Abstract
This study deals with the problem of including the risk of wind damage in long-term forestry management. A model based on Graph-Based Markov Decision Processes (GMDP) is suggested for development of silvicultural management policies. The model can both take stochastic wind events into account and be applied to forest estates containing a large number of stands. The model is demonstrated for a forest estate in southern Sweden. Treatment of the stands according to the management policy specified by the GMDP model increased the expected net present value (NPV) of the whole forest only slightly, less than 2%, under different wind-risk assumptions. Most of the stands were managed in the same manner as when the risk of wind damage was not considered. For the stands that were treated differently, however, the expected NPV increased by 3% to 8%.
Similar content being viewed by others

References
Blennow, K., & Sallnäs, O. (2004). WINDA – a system of models for assessing the probability of wind damage to forest stands within a landscape. Ecological Modelling, 175, 87–99.
Boychuk, D., & Martell, D. L. (1996). A multistage stochastic programming model for sustainable forest-level timber supply under risk of fire. Forest Science, 42(1), 10–26.
Chornei, R. K., Daduna, H., & Knopov, P. S. (2006). Control of spatially structured random processes and random fields with applications. Berlin: Springer.
Falcão, A. O., & Borges, J. G. (2002). Combining random and systematic search heuristic procedures for solving spatially constrained forest management scheduling problems. Forest Science, 48(3), 608–621.
Forsell, N., & Sabbadin, R. (2006). Approximate linear-programming algorithms for graph-based Markov decision processes. In: Proceedings of 17th European Conference on Artificial Intelligence, Riva Del Garda, Italy, pp. 590–594.
Gardiner, B. A., Stacey, G. R., Belcher, R. E., & Wood, C. J. (1997). Field and wind tunnel assessments of the implications of respacing and thinning for tree stability. Forestry, 70, 233–252.
Guestrin, C., Lagoudakis, M. G., & Parr, R. (2002). Coordinated reinforcement learning. International Conference on Machine Learning, pp. 227–234.
Gunn, E. A. (2007). Models for strategic forest management. In: Handbook of operations research in natural resources (pp. 317–342). New York: Springer.
Hartman, R. (1976). The Harvesting decision when a standing forest has value. Economic Inquiry, XIV, 52–58.
Johnson, K. N., & Scheurman, H. L. (1977). Techniques for prescribing optimal timber harvest and investment under different objectives-discussion and synthesis. Forest Science, Monograph 18.
Kaya, I., & Buongiorno, J. (1987). Economic harvesting of uneven-aged northern hardwood stands under risk: A Markovian decision model. Forest Science, 33(1), 889–907.
Kok, J. R., & Vlassis, N. A. (2006). Collaborative multiagent reinforcement learning by payoff propagation. Journal of Machine Learning Research, 7, 1789–1828.
Lohmander, P., & Helles, P. (1987). Windthrow probability as a function of stand characteristics and shelter. Scandinavian Journal of Forest Research, 2, 227–238.
Constantino, I. 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, 16, 478–498.
Meilby, H., Strange, N., & Thorsen, B. J. (2001). Optimal spatial harvest planning under risk of windthrow. Forest Ecology and Management, 149, 15–31.
Murray, A. T., & Church, R. L. (1996). Analyzing cliques for imposing adjacency restrictions in forest models. Forest Science, 42(2), 166–175.
Olofsson, E. (2006). Supporting management of the risk of wind damage in south Swedish forestry. Ph.D. thesis, Southern Swedish Forest Research Centre, SLU.
Olofsson, E., & Blennow, K. (2005). Decision support for identifying spruce forest stand edges with high probability of wind damage. Forest Ecology and Management, 207, 87–98.
Peltola, H., Kellomäki, S., Väisänen, H., & Ikonen, V. P. (1999). A mechanistic model for assessing the risk of wind and snow damage to single trees and stands of Scots pine, Norway spruce, and birch. Canadian Journal of Forest Research, 29, 647–661.
Persson, P. (1975). Windthrow in forests – its causes and the effect of forestry measures. Royal College of Forestry, Department of Forest Yield Research, Stockholm, Research Notes 36.
Peyrard, N., & Sabbadin, R. (2006). Mean field approximation of the policy iteration algorithm for graph-based Markov decision processes. In: Proceedings of 17th European Conference on Artificial Intelligence, Riva Del Garda, Italy, pp. 595–599.
Puterman, M. L. (1994). Markov decision processes, New York: Wiley.
Quine, C., Coutts, M., Gardiner, B., & Pyatt, G. (1995). Forest and wind: management to minimise damage. London, Bulletin 114, HMSO.
Christian, P. R., & George, C., (1999). Monte Carlo statistical methods. New York: Springer.
Schelhaas, M., Nabuurs, G., & Schuck, A. (2003). Natural disturbances in the European forests in the 19th and 20th centuries. Global Change Biology, 9, 1620–1633.
Schroeder, L. M., & Eidmann, H. H. (1993). Attacks of bark- and wood-boring Coleoptera on snow-broken conifers over a two-year period. Scandinavian Journal of Forest Research, 8, 257–265.
Scilab (2004). Scilab – a free scientific software package. INRIA. France. http://www.scilab.org.
Sondell, J. (2006). Erferenheter från “operation Gudrun”. Skogforsk Resultat, nr. 7.
Snyder, S., & ReVelle, C. (1996). The grid packing problem: selecting a harvesting pattern in an area with forbidden regions. Forest Science, 42(1), 27–34.
Snyder, S., & ReVelle, C. (1997). Dynamic selection of harvests with adjacency restrictions: the SHARe model. Forest Science, 43(2), 213–222.
Sutton, R. (1991). Planning by incremental dynamic programming. In: Proceedings of the 8th international workshop on machine learning, pp. 353–357.
Valinger, E., & Fridman, J. (1997). Modelling probability of snow and wind damage in Scots pine stands using tree characteristics. Forest Ecology and Management, 97, 215–222.
Valinger, E., & Pettersson, N. (1996). Wind and snow damage in a thinning and fertilization experiment in Picea abies in southern Sweden. Forestry, 69, 25–33.
Weintraub, A., Barahona, F., & Epstein, R. (1994). A column generation algorithm for solving general forest planning problems with adjacency constraints. Forest Science, 40(1), 142–161.
Wikström, P. (2000). A solution method for uneven-aged management applied to Norway spruce. Forest Science, 46(3), 452–462.
Zeng, H., Pukkala, T., & Peltola, H. (2007). The use of heuristic optimization in risk management of wind damage in forest planning. Forest Ecology and Management, 241, 189–199.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Forsell, N., Wikström, P., Garcia, F. et al. Management of the risk of wind damage in forestry: a graph-based Markov decision process approach. Ann Oper Res 190, 57–74 (2011). https://doi.org/10.1007/s10479-009-0522-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-009-0522-7