Environmental Modeling & Assessment

, Volume 13, Issue 1, pp 1–15 | Cite as

Promoting Large, Compact Mature Forest Patches in Harvest Scheduling Models

  • Sándor F. TóthEmail author
  • Marc E. McDill


Spatially explicit harvest scheduling models that can promote the development of dynamic mature forest patches have been proposed in the past. This paper introduces a formulation that extends these models by allowing the total perimeter of the patches to be constrained or minimized. Test run results suggest that the proposed model can produce solutions with fewer, larger, and more compact patches. In addition, patches are more likely to be temporally connected with this formulation. Methods for identifying the tradeoffs between the net present value of the forest and the size and perimeter of the evolving patches are demonstrated for a hypothetical forest.


spatially explicit forest planning integer programming dynamic habitat patches minimum perimeter tradeoffs 



The authors thank the Editor-in-Chief and the anonymous reviewers for their helpful comments. They also thank the Pennsylvania Bureau of Forestry for providing financial support for this research.


  1. 1.
    Carter, D. R., Vogiatzis, M., Moss, C. B., & Arvanitis, L. G. (1997). Ecosystem management or infeasible guidelines? Implications of adjacency restrictions for wildlife habitat and timber production. Canadian Journal of Forest Research, 27, 1302–1310.CrossRefGoogle Scholar
  2. 2.
    Fischer, D. T., & Church, R. L. (2003). Clustering and compactness in reserve site selection: An extension of the biodiversity management area selection model. Forest Science, 49(4), 555–565.Google Scholar
  3. 3.
    Franklin, J. F., & Forman, R. T. (1987). Creating landscape patterns by forest cutting: Ecological consequences and principles. Landscape Ecology, 1, 5–18.CrossRefGoogle Scholar
  4. 4.
    Gates, J. E., & Gysel, L. W. (1978). Avian nest dispersion and fledgling success in field-forest ecotones. Ecology, 59, 871–883.CrossRefGoogle Scholar
  5. 5.
    Gustafson, E. J., & Crow, T. R. (1998). Simulating spatial and temporal context of forest management using hypothetical landscapes. Environmental Management, 22(5), 777–787.CrossRefGoogle Scholar
  6. 6.
    Harris, L. D. (1984). The fragmented forest: Island biogeography theory and the preservation of biotic diversity (p. 211). Chicago, IL: The University of Chicago Press.Google Scholar
  7. 7.
    ILOG (2003). CPLEX 9.0 Reference Manual, in ILOG Optimization Suite 2.0 Documentation.Google Scholar
  8. 8.
    Johnson, K. N., & Scheurman, H. L. (1977). Techniques for prescribing optimal timber harvest and investment under different objectives – discussion and synthesis. Forest Science Monographs, 18.Google Scholar
  9. 9.
    Jones, J. G., Meneghin, B. J., & Kirby, M. W. (1991). Formulating adjacency constraints in linear optimization models for scheduling projects in tactical planning. Forest Science, 37(5), 1283–1297.Google Scholar
  10. 10.
    Litvaitis, J. A. (1993). Response of early successional vertebrates to historic changes in land use. Conservation Biology, 7(4), 866–873.CrossRefGoogle Scholar
  11. 11.
    Marianov, V., ReVelle, C. S., & Snyder, S. (In Review). Selecting compact habitat reserves for species with differential habitat size needs.Google Scholar
  12. 12.
    Matlack, G. R., & Litvaitis, J. A. (2000). Forest edges. In M. L. Hunter (Ed.), Maintaining biodiversity in forest ecosystems (p. 698). Cambridge, UK: Cambridge Univ. Press.Google Scholar
  13. 13.
    McDill, M. E., Rebain, S., & Braze, J. (2002). Harvest scheduling with area-based adjacency constraints. Forest Science, 48(4), 631–642.Google Scholar
  14. 14.
    McDonnell, M. D., Possingham, H. P., Ball, I. R., & Cousins, E. A. (2002). Mathematical methods for spatially cohesive reserve design. Environmental Modeling and Assessment, 7, 107–114.CrossRefGoogle Scholar
  15. 15.
    Murray, A. T. (1999). Spatial restrictions in harvest scheduling. Forest Science, 45(1), 45–52.Google Scholar
  16. 16.
    Murray, A. T., & Church., R. L. (1996a). Analyzing cliques for imposing adjacency restrictions in forest models. Forest Science, 42(2), 166–175.Google Scholar
  17. 17.
    Murray, A. T., & Church, R. L. (1996b). Constructing and selecting adjacency constraints. INFOR, 34(3), 232–248.Google Scholar
  18. 18.
    Önal, H., & Briers, R. A. (2002). Incorporating spatial criteria in optimum reserve network selection. Proceedings of the Royal Society of London B, 269, 2437–2441.CrossRefGoogle Scholar
  19. 19.
    Önal, H., & Briers, R. A. (2003). Selection of a minimum-boundary reserve network using integer programming. Proceedings of the Royal Society of London B, 270, 1487–1491.CrossRefGoogle Scholar
  20. 20.
    Önal, H., & Briers, R. A. (2006). Optimal selection of a connected reserve network. Operations Research, 54(2), 379–388.CrossRefGoogle Scholar
  21. 21.
    Paton, P. W. C. (1994). The effect of edge on avian nest success: How strong is the evidence? Conservation Biology, 8, 17–26.CrossRefGoogle Scholar
  22. 22.
    Rebain, S., & McDill, M. E. (2003a). Can mature patch constraints mitigate the fragmenting effect of harvest opening size restrictions? International Transactions in Operational Research, 10(5), 499–513.CrossRefGoogle Scholar
  23. 23.
    Rebain, S., & McDill, M. E. (2003b). A mixed-integer formulation of the minimum patch size problem. Forest Science, 49(4), 608–618.Google Scholar
  24. 24.
    Snyder, S., & ReVelle, C. (1996a). Temporal and spatial harvesting of irregular systems of parcels. Canadian Journal of Forest Research, 26, 1079–1088.CrossRefGoogle Scholar
  25. 25.
    Snyder, S., & ReVelle, C. (1996b). The grid packing problem: Selecting a harvest pattern in an area with forbidden regions. Forest Science, 42(1), 27–34.Google Scholar
  26. 26.
    Snyder, S., & ReVelle, C. (1997a). Multiobjective grid packing model: An application in forest management. Location Science, 5(3), 165–180.CrossRefGoogle Scholar
  27. 27.
    Snyder, S., & ReVelle, C. (1997b). Dynamic selection of harvests with adjacency restrictions: The SHARe Model. Forest Science, 43(2), 213–222.Google Scholar
  28. 28.
    Spies, T. A., & Turner, M. G. (1999). Dynamic forest mosaics. In M. L. Hunter (Ed.), Maintaining biodiversity in forest ecosystems (p. 698). Cambridge, UK: Cambridge Univ. Press.Google Scholar
  29. 29.
    Tahvonen, O. (2004). Timber production versus old-growth preservation with endogenous prices and forest age-classes. Canadian Journal of Forest Research, 34(6), 1296–1310.Google Scholar
  30. 30.
    Thompson, E. F., Halterman, B. G., Lyon, T. J., & Miller, R. L. (1973). Integrating timber and wildlife management planning. The Forestry Chronicle, 247–250.Google Scholar
  31. 31.
    Tóth, S. F., McDill, M. E., & Rebain, S. (2006). Finding the efficient frontier of a bi-criteria, spatially-explicit harvest scheduling problem. Forest Science, 52(1), 93–107.Google Scholar
  32. 32.
    Williams, J. C., & ReVelle, C. S. (1996). A 0–1 programming approach to delineating protected reserves. Environment and Planning. B, Planning and Design, 23, 607–624.CrossRefGoogle Scholar
  33. 33.
    Williams, J. C., & ReVelle, C. S. (1998). Reserve assemblage of critical areas: A zero–one programming approach. European Journal of Operational Research, 104, 497–509.CrossRefGoogle Scholar
  34. 34.
    Williams, J. C., ReVelle, C. S., & Levin, S. A. (2005). Spatial attributes and reserve design models: A review. Environmental Modeling and Assessment, 10, 163–181.CrossRefGoogle Scholar
  35. 35.
    Wright, J., ReVelle, C. S., & Cohon, J. L. (1983). A multiobjective integer programming model for the land acquisition problem. Regional Science and Urban Economics, 13, 31–53.CrossRefGoogle Scholar
  36. 36.
    Yahner, R. H. (1988). Changes in wildlife communities near edges. Conservation Biology, 2, 333–339.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Natural Resource Ecology and ManagementOklahoma State UniversityStillwaterUSA
  2. 2.Penn State School of Forest ResourcesUniversity ParkUSA

Personalised recommendations