Nothing Special   »   [go: up one dir, main page]
Skip to main content

Advertisement

Springer Nature Link
Log in

Modeling forest core area with integer programming

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Abundant and continuous old forest tend to be fragmented into isolated and small patches because of human harvest activities. Dispersive and isolated old forest patches cannot provide abundant interior habitat to wildlife, which is a fatal threat for specific plant communities and wildlife species. In this paper, an Integer Programming model for forest planning is designed to maximize the economical benefit of the forest and to guarantee a minimum area of interior old forest for wildlife habitat, the so-called core area satisfying minimum mature age requirements. The minimum core area constraints, to some degree, can help mitigate the negative impact of harvest activities to divide forest habitat into many small patches. The model is implemented in a commercial Integer Programming solver and it is applied to several hypothetical landscapes. The results show the possibility of incorporating a core area requirement into a forest planning model, and the possibility to obtain solutions within a reasonable computational time. Instances with up to 1600 management units have been solved in seconds to an optimality gap of 1% (0.1% in some cases).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Baskent, E., & Jordan, G. (1995). Characterizing spatial structure of forest landscapes. Canadian Journal of Forest Research, 25, 1830–1849.

    Article  Google Scholar 

  • Bettinger, P., & Boston, K. (2001). Development of spatially feasible forest plans: a comparison of two modeling approaches. Silva Fennica, 35(4), 425–435.

    Google Scholar 

  • Bettinger, P., & Zhu, J. P. (2006). A new heuristic method for solving spatially constrained forest planning problems based on mitigation of infeasibilities radiating outward from a forced choice. Silva Fennica, 40(2), 315–333.

    Google Scholar 

  • Bettinger, P., Boston, K., & Sessions, J. (1999). Intensifying a heuristic forest harvest scheduling search procedure with 2-opt decision choices. Canadian Journal of Forest Research, 29, 1784–1792.

    Article  Google Scholar 

  • Bettinger, P., Graetz, D., Boston, K., Sessions, J., & Chung, W. (2002). Eight heuristic planning techniques applied to three increasingly difficult wildlife planning problems. Silva Fennica, 36(2), 561–584.

    Google Scholar 

  • Boston, K., & Bettinger, P. (2002). Combining tabu search and genetic algorithm heuristic techniques to solve spatial harvest scheduling problem. Forest Science, 48(1), 35–46.

    Google Scholar 

  • Brumelle, S., Granot, D., Halme, M., & Vertinsky, H. (1998). A tabu search algorithm for finding good forest harvest schedules satisfying green-up constraints. European Journal of Operational Research, 106, 408–424.

    Article  Google Scholar 

  • Caro, F., Constantino, M., Martins, I., & Weintraub, A. (2003). A 2-opt tabu search procedure for the multiperiod forest harvesting problem with adjacency, greenup, old growth, and even flow constraints. Forest Science, 49(5), 738–751.

    Google Scholar 

  • Constantino, M., Martins, I., & Borges, J. G. (2008). A new mixed integer programming model for harvest scheduling subject to maximum area restrictions. Operations Research, 56, 542–551.

    Article  Google Scholar 

  • Falcão, A. (1997). Dunas-a growth model for the national forest of leiria. In Proceedings of empirical and process-based models for forest tree and stand growth simulation, Oeiras, Portugal (pp. 20–26).

  • Falcão, A. O., & Borges, J. G. (2002). Combining random and systematic search heuristic procedures for solving spatially constrained forest management scheduling models. Forest Science, 48(3), 608–621.

    Google Scholar 

  • Hoganson, H. M., Bixby, J., Bergmann, S., & Borges, J. G. (2004). Large-scale planning address interior space production three case studies from northern Minnesota. Silva Lusitana, 12(especial), 35–47.

    Google Scholar 

  • Lockwood, C., & Moore, T. (1993). Harvest scheduling with spatial constraints: a simulated annealing approach. Canadian Journal of Forest Research, 23, 468–478.

    Article  Google Scholar 

  • McDill, M. E., & Amateis, R. L. (1992). Measuring forest site quality using the parameters of a dimensionally compatible height growth function. Forest Science, 38(2), 409–429.

    Google Scholar 

  • McDill, M. E., Rebain, S. A., & Braze, J. (2002). Harvest scheduling with area-based adjacency constraints. Forest Science, 48(4), 631–642.

    Google Scholar 

  • Murray, A. T. (1999). Spatial restrictions in harvest scheduling. Forest Science, 45(1), 45–52.

    Google Scholar 

  • Murray, A. T., & Church, R. L. (1996). Analyzing cliques for imposing adjacency restrictions in forest models. Forest Science, 42(2), 166–175.

    Google Scholar 

  • Öhman, K. (2000). Creating continuous areas of old forest in long-term forest planning. Canadian Journal of Forest Research, 30, 1817–1823.

    Article  Google Scholar 

  • Öhman, K., & Eriksson, L. O. (1998). The core area concept in forming contiguous areas for long-term forest planning. Canadian Journal of Forest Research, 28, 1032–1039.

    Article  Google Scholar 

  • Öhman, K., & Eriksson, L. O. (2002). Allowing for spatial consideration in long-term forest planning by linking linear programming with simulated annealing. Forest Ecology and Management, 161, 221–230.

    Article  Google Scholar 

  • Öhman, K., & Lämås, T. (2005). Reducing forest fragmentation in long-term forest planning by using the shape index. Forest Ecology and Management, 212, 346–357.

    Article  Google Scholar 

  • Rebain, S., & McDill, M. E. (2003). A mixed-integer formulation of the minimum patch size problem. Forest Science, 49(4), 608–618.

    Google Scholar 

  • Tóth, S. F., & McDill, M. E. (2008). Promoting large, compact mature forest patches in harvest scheduling models. Environmental Modeling and Assessment, 13(1), 1–15.

    Article  Google Scholar 

  • Wei, Y., & Hoganson, H. M. (2005). Landscape impacts from valuing core area in national forest planning. Forest Ecology and Management, 218, 89–106.

    Article  Google Scholar 

  • Wei, Y., & Hoganson, H. M. (2006). Spatial information for scheduling core area production in forest planning. Canadian Journal of Forest Research, 36, 23–33.

    Article  Google Scholar 

  • Weintraub, A., & Murray, A. T. (2006). Review of combinatorial problems induce by spatial forest harvesting planning. Discrete Applied Mathematics, 154, 867–879.

    Article  Google Scholar 

  • Wolsey, L. A. (1998). Integer programming. New York: Wiley.

    Google Scholar 

  • Xpress-MP (2007). www.dashoptimizatiom.com.

Download references

Author information

Authors and Affiliations

  1. Business School, University of Shanghai for Science and Technology, Mail box 459, 516 Jungong Road, Shanghai, 200093, China

    Huizhen Zhang

  2. Faculdade de Ciências, Centro de Investigação Operacional, Universidade de Lisboa, Lisbon, Portugal

    Huizhen Zhang

  3. Faculdade de Ciências, DEIO/ Centro de Investigação Operacional, Universidade de Lisboa, Bloco C6, piso 4, Cidade Universitária, 1749-016, Lisbon, Portugal

    Miguel Constantino

  4. Faculdade de Ciências, Departamento de Informática/ Lasige, Universidade de Lisboa, Bloco C6, piso 3, Cidade Universitária, 1749-016, Lisbon, Portugal

    André Falcão

Authors
  1. Huizhen Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miguel Constantino
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. André Falcão
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huizhen Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, H., Constantino, M. & Falcão, A. Modeling forest core area with integer programming. Ann Oper Res 190, 41–55 (2011). https://doi.org/10.1007/s10479-009-0517-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-009-0517-4

Keywords

Search

Navigation