Forest harvest scheduling with clearcut and core area constraints
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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.
KeywordsForest planning Core area Edge effect Clearcut Integer programming Branch-and-bound
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.
- 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
- Diestel, R. (2012). Graph theory, volume 173 of graduate texts in mathematics. Berlin, Heidelberg: Springer.Google Scholar
- 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
- 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
- Harris, L. D. (1984). The fragmented forest: Island biogeography theory and the preservation of biotic diversity. Chicago: University of Chicago press.Google Scholar
- 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
- 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
- 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
- McDermott, C., Cashore, B. W., & Kanowski, P. (2010). Global environmental forest policies: An international comparison. Earthscan.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
- 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.
- 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
- 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
- Paradis, G., & Richards. E. (2001). Flg: A forest landscape generator. CORS-SCRO Bulletin, 35(3), 28–31.Google Scholar
- Rebain, S., & McDill, M. E. (2003b). A mixed-integer formulation of the minimum patch size problem. Forest Science, 49(4), 608–618.Google Scholar
- 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
- 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