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A Mixed-Integer Formulation of the Minimum Patch Size Problem

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Abstract:



Forest harvest scheduling models have addressed wildlife habitat concerns in a variety of ways. One way is through minimum patch size constraints specifying that a certain amount of the forest must consist of patches meeting both minimum size and minimum age requirements. Patch size requirements may be necessary because a forest with only small patches of mature habitat may not be able to support populations of some wildlife species. Maximum harvest opening size constraints, which are often imposed for legal or policy reasons, tend to divide forest habitat into small patches. Minimum patch size constraints may be able to help mitigate the negative impact of maximum harvest opening size restrictions. Patch size requirements have been considered elsewhere, but a mixed-integer linear programming (MILP) formulation has never been presented. This article presents such a formulation, which allows minimum patch size problems to be solved using the branch and bound algorithm available through commercial solver packages. An example problem is formulated, solved, and discussed. For. Sci. 49(4):608–618.

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

Document Type: Miscellaneous

Affiliations: 1: Biometrician USDA Forest Service, Ft. Collins, CO, 80526, Phone: 970-295-5793; Fax: 970-295-5755 sarebain@fs.fed.us 2: Associate Professor of Forest Management School of Forest Resources, The Pennsylvania State University, mem14@psu.edu

Publication date: August 1, 2003

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

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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