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Nonlinear Programming Approaches to Multistand Timber Harvest Scheduling

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Abstract:

This paper describes several nonlinear programming formulations of multistand (analysis area) timber harvest scheduling problems and compares these formulations with more traditional approaches. The strengths of the nonlinear programming approaches include the abilities to represent explicit nonlinear timber yield functions and to define continuous harvest timing variables. Optimal control theory has these capabilities but, to date, the technique has not proven applicable to multistand problems or to problems with common exogenous constraints. Linear programming works well with multistand problems but utilizes piecewise approximations of yield functions and discrete time periods. Both nonlinear and linear programming can accommodate common programming constraints such as output targets and limits on inputs. The nonlinear programming formulations were solved using a version of the generalized reduced gradient algorithm. It was discovered that a local optimum exists for each number of harvests on each analysis area. Because nonlinear programming finds local optima, the global optimum was determined with multiple advanced starts. A nonlinear programming formulation that can handle time-period-based constraints is provided, but could not be solved. For. Sci. 36(4):894-907.

Keywords: Linear programming; constrained optimization; optimal control theory

Document Type: Journal Article

Affiliations: Project Leader, Rocky Mountain Forest and Range Experiment Station, USDA Forest Service, Fort Collins, CO.

Publication date: December 1, 1990

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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