, Z.; Li, S.;

Lelas, V.; Sullivan, D. W. 1996. Survey of

mathematical programming models in air

pollution management. European Journal of

Operational Research. 96: 1-35.

Describes current MODM research in air pollution

management to include institutions involved, regulatory

activity, risk management, and selection of management

goals and attributes. Basic mathematical programming

approaches that are surveyed include deterministic

programming, which is illustrated using linear

programming and goal programming, and stochastic

programming, which is illustrated with a chanceconstrained programming model. The application of

these and two additional approaches to problems related

to management are discussed.

113. Hokkanen, Joonas; Salminen, Pekka. 1997.

Choosing a solid waste management system using

multicriteria decision analysis. European Journal of

Operational Research. 98: 19 36.

ELECTRE III was applied to the selection of a

municipal solid waste-management system in northern

Finland. This method was chosen because it is fast and

easy to use, data were imprecise, and numerous

decisionmakers were involved who provided little

information on preferences. Results are presented as a

ranking of the alternatives; the impact of sensitivity

analysis on those rankings is discussed. This technique is

useful for situations in which keeping decisionmakers

informed is a requirement.

114. Tecle, Aregai; Fogel, Martin. 1986. Multiobjective

wastewater management planning in a semiarid

region. Hydrology and Water Resources in Arizona

and the Southwest. 16: 43-61.

ELECTRE and compromise programming were used in

the selection of the “best” design for a wastewater

treatment facility in Nogales, Arizona. The same

alternative was selected with both models.

Decision-Support Systems

115. Brack, Christopher L.; Marshall, Peter L. 1996. A

test of knowledge-based forest operations

scheduling procedures. Canadian Journal of Forest

Research. 26: 1193-1202.

Solution outputs were compared for three knowledgebased search routines, two expert systems, linear

programming (LP), mixed integer programming (IP),

and simulation methods that were applied to two forest

plantations in Australia. A set of operations schedules

were compared for each site. An algorithm rated each

alternative on the basis of timber-yield flows, scenic

beauty, stand health, and water quality. The expert

systems and search routines performed well relative to

the IP and simulation techniques. The LP model

generated higher timber flows than most of the other

methods; one expert system produced an even higher

flow using nonstandard management regimes.

Knowledge-based approaches and expert systems do not

attempt to create optimal plans, but their flexibility can

generate good solutions.

116. Gurocak, Elizabeth Reilly; Whittlesey, Norman K.

1998. Multiple criteria decisionmaking: a case

study of the Columbia River salmon recovery plan.

Environmental and Resource Economics. 12(4): 479-

495.

A salmon recovery plan for the Columbia River was used

as a case study to compare the performance of two

MCDM—simple additive weighting and the interactive

method—with a fuzzy expert system. Each method

ranked alternatives on the basis of five attributes. The

methods are compared on the outputs obtained by the

highest ranked alternatives. Unlike the MCDM solutions,

alternatives selected by the fuzzy expert system always

were appropriate, that is, decision rules were satisfied.

117. Hong, Hyoo B.; Vogel, Doug R. 1991. Data and

model management in a generalized MCDM-DSS.

Decision Sciences. 22: 1-25.

Describes a method for designing a decision-support

system (DSS) that supports an organization in

formulating and solving multi-criteria problems. The

typical multi-attribute method of representing

alternatives is reviewed. Multi-criteria models are

categorized, and various choice methods are described.

Whether compensatory or noncompensatory, the models

are categorized according to the cognitive demands on

decisionmakers. Choice rules discussed include the
24

additive, additive-difference, dominance, conjunctive,

disjunctive, lexicographic, and elimination by aspects

models. A set of principles for guiding the selection of an

appropriate choice rule is suggested, and the process of

executing the chosen model is described. The basic DSS

architecture and prototype model (ISBIS) are described,

and two examples of the applicability of the approach

are provided.

118. Malczewski, Jacek; Jackson, Marlene. 2000.

Multicriteria spatial allocation of educational

resources: an overview. Socio-Economic Planning

Sciences. 34: 219-235.

In response to criticism of optimization (MODM)

techniques, decision-support systems are being used to

facilitate the allocation of education resources. Typical

allocational issues related to educational resources are

reviewed, and basic multiobjective formulation and

several models that have been applied to allocation issues

are presented. Typical planning attempts use data

envelope analysis (which is based on a mathematical

programming model), parametric programming, and

goal programming. As an alternative approach to

educational resource planning, it is proposed that multicriteria decision techniques and a geographic

information system be combined into an interactive

Spatial Decision-Support System (SDSS) to take

advantage of the visualization capabilities of an

interactive SDSS.

119. Naesset, Erik. 1997. A spatial decision support

system for long-term forest management planning

by means of linear programming and a

geographical information system. Scandinavian

Journal of Forest Research. 12: 77-88.

Describes SGIS, a decision-support system that

integrates a geographic information system and linear

programming into a strategic planning system. Although

limited to areas with no more than 2,000 stands, SGIS

simulates the effects of treatment schedules, selects the

optimal schedule, and generates maps and tables. SGIS

was applied to a 719-ha, 872-unit forest in southeast

Norway to determine the impact of establishing

restricted-use buffers around water bodies with respect to

net present value (NPV) and timber volume. The buffer

areas resulted in a reduction in NPV of nearly 7 percent

and reduction in timber volume of about 10 percent.

Although SGIS is a valuable planning tool, it is not

applicable to large areas nor can it incorporate spatial

constraints into the optimization process.

120. Olson, Craig M.; Orr, Bruce. 1999. Combining

tree growth, fish and wildlife habitat, mass

wasting, sedimentation, and hydrologic models in

decision analysis and long term forest land

planning. Forest Ecology and Management. 114:

339-348.

Discusses the trend toward using MCDM in

conjunction with other processes and models to develop

a more diverse and comprehensive approach to forest

management planning. The methodology outlined is

intended for landscape-scale management situations and

has been applied to areas ranging in size from 50,000 to

230,000 acres. Models that were incorporated into this

planning process include digital terrain models, sitequality information, vegetation-class data, timber growth

and yield models, and a watershed risk index. Linear

programming was used to maximize the present net

value of management activities subject to numerous

constraints.

121. Purao, Sandeep; Jain, Hemant K.; Nazareth, Derek

L. 1999. Supporting decision making in

combinatorially explosive multicriteria situations.

Decision Support Systems. 26: 225-247.

Presents a decision support system based on multiobjective and multi-attribute decision theory as an

effective method for addressing problems characterized

by a “combinatorially explosive” number of solutions

and many conflicting criteria. A weakness of three

categories of solution procedures, analytical, genetic

algorithm-based, and heuristic approaches, is their

inability to support decisionmaker learning. The first

step in the proposed decision support system entails a

“broad exploration of the search space.” Information

gathered on search space limits and behavior is given to

the decisionmaker to facilitate educated preference input

in later stages. The second step consists of deep probes

into promising search space regions. The decisionmaker

is guided in an iterative and systematic process of

exploring alternatives, steering the direction of the search

by the specification of his or her preferences. The model

provides information about unexplored regions of the

decision space to the decisionmaker by assessing the

likelihood of improving on the current solution’s levels

of attainment for each criterion. When applied to a

client/server architecture problem, this method places

only moderate demands on the decisionmaker and

quantifies the risk of stopping the search process at any

point.

122. Rauscher, H. Michael. 1999. Ecosystem

management decision support for federal forests in

the United States: a review. Forest Ecology and

Management. 114: 173 197.

Presents a generic decision-support system (DDS) for

ecosystem management on federal forests. The typical
25

adaptive management process as it is applied to

ecosystem management is discussed and 33 ecosystem

management DSS are compared. Decision methods

(MODM) are discussed as a single component in a

much larger planning process.

123. Tecle, Aregai; Shrestha, Bijaya P.; Duckstein,

Lucien. 1998. A multiobjective decision support

system for multiresource forest management.

Group Decision and Negotiation. 7: 23-40.

Describes FORMDSS, an interactive, multiobjective

decision support system that incorporates both

compromise programming and cooperative game theory

into a single tool for resource management. Data are

from a pine forest in north-central Arizona managed for

multiple objectives. Five objectives, each of which is

based on a single variable—square feet of tree basal area

per acre—are intended to represent the views of a

different interest group or decisionmaker. For each

objective, a graph specifies the relationship between basal

area and a particular resource goal, and indicates the

level of utility that would be achieved by a group

advocating the maximization of that resource. This

relationship is described mathematically as a timeinvariant continuous function. Tradeoffs that occur

across different basal-area densities are demonstrated for

both MCDM. The objectives were given equal weights

to identify a narrow range of basal-area densities that all

(hypothetical) decisionmakers found satisfactory.

FORMDSS can handle any number of objective

functions, allows for easy modification of preference

structures and other model parameters, and facilitates

understanding through graphical representation of

model inputs and outputs.

124. Varma, Vive K.; Ferguson, Ian; Wild, Ian. 2000.

Decision support system for the sustainable forest

management. Forest Ecology and Management. 128:

49-55.

Describes a decision support system for forest

management that combines geographic information

systems (GIS), a heuristic, and linear programming (LP)

in a flexible model that addresses uncertainty and

maximizes the utility derived from the products

generated through alternative management plans. LP

generates the optimal land allocation solution and then

the spatial distribution of these uses is solved with a

heuristic algorithm. Although this heuristic does not

guarantee that the optimal utility level generated in the

LP model will be attained, this approach should be

effective when sustainability in forest management is an

issue.
26

Allen, Julia

28

Anderson, David J.

25

Apostolakis, G. E.

111

Barahona, Francisco

58

Barber, Klaus

37

Bare, B. Bruce

1, 25, 29, 32, 70

Belaineh, Getachew

90

Bell, Enoch F. 2

Bella, Aimee

91

Bender, H. Wise

83

Bettinger, Pete

60, 61, 62, 63

Bevers, Michael

45

Bodie, J. Douglas

69

Bogardi, J. J.

108

Bojorquez-Tapia, L. A.

88

Bonano, E. J.

111

Borges, Jose G.

49

Bos, Jan

64

Boscolo, M.

7, 30

Boston, Kevin

60, 62

Brack, Christopher L.

115

Briggs, David G. 1

Brodie, J. Douglas

38, 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, Christian

36

Center, Calum J.

15

Chang, Ni-Bin

92

Chang, S. J.

17

Chankong, Vira

102

Chevalier, P.

42

Cholaky, Alejandro

39

Choo, Eng U.

77

Chung, Joosang

14

Church, Richard L.

37, 40, 52, 53, 72

Cooper, W. W.

112

da Conceicao, Cunha

93

Daellenbach, H. G.

41

Dahir, S. 8

Das, Pransanta

94

de Kluyver, C. A.

41

de Steiguer, J.E.

18

Dent, J. B.

21

Duckstein, Lucien

24, 86, 91, 95, 96, 98, 99, 123

Dyer, A. Allen

87

Easley, Robert F.

78

Epstein, R.

42

Epstein, Rafael

58, 59

Evans, James R.

76

Faaland, Bruce H.

70

Ferguson, Ian

124

Flug, Marshall

97

Fogel, Martin M.

86, 114

Fortson, James C.

105

Gabarro, J.

42

Garcia, Oscar 5

Gershon, Mark

79, 98, 99

Ghassemi, A.

111

Gilless, J. K. 4

Guinard, Monique

43, 72

Gurocak, E. R.

116

Haight, Robert G.

44

Haimes, Yacov Y.

94, 100

Hajkowicz, Stefan A.

80

Hall, Warren A.

100

Hamadeh, Wael

102

Author Index
27

Hemphill, H.

112

Hipel, Keith W.

101

Hobbs, Benjamin F.

102

Hof, John

45, 46, 47, 48

Hoganson, Howard

49

Hokkanen, Joonas

82, 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, Marlene

118

Jain, Hemant K.

121

Jamnick, Mark S.

10

Jennings, S.

111

Jofre, Alejandro

36

Johnson, Norman

11, 61, 63

Jones, J. Greg

50, 73

Joyce, Linda

46, 47

Julio, Berbel

20

Kangas, Jyrki

66, 85

Keeney, Ralph L.

103

Kirby, Malcom W.

50

Klemperer, W. David

65

Kolbe, A.

31

Korhonen, Pekka

24

Kowero, G.

21

Lahdelma, Risto

82

Lancia, Richard

14

Laszlo, David

95

Lelas, V.

112

Lennartz, Mike

14

Li, S.

112

Lin, C.R.

8, 26

Lockwood, Carey

67

Lu, H.C.

8, 12

Lund, Jay R.

104

Magendzo, Adrian

73

Magendzo, Ariel

73

Malchuk, Daniel

73

Malczewski, Jacek

88, 118

Manley, Bruce

59

Mardle, Simon

109

Marshall, Peter L.

115

Martin, W.E.

83

McAniff, Richard

98

McDonald, Geoff T.

80

Meacham, Mary

73

Mendoza, Guillermo A.

29, 32, 89

Meneghin, Bruce J.

50

Moore, Tom

67

Moreno-Sanchez, R.

88

Murphy, Glen

59

Murphy, James L.

13

Murray, Alan T.

37, 40, 51, 52, 53, 68, 72

Naesset, Erik

119

Nazareth, Derek L.

121

Needham, Jason T.

104

Neely, Walter P.

105

Nelson, John

38, 69

Nhantumbo, I.

21

Nieto, E.

42

Nieuwenhuis, Maarten 6

North, Ronald M.

105

O’Hara, Anthony

70

Olson, Craig M.

120

Omi, Philip N.

13
28

Onal, Hayri

110

Ongay-Delhumeau, E.

88

Opricovic, Serafim

96

Orr, Bruce

120

Pascoe, Sean

109

Peralta, Richard C.

90

Perlack, R. D.

35

Peyron, J. L.

16

Pouwels, H. M.

106

Prato, T.

84

Pukkala, Timo

66, 85

Purao, Sandeep

121

Puumalainen, Janna

27

Raphael, Martin G.

48

Rauscher, H. Michael

122

ReVelle, Charles

55, 56, 57

Roise, Joseph P.

1, 14, 54

Rowse, John

15

Ryu, Choonho

43

Salminen, Pekka

82, 113

Salter, P. F.

111

Schoner, Bertram

77

Schreuder, Gerard F. 1

Schuler, Albert T.

23

Schulte, B.

33

Scott, John F.

97

Seitz, Heather L. H.

97

Sessions, John

38, 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, Stephanie

55, 56, 57

Sousa, Joaquim

93

Sousa, Maris

93

Spielberg, Kurt

43

Sprouse, William

89

Stakhiv, Eugene Z.

102

Steuer, Ralph E.

23

Sullivan, D. W.

112

Szidarovsky, Ferenc

91

Tecle, Aregai

24, 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, William

77

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, Ian

124

Willis, C. E.

35

Wind, H.G.

106

Witter, V. J.

106

Wood, Eric F.

103

Wu, S. L.

92

Yoon, Jae-Heung

107

Yoshimoto, Atsushi

74, 75

Zamora, Richardo

20

Zanakis, Stelios H.

76

Zsuffa, I.

108
29

Glossary

0 — 1 Integer Programming (see Binary Integer

Programming).

1 opt, 2 opt — concepts in heuristic timber harvest

scheduling. With 1-opt moves, only one attribute of one

decision choice is altered, i.e., a unit is removed from the

harvesting schedule. In 2-opt moves, that attribute is

changed for two decision choices simultaneously, i.e.,

one unit is added to the harvest schedule while another

is removed.

Adjacency Constraints — constraints in mathematical

programming that control the occurrence of spatially

related activities, e.g., the harvesting of timber in

adjacent forest plots.

Algorithm — in mathematics, any computational

procedure (see Simplex Method as an example).

Analytic Hierarchical Process (AHP) — a decision

method in which a complex problem is structured as a

hierarchy involving goals, criteria, objectives and

alternatives; pair-wise comparisons of criteria and

alternatives result in the specification of a preferred

solution.

Area-Restricted Model (ARM) — a concept in timber

harvest modeling with adjacency constraints. If

management units are significantly smaller than the area

limit of the adjacency constraint, then harvest of

adjacent units does not necessarily violate the constraints

and the ARM is used (see URM).

Binary Coded Genetic Algorithm (BIGA). See Genetic

Algorithm and 0 - 1 Integer Programming.

Binary Integer Programming — a form of integer

programming in which the values of the decision

variables are restricted to 1 or 0.

Branch and Bound Algorithm — a technique that uses

an efficient search algorithm for solving integer

programming problems.

Bridging Analysis Models (BAM) — a method for

decomposing optimal strategic-level solutions into

optimal tactical-level plans on forests.

Compromise Programming (CP) — a solution

technique that uses distance metrics to weight various

objectives to account for their different importance to

the decisionmaker. The alternative with the lowest

summed deviation from the objectives is designated as

the “best” solution.

Constraints — limits placed on and thus defining a

problem’s solution space, usually in the form of

equations stated as mathematical equalities or

inequalities.

Cooperative Game Theory — a form of game theory in

which the participants cooperate to find a solution as

opposed to noncooperative solutions, i.e., participants

compete against each other.

Decision Support Systems (DSS) — a class of

interactive computer-based systems and subsystems that

help decisionmakers use data, documents, knowledge,

and/or models to identify and solve problems and make

decisions.

Dominated Solutions (see Inferior Solutions).

Dynamic Programming (DP) — a problem-solving

approach that allows a large problem to be broken into a

series of smaller problems or stages. The solution of all

the smaller individual problems results in an optimal

solution to the large problem.

Economically Inefficient (efficient) Solutions —

solutions to economic cost-benefit analyses where costs

are greater (less) than benefits.

ELECTRE, ELECTRE 1, 2, 3 — MADM techniques

that facilitate decisionmaking by reducing the number of

feasible alternatives to be considered.

Feasible Solution — A solution that satisfies all of the

specified constraints (see Infeasible Solution).

FORMDSS — an interactive, multiobjective decision

support system that incorporates both compromise

programming and cooperative game theory into a single

tool for resource management.

FORPLAN — FORest PLANning model; a linear

programming approach used by the USDA Forest

Service for land management planning.

Four Color Theorem — related to timber harvest

scheduling with adjacency constraints. For problems that

require adjacent units to be harvested no less than a

specified number of years apart (the exclusion period),

this theorem implies that a feasible solution is possible so

long as the project period length divided by the

exclusion period length is less than or equal to four. The
30

theorem name is derived from the four colors used in

mapmaking, for example, to distinguish different

political states on a map.

Fuzzy Logic — an approach to computing based on

degrees of truth rather than the usual “true or false” (i.e.,

1 or 0). Includes 0 and 1 as extreme cases of truth, but

also the various states of truth in between so that, for

example, the result of a comparison between two things

could be not “tall” or “short” but “ .38 of tallness.”

Fuzzy Programming — mathematical programming

that uses fuzzy logic (see Fuzzy Logic).

Generating Methods — Techniques for identifying

tradeoffs that are necessary among each of the decision

alternatives. This information is presented to the

decisionmaker who selects the most preferred option.

Genetic Algorithm (GA) — a heuristic solution

algorithm in which the first step is generating a

“population” of random solutions that are represented as

“strings” composed of binary values for each decision

variable. Each value corresponds to an “allele” on the

string, which represents DNA; hence the name.

Geographic Information System (GIS) — a computer

system for entering, processing, analyzing, and

displaying spatial data and information, often a map-like

format.

Goal Programming (GP) — a technique for solving

multiobjective decision problems within the framework

of linear programming. Target values are established for a

set of separate goals and the programming objective is to

minimize the collective deviation from these targets.

HERO — a utility-based heuristic method for

addressing harvest scheduling problems that explicitly

considers biodiversity.

Heuristic Techniques — methods for problem solving

through experimentation and especially trial and error.

They are typically used for computationally hard-tosolve problems and seek a compromise between a quick

feasible solution and a feasible solution that is optimal.

Hierarchy — a structure for a decision problem using

various levels consisting of goals, criteria, objectives, and

decision alternatives (see AHP).

Infeasible Solution — occurs when two or more

constraints have been specified that cannot be satisfied

simultaneously, for example, simultaneous satisfaction of

x> 100 and x< 75 is infeasible.

Inferior Solutions — solutions that are not Pareto

optimal; also known as locally efficient solutions or

dominated solutions.

Integer Programming (IP) — a problem-solving

approach like linear programming except that decision

variables are integers rather than continuous values.

Integrated Resource Planning Model (IRPM) — an

integer programming planning model used by the

USDA Forest Service.

Lagrangian Relaxation — a mathematical

programming technique for performing constrained

optimization through the introduction of Lagrangian

multipliers—which are arbitrary non-zero constraints—

to the constraints.

Lexicographic Goal Programming — a technique that

assigns absolute priorities to the goals. Also called

preemptive GP, this approach satisfies the multiple

objectives sequentially in the order established by the

priorities.

Linear Programming (LP) — a mathematical problemsolving approach that entails maximization or

minimization of a single linear objective function subject

to multiple linear constraints.

MAXMIN Model — attempts to maximize the

minimum payoff; generally said to be a betting

pessimist’s strategy. Some argue that MAXMIN finds a

socially “just” solution in the sense that it identifies the

best possible outcome for members of society who are

most needy.

Metropolis Algorithm (MA) — a timber-harvest

scheduling algorithm related to the Monte Carlo

heuristic technique.

Mixed Integer Program — a mathematical program

that uses both integer and continuous decision variable.

Model I Formulation, Model II Formulation — two

methods for defining decision variables in a timber

harvest scheduling problem. With Model I, decision

variables are the same for both original and regenerated

stands. With Model II, different decision variables are

defined for the original and the regenerated stands.
31

Modeling to Generate Alternatives (MGA) — the use

of mathematical programming models to generate a

series of possible alternative decision choices from which

the decisionmaker chooses the preferred alternative.

Monte Carlo Heuristic Techniques — heuristic

solution methods using simulations analogous to the

probabilistic outcomes of roulette played in the casinos

of Monte Carlo.

Monte Carlo Integer Programming — a heuristic

solution method for integer programs involving the use

of probabilistic inputs generated by a Monte Carlo

process.

Multi-Attribute Decision Models (MADM) — a

subdivision of MCDM, MADM support the selection

of the “best” decision alternative from among several

possibilities. Examples of MADM methods include the

Analytic Hierarchy Process and Multi-Attribute Utility

Theory.

Multi-Attribute Utility Theory (MAUT) — assumes

that an individual can select among obtainable

alternatives in a way that maximizes the amount of

satisfaction he/she derives from that choice. This theory

assumes that individuals are aware of the alternatives

available to them and are capable of evaluating those

alternatives.

Multi-Criteria Decision Models (MCDM) — refers to

a variety of quantitative techniques used to facilitate

decisions involving multiple, competing objectives or

goals. MCDM were first developed for military strategic

decisionmaking but have been expanded to include such

diverse fields as financial planning, real estate

investment, reservoir control, water distribution, solid

waste management, energy planning, manufacturing,

and forest management. Often subdivided into MODM

(Multi-Objective Decision Models) and MADM (MultiAttribute Decision Models).

Multi-Objective Decision Model (MODM) — a

subdivision of MCDM, MODM support the design of

superior decision alternatives; methods include linear,

goal, and integer programming.

Multi-Objective Programming (MOP) — programs

that require the simultaneous optimization of more than

one objective function. This method optimizes each

separate objective function followed by an interactive

search for a compromise solution that is Pareto optimal;

also called Multi-Objective Linear Programming.

Network Analysis — a graphical description of a

decision problem in terms of nodes and interconnected

arcs enabling solutions to problems related to

transportation, information systems, and project

scheduling.

Non-Inferior Set Estimation (NISE) — a multiobjective programming solution algorithm that uses

repeated linear programming solutions to generate an

estimate of a non-inferior set.

Non-convex Decision Space — a decision space or

choice not involving a decreasing rate of technical

substitution, i.e., not bowed toward the origin.

Non-Dominated Solutions (see Non-Inferior

Solutions).

Non-Inferior Solutions — solutions that are Pareto

optimal; also known as globally efficient or nondominated solutions.

Non-linear Programming — an alternative to linear

programming that uses a non-linear objective function.

Objective Function — an equation that expresses

mathematically the goal of a decision problem/ usually

stated as a maximization of minimization problem.

Optimal Solution — a best solution, i.e., the

attainment of a maximum or minimum value subject to

specified constraints.

Pareto Optimal — a feasible solution such that no other

possible solution is superior to it.

PARETO RACE — a type of decision support system

that enables a decisionmaker to freely search the efficient

frontier of a multiple objective quadratic-linear

programming problem by controlling the speed and

direction of motion.

Programming — a general term applied to a host of

mathematical planning techniques, including linear,

goal, integer, and non-linear programming.

Recursive Dynamic Programming — a solution

method by which a large problem is divided into smaller

problems or stages; each of the smaller problems is

solved in sequence, feeding into the next higher stage.

SGIS — a decision support system that integrates a

geographic information system and linear programming

into a single planning system.
32

SHARe Model — a harvest planning model that uses

spatial constraints but also allows temporal management

considerations.

Shortest Path Network Flow Model — a network

model by which the optimal problem solution is found

by the shortest path between any pair of nodes in the

network.

Simple Additive Weighting (SAW) — an MCDM

method.

Simplex Method — an algebraic procedure for solving

linear programming problems.

Simulated Annealing (SA) — a heuristic solution

method based on simulation of the material tempering

process know as annealing.

Simulation Modeling — a technique in which

computers typically are used to model the operation of a

complex system by abstracting, simplifying, and hence

simulating the true system.

SNAP 11+ — a harvest scheduling program that uses an

integer programming formulation and a heuristic

solution algorithm.

STEM — a Modeling to Generate Alternatives

technique for forest planning applications.

Stochastic Programming — a form of mathematical

programming in which the inputs are uncertain and

subject to variation; this contrasts with deterministic

models in which the inputs are certain and not subject to

variation.

Successive Approximation Linear Quadratic

Regulator (SALQR) — a software program that has

been used for optimization problems in which nonlinear simulation equations are made linear in the

optimization step.

Surrogate Worth Trade-Off (SWT) — a utility-based

algorithm.

TABU search — a heuristic solution method that relies

upon near-neighbor solutions that can be reached

directly from an initial solution by a single move, i.e.,

adding a unit, removing a unit, or exchanging two units.

Trigger Constraints — constraints of mathematical

programming problems invoked or “triggered” by

predetermined conditions.

Unit Restrictive Model (URM) — refers to timber

harvesting with adjacency constraints. Applied when

management units are so large that the harvest of two

adjacent units would necessarily violate adjacency

constraints (see ARM).

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

Weighting Methods — used to indicate the relative

importance of the evaluation criteria to the

decisionmaker. Examples of weighting methods are fixed

point scoring, rating, ordinal ranking, graphical

weighting, and paired comparisons.
Printed on Recycled Paper

de Steiguer, J. E.; Liberti, Leslie; Schuler, Albert; Hansen, Bruce. 2003. Multicriteria 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 when

developing land-management plans. Conflicts may encompass economic,

environmental, social, cultural, technical, and aesthetic objectives. Selecting the

best combination of management uses from numerous objectives is difficult and

challenging. Multi-Criteria Decision Models (MCDM) provide a systematic means for

comparing tradeoffs and selecting alternatives that best satisfy the decisionmaker’s

objectives. In recent years, the use of MCDM in forestry and natural resources

management has generated a substantial body of literature. This annotated

bibliography includes 124 important references ranging from theoretical studies to

real-world applications of MCDM.

Keywords: linear programming, goal programming, mathematical programming,

dynamic programming, hierarchical programming, heuristics
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