Difference between revisions of "Spectrum"

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	=== Brief overview ===		=== Brief overview ===
	Spectrum is a linear programming based model designed to schedule management treatments to achieve ecosystem management and financial, or other goals. Model formulation is flexible, allowing representation of simple and complex environmental interactions.		Spectrum is a linear programming based model designed to schedule management treatments to achieve ecosystem management and financial, or other goals. Model formulation is flexible, allowing representation of simple and complex environmental interactions.
−	In a Spectrum model a user constructs a representation of natural processes and possible management actions and  on a landscape. They also construct a representation of decision criteria in the form of management objectives and physical constraints.	+	In a Spectrum model a user constructs a representation of natural processes and possible management actions on a landscape. They also construct a representation of decision criteria in the form of management objectives and physical constraints.  A linear programming solver chooses the best mix of management options to meet specified goals and objectives.
	[[Category:Decision support system]]		[[Category:Decision support system]]
	[[Category:USA DSS]]		[[Category:USA DSS]]
	[[Category:linear programming]]		[[Category:linear programming]]
−		+	[[File:SpectrumBrochure.jpg | frame ]]
	__TOC__		__TOC__
	=== Scope of the system ===		=== Scope of the system ===
−	* tool encourages decision maker to discover new problems or opportunities by exposing to new information or results
−	* tool helps decision makers in recognizing upcoming problems for which solutions have been developed previously
−	* tool allows decision maker to actively create new knowledge when faced with a new problem and to develop novel solutions
−	* tool allows decision maker to capture knowledge, making it available to decision makers who are seeking solutions from previously solved problems
	=== System origin ===		=== System origin ===
Line 28:		Line 24:
	=== Support for specific issues  ===		=== Support for specific issues  ===
−	Is the system designed to take into account specific uses? E.g. guidance on ways to characterize biodiversity, economic-biodiversity tradeoff analysis methods, risk assessment methods, landscape analysis methods, timber harvest effects, climate change effects, biological effects (pests, pathogens, invasives), fire,...	+	Spectrum is a flexible modeling system that can be used for a variety of land management planning problems.
	=== Support for specific thematic areas of a problem type  ===		=== Support for specific thematic areas of a problem type  ===
−	* Silvicultural	+	Spectrum is useful for a wide range of applications:
−	* Certification	+	*Forest Plan amendment and revision
−	* Conservation	+	*Landscape/watershed scale analysis
−	* Restoration	+	*Designing sustainable management strategies
−	* Transportation	+	*Land and resource allocation
−	* Development choices / land use zoning	+	*Estimating levels of goods and services
−	* Policy/intervention alternatives	+	*Finding pathways to desired conditions
−	* Sustainability impact assessment (SIA)	+	*Management activity scheduling
		+	*Environmental effects analysis
		+	*Economic analysis
		+	*Tradeoff analysis
		+	*Sensitivity analysis
		+	*Policy analysis
	=== Capability to support decision making phases  ===		=== Capability to support decision making phases  ===
−	''(NOTE I do not quite know what to do with this, as I do not understand it myself, although it seems related to system use)''
	(Click [[Simon's decision making model|here]] to see a more detailed explanation)		(Click [[Simon's decision making model|here]] to see a more detailed explanation)
−	* Intelligence (+ explicit description of the support given by the DSS)	+	* Intelligence
−	* Design (+ explicit description of the support given by the DSS)	+	No specific functionality for this phase
−	* Choice (+ explicit description of the support given by the DSS)	+	* Design
−	* Monitor (+ explicit description of the support given by the DSS)	+	Spectrum offers extensive automation in the generation of management options for land units.  It also offers automation for the creation of objectives and constraints to be applied to any sub-unit of the forest, for any portion of the planning horizon.
		+	* Choice
		+	Spectrum offers many objective function formulations for the linear programming problem.
		+	* Monitor
		+	No specific functionality for this phase
	=== Related systems  ===		=== Related systems  ===
−	Describe (and/or link to) other systems related	+	Spectrum has a custom utility to import data from the USFS Forest Vegetation Simulator (FVS).
	== Data and data models ==		== Data and data models ==
	=== Typical spatial extent of application  ===		=== Typical spatial extent of application  ===
−	Define the scale of use for the application (user defined, regional, multi-owner forest single ownership forest, Multiple scale interaction)	+	The spatial scale for a Spectrum model is user defined. USFS models are usually constructed for an entire National Forest which can be one hundred thousand to four million acres in size.  In these models, analysis units are usually discontiguous parcels of land with similar attributes.  Other uses of Spectrum are more tactical, modelling management options on thousands of acres with analysis units representing contiguous management parcels.
	=== Forest data input  ===		=== Forest data input  ===
−	Describe the basic forest input (forest level, stand level, or individual tree level), and appropriate meta-data, such as data provenance (Areal coverage, Sample of plots, stands, Contiguous forest cover). GIS information is to be considered here, namely include cover tyes and type of information (raster or vectorial, necessity of topological information)  If necessary describe surrogate sources of information
−	If necessary describe other types of required data (economic, social)	+	[[File:SpectrumSystem2.jpg | frame | Data components of a Spectrum model]]
		+
		+	Spectrum is a modeling system and contains no data itself.  Land units are described with up to six user defined attributes.  Management actions are also user defined and are assigned as a management option to land units.  Most forest outputs are input as forest strata level growth and yield tables.  These tables can contain any number of metrics.  Management actions are described as a series of activities that occur through time. Other outcomes and effects are calculated in quantitative relationships with these primary outputs and management activities.  Natural processes are represented by state variables related to activities and outputs as they change through time.  All activities and outputs may have associated costs and revenues.
		+
		+	Management objectives are represented as controls on levels of activities, outputs or states through time. These controls are input as simple equations that control the absolute level of a variable, the relative value of a variable to another or the relative change in a variable's  value from one period to another.
		+
		+	Most bulky data sections have utilities that allow import from comma-delimited files.  A special import utility allows import from the Forest Vegetation Simulator (FVS).
	=== Type of information input from user (via GUI) ===		=== Type of information input from user (via GUI) ===
−	Describe what is the information that the user directly inputs in the system if any): expert knowledge, opinion, goals and production objectives, preferences, stand/site information....	+	As a modeling system, Spectrum contains no data.  The user enters all data via a user interface.  Import utilities are employed to take large data pieces, like yield tables and analysis unit lists, from comma-delimited files.  A special import utility is used to import yield information from the USFS Forest Vegetation Simulator (FVS). All data are stored in dBase type data tables, so advanced users can manipulate data with other database applications such as MS Access.
	== Models ==		== Models ==
	=== Forest models ===		=== Forest models ===
−	Growth, Yield, Carbon, Wood quality, biodiversity and habitat suitability, environmental and external effects (fire, storms, pests, diseases, climate change, etc)	+	Spectrum is designed to import forest growth information from other forest models.  A general import format is supported along with a custom utility for import from the Forest Vegetation Simulator.
		+	[[File:SpectrumModel2Diagram.jpg | frame | A decision tree modeled with Spectrum generalized Model 2 formulation]]
		+	Spectrum also provides a modeling structure for representing natural disturbance and ecological simulation:
		+	*Probabilistic mortality
		+	*State, flow and accessory variables for ecological process simulation
		+	*Decision tree for modifying successional pathway
		+	*Spatial relationships and dynamics
		+
		+	These formulations are supported by a generalized Model 2<ref>Johnson, K. Norman, and Scheurman, H. Lynn. Techniques for Prescribing Optimal Timber Harvest and Investment Under Different Objectives - Discussion and Synthesis. 1977. Forest Science Monograph. </ref> structure in the LP matrix.
	=== Social models  ===		=== Social models  ===
−	historical and cultural values of sites, values due to peace and quiet, esthetic values, values due to recreational activities, ethical values): E. g. Recreation, Health, Game
−
	== Decision Support ==		== Decision Support ==
	=== Definition of management interventions ===		=== Definition of management interventions ===
−	Define what is available for the manager to intervene in the forest: time of harvest, plantations, thinnings, reconversions...	+	All traditional silvicultural treatments can be represented.  Yield table representations of treatments from growth and yield simulators can be imported.  Also, from a single yield table representing natural growth, many harvest timing options can be generated with harvests represented as a proportion of the inventory.  Other activities associated with treatments can be generated with time, age or sequence relationships to forest outputs.
−	Existence of prescription writer, simple enumeration of all possibilities, scenario simulation , etc.	+
		+	There is a great deal of functionality for creating many management options with minimal data redundancy.
	=== Typical temporal scale of application ===		=== Typical temporal scale of application ===
−	Define the temporal scale of the application: E.g., operational and immediate level, Tactical planning (short term) and strategic level.	+	Spectrum can represent '''90 time periods''' or steps of user-defined length. The most typical use is for long range planning of 150 to 200 years using 10-year periods.  Five-year and one-year time steps have also been used.
	=== Types of decisions supported  ===		=== Types of decisions supported  ===
−	*Management level	+	Spectrum is a flexible modeling tool that can be used to answer a wide range of planning questions:
−	**strategic decisions	+
−	**administrative decisions	+	* What is the  Long Term Sustained Yield Capacity (LTSYC) of the forest?
−	**operating control decisions	+	* What are the likely timber production amounts and what silvicultural systems will be used?
−	* Management function	+	* What will the forest look like in 100 years under a management scenario?
−	* planning decisions	+	* Are desired conditions feasible?
−	**organizing decisions	+	* How long to reach desired conditions?
−	**command decisions	+	* What are the tradeoffs between desired conditions?
−	**control decisions	+
−	** coordination decisions	+
−	*decision making situation	+
−	**unilateral	+
−	** collegial	+
−	**Bargaining / participative decision making	+
	=== Decision-making processes and models ===		=== Decision-making processes and models ===
−	*Logic modeling	+	Spectrum is a linear programming based system.  It offers great flexibility in the types of objective function formulations that can be constructed.
−	*Operations research modeling	+	* Maximization
−	**Direct approaches	+	* Minimization
−	**Heuristic manipulation of simulation models	+	* Iterative Max or Min - maximize X then maximize Y subject to level achieved for X
−	*Business modeling	+	* Goal programming
−	*Simulation (with and without stochasticity)	+	**minimize deviations above targets
−	*Multiple criteria/ranking	+	**minimize deviations below targets
−	*Other	+	**minimize deviations above or below targets
		+	**minimize deviations from a relative target (variable X should be close to 5% of variable Y)
		+	* MAX/MIN<ref>HOF, J.G., J.B. PICKENS, AND E.T. BARTLETT. 1986. A MAXMIN approach to
		+	nondeclining yield timber harvest scheduling problems. For. Sci.
		+	32(3):653–666. </ref> - maximize the minimum occurrence of a critical resource
		+	* MIN/MAX - minimize the highest level of occurrence of a undesirable outcome
	== Output ==		== Output ==
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	=== Types of  outputs ===		=== Types of  outputs ===
−	Types of outputs produced (tables, maps, 3-D visualizations, pre-programmed summaries, etc)	+	The Spectrum report writer interprets the results of a "solution" and can produce outputs in several forms:
		+	* Formatted reports for a variety of model outputs to user defined summary level (forest-wide, sub-unit etc.)
		+	* Comma delimited files with the same content and flexibility of formatted reports.
		+	* Database tables (dBase format) with fine-grained results that can be queried and aggregated in the Spectrum Report Template.
	=== Spatial analysis capabilities  ===		=== Spatial analysis capabilities  ===
−	* integrated capabilities
−	* facilitates links to GIS (wizards, etc.)
−	* provides standard data import/export formats
−	* allows spatial analysis (e.g. topology overlays (e.g. multi layering of different maps, selection of objects based on selection criteria, aggregation by attributes (e.g. areas of similar characteristics), Linking by logical means, Statistics by area, analysis with digital terrain model)
	=== Abilities to address interdisciplinary, multi-scaled, and political issues  ===		=== Abilities to address interdisciplinary, multi-scaled, and political issues  ===
−	Evaluate interactions between different basic information types (biophysical, economic, social). Produce coordinated results for decision makers operating at different spatial scales facilitate social negotiation and learning
	== System ==		== System ==
Line 137:		Line 150:
	=== Architecture and major DSS components ===		=== Architecture and major DSS components ===
−	Describe the basic architecture of the system in software and hardware. Desktop client-server, web based, as well as the integration with available systems. Basic data flow, focusing on retrieval of required input and propagation and implementations of decisions. Mention its modular and scalability capabilities.	+	Spectrum is a desktop application that runs in Windows operating systems.  It requires the use of a commercial LP solver software and uses the MPSIII product from Ketron Optimization. Data are input into the system via forms or imported from comma-delimited files. Model results are output in a variety of forms: formatted reports, comma-delimited files or dBase tables.
	=== Usage ===		=== Usage ===
−	Describe the level of use: Research level use, Industry use, Government use	+	Spectrum is used by government, industry and research<ref>Bevers, Michael and Hof, John. 1999. Spatially Optimizing Wildlife Habitat Edge Effects in Forest Management Linear and Mixed-Integer Programs. Forest Science 45(2): 249-258 </ref> entities.
	=== Computational limitations ===		=== Computational limitations ===
Line 148:		Line 161:
	=== User interface ===		=== User interface ===
−	Describe the quality of user interface and the Prerequisite knowledge for using the system	+	Spectrum has a fully functional user interface in which all the tasks of model editing, matrix generation, LP solving and solution interpretation can be accomplished.  Formatted reports can be viewed from the interface, but complex graphing and reporting of results are done with spreadsheet or database software.
	=== Documentation and support ===		=== Documentation and support ===
Line 154:		Line 167:
	The USFS Planning Analysis Group in Fort Collins, Colorado, provides user support for Spectrum to USDA Forest Service employees. Others can use the contacts below to inquire about support options:		The USFS Planning Analysis Group in Fort Collins, Colorado, provides user support for Spectrum to USDA Forest Service employees. Others can use the contacts below to inquire about support options:
	* Mail can be addressed to:		* Mail can be addressed to:
−	: Planning Analysis Group<br />	+	: Planning Analysis Group
−	USDA Forest Service<br />	+	: USDA Forest Service
−	2150 Centre Ave. Bldg. A<br />	+	: 2150 Centre Ave., Bldg. A
−	Fort Collins, CO. 80526<br />	+	: Fort Collins, CO. 80526
−	Attn: Spectrum	+	: Attn: Spectrum
	* E-Mail can be addressed to: bmeneghin@fs.fed.us		* E-Mail can be addressed to: bmeneghin@fs.fed.us
	=== Installation ===		=== Installation ===
−	* Prerequisite knowledge: Level of effort to become functional	+	The [https://fsplaces.fs.fed.us/fsfiles/unit/wo/emc/imi/IMI_OPEN_TeamRoom.nsf/1ba02e5ee0ba987c8525663a006cb7ec/5a6444c3218e258b8725711c007cdffa/$FILE/Spectrum30_Overview.pdf Spectrum Overview ] provides a good introduction to Spectrum.
−	* Cost: (purchase price, development costs, demonstrated return on investment, cost of use, training costs, licence and maintenance costs)	+
−	* Demo: allows the download/utilization of a trial version. If yes, where is it available and what are the trial conditions.	+	The Spectrum installation package contains example tutorial models with annotations in the model description.  You can contact [http://www.ketronms.com/  Ketron] for a trial version of the MPSIII solver and pricing.
		+
		+	Spectrum requires general knowledge of forest management and knowledge of linear programming techniques <ref>Kent, Brian M. 1989. Forest Service Land Management Planners' Introduction to Linear Programming.  USDA Forest Service, Rocky Mountain Forest and Range Experiment Station, General Technical Report RM-173, Fort Collins, CO. </ref>.
	==References==		==References==
Line 172:		Line 187:
	===External resources===		===External resources===
−	[http://www.fs.fed.us/institute/planning_center/plan_spectrum.html Spectrum web site]	+	[https://fsplaces.fs.fed.us/fsfiles/unit/wo/emc/imi/IMI_OPEN_TeamRoom.nsf/1ba02e5ee0ba987c8525663a006cb7ec/9d6ec3fa57ddc68f8725711d007210b7?OpenDocument Spectrum web site]

---

Latest revision as of 00:33, 1 November 2014

General System description

System name: Spectrum

Brief overview

Spectrum is a linear programming based model designed to schedule management treatments to achieve ecosystem management and financial, or other goals. Model formulation is flexible, allowing representation of simple and complex environmental interactions.

In a Spectrum model a user constructs a representation of natural processes and possible management actions on a landscape. They also construct a representation of decision criteria in the form of management objectives and physical constraints. A linear programming solver chooses the best mix of management options to meet specified goals and objectives.

Scope of the system

System origin

Spectrum is based on the FORPLAN system developed by Dr. K. Norman Johnson and colleagues at Utah State and Colorado State Universities, and the members of the U.S. Forest Service (USFS) WO-LMP Systems Application Unit (now EMC-PAG) in Fort Collins, Colorado. FORPLAN Version 1 was developed in 1980, followed by FORPLAN Version 2 in 1983. FORPLAN became the "required primary analysis tool" for the development of National Forest land management plans by the USFS.

In 1991 the USFS Rocky Mountain Forest and Range Experiment Station, in cooperation with the USFS Ecosystem Management Analysis Center, moved the current UNISYS mainframe release of FORPLAN to the microcomputing environment and discontinued development efforts for the mainframe environment. These two groups collaborated in the development of Spectrum. Spectrum was designed to have a graphical user interface; execute on PCs; retain FORPLAN analytical capabilities with expanded modeling options and size limits; and provide new analytical capability to address ecosystem management issues.

The Spectrum system is available for no charge to the public. It does require the use of a commercial LP solver software, and uses the MPSIII system from Ketron Optimization.

Support for specific issues

Spectrum is a flexible modeling system that can be used for a variety of land management planning problems.

Support for specific thematic areas of a problem type

Spectrum is useful for a wide range of applications:

• Forest Plan amendment and revision
• Landscape/watershed scale analysis
• Designing sustainable management strategies
• Land and resource allocation
• Estimating levels of goods and services
• Finding pathways to desired conditions
• Management activity scheduling
• Environmental effects analysis
• Economic analysis
• Tradeoff analysis
• Sensitivity analysis
• Policy analysis

Capability to support decision making phases

(Click here to see a more detailed explanation)

• Intelligence

No specific functionality for this phase

• Design

Spectrum offers extensive automation in the generation of management options for land units. It also offers automation for the creation of objectives and constraints to be applied to any sub-unit of the forest, for any portion of the planning horizon.

• Choice

Spectrum offers many objective function formulations for the linear programming problem.

• Monitor

No specific functionality for this phase

Related systems

Spectrum has a custom utility to import data from the USFS Forest Vegetation Simulator (FVS).

Data and data models

Typical spatial extent of application

The spatial scale for a Spectrum model is user defined. USFS models are usually constructed for an entire National Forest which can be one hundred thousand to four million acres in size. In these models, analysis units are usually discontiguous parcels of land with similar attributes. Other uses of Spectrum are more tactical, modelling management options on thousands of acres with analysis units representing contiguous management parcels.

Forest data input

Spectrum is a modeling system and contains no data itself. Land units are described with up to six user defined attributes. Management actions are also user defined and are assigned as a management option to land units. Most forest outputs are input as forest strata level growth and yield tables. These tables can contain any number of metrics. Management actions are described as a series of activities that occur through time. Other outcomes and effects are calculated in quantitative relationships with these primary outputs and management activities. Natural processes are represented by state variables related to activities and outputs as they change through time. All activities and outputs may have associated costs and revenues.

Management objectives are represented as controls on levels of activities, outputs or states through time. These controls are input as simple equations that control the absolute level of a variable, the relative value of a variable to another or the relative change in a variable's value from one period to another.

Most bulky data sections have utilities that allow import from comma-delimited files. A special import utility allows import from the Forest Vegetation Simulator (FVS).

Type of information input from user (via GUI)

As a modeling system, Spectrum contains no data. The user enters all data via a user interface. Import utilities are employed to take large data pieces, like yield tables and analysis unit lists, from comma-delimited files. A special import utility is used to import yield information from the USFS Forest Vegetation Simulator (FVS). All data are stored in dBase type data tables, so advanced users can manipulate data with other database applications such as MS Access.

Models

Forest models

Spectrum is designed to import forest growth information from other forest models. A general import format is supported along with a custom utility for import from the Forest Vegetation Simulator.

Spectrum also provides a modeling structure for representing natural disturbance and ecological simulation:

• Probabilistic mortality
• State, flow and accessory variables for ecological process simulation
• Decision tree for modifying successional pathway
• Spatial relationships and dynamics

These formulations are supported by a generalized Model 2^[1] structure in the LP matrix.

Social models

Decision Support

Definition of management interventions

All traditional silvicultural treatments can be represented. Yield table representations of treatments from growth and yield simulators can be imported. Also, from a single yield table representing natural growth, many harvest timing options can be generated with harvests represented as a proportion of the inventory. Other activities associated with treatments can be generated with time, age or sequence relationships to forest outputs.

There is a great deal of functionality for creating many management options with minimal data redundancy.

Typical temporal scale of application

Spectrum can represent 90 time periods or steps of user-defined length. The most typical use is for long range planning of 150 to 200 years using 10-year periods. Five-year and one-year time steps have also been used.

Types of decisions supported

Spectrum is a flexible modeling tool that can be used to answer a wide range of planning questions:

• What is the Long Term Sustained Yield Capacity (LTSYC) of the forest?
• What are the likely timber production amounts and what silvicultural systems will be used?
• What will the forest look like in 100 years under a management scenario?
• Are desired conditions feasible?
• How long to reach desired conditions?
• What are the tradeoffs between desired conditions?

Decision-making processes and models

Spectrum is a linear programming based system. It offers great flexibility in the types of objective function formulations that can be constructed.

• Maximization
• Minimization
• Iterative Max or Min - maximize X then maximize Y subject to level achieved for X
• Goal programming
  • minimize deviations above targets
  • minimize deviations below targets
  • minimize deviations above or below targets
  • minimize deviations from a relative target (variable X should be close to 5% of variable Y)
• MAX/MIN^[2] - maximize the minimum occurrence of a critical resource
• MIN/MAX - minimize the highest level of occurrence of a undesirable outcome

Output

Types of outputs

The Spectrum report writer interprets the results of a "solution" and can produce outputs in several forms:

• Formatted reports for a variety of model outputs to user defined summary level (forest-wide, sub-unit etc.)
• Comma delimited files with the same content and flexibility of formatted reports.
• Database tables (dBase format) with fine-grained results that can be queried and aggregated in the Spectrum Report Template.

Spatial analysis capabilities

Abilities to address interdisciplinary, multi-scaled, and political issues

System

System requirements

Spectrum requires the following operating system and support software:

• Windows 98, Windows 2000, Windows XP (untested on Windows Vista, Windows 7)
• C-Whiz linear programming solver by Ketron for solving models,
• Adobe Acrobat Reader, V6.x or greater for viewing help files,
• Text file viewing software such as Notepad or Wordpad

Spectrum continues to be maintained by the U.S. Forest Service

Architecture and major DSS components

Spectrum is a desktop application that runs in Windows operating systems. It requires the use of a commercial LP solver software and uses the MPSIII product from Ketron Optimization. Data are input into the system via forms or imported from comma-delimited files. Model results are output in a variety of forms: formatted reports, comma-delimited files or dBase tables.

Usage

Spectrum is used by government, industry and research^[3] entities.

Computational limitations

• The planning horizon can be up to 90 periods of any length.
• There are no limits to the number of analysis units that can be represented.
• There are a small number of model parameters that have limits - see the user guide for details.

User interface

Spectrum has a fully functional user interface in which all the tasks of model editing, matrix generation, LP solving and solution interpretation can be accomplished. Formatted reports can be viewed from the interface, but complex graphing and reporting of results are done with spreadsheet or database software.

Documentation and support

Spectrum has a full electronic user guide in .PDF format. The user interface has context sensitive links to that user guide. The USFS Planning Analysis Group in Fort Collins, Colorado, provides user support for Spectrum to USDA Forest Service employees. Others can use the contacts below to inquire about support options:

• Mail can be addressed to:

Planning Analysis Group

USDA Forest Service

2150 Centre Ave., Bldg. A

Fort Collins, CO. 80526

Attn: Spectrum

• E-Mail can be addressed to: bmeneghin@fs.fed.us

Installation

The Spectrum Overview provides a good introduction to Spectrum.

The Spectrum installation package contains example tutorial models with annotations in the model description. You can contact Ketron for a trial version of the MPSIII solver and pricing.

Spectrum requires general knowledge of forest management and knowledge of linear programming techniques ^[4].

References

Cited references

1. ↑ Johnson, K. Norman, and Scheurman, H. Lynn. Techniques for Prescribing Optimal Timber Harvest and Investment Under Different Objectives - Discussion and Synthesis. 1977. Forest Science Monograph.
2. ↑ HOF, J.G., J.B. PICKENS, AND E.T. BARTLETT. 1986. A MAXMIN approach to nondeclining yield timber harvest scheduling problems. For. Sci. 32(3):653–666.
3. ↑ Bevers, Michael and Hof, John. 1999. Spatially Optimizing Wildlife Habitat Edge Effects in Forest Management Linear and Mixed-Integer Programs. Forest Science 45(2): 249-258
4. ↑ Kent, Brian M. 1989. Forest Service Land Management Planners' Introduction to Linear Programming. USDA Forest Service, Rocky Mountain Forest and Range Experiment Station, General Technical Report RM-173, Fort Collins, CO.

External resources

Spectrum web site