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Finding the Efficient Frontier of a Bi-Criteria, Spatially Explicit, Harvest Scheduling Problem

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This article evaluates the performance of five traditional methods and one new method of generating the efficient frontier for a bi-criteria, spatially explicit harvest scheduling problem. The problem is to find all possible efficient solutions, thus defining the trade-offs between two objectives: (1) maximizing the net present value of the forest and (2) maximizing the minimum area over the planning horizon in large, mature forest patches. The methods for generating the efficient frontier were tested using a hypothetical forest consisting of 50 stands. The methods were compared based on the number of efficient solutions each method can identify and on how quickly the solutions were identified. The potential to generalize these algorithms to 3- or n-criteria cases is also assessed. Three of the traditional approaches, the - constraining; the triangles method, the decomposition algorithm based on the Tchebycheff metric; and the new, proposed method are capable of generating all or most of the efficient solutions. However, the triangles and the new method far outperformed the other approaches in terms of solution time. The new method, called alpha-delta, appears to be the simplest to generalize to the tri-criteria case.

Keywords: 0–1 programming; Multicriteria optimization; trade-off analysis; wildlife habitat

Document Type: Research Article

Affiliations: 1: Sándor F. Tóth, Research Associate, Penn State School of Forest Resources, 214B Ferguson Bldg., University Park, PA 16802—Phone: (814) 865-1602;, Fax: (814) 865-3725, Email: 2: Marc E. McDill, Associate Professor, Penn State School of Forest Resources, 214B Ferguson Bldg., University Park, PA 16802—Phone: (814) 865-1602;, Email: 3: Stephanie A. Rebain, Forester, USDA Forest Service, Forest Management Service Center, 2150A Centre Avenue, Suite 341A, Ft. Collins, CO 80526-1891—Phone: (970) 295-5793;, Email:

Publication date: 2006-01-01

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

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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