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Comparing Adjacency Constraint Formulations for Randomly Generated Forest Planning Problems with Four Age-Class Distributions

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Three types of adjacency constraint formulations—pairwise, Type I ND (nondominated), and NOAM (new ordinary adjacency matrix)—were compared on 900 hypothetical, randomly generated, spatially explicit forest management problems with between 50 and 350 stands. Forests were generated using four age-class distributions, nominally called immature, regulated, overmature, and old-growth. Management planning problems with adjacency constraints were formulated for these forests in Model 1 format based on a planning horizon consisting of three 20 yr periods. The problems also included flow constraints and minimum average age requirements for the ending forest. For all age-class distributions, the Type I ND constraint type resulted in significantly lower solution times than either the Pairwise or the NOAM constraint types. NOAM constraints performed better than Pairwise constraints for immature forest problems, but Pairwise constraints performed better than NOAM constraints for overmature and old-growth forest problems. There was no difference between these two constraint types for regulated forest problems. Results also show that the age-class distribution of the forest is one of the most important factors determining the time needed to solve forest management problems with adjacency constraints. In general, the more mature the forest, the harder the problem is to solve. In particular, problems based on the old-growth age-class distribution typically took much longer to solve than comparable problems based on the other age-class distributions. FOR. SCI. 46(3): 423–536.

Keywords: Forest management; area-based forest planning; environmental management; forest; forest management; forest resources; forestry; forestry research; forestry science; harvest scheduling; integer programming; natural resource management; natural resources; spatial optimization

Document Type: Miscellaneous

Affiliations: 1: Assistant Professor of Forest Management School of Forest Resources, The Pennsylvania State University, 214B Ferguson Building, University Park, PA, 16802-4301, Phone: (814) 865-1602; Fax: (814) 865-3725 2: Project Associate School of Forest Resources, The Pennsylvania State University,

Publication date: 2000-08-01

More about this publication?
  • 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

    Average time from submission to first decision: 62.5 days*
    June 1, 2016 to Feb. 28, 2017

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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