Annals of Operations Research

, Volume 258, Issue 2, pp 453–478 | Cite as

Forest harvest scheduling with clearcut and core area constraints

  • Teresa Neto
  • Miguel Constantino
  • Isabel Martins
  • João Pedro Pedroso
CLAIO 2014

Abstract

Many studies regarding environmental concerns in forest harvest scheduling problems deal with constraints on the maximum clearcut size. However, these constraints tend to disperse harvests across the forest and thus to generate a more fragmented landscape. When a forest is fragmented, the amount of edge increases at the expense of the core area. Highly fragmented forests can neither provide the food, cover, nor the reproduction needs of core-dependent species. This study presents a branch-and-bound procedure designed to find good feasible solutions, in a reasonable time, for forest harvest scheduling problems with constraints on maximum clearcut size and minimum core habitat area. The core area is measured by applying the concept of subregions. In each branch of the branch-and-bound tree, a partial solution leads to two children nodes, corresponding to the cases of harvesting or not a given stand in a given period. Pruning is based on constraint violations or unreachable objective values. The approach was tested with forests ranging from some dozens to more than a thousand stands. In general, branch-and-bound was able to quickly find optimal or good solutions, even for medium/large instances.

Keywords

Forest planning Core area Edge effect Clearcut Integer programming Branch-and-bound 

Notes

Acknowledgments

This work was partly funded by FCT—Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) within projects UID/EEA/50014/2013 and UID/MAT/04561/2013. We would like to thank four anonymous reviewers for their constructive comments on a previous version of this paper.

Supplementary material

References

  1. Baskent, E. Z., & Jordan, G. A. (1995). Characterizing spatial structure of forest landscapes. Canadian Journal of Forest Research, 25(11), 1830–1849.CrossRefGoogle Scholar
  2. 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
  3. 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(3), 542–551.CrossRefGoogle Scholar
  4. Crowe, K., Nelson, J., & Boyland, M. (2003). Solving the area-restricted harvest-scheduling model using the branch and bound algorithm. Canadian Journal of Forest Research, 33(9), 1804–1814.CrossRefGoogle Scholar
  5. Davis, L. S. (1977). Understanding shape: Angles and sides. IEEE Transactions on Computers, 100(3), 236–242.CrossRefGoogle Scholar
  6. Diestel, R. (2012). Graph theory, volume 173 of graduate texts in mathematics. Berlin, Heidelberg: Springer.Google Scholar
  7. Falcão, A. O., & Borges, J. (2002). Combining random and systematic search heuristic procedures for solving spatially constrained forest management scheduling models. Forest Science, 48(3), 608–621.Google Scholar
  8. Franklin, J. F., & Forman, R. T. (1987). Creating landscape patterns by forest cutting: Ecological consequences and principles. Landscape Ecology, 1(1), 5–18.CrossRefGoogle Scholar
  9. Goycoolea, M., Murray, A. T., Barahona, F., Epstein, R., & Weintraub, A. (2005). Harvest scheduling subject to maximum area restrictions: Exploring exact approaches. Operations Research, 53(3), 490–500.CrossRefGoogle Scholar
  10. Goycoolea, M., Murray, A., Vielma, J. P., & Weintraub, A. (2009). Evaluating approaches for solving the area restriction model in harvest scheduling. Forest Science, 55(2), 149–165.Google Scholar
  11. Harris, L. D. (1984). The fragmented forest: Island biogeography theory and the preservation of biotic diversity. Chicago: University of Chicago press.Google Scholar
  12. Hof, J., Bevers, M., Joyce, L., & Kent, B. (1994). An integer programming approach for spatially and temporally optimizing wildlife populations. Forest Science, 40(1), 177–191.Google Scholar
  13. Hoganson, H., Wei, Y., & Hokans, R. (2005). Integrating spatial objectives into forest plans for Minnesota’s National Forests. Technical Report 656, USDA Forest Service—General Technical Report PNW-GTR, 10.Google Scholar
  14. Kurttila, M., Pukkala, T., & Loikkanen, J. (2002). The performance of alternative spatial objective types in forest planning calculations: A case for flying squirrel and moose. Forest Ecology and Management, 166(1), 245–260.CrossRefGoogle Scholar
  15. Martins, I., Constantino, M., & Borges, J. (1999). Forest management models with spatial structure constraints. Working paper 2, CIO/Faculdade de CiÍncias de Lisboa.Google Scholar
  16. Martins, I., Constantino, M., & Borges, J. G. (2005). A column generation approach for solving a non-temporal forest harvest model with spatial structure constraints. European Journal of Operational Research, 161(2), 478–498.CrossRefGoogle Scholar
  17. Martins, I., Alvelos, F., & Constantino, M. (2012). A branch-and-price approach for harvest scheduling subject to maximum area restrictions. Computational Optimization and Applications, 51(1), 363–385.CrossRefGoogle Scholar
  18. McDermott, C., Cashore, B. W., & Kanowski, P. (2010). Global environmental forest policies: An international comparison. Earthscan.Google Scholar
  19. McDill, M. E., Rebain, S. A., & Braze, J. (2002). Harvest scheduling with area-based adjacency constraints. Forest Science, 48(4), 631–642.Google Scholar
  20. McGarigal, K., Cushman, S. A., Neel, M. C., & Ene, E.: FRAGSTATS: Spatial pattern analysis program for categorical maps. University of Massachusetts, Amherst, 2002. URL http://www.umass.edu/landeco/research/fragstats/fragstats.html.
  21. Moellering, H., & Rayner, J. N. (1981). The harmonic analysis of spatial shapes using dual axis fourier shape analysis (dafsa). Geographical Analysis, 13(1), 64–77.CrossRefGoogle Scholar
  22. Murray, A. T., & Weintraub, A. (2002). Scale and unit specification influences in harvest scheduling with maximum area restrictions. Forest Science, 48(4), 779–789.Google Scholar
  23. Neto, T., Constantino, M., Martins, I., & Pedroso, J. P. (2013). A branch-and-bound procedure for forest harvest scheduling problems addressing aspects of habitat availability. International transactions in operational research, 20(5), 689–709.CrossRefGoogle Scholar
  24. Öhman, K. (2000). Creating continuous areas of old forest in long-term forest planning. Canadian Journal of Forest Research, 30(11), 1817–1823.CrossRefGoogle Scholar
  25. 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(7), 1032–1039.CrossRefGoogle Scholar
  26. Öhman, K., & Lämås, T. (2005). Reducing forest fragmentation in long-term forest planning by using the shape index. Forest Ecology and Management, 212(1), 346–357.CrossRefGoogle Scholar
  27. Öhman, K., & Wikström, P. (2008). Incorporating aspects of habitat fragmentation into long-term forest planning using mixed integer programming. Forest Ecology and Management, 255(3), 440–446.CrossRefGoogle Scholar
  28. Öhman, K., Pukkala, T., et al. (2002). Spatial optimisation in forest planning: A review of recent swedish research. Multi-objective forest planning (Vol. 6, pp. 153–172).Google Scholar
  29. Paradis, G., & Richards. E. (2001). Flg: A forest landscape generator. CORS-SCRO Bulletin, 35(3), 28–31.Google Scholar
  30. Rebain, S., & McDill, M. E. (2003a). Can mature patch constraints mitigate the fragmenting effects of harvest opening size restrictions? International Transactions in Operational Research, 10(5), 499–513.CrossRefGoogle Scholar
  31. Rebain, S., & McDill, M. E. (2003b). A mixed-integer formulation of the minimum patch size problem. Forest Science, 49(4), 608–618.Google Scholar
  32. Saura, S., & Pascual-Hortal, L. (2007). A new habitat availability index to integrate connectivity in landscape conservation planning: Comparison with existing indices and application to a case study. Landscape and Urban Planning, 83(2), 91–103.CrossRefGoogle Scholar
  33. 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
  34. Vielma, J. P., Murray, A. T., Ryan, D. M., & Weintraub, A. (2007). Improving computational capabilities for addressing volume constraints in forest harvest scheduling problems. European Journal of Operational Research, 176(2), 1246–1264.CrossRefGoogle Scholar
  35. Wei, Y., & Hoganson, H. M. (2007). Scheduling forest core area production using mixed integer programming. Canadian Journal of Forest Research, 37(10), 1924–1932.CrossRefGoogle Scholar
  36. Wei, Y., & Hoganson, H. M. (2008). Tests of a dynamic programming-based heuristic for scheduling forest core area production over large landscapes. Forest Science, 54(3), 367–380.Google Scholar
  37. Wentz, E. A. (2000). A shape definition for geographic applications based on edge, elongation, and perforation. Geographical Analysis, 32(2), 95–112.CrossRefGoogle Scholar
  38. Xia, L. (1996). Technical note: A method to improve classification with shape information. International Journal of Remote Sensing, 17(8), 1473–1481.CrossRefGoogle Scholar
  39. Yoshimoto, A., & Brodie, J. D. (1994). Comparative analysis of algorithms to generate adjacency constraints. Canadian Journal of Forest Research, 24(6), 1277–1288.CrossRefGoogle Scholar
  40. Zhang, H., Constantino, M., & Falcão, A. (2011). Modeling forest core area with integer programming. Annals of Operations Research, 190(1), 41–55.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Teresa Neto
    • 1
  • Miguel Constantino
    • 2
  • Isabel Martins
    • 3
  • João Pedro Pedroso
    • 4
  1. 1.Escola Superior de Tecnologia e Gestão de ViseuInstituto Politécnico de ViseuViseuPortugal
  2. 2.Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Faculdade de CiênciasUniversidade de LisboaLisbonPortugal
  3. 3.Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Instituto Superior de AgronomiaUniversidade de LisboaLisbonPortugal
  4. 4.INESC TEC and Faculdade de CiênciasUniversidade do PortoPortoPortugal

Personalised recommendations